SFD OlderCodes.vp Older Codes
User Manual: SFD-OlderCodes
Open the PDF directly: View PDF .
Page Count: 106
Download | |
Open PDF In Browser | View PDF |
Steel Frame Design Manual AISC ASD 01 & AISC ASD 89 Steel Frame Design Manual AISC ASD-1989 and AISC ASD-01 For CSiBridge® ISO BRG102816M31 Rev 0 Proudly developed in the United States of America October 2016 Copyright Copyright Computers & Structures, Inc., 1978-2016 All rights reserved. The CSI Logo®, SAP2000®, ETABS®, and SAFE® are registered trademarks of Computers & Structures, Inc. Watch & LearnTM is a trademark of Computers & Structures, Inc. The computer programs SAP2000®, CSiBridge®, and ETABS® and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest with Computers & Structures, Inc. Unlicensed use of these programs or reproduction of documentation in any form, without prior written authorization from Computers & Structures, Inc., is explicitly prohibited. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior explicit written permission of the publisher. Further information and copies of this documentation may be obtained from: Computers & Structures, Inc. http://www.csiamerica.com/ info@csiamerica.com (for general information) support@csiamerica.com (for technical support) DISCLAIMER CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THE DEVELOPMENT AND DOCUMENTATION OF THIS SOFTWARE. HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON THE ACCURACY OR THE RELIABILITY OF THIS PRODUCT. THIS PRODUCT IS A PRACTICAL AND POWERFUL TOOL FOR STRUCTURAL DESIGN. HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC ASSUMPTIONS OF THE SOFTWARE MODELING, ANALYSIS, AND DESIGN ALGORITHMS AND COMPENSATE FOR THE ASPECTS THAT ARE NOT ADDRESSED. THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE CHECKED BY A QUALIFIED AND EXPERIENCED ENGINEER. THE ENGINEER MUST INDEPENDENTLY VERIFY THE RESULTS AND TAKE PROFESSIONAL RESPONSIBILITY FOR THE INFORMATION THAT IS USED. Table of Contents CHAPTER I Introduction 1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Recommended Reading . . . . . . . . . . . . . . . . . . . . . . . . . 4 CHAPTER II Design Algorithms 5 Design Load Combinations. . . . . . . . . . . . . . . . . . . . . . . . 6 Design and Check Stations . . . . . . . . . . . . . . . . . . . . . . . . 8 P-D Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Element Unsupported Lengths . . . . . . . . . . . . . . . . . . . . . . 9 Effective Length Factor (K) . . . . . . . . . . . . . . . . . . . . . . . 11 Choice of Input Units . . . . . . . . . . . . . . . . . . . . . . . . . . 14 CHAPTER III Check/Design for AISC-ASD01 Design Loading Combinations . . . . . . . . . . . . . . . Classification of Sections . . . . . . . . . . . . . . . . . . Special Seismic Provisions of Member Design . . . . . . . Ordinary Moment Frames (OMF) . . . . . . . . . Intermediate Moment Frames (IMF) . . . . . . . Special Moment Frames (SMF) . . . . . . . . . . Ordinary Concentrically Braced Frames (OCBF) . Special Concentrically Braced Frames (SCBF) . . Eccentrically Braced Frames (EBF) . . . . . . . . Calculation of Stresses . . . . . . . . . . . . . . . . . . . Calculation of Allowable Stresses . . . . . . . . . . . . . Allowable Stress in Tension . . . . . . . . . . . . . . Allowable Stress in Compression . . . . . . . . . . . Flexural Buckling . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 22 24 24 25 25 28 28 29 32 33 33 34 34 i CSI Steel Design Manual Flexural-Torsional Buckling. . . . . Allowable Stress in Bending . . . . . . . I-sections. . . . . . . . . . . . . . . Channel sections . . . . . . . . . . . T-sections and Double angles . . . . Box Sections and Rectangular Tubes Pipe Sections. . . . . . . . . . . . . Round Bars . . . . . . . . . . . . . Rectangular and Square Bars . . . . Single-Angle Sections. . . . . . . . General Sections . . . . . . . . . . . Allowable Stress in Shear . . . . . . . . Calculation of Stress Ratios . . . . . . . . . . Axial and Bending Stresses. . . . . . . . Shear Stresses. . . . . . . . . . . . . . . Joint Design . . . . . . . . . . . . . . . . . . Design of Continuity Plates . . . . . . . Design of Doubler Plates . . . . . . . . . Weak Beam Strong Column Measure . . Evaluation of Beam Connection Shears . Evaluation of Brace Connection Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER IV Check/Design for AISC-ASD89 Design Loading Combinations . . . . . . . . Classification of Sections . . . . . . . . . . . Calculation of Stresses . . . . . . . . . . . . Calculation of Allowable Stresses . . . . . . Allowable Stress in Tension . . . . . . . Allowable Stress in Compression . . . . Flexural Buckling . . . . . . . . . . Flexural-Torsional Buckling. . . . . Allowable Stress in Bending . . . . . . . I-sections. . . . . . . . . . . . . . . Channel sections . . . . . . . . . . . T-sections and Double angles . . . . Box Sections and Rectangular Tubes Pipe Sections. . . . . . . . . . . . . Round Bars . . . . . . . . . . . . . Rectangular and Square Bars . . . . Single-Angle Sections. . . . . . . . General Sections . . . . . . . . . . . Allowable Stress in Shear . . . . . . . . Calculation of Stress Ratios . . . . . . . . . . Axial and Bending Stresses. . . . . . . . Shear Stresses. . . . . . . . . . . . . . . ii 36 38 38 42 43 43 44 45 45 45 48 48 49 49 51 52 52 56 59 61 63 65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 68 72 73 73 73 73 75 80 80 83 84 85 86 86 86 87 89 89 91 91 93 CHAPTER XIII Design Output Table of Contents 311 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graphical Display of Design Output . . . . . . . . . . . . . . . . . Tabular Display of Design Output. . . . . . . . . . . . . . . . . . . 311 312 313 Member Specific Information . . . . . . . . . . . . . . . . . . . . . 314 iii Chapter I Introduction Overview SAP2000 and ETABS feature powerful and completely integrated modules for design of both steel and reinforced concrete structures. The program provides the user with options to create, modify, analyze and design structural models, all from within the same user interface. The program is capable of performing initial member sizing and optimization from within the same interface. The program provides an interactive environment in which the user can study the stress conditions, make appropriate changes, such as revising member properties, and re-examine the results without the need to re-run the analysis. A single mouse click on an element brings up detailed design information. Members can be grouped together for design purposes. The output in both graphical and tabulated formats can be readily printed. The program is structured to support a wide variety of the latest national and international design codes for the automated design and check of concrete and steel frame members. The program currently supports the following steel design codes: • U.S. AISC 360-2005/IBC 2006 • U.S. AISC ASD-2001, • U.S. AISC LRFD-1999, Overview 1 CSI Steel Design Manual • U.S. AISC ASD-1989, • U.S. AISC-LRFD-1994, • UBC ASD-1997, • UBC LRFD-1997, • Canadian CAN/CSA-S16.1-1994, • British BS 5950-2200, • British BS 5950-1990, and • Eurocode 3 (ENV 1993-1-1). The design is based upon a set of user-specified loading combinations. However, the program provides a set of default load combinations for each design code supported in the program. If the default load combinations are acceptable, no definition of additional load combination is required. In the design process the program picks the least weight section required for strength for each element to be designed, from a set of user specified sections. Different sets of available sections can be specified for different groups of elements. Also several elements can be grouped to be designed to have the same section. In the check process the program produces demand/capacity ratios for axial load and biaxial moment interactions and shear. The demand/capacity ratios are based on element stress and allowable stress for allowable stress design, and on factored loads (actions) and factored capacities (resistances) for limit state design. The checks are made for each user specified (or program defaulted) load combination and at several user controlled stations along the length of the element. Maximum demand/capacity ratios are then reported and/or used for design optimization. All allowable stress values or design capacity values for axial, bending and shear actions are calculated by the program. Tedious calculations associated with evaluating effective length factors for columns in moment frame type structures are automated in the algorithms. The presentation of the output is clear and concise. The information is in a form that allows the designer to take appropriate remedial measures if there is member overstress. Backup design information produced by the program is also provided for convenient verification of the results. When using 1997 UBC-ASD or UBC-LRFD design codes, requirements for continuity plates at the beam to column connections are evaluated. The program performs a joint shear analysis to determine if doubler plates are required in any of the 2 Overview Chapter I Introduction joint panel zones. Maximum beam shears required for the beam shear connection design are reported. Also maximum axial tension or compression values that are generated in the member are reported. Special 1997 UBC-ASD and UBC-LRFD seismic design provisions are implemented in the current version of the program. The ratio of the beam flexural capacities with respect to the column reduced flexural capacities (reduced for axial force effect) associated with the weak beam-strong column aspect of any beam/column intersection, are reported for special moment resisting frames. Capacity requirements associated with seismic framing systems that require ductility are checked. Special requirements for seismic design are not implemented in the current version of SAP2000. English as well as SI and MKS metric units can be used to define the model geometry and to specify design parameters. Organization This manual is organized in the following way: Chapter II outlines various aspects of the steel design procedures of the program. This chapter describes the common terminology of steel design as implemented in the program. Each of eleven subsequent chapters gives a detailed description of a specific code of practice as interpreted by and implemented in the program. Each chapter describes the design loading combinations to be considered; allowable stress or capacity calculations for tension, compression, bending, and shear; calculations of demand/capacity ratios; and other special considerations required by the code. • Chapter III gives a detailed description of the AISC ASD code (AISC 2001) as implemented in the program. • Chapter IV gives a detailed description of the AISC ASD steel code (AISC 1989) as implemented in the program. • Chapter V gives a detailed description of the AISC LRFD code (AISC 1999) as implemented in the program. • Chapter VI gives a detailed description of the AISC LRFD steel code (AISC 1993) as implemented in the program. • Chapter VII gives a detailed description of the British code BS 5950 (BSI 2000) as implemented in the program. Organization 3 CSI Steel Design Manual • Chapter IIIV gives a detailed description of the British code BS 5950 (BSI 1990) as implemented in the program. • Chapter IX gives a detailed description of the Canadian code (CISC 1994) as implemented in the program. • Chapter X gives a detailed description of the Eurocode 3 (CEN 1992) as implemented in the program. • Chapter XI gives a detailed description of the UBC ASD (UBC 1997) as implemented in the program. • Chapter XII gives a detailed description of the UBC (UBC 1997) as implemented in the program. Chapter XIII outlines various aspects of the tabular and graphical output from the program related to steel design. Recommended Reading It is recommended that the user read Chapter II “Design Algorithms” and one of eleven subsequent chapters corresponding to the code of interest to the user. Finally the user should read “Design Output” in Chapter XIII for understanding and interpreting the program output related to steel design. 4 Recommended Reading C h a p t e r II Design Algorithms This chapter outlines various aspects of the steel check and design procedures that are used by the program. The steel design and check may be performed according to one of the following codes of practice. • American Institute of Steel Construction’s “Allowable Stress Design and Plastic Design Specification for Structural Steel Buildings”, AISC-ASD (AISC 2001). • American Institute of Steel Construction’s “Allowable Stress Design and Plastic Design Specification for Structural Steel Buildings”, AISC-ASD (AISC 1989). • American Institute of Steel Construction’s “Load and Resistance Factor Design Specification for Structural Steel Buildings”, AISC-LRFD (AISC 1999) • American Institute of Steel Construction’s “Load and Resistance Factor Design Specification for Structural Steel Buildings”, AISC-LRFD (AISC 1994). • British Standards Institution’s “Structural Use of Steelwork in Building”, BS 5950 (BSI 2000). • British Standards Institution’s “Structural Use of Steelwork in Building”, BS 5950 (BSI 1990). 5 CSI Steel Design Manual • Canadian Institute of Steel Construction’s “Limit States Design of Steel Structures”, CAN/CSA-S16.1-94 (CISC 1995). • European Committee for Standardization’s “Eurocode 3: Design of Steel Structures C Part 1.1: General Rules and Rules for Buildings”, ENV 1993-1-1 (CEN 1992). • International Conference of Building Officials’ “1997 Uniform Building Code: Volume 2: Structural Engineering Design Provisions” Chapter 22 Division III “Design Standard for Specification for Structural Steel Buildings ¾ Allowable Stress Design and Plastic Design”, UBC-ASD (ICBO 1997). • International Conference of Building Officials’ “1997 Uniform Building Code: Volume 2: Structural Engineering Design Provisions” Chapter 22 Division II “Design Standard for Load and Resistance factor Design Specification for Structural Steel Buildings”, UBC-LRFD (ICBO 1997). Details of the algorithms associated with each of these codes as implemented and interpreted in the program are described in subsequent chapters. However, this chapter provides a background which is common to all the design codes. It is assumed that the user has an engineering background in the general area of structural steel design and familiarity with at least one of the above mentioned design codes. For referring to pertinent sections of the corresponding code, a unique prefix is assigned for each code. For example, all references to the AISC-LRFD code carry the prefix of “LRFD”. Similarly, – References to the AISC-ASD code carry the prefix of “ASD” – References to the Canadian code carry the prefix of “CISC” – References to the British code carry the prefix of “BS” – References to the Eurocode carry the prefix of “EC3” – References to the UBC-ASD code carry the prefix of “UBC Design Load Combinations The design load combinations are used for determining the various combinations of the load cases for which the structure needs to be designed/checked. The load combination factors to be used vary with the selected design code. The load combination factors are applied to the forces and moments obtained from the associated 6 Design Load Combinations Chapter II Design Algorithms load cases and the results are then summed to obtain the factored design forces and moments for the load combination. For multi-valued load combinations involving response spectrum, time history, moving loads and multi-valued combinations (of type enveloping, square-root of the sum of the squares or absolute) where any correspondence between interacting quantities is lost, the program automatically produces multiple sub combinations using maxima/minima permutations of interacting quantities. Separate combinations with negative factors for response spectrum cases are not required because the program automatically takes the minima to be the negative of the maxima for response spectrum cases and the above described permutations generate the required sub combinations. When a design combination involves only a single multi-valued case of time history or moving load, further options are available. The program has an option to request that time history combinations produce sub combinations for each time step of the time history. Also an option is available to request that moving load combinations produce sub combinations using maxima and minima of each design quantity but with corresponding values of interacting quantities. For normal loading conditions involving static dead load, live load, wind load, and earthquake load, and/or dynamic response spectrum earthquake load, the program has built-in default loading combinations for each design code. These are based on the code recommendations and are documented for each code in the corresponding chapters. For other loading conditions involving moving load, time history, pattern live loads, separate consideration of roof live load, snow load, etc., the user must define design loading combinations either in lieu of or in addition to the default design loading combinations. The default load combinations assume all static load cases declared as dead load to be additive. Similarly, all cases declared as live load are assumed additive. However, each static load case declared as wind or earthquake, or response spectrum cases, is assumed to be non additive with each other and produces multiple lateral load combinations. Also wind and static earthquake cases produce separate loading combinations with the sense (positive or negative) reversed. If these conditions are not correct, the user must provide the appropriate design combinations. The default load combinations are included in design if the user requests them to be included or if no other user defined combination is available for concrete design. If any default combination is included in design, then all default combinations will Design Load Combinations 7 CSI Steel Design Manual automatically be updated by the program any time the user changes to a different design code or if static or response spectrum load cases are modified. Live load reduction factors can be applied to the member forces of the live load case on an element-by-element basis to reduce the contribution of the live load to the factored loading. The user is cautioned that if moving load or time history results are not requested to be recovered in the analysis for some or all the frame members, then the effects of these loads will be assumed to be zero in any combination that includes them. Design and Check Stations For each load combination, each element is designed or checked at a number of locations along the length of the element. The locations are based on equally spaced segments along the clear length of the element. The number of segments in an element is requested by the user before the analysis is made. The user can refine the design along the length of an element by requesting more segments. The axial-flexure interaction ratios as well as shear stress ratios are calculated for each station along the length of the member for each load combination. The actual member stress components and corresponding allowable stresses are calculated. Then, the stress ratios are evaluated according to the code. The controlling compression and/or tension stress ratio is then obtained, along with the corresponding identification of the station, load combination, and code-equation. A stress ratio greater than 1.0 indicates an overstress or exceeding a limit state. P-D Effects The program design algorithms require that the analysis results include the P-D effects. The P-D effects are considered differently for “braced” or “nonsway” and “unbraced” or “sway” components of moments in frames. For the braced moments in frames, the effect of P-D is limited to “individual member stability”. For unbraced components, “lateral drift effects” should be considered in addition to individual member stability effect. In the program, it is assumed that “braced” or “nonsway” moments are contributed from the “dead” or “live” loads. Whereas, “unbraced” or “sway” moments are contributed from all other types of loads. For the individual member stability effects, the moments are magnified with moment magnification factors as in the AISC-LRFD code is considered directly in the design equations as in the Canadian, British, and European codes. No moment magnification is applied to the AISC-ASD code. 8 Design and Check Stations Chapter II Design Algorithms For lateral drift effects of unbraced or sway frames, the program assumes that the amplification is already included in the results because P-D effects are considered for all but AISC-ASD code. The users of the program should be aware that the default analysis option in the program is turned OFF for P-D effect. The default number of iterations for P-D analysis is 1. The user should turn the P-D analysis ON and set the maximum number of iterations for the analysis. No P-D analysis is required for the AISCASD code. For further reference, the user is referred to CSI Analysis Reference Manual (CSI 2005). Element Unsupported Lengths To account for column slenderness effects, the column unsupported lengths are required. The two unsupported lengths are l 33 and l 22 . See Figure II-1. These are the lengths between support points of the element in the corresponding directions. The length l 33 corresponds to instability about the 3-3 axis (major axis), and l 22 corresponds to instability about the 2-2 axis (minor axis). The length l 22 is also used for lateral-torsional buckling caused by major direction bending (i.e., about the 3-3 axis). See Figure II-2 for correspondence between the program axes and the axes in the design codes. Normally, the unsupported element length is equal to the length of the element, i.e., the distance between END-I and END-J of the element. See Figure II-1. The program, however, allows users to assign several elements to be treated as a single member for design. This can be done differently for major and minor bending. Therefore, extraneous joints, as shown in Figure II-3, that affect the unsupported length of an element are automatically taken into consideration. Element Unsupported Lengths 9 CSI Steel Design Manual Axis 2 Axis 1 l 33 End j l 22 End I Axis 3 Figure II-1 Major and Minor Axes of Bending In determining the values for l 22 and l 33 of the elements, the program recognizes various aspects of the structure that have an effect on these lengths, such as member connectivity, diaphragm constraints and support points. The program automatically locates the element support points and evaluates the corresponding unsupported element length. Therefore, the unsupported length of a column may actually be evaluated as being greater than the corresponding element length. If the beam frames into only one direction of the column, the beam is assumed to give lateral support only in that direction. The user has options to specify the unsupported lengths of the elements on an element-by-element basis. 10 Element Unsupported Lengths Chapter II Design Algorithms 2 3 3 2 y y x x y ASD89, LRFD95 & AASHTO x SAP2000 x z y x x y y CISC95 BS5950 y y z EUROCODE 3 Figure II-2 Correspondence between the program Axes and Code Axes Effective Length Factor (K) The column K-factor algorithm has been developed for building-type structures, where the columns are vertical and the beams are horizontal, and the behavior is basically that of a moment-resisting nature for which the K-factor calculation is relatively complex. For the purpose of calculating K-factors, the elements are identified as columns, beams and braces. All elements parallel to the Z-axis are classified as columns. All elements parallel to the X-Y plane are classified as beams. The rest are braces. Effective Length Factor (K) 11 CSI Steel Design Manual Figure II-3 Unsupported Lengths are Affected by Intermediate Nodal Points The beams and braces are assigned K-factors of unity. In the calculation of the K-factors for a column element, the program first makes the following four stiffness summations for each joint in the structural model: æ Ec Ic è Lc ö ÷ ÷ øx æ Ec Ic ö S cy = å çç ÷ ÷ è Lc ø y S cx = å çç æ Eb Ib è Lb ö ÷ ÷ øx æ Eb Ib ö S by = å çç ÷ ÷ è Lb ø y S bx = å çç where the x and y subscripts correspond to the global X and Y directions and the c and b subscripts refer to column and beam. The local 2-2 and 3-3 terms EI 22 l 22 and EI 33 l 33 are rotated to give components along the global X and Y directions to form the ( EI / l) x and ( EI / l) y values. Then for each column, the joint summations at END-I and the END-J of the member are transformed back to the column local 1-2-3 coordinate system and the G-values for END-I and the END-J of the member are calculated about the 2-2 and 3-3 directions as follows: 12 Effective Length Factor (K) Chapter II Design Algorithms S I c 22 S I b 22 S I c 33 = I S b 33 S J c 22 S J b 22 S J c 33 = J S b 33 G I 22 = G J 22 = G I 33 G J 33 If a rotational release exists at a particular end (and direction) of an element, the corresponding value is set to 10.0. If all degrees of freedom for a particular joint are deleted, the G-values for all members connecting to that joint will be set to 1.0 for the end of the member connecting to that joint. Finally, if G I and G J are known for a particular direction, the column K-factor for the corresponding direction is calculated by solving the following relationship for a: a 2 G I G J - 36 a = I J tan a 6( G +G ) from which K = p / a. This relationship is the mathematical formulation for the evaluation of K factors for moment-resisting frames assuming sidesway to be uninhibited. For other structures, such as braced frame structures, trusses, space frames, transmission towers, etc., the K-factors for all members are usually unity and should be set so by the user. The following are some important aspects associated with the column K-factor algorithm: • An element that has a pin at the joint under consideration will not enter the stiffness summations calculated above. An element that has a pin at the far end from the joint under consideration will contribute only 50% of the calculated EI value. Also, beam elements that have no column member at the far end from the joint under consideration, such as cantilevers, will not enter the stiffness summation. • If there are no beams framing into a particular direction of a column element, the associated G-value will be infinity. If the G-value at any one end of a column for a particular direction is infinity, the K-factor corresponding to that direction is set equal to unity. • If rotational releases exist at both ends of an element for a particular direction, the corresponding K-factor is set to unity. • The automated K-factor calculation procedure can occasionally generate artificially high K-factors, specifically under circumstances involving skewed beams, fixed support conditions, and under other conditions where the program may have difficulty recognizing that the members are laterally supported and K-factors of unity are to be used. Effective Length Factor (K) 13 CSI Steel Design Manual • All K-factors produced by the program can be overwritten by the user. These values should be reviewed and any unacceptable values should be replaced. Choice of Input Units English as well as SI and MKS metric units can be used for input. But the codes are based on a specific system of units. All equations and descriptions presented in the subsequent chapters correspond to that specific system of units unless otherwise noted. For example, AISC-ASD code is published in kip-inch-second units. By default, all equations and descriptions presented in the chapter “Check/Design for AISC-ASD89” correspond to kip-inch-second units. However, any system of units can be used to define and design the structure in the program. 14 Choice of Input Units C h a p t e r III Check/Design for AISC-ASD01 This chapter describes the details of the structural steel design and stress check algorithms that are used by the program when the user selects the AISC-ASD01 design code (AISC 2001). Various notations used in this chapter are described in Table IV-1. For referring to pertinent sections and equations of the original ASD code, a unique prefix “ASD” is assigned. However, all references to the “Specifications for Allowable Stress Design of Single-Angle Members” carry the prefix of “ASD SAM”. The design is based on user-specified loading combinations. But the program provides a set of default load combinations that should satisfy requirements for the design of most building type structures. In the evaluation of the axial force/biaxial moment capacity ratios at a station along the length of the member, first the actual member force/moment components and the corresponding capacities are calculated for each load combination. Then the capacity ratios are evaluated at each station under the influence of all load combinations using the corresponding equations that are defined in this chapter. The controlling capacity ratio is then obtained. A capacity ratio greater than 1.0 indicates overstress. Similarly, a shear capacity ratio is also calculated separately. 15 CSI Steel Design Manual Cross-sectional area, in2 Effective cross-sectional area for slender sections, in2 Area of flange , in2 Gross cross-sectional area, in2 Major and minor shear areas, in2 Web shear area, dt w , in2 Bending Coefficient Moment Coefficient Warping constant, in6 Outside diameter of pipes, in Modulus of elasticity, ksi Allowable axial stress, ksi Allowable bending stress, ksi Allowable major and minor bending stresses, ksi Critical compressive stress, ksi 12 p 2 E A Ae Af Ag A v2 , A v3 Aw Cb Cm Cw D E Fa Fb Fb 33 , Fb 22 Fcr = = = = = = = = = = = = = = = ¢ Fe33 = ¢ Fe22 = 23 (K 22 l22 r 22 ) Fv Fy K K 33 , K 22 M 33 , M 22 M ob P Pe Q Qa Qs S S 33 , S 22 = = = = = = = = = = = = = Allowable shear stress, ksi Yield stress of material, ksi Effective length factor Effective length K-factors in the major and minor directions Major and minor bending moments in member, kip-in Lateral-torsional moment for angle sections, kip-in Axial force in member, kips Euler buckling load, kips Reduction factor for slender section, = Qa Qs Reduction factor for stiffened slender elements Reduction factor for unstiffened slender elements Section modulus, in3 Major and minor section moduli, in3 23 (K 33 l33 r 33 ) 2 12 p 2 E 2 Table III-1 AISC-ASD Notations 16 Chapter III Check/Design for AISC-ASD01 S eff ,33 , S eff ,22 Sc V2 , V3 b = = = = be bf d fa fb f b 33 , f b 22 fv f v2 , f v3 h he k kc = = = = = = = = = = = = l33 , l22 lc r r 33 , r 22 rz t tf tw bw = = = = = = = = = Effective major and minor section moduli for slender sections, in3 Section modulus for compression in an angle section, in3 Shear forces in major and minor directions, kips Nominal dimension of plate in a section, in longer leg of angle sections, bf - 2t w for welded and bf -3t w for rolled box sections, etc. Effective width of flange, in Flange width, in Overall depth of member, in Axial stress either in compression or in tension, ksi Normal stress in bending, ksi Normal stress in major and minor direction bending, ksi Shear stress, ksi Shear stress in major and minor direction bending, ksi Clear distance between flanges for I shaped sections ( d - 2t f ), in Effective distance between flanges less fillets, in Distance from outer face of flange to web toe of fillet , in Parameter used for classification of sections, 4.05 if h t w > 70 , 0.46 [h t w ] 1 if h t w £ 70 . Major and minor direction unbraced member lengths, in Critical length, in Radius of gyration, in Radii of gyration in the major and minor directions, in Minimum Radius of gyration for angles, in Thickness of a plate in I, box, channel, angle, and T sections, in Flange thickness, in Web thickness, in Special section property for angles, in Table III-1 AISC-ASD Notations (cont.) 17 CSI Steel Design Manual English as well as SI and MKS metric units can be used for input. But the code is based on Kip-Inch-Second units. For simplicity, all equations and descriptions presented in this chapter correspond to Kip-Inch-Second units unless otherwise noted. Design Loading Combinations The design load combinations are the various combinations of the load cases for which the structure needs to be checked. For the AISC-ASD01 code, if a structure is subjected to dead load (DL), live load (LL), wind load (WL), and earthquake induced load (EL), and considering that wind and earthquake forces are reversible, then the following load combinations may have to be defined (ASD A4). The DL multiplier and r factors are specified in ASCE 7-02: 1.0 DL 1.0 DL + 1.0 LL (ASCE 2.4.1-1) (ASCE 2.4.1-2) 1.0 DL ± 1.0 WL 0.6 DL ± 1.0 WL 1.0 DL + 0.75 (1.0 LL ± 1.0 WL) (ASCE 2.4.1-5) (ASCE 2.4.1-7) (ASCE 2.4.1-6) 1.0 DL (0.6 - 0.7 DL multiplier ) ± 0.7 r EL (ASCE 2.4.1-8) 1.0 DL (1 + 0.7 DL multiplier ) ± 1.0 r EL (ASCE 2.4.1-5) 1.0 DL + 0.75 (0.7 DL multiplier + 1.0 LL ± 0.7 r EL) (ASCE 2.4.1-6) It is noted here that whenever special seismic loading combinations are required by the code for special circumstances, the program automatically generates those load combinations internally. The following additional seismic load combinations are frequently checked for specific types of members and special circumstances. (0.9-0.2SDS) DL ± W 0 EL (ASCE 9.5.2.7.1, 2.3, LRFD SEISMIC 4.1) (1.2 + 0.2SSDS) DL + 1.0 LL ± W 0 EL where, W 0 is the seismic force amplification factor which is required to account for structural overstrength. The default value of W 0 is taken as 3.0 in the program. If the user defines one or more auto-seismic loads, then the value of W 0 defined for each auto-seismic load cases. Also if special seismic data is defined by the user, the user specifies an W 0 value, and the user requests the program to include the special seismic design data, then the user specified W 0 takes precedence over the default 18 Design Loading Combinations Chapter III Check/Design for AISC-ASD01 Figure III-1 AISC-ASD Definition of Geometric Properties Design Loading Combinations 19 CSI Steel Design Manual Section Description Ratio Checked Compact Section b f 2t f ( rolled) £ 65 Fy b f 2t f (welded) £ 65 Fy Noncompact Section £ 95 £ 95 Slender Section Fy No limit Fy / k c No limit For f a I-SHAPE d tw Fy £ 0.16 640 f £ (1 - 3.74 a ) , Fy Fy No limit No limit For f a / Fy > 0.16 £ 257 / Fy . If compression only, £ 253 Fy h tw b tf d tw No limit £ 190 Fy otherwise £ 760 Fb £ 238 Fy 14000 Fy ( Fy + 16.5) £ 260 No limit As for I-shapes No limit No limit h tw No limit As for I-shapes As for I-shapes Other t w ³ t f 2 , d w £ 6b f None None BOX b tf As for I-shapes As for I-shapes No limit d tw As for I-shapes No limit No limit No limit As for I-shapes As for I-shapes h tw CHANNEL Other No limit No limit Table III-2 Limiting Width-Thickness Ratios for Classification of Sections Based on AISC-ASD 20 £ Design Loading Combinations If welded b f dw t f tw If rolled b f dw t f tw £ 0.25, £ 3.0 £ 0.5, £ 2.0 Chapter III Check/Design for AISC-ASD01 Section Description Ratio Checked bf 2t f d tw Compact Section £ 65 Fy Not applicable Noncompact Section £ 95 Fy No limit £ 127 Fy No limit T-SHAPE Other No limit Slender Section No limit If welded b f d w ³ 0.5, t f t w ³ 1.25 If rolled b f d w ³ 0.5, t f t w ³ 1.10 DOUBLE ANGLES b t Not applicable £ 76 Fy No limit ANGLE b t Not applicable £ 76 Fy No limit £ 3,300 Fy £ 3,300 Fy PIPE D t ROUND BAR ¾ Assumed Compact RECTANGLE ¾ Assumed Noncompact GENERAL ¾ Assumed Noncompact £ 13,000 Fy (Compression only) No limit for flexure Table III-2 Limiting Width-Thickness Ratios for Classification of Sections Based on AISC-ASD (Cont.) values and those defined for the auto-seismic load cases. Moreover, W 0 can be overwritten for each individual member. The overwritten W 0 gets the highest precedence. The guidelines for selecting a reasonable value for W 0 can be found in ANSI/AISC 341 SEISMIC section 4.1 and Table I-4-1. These are also the default design load combinations in the program whenever the AISC-ASD01 code is used. The user should use other appropriate loading combiDesign Loading Combinations 21 CSI Steel Design Manual nations if roof live load is separately treated, if other types of loads are present, or if pattern live loads are to be considered. When designing for combinations involving earthquake and Wind loads, allowable stresses are NOT increased by the 4/3 factor per the ASD Supplement No. 1 which references ASCE7. For seismic combinations, the allowable stresses are increased by 1.7 factor in accordance with ANSI/AISC 341 Seismic Section 4.2. Live load reduction factors can be applied to the member forces of the live load case on an element-by-element basis to reduce the contribution of the live load to the factored loading. Classification of Sections The allowable stresses for axial compression and flexure are dependent upon the classification of sections as either Compact, Noncompact, Slender, or Too Slender. The program classifies the individual members according to the limiting width/thickness ratios given in Table III-2 (ASD B5.1, F3.1, F5, G1, A-B5-2). The definition of the section properties required in this table is given in Figure III-1 and Table III-1. If the section dimensions satisfy the limits shown in the table, the section is classified as either Compact, Noncompact, or Slender. If the section satisfies the criteria for Compact sections, then the section is classified as Compact section. If the section does not satisfy the criteria for Compact sections but satisfies the criteria for Noncompact sections, the section is classified as Noncompact section. If the section does not satisfy the criteria for Compact and Noncompact sections but satisfies the criteria for Slender sections, the section is classified as Slender section. If the limits for Slender sections are not met, the section is classified as Too Slender. Stress check of Too Slender sections is beyond the scope of the program. In general the design sections need not necessarily be Compact to satisfy ANSI/AISC 341-02 codes. However, for certain special seismic cases they have to be Compact and have to satisfy special slenderness requirements. See subsection “Seismic Requirements” later in this manual. The sections which do satisfy these additional requirements are classified and reported as “SEISMIC” in the program. These special requirements for classifying the sections as “SEISMIC” in the program are given in Table III-3 (ANSI/AISC 341SEISMIC 8.2, Table I-8-1). If these criteria are not satisfied, when the code requires them to be satisfied, the user must modify the section property. In this case the program gives an error message in the output file. 22 Classification of Sections Chapter III Check/Design for AISC-ASD01 Description of Section WidthThickness Ratio (l) COMPACT (SEISMIC ZONE) (l ps ) NONCOMPACT (Uniform Compression) (M 22 » M 33 » 0) (l r ) b f 2t f (rolled) £ 0.3 E Fy £ 056 . E Fy b f 2t f (welded) £ 0.3 E Fy £ 056 . E Fy £ 1.49 E Fy £ 0.64 E Fy £ 1.49 E Fy For Pu I-SHAPE hc tw j b Py £ 0.125, E æç P ö £ 314 . 1 - 1.54 u ÷ Fy çè j b Py ÷ ø For Pu j b Py > 0.125 ìï E æç P ö E üï . 2.33 - u ÷ £ í112 ³ 1.49 ý ç ÷ Fy è j b Py ø Fy ïþ ïî b tf hc t w BOX 0. 64 E Fy Not applicable CHANNEL, DOUBLE CHANNEL bf hc tf tw As for I-shapes As for I-shapes As for I-shapes As for I-shapes T-SHAPE bf d 2t f tw Not applicable Not applicable As for I-shapes £ 075 . E Fy ANGLE b t 0.3 E Fy £ 0.45 E Fy DOUBLE-ANGLE (Separated) b t 0.3 E Fy £ 0.45 E Fy Table III-3 Limiting Width-Thickness Ratios for Classification of Sections (Special Cases) based on AISC-LRFD Classification of Sections 23 CSI Steel Design Manual In classifying web slenderness of I-shapes, Box, and Channel sections, it is assumed that there are no intermediate stiffeners (ASD F5, G1). Double angles are conservatively assumed to be separated. Special Seismic Provisions of Member Design When using the AISC-ASD01 option, the following Framing Systems are recognized (ANSI/AISC 341 SEISMIC 9, 10, 11, 12, 13, 14, 15): • Ordinary Moment Frame (OMF) • Intermediate Moment Frame (IMF) • Special Moment Frame (SMF) • Ordinary Concentrically Braced Frame (OCBF) • Special Concentrically Braced Frame (SCBF) • Eccentrically Braced Frame (EBF) • Special Truss Moment Frame (STMF) By default the frame type is taken as Special Moment-Resisting Frame (SMRF) in the program. However, the frame type can be overwritten in the Preference form to change the default and in the Overwrites form on a member by member basis. If any member is assigned with a frame type, the change of the frame type in the Preference will not modify the frame type of the individual member for which it is assigned. Currently the program does not apply any special requirement for STMF. The special seismic requirements checked by the program for member design are dependent on the type of framing used and are described below for each type of framing. Thus special provisions for buildings are only applied if the building frame is classified as seismic design category (SDC) D or E. (ANSI/AISC 341 SEISMIC 1). No special requirement is checked for frames with seismic design category A, B, or C. Ordinary Moment Frames (OMF) For this framing system, the following additional requirements are checked and reported (ANSI/AISC 341 SEISMIC 11): Pu in columns due to prescribed loading combinations without considjPn eration of amplified seismic load is greater than 0.4, the axial compressive and tensile strengths are checked in absence of any applied moment and shear for • When 24 Special Seismic Provisions of Member Design Chapter III Check/Design for AISC-ASD01 the following Special Seismic Load Combinations (ANSI/AISC 341 SEISMIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3). (0.9 - 0.2S )DL ± W DS 0 EL (12. + 0.2S )DL + 10. LL ± W DS 0 EL Intermediate Moment Frames (IMF) For this framing system, the following additional requirements are checked and reported (ANSI/AISC 341 SEISMIC 10): Pu in columns due to prescribed loading combinations without considjPn eration of amplified seismic load is greater than 0.4, the axial compressive and tensile strengths are checked in absence of any applied moment and shear for the following Special Seismic Load Combinations (ANSI/AISC 341 SEISMIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2). • When (0.9 - 0.2SDS)DL ± W 0 EL (12. + 0.2SDS)DL + 10. LL ± W 0 EL Special Moment Frames (SMF) For this framing system, the following additional requirements are checked or reported (ANSI/AISC 341 SEISMIC 9): Pu in columns due to prescribed loading combinations without considjPn eration of amplified seismic load is greater than 0.4, the axial compressive and tensile strengths are checked in absence of any applied moment and shear for the following Special Seismic Load Combinations (AISC SEISMIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2). • When (0.9 - 0.2S )DL ± W DS 0 EL (12. + 0.2S )DL + 10. LL ± W DS 0 EL Special Seismic Provisions of Member Design 25 CSI Steel Design Manual Section Type I-SHAPE Reduction Factor for Unstiffened Slender Elements (Qs ) ì 1.0 ïï Qs = í1.293 - 0.00309[bf 2 t f ] Fy k c 2 ï ïî 26,200 k c [bf 2 t f ] Fy { } if if 95 if bf 2 t f £ 95 Fy k c , Fy k c < bf 2 t f < 195 Fy k c , bf 2 t f ³ 195 Fy k c . Equation Reference ASD A-B5-3, ASD A-B5-4 BOX Qs = 1 ASD A-B5.2c CHANNEL As for I-shapes with b f 2t f replaced by b f t f . ASD A-B5-3, ASD A-B5-4 For flanges, as for flanges in I-shapes. For web see below. T-SHAPE ì 1.0 , if ïï Qs £ í1.908 - 0.00715[d t w ] Fy , if 2 ï if ïî 20,000 [d t w ] Fy , { } 127 ì 1.0 , if ïï Qs = í1.340 - 0.00447[b t] Fy , if 2 ï if ïî 15,500 [b t] Fy , 76 ANGLE ì 1.0 , if ïï Qs = í1.340 - 0.00447[b t] Fy , if 2 ï if ïî 15,500 [b t] Fy , 76 { } } Fy , Fy < d t w < 176 Fy , d t w ³ 176 DOUBLEANGLE { d t w £ 127 b t £ 76 Fy . Fy , Fy < b t < 155 Fy , b t ³ 155 Fy . b t £ 76 Fy , Fy < b t < 155 Fy , b t ³ 155 Fy . ASD A-B5-3, ASD A-B5-4, ASD A-B5-5, ASD A-B5-6 ASD A-B5-1, ASD A-B5-2, SAM 4-3 ASD A-B5-1, ASD A-B5-2, SAM 4-3 PIPE Qs = 1 ASD A-B5.2c ROUND BAR Qs = 1 ASD A-B5.2c RECTANGULAR Qs = 1 ASD A-B5.2c GENERAL Qs = 1 ASD A-B5.2c Table III-4 Reduction Factor for Unstiffened Slender Elements, Q s 26 Special Seismic Provisions of Member Design Chapter III Check/Design for AISC-ASD01 Section Type I-SHAPE Effective Width for Stiffened Sections ì ï h, ï he = í ï 253 t w ïî f ì ï h, ï he = í ï 253 t w ïî f BOX CHANNEL é 44.3 ù ú, ê1 ( h tw ) f û ë é 44.3 ù ú, ê1 ( h tw ) f û ë if h 195.74 , £ tw f if h 195.74 > . tw f if h 195.74 , £ tw f if h 195.74 > . tw f ì if ï b, ï be = í 253 t f é 50.3 ù ï ú , if ê1 ï f êë ( h t f ) f úû î ì if ï h, ï he = í ù é ï 253 t w ê1 - 44.3 ú , if ïî f ë ( h t w ) f û b 183.74 , £ tf f b 183.74 . > t f h 195.74 , £ tw f h 195.74 > . tw f Equation Reference (compression only, f = P ) Ag (compression only, f = P ) Ag ASD A-B5-8 (compr., flexure, f = 0.6 Fy ) ASD A-B5-7 P ) Ag ASD A-B5-8 (compression only, f = ASD A-B5-8 T-SHAPE be = b ASD A-B5.2c DOUBLEANGLE be = b ASD A-B5.2c ANGLE be = b ASD A-B5.2c PIPE Q a = 1, (However, special expression for allowable axial stress is given.) ASD A-B5-9 ROUND BAR Not applicable ¾ RECTANGULAR be = b ASD A-B5.2c GENERAL Not applicable ¾ Table III-5 Effective Width for Stiffened Sections Special Seismic Provisions of Member Design 27 CSI Steel Design Manual • The I-, Channel-, and Double-Channel Shaped beams and columns are additionally checked for compactness criteria as described in Table VI-1 (AISC SEISMIC 9.4, 8.2, Table I-8-1). If this criteria is satisfied the section is reported as SEISMIC as described earlier under section classifications. If this criteria is not satisfied the, the program issues an error message. • The program checks the laterally unsupported length of beams to be less than 0.08( E Fy ) r y . If this criteria is not satisfied, the program issues an error message.(ANSI/AISC 341 SEISMIC 9.8) • The program checks the slenderness ratio, L®, for columns to be less than 60 (ANSI/AISC 341 SEISMIC 9.7.b(2)). If the criteria is not satisfied, the program issues an error message. Ordinary Concentrically Braced Frames (OCBF) For this framing system, the following additional requirements are checked or reported (ANSI/AISC 341 SEISMIC 14): • The columns and beams (NOT braces) are designed for the following special amplified seismic load combinations (AISC/ANSI 341 SEISMIC 14.2, ASCI 9.5.2.7.1, 2.3.2.1, 2.3.2). (0.9 - 0.2S )DL ± W EL (12. + 0.2S )DL + 10. LL ± W DS DS 0 0 EL Kl ratio of the braces for V or inverted-V configurations is r E (ANSI/AISC 341 SEISMIC 14.2). If this critechecked not to exceed 4 . 23 Fy • The maximum ria is not met, an error message is reported in the output. Special Concentrically Braced Frames (SCBF) For this framing system, the following additional requirements are checked or reported (ANSI/AISC 341 SEISMIC 13): Pu in columns due to prescribed loading combinations without considjPn eration of amplified seismic load is greater than 0.4, the axial compressive and tensile strengths are checked in absence of any applied moment and shear for • When 28 Special Seismic Provisions of Member Design Chapter III Check/Design for AISC-ASD01 the following Special Seismic Load Combinations (ANSI/AISC 341 SEISMIC 8.34.1, ASCE 9.5.2.7.1, 2.3.2). (0.9 - 0.2S )DL ± W DS 0 EL (12. + 0.2S )DL + 10. LL ± W DS 0 EL • All beam, columns and brace members are checked to be Compact according to Table V-2(ANSI/AISC 341 SEISMIC 13.5, 13.2d, 8.2, Table I-8-1). If this criteria is satisfied the section is reported as SEISMIC as described earlier under section classifications. If this criteria is not satisfied the program issues an error message. This special criteria is only checked for I, Channel, Double-Channel, Angle, Double-Angle, Box and Pipe sections. • The compressive strength for braces is taken as j c Pn . (ANSI/AISC 341 SEISMIC 13.26) Pu £ j c Pn • The maximum K l r ratio of the braces is checked not to exceed 5.87 Fy E . If this check is not met, the program issues an error message. Note: Beams intersected by Chevron (V or inverted-V) braces are NOT currently checked to have a strength to support loads for the following two conditions (ANSI/AISC 341 SEISMIC 13.4a): a A beam that is intersected by braces shall be designed to support the effects of all tributary dead and live loads form load combinations stipulated by the code, assuming the bracings are not present, and b A beam that is intersected by braces shall be designed to resist the effects of load combinations stipulated by the code, except that a load q b shall be substituted for the term E. q b is given by the difference of R y Fy A for the tension brace and 0.3 j c Pn for the compression brace. Users need to check for this requirement independently. Eccentrically Braced Frames (EBF) For this framing system, the program looks for and recognizes the eccentrically braced frame configurations shown in Figure VI-II. The following additional re- Special Seismic Provisions of Member Design 29 CSI Steel Design Manual quirements are checked or reported for the beams, columns and braces associated with these configurations (ANSI/AISC 341 SEISMIC 15). Pu in columns due to prescribed loading combinations without considjPn eration of amplified seismic load is greater than 0.4, the axial compressive and tensile strengths are checked in absence of any applied moment and shear for the following Special Seismic Load Combinations (ANSI/AISC 341 SEISMIC 8.3, 4.1, ASCE 9.5.2.7.1, 2.3.2). • When (0.9 - 0.2S )DL ± W DS 0 EL (12. + 0.2S )DL + 10. LL ± W DS 0 EL • The I-shaped, Channel-shaped, and Double-Channel Shaped beams are additionally checked for compactness criteria as described in Table VI-III (ANSI/AISC 341 SEISMIC 15.2, 8.2, Table I-8-1). If this criteria is satisfied the section is reported as SEISMIC as described earlier under section classifications. If this criteria is not satisfied the user must modify the program issues an error message. • The link beam yield strength, Fy , is checked not to exceed the following (AISC SEISMIC 15.2): Fy £ 50 ksi (ANSI/AISC 341 SEISMIC 15.2) If the check is not satisfied, the program issue an error message. • The shear strength for link beams is taken as follows (AISC SEISMIC 15.2): Vu £ j v Vn , (ANSI/AISC 341 SEISMIC 15.2) where, j Vn = min(j V pa , j 2 M pa e) , V pa = V p æP 1-ç u çP è y 2 ö ÷ , ÷ ø é P ù M pa = 1.18 M p ê1 - u ú , ë Py û 30 (ANSI/AISC 341 SEISMIC 15.2) Special Seismic Provisions of Member Design (ANSI/AISC 341 SEISMIC 15.1) (ANSI/AISC 341 SEISMIC 15.2) Chapter III Check/Design for AISC-ASD01 V p = 0.6 Fy ( d - 2t f ) t w , (ANSI/AISC 341 SEISMIC 15.2) M p = Z Fy , (ANSI/AISC 341 SEISMIC 15.2) j = jv (ANSI/AISC 341 SEISMIC 15.2) (default is 0.9) , Py = A g Fy . (ANSI/AISC 341 SEISMIC 15.2) • If Pu > 0.15 A g Fy , the link beam length, e, is checked not to exceed the following (ANSI/AISC 341 SEISMIC 15.2): ìé Aw ù é M p ù ï ê1.15 - 0.5 r ¢ ú ê1.6 ú if Ag û ë Vp û ïë e £í é Mp ù ï if ê1.6 ú ï V p ë û î r¢ Aw ³ 0.3 , Ag r¢ Aw < 0.3 , Ag (ANSI/AISC 341 SEISMIC 15.2) where, A w = ( d - 2t f ) t w , and (ANSI/AISC 341 SEISMIC 15.2) r ¢ = Pu Vu . (ANSI/AISC 341 SEISMIC 15.2) If the check is not satisfied, the program reports an error message. • The link beam rotation, q, of the individual bay relative to the rest of the beam is calculated as the story drift D M times bay length divided by the total lengths of link beams in the bay. The link beam rotation, q, is checked as follows (ANSI/AISC 341 SEISMIC 15.2). q £ 0.08 radian , where link beam clear length, e £ 1.6 M s Vs , q £ 0.03 radian , where link beam clear length, e ³ 2.6 M s Vs , and q £ value interpolated between 0.08 and 0.02 as the link beam clear length varies from 1.6 M s Vs to 2.6 M s Vs . • The beam strength outside the link is checked to be at least 1.1 times the beam forces corresponding to the controlling link beam shear strength (ANSI/AISC 341 SEISMIC 15.6). The controlling link beam nominal shear strength is taken as follows: min(V pa , 2 M pa e) , (ANSI/AISC 341 SEISMIC 15.6, 15.2) Special Seismic Provisions of Member Design 31 CSI Steel Design Manual The values of V pa and M pa are calculated following the procedure described above (ANSI/AISC 341SEISMIC 15.2). The correspondence between brace force and link beam force is obtained from the associated load cases, whichever has the highest link beam force of interest. All braces are checked to be at least compact per regular ANSI/AISC 341code (ANSI/AISC 341 SEISMIC 15.6). If this criteria is not satisfied, the program issues an error message. The brace strength is checked for 1.25R y times the brace forces corresponding to the controlling link beam nominal shear strength (ANSI/AISC 341 SEISMIC 15.6). The controlling link beam nominal shear strength and the corresponding forces are obtained by the process described earlier. The I-, Channel-, and Double-Channel- shaped column sections are checked to be at least compact per regular ANSI/AISC 341 code (ANSI/AISC 341 SEISMIC 8.2, Table I-8-1, LRFD B.5.1). If this criterion is not satisfied, the program issues an error message. • The column strength is checked for 1.1R y times the column forces corresponding to the controlling link beam nominal shear strength (ANSI/AISC 341 SEISMIC 15.8). The controlling link beam nominal shear strength and the corresponding forces are obtained by the process described above. Note: Axial forces in the beams are included in checking the beams. The user is reminded that using a rigid diaphragm model will result in zero axial forces in the beams. The user must disconnect some of the column lines from the diaphragm to allow beams to carry axial loads. It is recommended that only one column line per eccentrically braced frame be connected to the rigid diaphragm or a flexible diaphragm model be used. Calculation of Stresses The stresses are calculated at each of the previously defined stations. The member stresses for non-slender sections that are calculated for each load combination are, in general, based on the gross cross-sectional properties.: f a = P/A f b 33 = M 33 /S 33 f b 22 = M 22 /S 22 f v 2 = V2 /A v 2 f v 3 = V3 /A v 3 32 Calculation of Stresses Chapter III Check/Design for AISC-ASD01 If the section is slender with slender stiffened elements, like slender web in I, Channel, and Box sections or slender flanges in Box, effective section moduli based on reduced web and reduced flange dimensions are used in calculating stresses. f a = P/A f b 33 = M 33 /S eff , 33 f b 22 = M 22 /S eff , 22 f v 2 = V2 /A v 2 f v 3 = V3 /A v 3 (ASD A-B5.2d) (ASD A-B5.2d) (ASD A-B5.2d) (ASD A-B5.2d) (ASD A-B5.2d) The flexural stresses are calculated based on the properties about the principal axes. For I, Box, Channel, T, Double-angle, Pipe, Circular and Rectangular sections, the principal axes coincide with the geometric axes. For Single-angle sections, the design considers the principal properties. For general sections it is assumed that all section properties are given in terms of the principal directions. For Single-angle sections, the shear stresses are calculated for directions along the geometric axes. For all other sections the shear stresses are calculated along the geometric and principle axes. Calculation of Allowable Stresses The allowable stresses in compression, tension, bending, and shear are computed for Compact, Noncompact, and Slender sections according to the following subsections. The allowable flexural stresses for all shapes of sections are calculated based on their principal axes of bending. For the I, Box, Channel, Circular, Pipe, T, Double-angle and Rectangular sections, the principal axes coincide with their geometric axes. For the Angle sections, the principal axes are determined and all computations related to flexural stresses are based on that. If the user specifies nonzero allowable stresses for one or more elements in the design over write form, these values will override the above mentioned calculated values for those elements as defined in the following subsections. The specified allowable stresses should be based on the principal axes of bending. Allowable Stress in Tension The allowable axial tensile stress value Fa is assumed to be 0.60 Fy . Fa = 0.6 Fy (ASD D1, ASD SAM 2) Calculation of Allowable Stresses 33 CSI Steel Design Manual It should be noted that net section checks are not made. For members in tension, if l r is greater than 300, a message to that effect is printed (ASD B7, ASD SAM 2). For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33 in computing l r . Allowable Stress in Compression The allowable axial compressive stress is the minimum value obtained from flexural buckling and flexural-torsional buckling. The allowable compressive stresses are determined according to the following subsections. For members in compression, if Kl r is greater than 200, a warning message is printed (ASD B7, ASD SAM 4). For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33 in computing Kl r . Flexural Buckling The allowable axial compressive stress value, Fa , depends on the slenderness ratio Kl r based on gross section properties and a corresponding critical value, C c , where K l ü ìK l Kl = max í 33 33 , 22 22 ý , and r r22 þ î r33 Cc = 2p 2 E . Fy (ASD E2, ASD SAM 4) For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33 in computing Kl r . For Compact or Noncompact sections Fa is evaluated as follows: ì ( Kl/r ) 2 ü 1.0 í ý Fy 2C c2 þ î Fa = 5 + 3 Fa = 34 3 ( Kl/r ) 8 Cc - (Kl/r) 12 p 2 E , 23 ( Kl r ) 2 Calculation of Allowable Stresses 3 , if Kl £ Cc , r (ASD E2-1, SAM 4-1) if Kl > Cc . r (ASD E2-2, SAM 4-2) 8 C c3 Chapter III Check/Design for AISC-ASD01 If Kl r is greater than 200, then the calculated value of Fa is taken not to exceed the value of Fa calculated by using the equation ASD E2-2 for Compact and Noncompact sections (ASD E1, B7). For Slender sections, except slender Pipe sections, Fa is evaluated as follows: Fa = Q Fa = ìï ( Kl/r ) 2 üï F í1.0 2 ý y 2C c¢ þï îï 3 ( Kl/r ) 5 + 3 8 C c¢ 12 p 2 E , 23 ( Kl r ) 2 (Kl/r) 8 C c¢ 3 , if Kl £ C c¢ , (ASD A-B5-11, SAM 4-1) r if Kl > C c¢ . (ASD A-B5-12, SAM 4-2) r 3 where, C c¢ = 2p 2 E . Q Fy (ASD A-B5.2c, ASD SAM 4) For slender sections, if Kl r is greater than 200, then the calculated value of Fa is taken not to exceed its value calculated by using the equation ASD A-B5-12 (ASD B7, E1). For slender Pipe sections Fa is evaluated as follows: Fa = 662 + 0.40 Fy D t (ASD A-B5-9) The reduction factor, Q, for all compact and noncompact sections is taken as 1. For slender sections, Q is computed as follows: Q = Q s Q a , where (ASD A-B5.2.c, SAM 4) Q s = reduction factor for unstiffened slender elements, and (ASD A-B5.2.a) Q a = reduction factor for stiffened slender elements. (ASD A-B5.2.c) The Q s factors for slender sections are calculated as described in Table III-4 (ASD A-B5.2a, ASD SAM 4). The Q a factors for slender sections are calculated as the ratio of effective cross-sectional area and the gross cross-sectional area. Calculation of Allowable Stresses 35 CSI Steel Design Manual Qa = Ae Ag (ASD A-B5-10) The effective cross-sectional area is computed based on effective width as follows: A e = A g - å (b - be ) t b e for unstiffened elements is taken equal to b, and b e for stiffened elements is taken equal to or less than b as given in Table III-5 (ASD A-B5.2b). For webs in I, box, and Channel sections, h e is used as b e and h is used as b in the above equation. Flexural-Torsional Buckling The allowable axial compressive stress value, Fa , determined by the limit states of torsional and flexural-torsional buckling is determined as follows (ASD E3, C-E3): 2 ì Kl/r ) üï ( ï e í1.0 ý Fy ¢2 2C c ïþ ïî , if ( Kl/r ) £ C c¢ , Fa = Q 3 e Kl/r ) 3 ( Kl/r ) ( 5 e e + 3 3 8 C c¢ 8 C c¢ Fa = 12 p 2 E 23 ( Kl/r ) 2 , if ( Kl/r ) > C c¢ . e (E2-1, A-B5-11) (E2-2, A-B5-12) e where, 2p 2 E , and Q Fy C c¢ = (Kl/r) = e p2E . Fe (ASD E2, A-B5.2c, SAM 4) (ASD C-E2-2, SAM 4-4) ASD Commentary (ASD C-E3) refers to the 1986 version of the AISC-LRFD code for the calculation of Fe . The 1993 version of the AISC-LRFD code is the same as the 1986 version in this respect. Fe is calculated in the program as follows: • For Rectangular, I, Box, and Pipe sections: 36 Calculation of Allowable Stresses Chapter III Check/Design for AISC-ASD01 é 2 ù p EC w 1 ê + GJ ú Fe = 2 ê (K l ) ú I 22 + I 33 ë zz û (LRFD A-E3-5) • For T-sections and Double-angles: æ F + Fez Fe = çç e22 2H è ö ÷ ÷ ø é 4 Fe22 Fez H ê1 - 1 ( Fe22 + Fez ) 2 êë ù ú úû (LRFD A-E3-6) ö ÷ ÷ ø é 4 Fe33 Fez H ê1 - 1 ( Fe33 + Fez ) 2 êë ù ú úû (LRFD A-E3-6) 4 Fe33 Fez H ù ö é 1 1 ÷ ú ê ÷ ( Fe33 + Fez ) 2 úû ø êë (ASD SAM C-C4-1) • For Channels: æ F + Fez Fe = çç e33 2H è • For Single-angle sections with equal legs: æ F + Fez Fe = çç e33 2H è • For Single-angle sections with unequal legs, Fe is calculated as the minimum real root of the following cubic equation (ASD SAM C-C4-2, LRFD A-E3-7): ( Fe - Fe33 )( Fe - Fe22 )( Fe -Fez ) - Fe2 ( Fe -Fe22 ) x 02 r02 - Fe2 ( Fe - Fe33 ) y 02 r02 =0, where, x 0 , y0 are the coordinates of the shear center with respect to the centroid, x 0 = 0 for double-angle and T-shaped members (y-axis of symme- try), r0 = x 02 + y 02 + æ x 2 + y2 H = 1 - çç 0 2 0 è r0 Fe33 = I 22 + I 33 = polar radius of gyration about the shear center, Ag ö ÷, ÷ ø (LRFD A-E3-9) p2E (K l 33 33 r33 ) 2 , (LRFD A-E3-10) Calculation of Allowable Stresses 37 CSI Steel Design Manual Fe22 = p2E (K 22 l 22 r22 ) 2 , (LRFD A-E3-11) é 2 ù p EC w ú 1 , + GJ Fez = ê 2 ê (K l ) ú Ar02 ë zz û (LRFD A-E3-12) K 22 , K 33 are effective length factors in minor and major directions, K z is the effective length factor for torsional buckling, and it is taken equal to K 22 in the program, l 22 , l 33 are effective lengths in the minor and major directions, lz is the effective length for torsional buckling, and it is taken equal to l 22 . For angle sections, the principal moment of inertia and radii of gyration are used for com put ing Fe (ASD SAM 4). Also, the maxi mum value of Kl, i.e, max( K 22 l 22 , K 33 l 33 ), is used in place of K 22 l 22 or K 33 l 33 in calculating Fe22 and Fe33 in this case. Allowable Stress in Bending The allowable bending stress depends on the following criteria: the geometric shape of the cross-section, the axis of bending, the compactness of the section, and a length parameter. I-sections For I-sections the length parameter is taken as the laterally unbraced length, l 22 , which is compared to a critical length, l c . The critical length is defined as ìï 76 b f 20, 000 A f l c = min í , d Fy ïî Fy Af 38 üï ý , where ïþ is the area of compression flange, Calculation of Allowable Stresses (ASD F1-2) Chapter III Check/Design for AISC-ASD01 Major Axis of Bending If l 22 is less than l c , the major allowable bending stress for Compact and Noncompact sections is taken depending on whether the section is welded or rolled and whether f y is greater than 65 ksi or not. For Compact sections: Fb 33 = 0.66 Fy if f y £ 65 ksi , (ASD F1-1) Fb 33 = 0.60 Fy if f y > 65 ksi , (ASD F1-5) For Noncompact sections: bf æ Fb 33 = ç 0.79 - 0.002 ç 2t f è ö Fy ÷ Fy , if rolled and f y £ 65 ksi, (ASD F1-3) ÷ ø æ bf Fb 33 = ç 0.79 - 0.002 ç 2tf è Fy ö ÷ F , if welded and f £ 65 ksi, (ASDF1-4) y y kc ÷ ø Fb 33 = 0.60 Fy if f y > 65 ksi.. (ASD F1-5) If the unbraced length l 22 is greater than l c , then for both Compact and Noncompact I-sections the allowable bending stress depends on the l 22 rT ratio. For l 22 £ rT 102, 000 C b , Fy Fb 33 = 0.60 Fy , for 102, 000 C b l < 22 £ Fy rT (ASD F1-6) 510, 000 C b , Fy é 2 Fy ( l 22 / rT ) 2 ù Fb 33 = ê ú Fy £ 0.60 Fy , and êë 3 1530, 000 C b úû for (ASD F1-6) l 22 510, 000 C b , > rT Fy Calculation of Allowable Stresses 39 CSI Steel Design Manual é 170, 000 C b ù Fb 33 = ê £ 0.60 Fy , 2 ú ë ( l 22 / rT ) û (ASD F1-7) and Fb 33 is taken not to be less than that given by the following formula: Fb 33 = 12, 000 C b l 22 ( d / A f ) (ASD F1-8) £ 0.6 Fy where, rT is the radius of gyration of a section comprising the compression flange and 1 3 the compression web taken about an axis in the plane of the web, æM C b = 1.75 +1.05 çç a è Mb ö ÷ ÷ + 0.3 ø æ Ma çç è Mb 2 ö ÷ ÷ £ 2.3, where ø (ASD F1.3) M a and M b are the end moments of any unbraced segment of the member and M a is numerically less than M b ; M a M b being positive for double curvature bending and negative for single curvature bending. Also, if any moment within the segment is greater than M b , C b is taken as 1.0. Also, C b is taken as 1.0 for cantilevers and frames braced against joint translation (ASD F1.3). The program defaults C b to 1.0 if the unbraced length, l 22 , of the member is redefined by the user (i.e. it is not equal to the length of the member). The user can overwrite the value of C b for any member by specifying it. The allowable bending stress for Slender sections bent about their major axis is determined in the same way as for a Noncompact section. Then the following additional considerations are taken into account. If the web is slender, then the previously computed allowable bending stress is reduced as follows: Fb¢33 = R PG R e Fb 33 , where R PG = 1.0 - 0.0005 Aw Af ( 12 + 3a - a 3 Re = 12 + 2 40 éh 760 ê Fb 33 êë t ) AA Aw Af Calculation of Allowable Stresses (ASD G2-1) ù ú £ 1.0 , úû (ASD G2) w f £ 1.0 , (hybrid girders) (ASD G2) Chapter III Check/Design for AISC-ASD01 R e =1.0 , (non-hybrid girders) (ASD G2) A w = Area of web, in 2 , A f = Area of compression flange, in 2 , a= 0.6 Fy Fb 33 (ASD G2) £ 1.0 Fb 33 = Allowable bending stress assuming the section is non-compact, and Fb¢33 = Allowable bending stress after considering web slenderness. In the above expressions, R e is taken as 1, because currently the program deals with only non-hybrid girders. If the flange is slender, then the previously computed allowable bending stress is taken to be limited as follows. Fb¢33 £ Q s (0.6 Fy ) , where (ASD A-B5.2a, A-B5.2d) Q s is defined earlier. Minor Axis of Bending The minor direction allowable bending stress Fb 22 is taken as follows: For Compact sections: Fb 22 = 0.75 Fy if f y £ 65 ksi , (ASD F2-1) Fb 22 = 0.60 Fy if f y > 65 ksi , (ASD F2-2) For Noncompact and Slender sections: bf æ Fb 22 = ç 1.075 - 0.005 ç 2t f è Fb 22 = 0.60 Fy ö Fy ÷ Fy , ÷ ø if f y £ 65 ksi, (ASD F2-3) if f y > 65 ksi.. (ASD F2-2) Calculation of Allowable Stresses 41 42 Calculation of Allowable Stresses Chapter III Check/Design for AISC-ASD01 If the web is slender, then the previously computed allowable bending stress is reduced as follows: Fb¢33 = R e R PG Fb 33 (ASD G2-1) If the flange is slender, the previously computed allowable bending stress is taken to be limited as follows: Fb¢33 £ Q s (0.6 Fy ) (ASD A-B5.2a, A-B5.2d) The definition for rT , C b , A f , A w , R e , R PG , Q s , Fb 33 , and Fb¢33 are given earlier. Minor Axis of Bending The minor direction allowable bending stress Fb 22 is taken as follows: (ASD F2-2) Fb 22 = 0.60 Fy T-sections and Double angles For T sections and Double angles, the allowable bending stress for both major and minor axes bending is taken as, Fb = 0.60 Fy . Box Sections and Rectangular Tubes For all Box sections and Rectangular tubes, the length parameter is taken as the laterally unbraced length, l 22 , measured compared to a critical length, l c . The critical length is defined as ì b 1200 b ü l c = max í(1950 + 1200 M a /M b ) , ý F Fy þ y î (ASD F3-2) where M a and M b have the same definition as noted earlier in the formula for 1200 b in the program. C b . If l 22 is specified by the user, l c is taken as Fy Major Axis of Bending If l 22 is less than l c , the allowable bending stress in the major direction of bending is taken as: Calculation of Allowable Stresses 43 CSI Steel Design Manual Fb 33 = 0.66 Fy (for Compact sections) (ASD F3-1) Fb 33 = 0.60 Fy (for Noncompact sections) (ASD F3-3) If l 22 exceeds l c , the allowable bending stress in the major direction of bending for both Compact and Noncompact sections is taken as: (ASD F3-3) Fb 33 = 0.60 Fy The major direction allowable bending stress for Slender sections is determined in the same way as for a Noncompact section. Then the following additional consideration is taken into account. If the web is slender, then the previously computed allowable bending stress is reduced as follows: Fb¢33 = R e R PG Fb 33 (ASD G2-1) The definition for R e , R PG , Fb 33 , and Fb¢33 are given earlier. If the flange is slender, no additional consideration is needed in computing allowable bending stress. However, effective section dimensions are calculated and the section modulus is modified according to its slenderness. Minor Axis of Bending If l 22 is less than l c , the allowable bending stress in the minor direction of bending is taken as: Fb 22 = 0.66 Fy (for Compact sections) (ASD F3-1) Fb 22 = 0.60 Fy (for Noncompact and Slender sections) (ASD F3-3) If l 22 exceeds l c , the allowable bending stress in the minor direction of bending is taken, irrespective of compactness, as: (ASD F3-3) Fb 22 = 0.60 Fy Pipe Sections For Pipe sections, the allowable bending stress for both major and minor axes of bending is taken as 44 Fb = 0.66 Fy (for Compact sections), and (ASD F3-1) Fb = 0.60 Fy (for Noncompact and Slender sections). (ASD F3-3) Calculation of Allowable Stresses Chapter III Check/Design for AISC-ASD01 Round Bars The allowable stress for both the major and minor axis of bending of round bars is taken as, Fb = 0.75 Fy . (ASD F2-1) Rectangular and Square Bars The allowable stress for both the major and minor axis of bending of solid square bars is taken as, Fb = 0.75 Fy . (ASD F2-1) For solid rectangular bars bent about their major axes, the allowable stress is given by Fb = 0.60 Fy , And the allowable stress for minor axis bending of rectangular bars is taken as, Fb = 0.75 Fy . (ASD F2-1) Single-Angle Sections The allowable flexural stresses for Single-angles are calculated based on their principal axes of bending (ASD SAM 5.3). Major Axis of Bending The allowable stress for major axis bending is the minimum considering the limit state of lateral-torsional buckling and local buckling (ASD SAM 5.1). The allowable major bending stress for Single-angles for the limit state of lateraltorsional buckling is given as follows (ASD SAM 5.1.3): é F ù Fb, major = ê0.55 - 0.10 ob ú Fob , Fy û ë if Fob £ Fy (ASD SAM 5-3a) é Fy ù Fb, major = ê0.95 - 0.50 ú Fy £ 0.66Fy , if Fob > Fy F ob êë úû (ASD SAM 5-3b) where, Fob is the elastic lateral-torsional buckling stress as calculated below. Calculation of Allowable Stresses 45 CSI Steel Design Manual The elastic lateral-torsional buckling stress, Fob , for equal-leg angles is taken as Fob = C b 28,250 , lt (ASD SAM 5-5) and for unequal-leg angles Fob is calculated as Fob = 143,100 C b I min S major é b 2 + 0.052( lt r ) 2 + b ù , w w min û l ë 2 (ASD SAM 5-6) where, t = min(t w , t f ) , l = max ( l 22 , l 33 ) , I min = minor principal moment of inertia, I max = major principal moment of inertia, S major = major section modulus for compression at the tip of one leg, rmin = radius of gyration for minor principal axis, é 1 bw = ê ë I max ò A ù z( w 2 + z 2 ) dA ú - 2z 0 , û (ASD SAM 5.3.2) z = coordinate along the major principal axis, w = coordinate along the minor principal axis, and z 0 = coordinate of the shear center along the major principal axis with respect to the centroid. b w is a special section property for angles. It is positive for short leg in compression, negative for long leg in compression, and zero for equal-leg angles (ASD SAM 5.3.2). However, for conservative design in the program, it is always taken as negative for unequal-leg angles. In the above expressions C b is calculated in the same way as is done for I sections with the exception that the upper limit of C b is taken here as 1.5 instead of 2.3. æM C b = 1.75 +1.05 çç a è Mb 46 ö ÷ ÷ + 0.3 ø Calculation of Allowable Stresses æ Ma çç è Mb 2 ö ÷ ÷ £ 1.5 ø (ASD F1.3, SAM 5.2.2) Chapter III Check/Design for AISC-ASD01 The allowable major bending stress for Single-angles for the limit state of local buckling is given as follows (ASD SAM 5.1.1): Fb, major = 0.66 Fy , if Fb, major = 0.60 Fy , if Fb, major = Q (0.60 Fy ) , if 65 < Fy 65 b , £ t Fy (ASD SAM 5-1a) b 76 , £ t Fy (ASD SAM 5-1b) 76 b , > t Fy (ASD SAM 5-1c) where, t = thickness of the leg under consideration, b = length of the leg under consideration, and Q = slenderness reduction factor for local buckling. (ASD A-B5-2, SAM 4) In calculating the allowable bending stress for Single-angles for the limit state of local buckling, the allowable stresses are calculated considering the fact that either of the two tips can be under compression. The minimum allowable stress is considered. Minor Axis of Bending The allowable minor bending stress for Single-angles is given as follows (ASD SAM 5.1.1, 5.3.1b, 5.3.2b): Fb,minor = 0.66 Fy , if Fb,minor = 0.60 Fy , if Fb,minor = Q (0.60 Fy ) , if 65 Fy < 65 b , £ t Fy (ASD SAM 5-1a) b 76 , £ t Fy (ASD SAM 5-1b) 76 b , > t Fy (ASD SAM 5-1c) In calculating the allowable bending stress for Single-angles it is assumed that the sign of the moment is such that both the tips are under compression. The minimum allowable stress is considered. Calculation of Allowable Stresses 47 CSI Steel Design Manual General Sections For General sections the allowable bending stress for both major and minor axes bending is taken as, Fb = 0.60 Fy . Allowable Stress in Shear The shear stress is calculated along the geometric axes for all sections. For I, Box, Channel, T, Double angle, Pipe, Circular and Rectangular sections, the principal axes coincide with their geometric axes. For Single-angle sections, principal axes do not coincide with the geometric axes. Major Axis of Bending The allowable shear stress for all sections except I, Box and Channel sections is taken in the program as: Fv = 0.40 Fy (ASD F4-1, SAM 3-1) The allowable shear stress for major direction shears in I-shapes, boxes and channels is evaluated as follows: Fv = 0.40 Fy , Fv = if Cv Fy £ 0.40 Fy , 2.89 if 380 h , and £ tw Fy (ASD F4-1) h £ 260 . tw (ASD F4-2) 380 Fy < where, ì 45, 000 k v , 2 ï F h t ï ( w) Cv = í y ï 190 k v , ï h t w Fy î 48 Calculation of Allowable Stresses if k h ³ 56,250 v , tw Fy if k h < 56,250 v , Fy tw (ASD F4) Chapter III Check/Design for AISC-ASD01 5.34 ì , 2 ï 4.00 + a h ( ) ï kv = í 4.00 ï5.34 + , 2 ï a h) ( î tw = a = if a £1, h if a >1 , h (ASD F4) Thickness of the web, Clear distance between transverse stiffeners, in. Currently it is taken conservatively as the length, l 22 , of the member in the pro- gram, h = Clear distance between flanges at the section, in. Minor Axis of Bending The allowable shear stress for minor direction shears is taken as: Fv = 0.40 Fy (ASD F4-1, SAM 3-1) Calculation of Stress Ratios In the calculation of the axial and bending stress capacity ratios, first, for each station along the length of the member, the actual stresses are calculated for each load combination. Then the corresponding allowable stresses are calculated. Then, the capacity ratios are calculated at each station for each member under the influence of each of the design load combinations. The controlling capacity ratio is then obtained, along with the associated station and load combination. A capacity ratio greater than 1.0 indicates an overstress. During the design, the effect of the presence of bolts or welds is not considered. Also, the joints are not designed. Axial and Bending Stresses With the computed allowable axial and bending stress values and the factored axial and bending member stresses at each station, an interaction stress ratio is produced for each of the load combinations as follows (ASD H1, H2, SAM 6): • If f a is compressive and f a Fa > 0.15, the combined stress ratio is given by the larger of Calculation of Stress Ratios 49 CSI Steel Design Manual fa C m 33 f b 33 C m 22 f b 22 , and (ASD H1-1, SAM 6.1) + + Fa æ fa ö fa ö æ çç 1 ÷ Fb 33 çç 1 ÷ Fb 22 F' e33 ÷ F' e22 ÷ è è ø ø fa Q (0.60 Fy ) + f b 33 f + b 22 , where Fb 33 Fb 22 (ASD H1-2, SAM 6.1) f a , f b 33 , f b 22 , Fa , Fb 33 , and Fb 22 are defined earlier in this chapter, C m 33 and C m 22 are coefficients representing distribution of moment along the member length. 1.00 , if length is overwritten, ì ï 1.00 , if tension member, ï 0.85 , if sway frame, ï ï M Cm = í 0.6 - 0.4 a , if nonsway, no transverse loading, ï M b ï 0.85 , if nonsway, trans. load, end restrained, ï ï 1.00 , if nonsway, trans. load, end unrestrained. î (ASD H1) For sway frame C m = 0.85 , for nonsway frame without transverse load C m = 0.6 - 0.4 M a M b , for nonsway frame with transverse load and end restrained compression member C m = 0.85 , and for nonsway frame with transverse load and end unrestrained compression member C m =1.00 (ASD H1), where M a M b is the ratio of the smaller to the larger moment at the ends of the member, M a M b being positive for double curvature bending and negative for single curvature bending. When M b is zero, C m is taken as 1.0. The program defaults C m to 1.0 if the unbraced length factor, l, of the member is redefined by either the user or the program, i.e., if the unbraced length is not equal to the length of the member. The user can overwrite the value of C m for any member. C m assumes two values, C m 22 and C m 33 , associated with the major and minor directions. Fe¢ is given by Fe¢ = 12 p 2 E . 23 ( Kl / r ) 2 (ASD H1) • If f a is compressive and f a Fa £ 0.15 , a relatively simplified formula is used for the combined stress ratio. 50 Calculation of Stress Ratios Chapter III Check/Design for AISC-ASD01 fa f f + b 33 + b 22 Fa Fb 33 Fb 22 (ASD H1-3, SAM 6.1) • If f a is tensile or zero, the combined stress ratio is given by the larger of fa f f + b 33 + b 22 , and Fa Fb 33 Fb 22 (ASD H2-1, SAM 6.2) f b 33 f + b 22 , where Fb 33 Fb 22 f a , f b 33 , f b 22 , Fa , Fb 33 , and Fb 22 are defined earlier in this chapter. However, either Fb 33 or Fb 22 need not be less than 0.6 Fy in the first equation (ASD H2-1). The second equation considers flexural buckling without any beneficial effect from axial compression. For circular and pipe sections, an SRSS combination is first made of the two bending components before adding the axial load component, instead of the simple addition implied by the above formulae. For Single-angle sections, the combined stress ratio is calculated based on the properties about the principal axis (ASD SAM 5.3, 6.1.5). For I, Box, Channel, T, Double-angle, Pipe, Circular and Rectangular sections, the principal axes coincide with their geometric axes. For Single-angle sections, principal axes are determined in the program. For general sections no effort is made to determine the principal directions. Shear Stresses From the allowable shear stress values and the factored shear stress values at each station, shear stress ratios for major and minor directions are computed for each of the load combinations as follows: fv2 , Fv and fv3 . Fv For Single-angle sections, the shear stress ratio is calculated for directions along the geometric axis. For all other sections the shear stress is calculated along the principle axes which coincide with the geometric axes. Calculation of Stress Ratios 51 SAP2000 Steel Design Manual Joint Design When using AISC-ASD01 design code, the structural joints are checked and/or designed for the following: • Check for the requirement of continuity plate and determination of its area • Check for the requirement of doubler plate and determination of its thickness • Check for the ratio of beam flexural strength to column flexural strength • Reporting the beam connection shear • Reporting the brace connection force Design of Continuity Plates In a plan view of a beam/column connection, a steel beam can frame into a column in the following ways: • The steel beam frames in a direction parallel to the column major direction, i.e. the beam frames into the column flange. • The steel beam frames in a direction parallel to the column minor direction, i.e. the beam frames into the column web. • The steel beam frames in a direction that is at an angle to both of the principal axes of the column, i.e. the beam frames partially into the column web and partially into the column flange. To achieve a proper beam/column moment connection strength, continuity plates such as shown in are usually placed on the column, in line with the top and bottom flanges of the beam, to transfer the compression and tension flange forces of the beam into the column. For connection conditions described in the last two steps above, the thickness of such plates is usually set equal to the flange thickness of the corresponding beam. However, for the connection condition described by the first step above, where the beam frames into the flange of the column, such continuity plates are not always needed. The requirement depends upon the magnitude of the beam-flange force and the properties of the column. This is the condition that the program investigates. Columns of I-sections only are investigated. The program evaluates the continuity plate requirements for each of the beams that frame into the column flange (i.e. parallel to the column major direction) and reports the maximum continuity plate area that is needed for each beam flange. The continuity plate requirements 52 Joint Design Chapter III Check/Design for AISC-ASD01 are evaluated for moment frames (OMF, IMF, SMF) only. No check is made for braced frames (OCBC, SCBF, EBF). The program first evaluates the need for continuity plates. Continuity plates will be required if any of the following four conditions are not satisfied: • The column flange design strength in bending must be larger than the beam flange force, i.e., jR n = (0.9)6.25 t fc2 Fyc ³ Pbf if not at top story (LRFD K1-1) jR n = ( 0.5)( 0.9)6 .25t fc2 Fyc ³ Pbc if at top story (LRFD K1-2) • The design strength of the column web against local yielding at the toe of the fillet must be larger than the beam flange force, i.e., jR n = (1.0) (5.0 k c +t fb ) Fyc t wc ³ Pbf , if not at top story (LRFD K1-2) jR n = (10 . )( 2.5k c + t fb ) Fyc t wc ³ Pbf , if at top story (LRFD K1-3) • The design strength of the column web against crippling must be larger than the beam flange force, i.e., jR n = (0.75) 0.80 t 2 wc é æt ê1+ 3ç fb çd ê è c ë öæ t wc ÷ç ÷ç t øè fc 1.5 ö ÷ ÷ ø ù t ú EFyc fc ³ Pbf , t wc ú û if not at top story jR n = ( 0.75)( 0.40)t 2 wc é æt ê1+ 3ç fb çd ê è c ë öæ t wc ÷ç ÷ç t øè fc 1.5 ö ÷ ÷ ø (LRFD K1-4) ù t ú EFyc fc ³ Pbf , t wc ú û it at top story (LRFD K1-5a) • The design compressive strength of the column web against buckling must be larger than the beam flange force, i.e., jR n = (0.9) jR n = (0.9) 3 24 t wc EFyc dc 3 12 t wc EFyc dc ³ Pbf , if not at top story ³ Pbf , if at top story (LRFD K1-8) (LRFD K1.9, E2) Joint Design 53 CSI Steel Design Manual If any of the conditions above are not met the program calculates the required continuity plate area as, A cp = A cp = Pbf (0.85)(0.9Fyc ) Pbf (0.85)(0.9Fyc ) 2 , if not at top story - 25 t wc (LRFD K1.9, E2) 2 , if at top story - 12 t wc (LRFD K1.9, E2) If A cp £ 0, no continuity plates are required. The formula above assumes the continuity plate plus a width of web equal to 12 t wc or 25t wc act as a compression member to resist the applied load (LRFD K1.9). The formula also assumes j = 0.85 and Fcr = 0.9Fyc . This corresponds to an assumption of l c = 0.5 in the column formulas (LRFD E2-2). The user should choose the continuity plate cross-section such that this is satisfied. As an example when using Fyc = 50 ksi and assuming the effective length of the stiffener as a column to be 0.75 h (LRFD K1.9) the required minimum radius of gyration of the stiffener cross-section would be r = 0.02 h to obtain l c = 0.5 (LRFD E2-4). If continuity plates are required, they must satisfy a minimum area specification defined as follows: • The minimum thickness of the stiffeners is taken in th program as follows: ìï üï Fyc . t cpmin = max í0.5 t fb , 179 b fb ý E ïî ïþ (LRFD K1.9.2) • The minimum width of the continuity plate on each side plus ½ the thickness of the column web shall not be less than 1/3 of the beam flange width, or æ b fp t wc ö ÷ b cpmin = 2 ç ç 3 ÷ 2 è ø (LRFD K1.9.1) • So that the minimum area is given by: Acpmin = t cpmin b cpmin (LRFD K1.9.1) Therefore, the continuity plate area provided by the program is either zero or the greater of A cp and A cpmin . In the equations above, 54 Joint Design Chapter III Check/Design for AISC-ASD01 A cp Fyc db dc h = = = = = kc = Mu Pbf = = Required continuity plate area Yield stress of the column and continuity plate material Beam depth Column depth Clear distance between flanges of column less fillets for rolled shapes Distance between outer face of the column flange and web toe of its fillet. Factored beam moment Beam flange force, assumed as M u ( d b - t fb ) Rn t fb t fc t wc j = = = = = Nominal strength Beam flange thickness Column flange thickness Column web thickness Resistance factor The special seismic requirements additionally checked by the program are dependent on the type of framing used and the Seismic Design Category. If the structure is identified as Seismic Design Category D or E, the special seismic requirements are satisfied (ANSI/AISC 341 SEISMIC 1). No special check is made if the Seismic Design Category is A, B, or C. Continuity plate requirements for seismic design are evaluated for moment frames (OMF, IMF, SMF) only. No checks are done for braced frames (LCBF, SCBF, and EBF). • For OMF the continuity plates are checked and designed for a beam flange force, Pbf = M pb ( d b - t fb ). Pbf = M pb (d b - t fb ) (ANSI/AISC 341 SEISMIC 11.5) • For SMF and IMF, the continuity plates are checked and designed for a beam flange force, Pbf = R y Fy b fb t fb . Pbf = R y Fy b fb t fb Note that the code insists on designing continuity pate to match with tested connection (ANSI/AISC 341 SEUISMIC 9.5, 10.5) Joint Design 55 CSI Steel Design Manual Design of Doubler Plates One aspect of the design of a steel framing system is an evaluation of the shear forces that exist in the region of the beam column intersection known as the panel zone. Shear stresses seldom control the design of a beam or column member. However, in a Moment-Resisting frame, the shear stress in the beam-column joint can be critical, especially in framing systems when the column is subjected to major direction bending and the joint shear forces are resisted by the web of the column. In minor direction bending, the joint shear is carried by the column flanges, in which case the shear stresses are seldom critical, and this condition is therefore not investigated by the program. Shear stresses in the panel zone, due to major direction bending in the column, may require additional plates to be welded onto the column web, depending upon the loading and the geometry of the steel beams that frame into the column, either along the column major direction, or at an angle so that the beams have components along the column major direction. See Figure . The program investigates such situations and reports the thickness of any required doubler plates. Only columns with I-shapes are investigated for doubler plate requirements. Also doubler plate requirements are evaluated for moment frames (OMF, IMF, SMF) only. No check is made for braced frames(OCBF, SCBF, EBF). The program calculates the required thickness of doubler plates using the following algorithms. The shear force in the panel zone, is given by nb Vp = å n =1 M bn cos q n d n - t fn - Vc The nominal panel shear strength is given by R v = 0.6 Fy d c t r , for Pu £ 0.4Py or if Pu is tensile, and é P ù R v = 0.6Fy d c t r ê1.4 - u ú , Py û ë for Pu > 0.4Py . (LRFD K1-9) (LRFD K1-10) By using V p = jR v , with j = 0.9 (by default), the required column web thickness t r can be found. The extra thickness, or thickness of the doubler plate is given by t dp = t r - t w , 56 Joint Design (LRFD F2-1) Chapter III Check/Design for AISC-ASD01 where, Fy tr t fn t dp t fc = Column and doubler plate yield stress = Required column web thickness = Flange thickness of n-th beam connecting to the column = Required doubler plate thickness = Column Flange thickness tw h Vp Vc Fy nb dn qn dc M bn = = = = = = = = = = Rv Pu Py = = = Column web thickness d c - 2t fc if welded, d c - 2 k c if rolled Panel zone shear Column shear in column above Beam flange forces Number of beams connecting to column Depth of n-th beam connecting to column Angle between n-th beam and column major direction Depth of column clear of fillets, equals d - 2 k Calculated factored beam moment from the corresponding loading combination Nominal shear strength of panel Column factored axial load Column axial yield strength, Fy A The largest calculated value of t dp calculated for any of the load combinations based upon the factored beam moments and factored column axial loads is reported. The special seismic requirements additionally checked by the program are dependent on the type of framing used and the Seismic Design Category. If the structure is identified as Seismic Design Category D or E, the special seismic requirements are satisfied (ANSI/AISC 341 SEISMIC 1). No special check is made if the Seismic Design Category is A, B, or C. Doubler plate requirements for seismic design are evaluated for SMF only. No further check/design is done for other types of frames. • For Special Moment-Resisting Frames, the panel zone doubler plate requirements that are reported will develop at least the beam moments equal to of the plastic moment capacity of the beam or beam moments due to specified load combinations involving seismic load (ANSI/AISC 341 SEISMIC 9.3a). • For seismic design, V p is calculated using the same equation as given above, except that M pb is taken as R y Fy Z 33 . Joint Design 57 CSI Steel Design Manual The capacity of the panel zone in resisting this shear is taken as (ANSI/AISC 341 SEISMIC 9-5): æ 3 b cf t cf2 j v Vn = 0.60 j v Fy d c t p ç 1 + ç db dc t p è ö ÷ ÷ ø for Pu £ 0.75Py (ANSI/AISC 341 SEISMIC 9-5) æ 3b cf t cf2 ç j v Vn = 0.6 j v Fy d c t p 1 + ç d b d ct p è öæ P ÷ç 19 . - 12 . u ÷ç Py øè ö ÷ ÷ ø for Pu > 0.75Py (ANSI/AISC 341 SEISMIC 9.3a, LRFD K1-12) giving the required panel zone thickness as tp = tp = Vp 0.6 j v Fy d c - 3 b cf t cf2 db dc , if Pu £ 0.75Py Vp æ æP 0.6 j v Fy d c ç 19 . - 12 . ç u çP ç è y è - 3b cf t cf2 öö ÷÷ ÷÷ øø dbdc , if Pu > 0.75Py (by default), (ANSI/AISC 341 SEISMIC 9.3a) and the required doubler plate thickness as t dp = t p - t wc where, 58 jv b cf t cf tp h db = = = = = = 0.90 by default, width of column flange, thickness of column flange, required column web thickness, d c - 2t fc if welded, d c - 2 k c if rolled, and depth of deepest beam framing into the major direction of the column. Py = Fy A Pu = Axial force in column Joint Design Chapter III Check/Design for AISC-ASD01 • For Special Moment-Resisting Frames, the panel zone column web thickness requirement the program checks the following: t³ ( d c - 2t fc ) + ( d b - 2t fb ) 90 (ANSI/AISC 341 SEISMIC 9.36) Here, t is taken as t wc + t dp when the double plate is plug welded to prevent local buckling. In such case t dp is increased if necessary to meet this criteria. If the doubler plate is not plug welded to the web, then t is taken as t wc and also as t dp for checking both the plates. If t wc cannot satisfy the criteria, then a failure condition is declared. If t dp does not satisfy this criteria, then its value is increased to meet this criteria. If the check is not satisfied, it is noted in the output. Weak Beam Strong Column Measure Only for Special Moment Frames with Seismic Design Category D and E, the code requires that the sum of column flexure strengths at a joint should be more than the sum of beam flexure strengths (ANSI/AISC 341 SEISMIC 1, 9.6). The column flexure strength should reflect the presence of axial force present in the column. The beam flexural strength should reflect potential increase in capacity for strain hardening to facilitate the review of the strong column weak beam criterion, the program will report a beam/column plastic moment capacity ratio for every joint in the structure. For the major direction of any column (top end) the beam to column strength ratio is obtained as nb åM R maj = * pbn cos q n n =1 (ANSI/AISC 341 SEISMIC 9.6) M *pcax + M *pcby For the minor direction of any column the beam to column strength ratio is obtained as nb åM R min = pbn sin q n n =1 M pcay + M pcby , (ANSI/AISC 341 SEISMIC 9.6) where, Joint Design 59 CSI Steel Design Manual R maj , min = Plastic moment capacity ratios, in the major and minor directions of the column, respectively Plastic moment capacity of n-th beam connecting M *pbn = qn = M *pcax , y = to column Angle between the n-th beam and the column major direction Major and minor plastic moment capacities, reduced for M *pcbx , y = axial force effects, of column above story level Major and minor plastic moment capacities, reduced for nb = axial force effects, of column below story level Number of beams connecting to the column The plastic moment capacities of the columns are reduced for axial force effects and are taken as ( M *pc = Z c Fyc - Puc A g ), (ANSI/AISC 341 SEISMIC 9.6) The plastic moment capacities of the beams are amplified for potential increase in capacity for strain hardening as, M *pb = 11 . R y Fyb Z b f mv , where, Zb = Plastic modulus of beam, Zc = Plastic modulus of column, Fyb = Yield stress of beam material, Fyc = Yield stress of column material, Puc = Axial compression force in column for the load combination under consideration, A gc = Gross area of column, f mv = The moment amplification factor. It is taken as the ratio of beam moment at the centerline of column to the moment the column face. This factor takes care of the M v of the code (ANSI/AISC 341 SEISMIC 9.6). Fmv is taken as follows: 1+ 60 dc , Lb Joint Design Chapter III Check/Design for AISC-ASD01 dc = Depth of column section, and Lb = Clear span length of the beam. For the above calculations the section of the column above is taken to be the same as the section of the column below assuming that the column splice will be located some distance above the story level. Evaluation of Beam Connection Shears For each steel beam in the structure the program will report the maximum major shears at each end of the beam for the design of the beam shear connections. The beam connection shears reported are the maxima of the factored shears obtained from the loading combinations. For special seismic design, the beam connection shears are not taken less than the following special values for different types of framing. The special seismic requirements additionally checked by the program are dependent on the type of framing used and the Seismic Design Category. If the structure is identified as Seismic De sign Cat e gory D or E, the spe cial seis mic re quire ments are sat is fied (ANSI/AISC 341 SEISMIC 1). No special check is made if the Seismic Design Category is A, B, or C. • For special moment frames, the beam connection shear is taken as the maximum of those from regular load combinations and those required for the development of full plastic moment capacity of the beams. The connection shear for the development of the full plastic moment capacity of beam is as follows: Vu = C M pb L +1.2 VDL + 0.5 VLL (ANSI/AISC 341 SEISMIC 9.2.a(3)) where M pb L VDL = = = = = = = VLL = V C Shear force corresponding to END I or END J of beam, 0 if beam ends are pinned, or for cantilever beam, 1 if one end of the beam is pinned, 2 if no ends of the beam are pinned, Plastic moment capacity of the beam, Z Fy , Clear length of the beam, Absolute maximum of the calculated factored beam shears at the corresponding beam ends from the dead load only, and Absolute maximum of the calculated factored beam Joint Design 61 CSI Steel Design Manual shears at the corresponding beam ends from the live load only. • For Intermediate Moment Frames and Ordinary Moment Frames, the beam connection shear is taken as the maximum of those from regular load combinations and those from special seismic consideration. the beam connection shear from special seismic consideration is taken as the minimum of those required for the development of full plastic moment capacity of the beam and those required for amplified seismic load and those required (ANSI/AISC 341 SEISMIC 10.2, 11.2). The connection shear for the development of the full plastic moment capacity of beam is as follows: Vu = CM pb L + 1. 2 VDL + 0.5VLL (ANSI/AISC 341 SEISMIC 10.2, 11.2) All parameters in the above equation have been described earlier. The load combinations for amplified seismic loads are (ANSI/AISC 341 SEISMIC 8.3, 4.1, ASCI 9.5.2.7.1, 2.3.2): (0.9 + 0.2S )DL ± W DS (12. + 0.2S DS 0 EL ) DL + 10 . LL ± W 0 EL) • For OCBF, the beam connection shear is taken as the maximum of those from regular load combinations and those from amplified seismic load combinations (ANSI/AISC 341 SEISMIC 14.2). • For SCBF, the beam connection shear is taken as the maximum of those from regular load combinations and those from amplified seismic load combination (ANSI/AISC 341 SEISMIC 13.4a(2)). Note: Beams intersected by Chevron (V or inverted-V) braces are NOT currently checked to have a strength to support loads for the following two conditions (ANSI/AISC 341 SEISMIC 13.4a): a A beam that is intersected by braces shall be designed to support the effects of all tributary dead and live loads form load combinations stipulated by the code, assuming the bracings are not present, and b A beam that is intersected by braces shall be designed to resist the effects of load combinations stipulated by the code, except that a load q b shall be substituted for the term E. q b is given by the difference of R y Fy A for the tension brace and 0.3f c Pn for the compression brace. 62 Joint Design Chapter III Check/Design for AISC-ASD01 Users need to check for this requirement independently. • For EBF, the beam connection shear is taken as the beam connection shear is taken as the maximum of those from regular load combinations and those from special seismic considerations. The beam connection shear from special seismic consideration is taken as the minimum of those required for yielding of link beam and those required for amplified seismic load (ANSI/AISC 341 SEISMIC 15.1, 15.4, 15.6). The load factor for the seismic component of loads in the combination is calculated to achieve forces related to yielding of link beam. For connection shear determination the forces are further amplified by 11 . R y (ANSI/AISC 341 SEISMIC 15.6(2)). The load combinations for Amplified Seismic Loads are given earlier. Evaluation of Brace Connection Forces For each steel brace in the structure the program reports the maximum axial force at each end of the brace for the design of the brace to beam connections. The brace connection forces reported are the maxima of the factored brace axial forces obtained from the loading combinations. For special seismic design, the brace connection forces are not taken less than the following special values for different types of framing. The special seismic requirements additionally checked by the program are dependent on the type of framing used and the Seismic Design Category. If the structure is identified as Seismic Design Category D or E, the special seismic requirements are satisfied (ANSI/AISC 341 SEISMIC 1). No special check is made if the Seismic Design Category is A, B, or C. Brace axial forces for seismic design are evaluated for braced frames (OCBF, SCBF, EBF) only. No special checks are done for moment frames (OMF, IMF, SMF). • For OBF, the bracing connection force is reported at least the expected tensile strength of the brace (R y Fy A g ) (ANSI/AISC 341 SEISMIC 14.2): • For SCBF, the bracing connection force is reported at least as the expected the tensile strength of the brace (R y Fy A g ) (ANSI/AISC 341 SEISMIC 13.3a). For EBF, the brace connection force is taken as the maximum of those from regular load combinations and those from special seismic consideration. The brace connection force from special seismic consideration is taken as the minimum of those required for yielding of link beam and those required for Amplified Seismic Load (ANSI/AISC 341 SEISMIC 15.1, 15.4, 15.6). The load factor for the seismic com- Joint Design 63 CSI Steel Design Manual ponent of loads in the combination is calculated to achieve forces related to yielding of Link beam. for connection force determination, the forces are further amplified by 125 . R y (ANSI/AISC 341 SEISMIC 15.6). The load combinations for Amplified Seismic Load are given earlier in this document. 64 Joint Design C h a p t e r IV Check/Design for AISC-ASD89 This chapter describes the details of the structural steel design and stress check algorithms that are used by the program when the user selects the AISC-ASD89 design code (AISC 1989). Various notations used in this chapter are described in Table III-1. For referring to pertinent sections and equations of the original ASD code, a unique prefix “ASD” is assigned. However, all references to the “Specifications for Allowable Stress Design of Single-Angle Members” carry the prefix of “ASD SAM”. The design is based on user-specified loading combinations. But the program provides a set of default load combinations that should satisfy requirements for the design of most building type structures. In the evaluation of the axial force/biaxial moment capacity ratios at a station along the length of the member, first the actual member force/moment components and the corresponding capacities are calculated for each load combination. Then the capacity ratios are evaluated at each station under the influence of all load combinations using the corresponding equations that are defined in this chapter. The controlling capacity ratio is then obtained. A capacity ratio greater than 1.0 indicates overstress. Similarly, a shear capacity ratio is also calculated separately. 65 CSI Steel Design Manual Cross-sectional area, in2 Effective cross-sectional area for slender sections, in2 Area of flange , in2 Gross cross-sectional area, in2 Major and minor shear areas, in2 Web shear area, dt w , in2 Bending Coefficient Moment Coefficient Warping constant, in6 Outside diameter of pipes, in Modulus of elasticity, ksi Allowable axial stress, ksi Allowable bending stress, ksi Allowable major and minor bending stresses, ksi Critical compressive stress, ksi 12 p 2 E A Ae Af Ag A v2 , A v3 Aw Cb Cm Cw D E Fa Fb Fb 33 , Fb 22 Fcr = = = = = = = = = = = = = = = ¢ Fe33 = ¢ Fe22 = 23 (K 22 l22 r 22 ) Fv Fy K K 33 , K 22 M 33 , M 22 M ob P Pe Q Qa Qs S S 33 , S 22 = = = = = = = = = = = = = Allowable shear stress, ksi Yield stress of material, ksi Effective length factor Effective length K-factors in the major and minor directions Major and minor bending moments in member, kip-in Lateral-torsional moment for angle sections, kip-in Axial force in member, kips Euler buckling load, kips Reduction factor for slender section, = Qa Qs Reduction factor for stiffened slender elements Reduction factor for unstiffened slender elements Section modulus, in3 Major and minor section moduli, in3 23 (K 33 l33 r 33 ) 2 12 p 2 E 2 Table IV-1 AISC-ASD Notations 66 Chapter IV Check/Design for AISC-ASD89 S eff ,33 , S eff ,22 Sc V2 , V3 b = = = = be bf d fa fb f b 33 , f b 22 fv f v2 , f v3 h he k kc = = = = = = = = = = = = l33 , l22 lc r r 33 , r 22 rz t tf tw bw = = = = = = = = = Effective major and minor section moduli for slender sections, in3 Section modulus for compression in an angle section, in3 Shear forces in major and minor directions, kips Nominal dimension of plate in a section, in longer leg of angle sections, bf - 2t w for welded and bf -3t w for rolled box sections, etc. Effective width of flange, in Flange width, in Overall depth of member, in Axial stress either in compression or in tension, ksi Normal stress in bending, ksi Normal stress in major and minor direction bending, ksi Shear stress, ksi Shear stress in major and minor direction bending, ksi Clear distance between flanges for I shaped sections ( d - 2t f ), in Effective distance between flanges less fillets, in Distance from outer face of flange to web toe of fillet , in Parameter used for classification of sections, 4.05 if h t w > 70 , 0.46 [h t w ] 1 if h t w £ 70 . Major and minor direction unbraced member lengths, in Critical length, in Radius of gyration, in Radii of gyration in the major and minor directions, in Minimum Radius of gyration for angles, in Thickness of a plate in I, box, channel, angle, and T sections, in Flange thickness, in Web thickness, in Special section property for angles, in Table IV-1 AISC-ASD Notations (cont.) 67 CSI Steel Design Manual English as well as SI and MKS metric units can be used for input. But the code is based on Kip-Inch-Second units. For simplicity, all equations and descriptions presented in this chapter correspond to Kip-Inch-Second units unless otherwise noted. Design Loading Combinations The design load combinations are the various combinations of the load cases for which the structure needs to be checked. For the AISC-ASD89 code, if a structure is subjected to dead load (DL), live load (LL), wind load (WL), and earthquake induced load (EL), and considering that wind and earthquake forces are reversible, then the following load combinations may have to be defined (ASD A4): DL DL + LL (ASD A4.1) (ASD A4.1) DL ± WL DL + LL ± WL (ASD A4.1) (ASD A4.1) DL ± EL DL + LL ± EL (ASD A4.1) (ASD A4.1) These are also the default design load combinations in the program whenever the AISC-ASD89 code is used. The user should use other appropriate loading combinations if roof live load is separately treated, if other types of loads are present, or if pattern live loads are to be considered. When designing for combinations involving earthquake and wind loads, allowable stresses are increased by a factor of 4/3 of the regular allowable value (ASD A5.2). Live load reduction factors can be applied to the member forces of the live load case on an element-by-element basis to reduce the contribution of the live load to the factored loading. Classification of Sections The allowable stresses for axial compression and flexure are dependent upon the classification of sections as either Compact, Noncompact, Slender, or Too Slender. The program classifies the individual members according to the limiting width/thickness ratios given in Table III-2 (ASD B5.1, F3.1, F5, G1, A-B5-2). The definition of the section properties required in this table is given in Figure III-1 and Table III-1. 68 Design Loading Combinations Chapter IV Check/Design for AISC-ASD89 Figure IV-1 AISC-ASD Definition of Geometric Properties Classification of Sections 69 CSI Steel Design Manual Section Description Ratio Checked Compact Section b f 2t f ( rolled) £ 65 Fy b f 2t f (welded) £ 65 Fy Noncompact Section £ 95 £ 95 Slender Section Fy No limit Fy / k c No limit For f a I-SHAPE d Fy £ 0.16 640 f £ (1 - 3.74 a ) , Fy Fy tw No limit No limit For f a / Fy > 0.16 £ 257 / Fy . If compression only, £ 253 Fy h tw b tf d tw No limit £ 190 Fy otherwise £ 760 Fb £ 238 Fy 14000 Fy ( Fy + 16.5) £ 260 No limit As for I-shapes No limit No limit h tw No limit As for I-shapes As for I-shapes Other t w ³ t f 2 , d w £ 6b f None None BOX b tf As for I-shapes As for I-shapes No limit d tw As for I-shapes No limit No limit No limit As for I-shapes As for I-shapes h tw CHANNEL Other No limit No limit Table IV-2 Limiting Width-Thickness Ratios for Classification of Sections Based on AISC-ASD 70 £ Classification of Sections If welded b f dw t f tw If rolled b f dw t f tw £ 0.25, £ 3.0 £ 0.5, £ 2.0 Chapter IV Check/Design for AISC-ASD89 Section Description Ratio Checked bf 2t f d tw Compact Section £ 65 Fy Not applicable Noncompact Section £ 95 Fy No limit £ 127 Fy No limit T-SHAPE Other No limit Slender Section No limit If welded b f d w ³ 0.5, t f t w ³ 1.25 If rolled b f d w ³ 0.5, t f t w ³ 1.10 DOUBLE ANGLES b t Not applicable £ 76 Fy No limit ANGLE b t Not applicable £ 76 Fy No limit £ 3,300 Fy £ 3,300 Fy PIPE D t ROUND BAR ¾ Assumed Compact RECTANGLE ¾ Assumed Noncompact GENERAL ¾ Assumed Noncompact £ 13,000 Fy (Compression only) No limit for flexure Table IV-2 Limiting Width-Thickness Ratios for Classification of Sections Based on AISC-ASD (Cont.) If the section dimensions satisfy the limits shown in the table, the section is classified as either Compact, Noncompact, or Slender. If the section satisfies the criteria for Compact sections, then the section is classified as Compact section. If the section does not satisfy the criteria for Compact sections but satisfies the criteria for Noncompact sections, the section is classified as Noncompact section. If the section does not satisfy the criteria for Compact and Noncompact sections but satisfies Classification of Sections 71 CSI Steel Design Manual the criteria for Slender sections, the section is classified as Slender section. If the limits for Slender sections are not met, the section is classified as Too Slender. Stress check of Too Slender sections is beyond the scope of SAP2000. In classifying web slenderness of I-shapes, Box, and Channel sections, it is assumed that there are no intermediate stiffeners (ASD F5, G1). Double angles are conservatively assumed to be separated. Calculation of Stresses The stresses are calculated at each of the previously defined stations. The member stresses for non-slender sections that are calculated for each load combination are, in general, based on the gross cross-sectional properties.: f a = P/A f b 33 = M 33 /S 33 f b 22 = M 22 /S 22 f v 2 = V2 /A v 2 f v 3 = V3 /A v 3 If the section is slender with slender stiffened elements, like slender web in I, Channel, and Box sections or slender flanges in Box, effective section moduli based on reduced web and reduced flange dimensions are used in calculating stresses. f a = P/A f b 33 = M 33 /S eff , 33 f b 22 = M 22 /S eff , 22 f v 2 = V2 /A v 2 f v 3 = V3 /A v 3 (ASD A-B5.2d) (ASD A-B5.2d) (ASD A-B5.2d) (ASD A-B5.2d) (ASD A-B5.2d) The flexural stresses are calculated based on the properties about the principal axes. For I, Box, Channel, T, Double-angle, Pipe, Circular and Rectangular sections, the principal axes coincide with the geometric axes. For Single-angle sections, the design considers the principal properties. For general sections it is assumed that all section properties are given in terms of the principal directions. For Single-angle sections, the shear stresses are calculated for directions along the geometric axes. For all other sections the shear stresses are calculated along the geometric and principle axes. 72 Calculation of Stresses Chapter IV Check/Design for AISC-ASD89 Calculation of Allowable Stresses The allowable stresses in compression, tension, bending, and shear are computed for Compact, Noncompact, and Slender sections according to the following subsections. The allowable flexural stresses for all shapes of sections are calculated based on their principal axes of bending. For the I, Box, Channel, Circular, Pipe, T, Double-angle and Rectangular sections, the principal axes coincide with their geometric axes. For the Angle sections, the principal axes are determined and all computations related to flexural stresses are based on that. If the user specifies nonzero allowable stresses for one or more elements in the program “Overwrites Element Design Data” form, these values will override the above mentioned calculated values for those elements as defined in the following subsections. The specified allowable stresses should be based on the principal axes of bending. Allowable Stress in Tension The allowable axial tensile stress value Fa is assumed to be 0.60 Fy . Fa = 0.6 Fy (ASD D1, ASD SAM 2) It should be noted that net section checks are not made. For members in tension, if l r is greater than 300, a message to that effect is printed (ASD B7, ASD SAM 2). For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33 in computing l r . Allowable Stress in Compression The allowable axial compressive stress is the minimum value obtained from flexural buckling and flexural-torsional buckling. The allowable compressive stresses are determined according to the following subsections. For members in compression, if Kl r is greater than 200, a warning message is printed (ASD B7, ASD SAM 4). For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33 in computing Kl r . Flexural Buckling The allowable axial compressive stress value, Fa , depends on the slenderness ratio Kl r based on gross section properties and a corresponding critical value, C c , where Calculation of Allowable Stresses 73 CSI Steel Design Manual K l ü ìK l Kl = max í 33 33 , 22 22 ý , and r r22 þ î r33 2p 2 E . Fy Cc = (ASD E2, ASD SAM 4) For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33 in computing Kl r . For Compact or Noncompact sections Fa is evaluated as follows: ì ( Kl/r ) 2 ü F í1.0 2 ý y C 2 c î þ Fa = 5 + 3 Fa = 3 ( Kl/r ) 8 Cc - (Kl/r) 3 , if Kl £ Cc , r (ASD E2-1, SAM 4-1) if Kl > Cc . r (ASD E2-2, SAM 4-2) 8 C c3 12 p 2 E , 23 ( Kl r ) 2 If Kl r is greater than 200, then the calculated value of Fa is taken not to exceed the value of Fa calculated by using the equation ASD E2-2 for Compact and Noncompact sections (ASD E1, B7). For Slender sections, except slender Pipe sections, Fa is evaluated as follows: Fa = Q Fa = ìï ( Kl/r ) 2 üï 1.0 F í 2 ý y ïî 2C c¢ ïþ 3 ( Kl/r ) 5 + 3 8 C c¢ 12 p 2 E , 23 ( Kl r ) 2 (Kl/r) 8 C c¢ 3 , if Kl £ C c¢ , (ASD A-B5-11, SAM 4-1) r if Kl > C c¢ . (ASD A-B5-12, SAM 4-2) r 3 where, C c¢ = 74 2p 2 E . Q Fy Calculation of Allowable Stresses (ASD A-B5.2c, ASD SAM 4) Chapter IV Check/Design for AISC-ASD89 For slender sections, if Kl r is greater than 200, then the calculated value of Fa is taken not to exceed its value calculated by using the equation ASD A-B5-12 (ASD B7, E1). For slender Pipe sections Fa is evaluated as follows: Fa = 662 + 0.40 Fy D t (ASD A-B5-9) The reduction factor, Q, for all compact and noncompact sections is taken as 1. For slender sections, Q is computed as follows: Q = Q s Q a , where (ASD A-B5.2.c, SAM 4) Q s = reduction factor for unstiffened slender elements, and (ASD A-B5.2.a) Q a = reduction factor for stiffened slender elements. (ASD A-B5.2.c) The Q s factors for slender sections are calculated as described in Table III-4 (ASD A-B5.2a, ASD SAM 4). The Q a factors for slender sections are calculated as the ratio of effective cross-sectional area and the gross cross-sectional area. Qa = Ae Ag (ASD A-B5-10) The effective cross-sectional area is computed based on effective width as follows: A e = A g - å (b - be ) t b e for unstiffened elements is taken equal to b, and b e for stiffened elements is taken equal to or less than b as given in Table III-5 (ASD A-B5.2b). For webs in I, box, and Channel sections, h e is used as b e and h is used as b in the above equation. Flexural-Torsional Buckling The allowable axial compressive stress value, Fa , determined by the limit states of torsional and flexural-torsional buckling is determined as follows (ASD E3, C-E3): 2 ì Kl/r ) üï ( ï e í1.0 ý Fy ¢2 2 C ïî ïþ c , if ( Kl/r ) £ C c¢ , Fa = Q 3 e Kl/r ) 3 ( Kl/r ) ( 5 e e + 3 3 8 C c¢ 8 C c¢ (E2-1, A-B5-11) Calculation of Allowable Stresses 75 CSI Steel Design Manual Section Type I-SHAPE Reduction Factor for Unstiffened Slender Elements (Qs ) ì 1.0 ïï Qs = í1.293 - 0.00309[bf 2 t f ] Fy k c 2 ï ïî 26,200 k c [bf 2 t f ] Fy { } if if 95 if bf 2 t f £ 95 Fy k c , Fy k c < bf 2 t f < 195 Fy k c , bf 2 t f ³ 195 Fy k c . Equation Reference ASD A-B5-3, ASD A-B5-4 BOX Qs = 1 ASD A-B5.2c CHANNEL As for I-shapes with b f 2t f replaced by b f t f . ASD A-B5-3, ASD A-B5-4 For flanges, as for flanges in I-shapes. For web see below. T-SHAPE ì 1.0 , if ïï Qs £ í1.908 - 0.00715[d t w ] Fy , if 2 ï if ïî 20,000 [d t w ] Fy , { } 127 ì 1.0 , if ïï Qs = í1.340 - 0.00447[b t] Fy , if 2 ï if ïî 15,500 [b t] Fy , 76 ANGLE ì 1.0 , if ïï Qs = í1.340 - 0.00447[b t] Fy , if 2 ï if ïî 15,500 [b t] Fy , 76 { } } Fy , Fy < d t w < 176 Fy , d t w ³ 176 DOUBLEANGLE { d t w £ 127 b t £ 76 Fy . Fy , Fy < b t < 155 Fy , b t ³ 155 Fy . b t £ 76 Fy , Fy < b t < 155 Fy , b t ³ 155 Fy . ASD A-B5-3, ASD A-B5-4, ASD A-B5-5, ASD A-B5-6 ASD A-B5-1, ASD A-B5-2, SAM 4-3 ASD A-B5-1, ASD A-B5-2, SAM 4-3 PIPE Qs = 1 ASD A-B5.2c ROUND BAR Qs = 1 ASD A-B5.2c RECTANGULAR Qs = 1 ASD A-B5.2c GENERAL Qs = 1 ASD A-B5.2c Table IV-3 Reduction Factor for Unstiffened Slender Elements, Q s 76 Calculation of Allowable Stresses Chapter IV Check/Design for AISC-ASD89 Section Type I-SHAPE Effective Width for Stiffened Sections ì ï h, ï he = í ï 253 t w ïî f ì ï h, ï he = í ï 253 t w ïî f BOX CHANNEL é 44.3 ù ú, ê1 ( h tw ) f û ë é 44.3 ù ú, ê1 ( h tw ) f û ë if h 195.74 , £ tw f if h 195.74 > . tw f if h 195.74 , £ tw f if h 195.74 > . tw f ì if ï b, ï be = í 253 t f é 50.3 ù ï ú , if ê1 ï f êë ( h t f ) f úû î ì if ï h, ï he = í ù é ï 253 t w ê1 - 44.3 ú , if ïî f ë ( h t w ) f û b 183.74 , £ tf f b 183.74 . > t f h 195.74 , £ tw f h 195.74 > . tw f Equation Reference (compression only, f = P ) Ag (compression only, f = P ) Ag ASD A-B5-8 (compr., flexure, f = 0.6 Fy ) ASD A-B5-7 P ) Ag ASD A-B5-8 (compression only, f = ASD A-B5-8 T-SHAPE be = b ASD A-B5.2c DOUBLEANGLE be = b ASD A-B5.2c ANGLE be = b ASD A-B5.2c PIPE Q a = 1, (However, special expression for allowable axial stress is given.) ASD A-B5-9 ROUND BAR Not applicable ¾ RECTANGULAR be = b ASD A-B5.2c GENERAL Not applicable ¾ Table IV-4 Effective Width for Stiffened Sections Calculation of Allowable Stresses 77 CSI Steel Design Manual Fa = 12 p 2 E 23 ( Kl/r ) 2 if ( Kl/r ) > C c¢ . , e (E2-2, A-B5-12) e where, C c¢ = 2p 2 E , and Q Fy (Kl/r) = e (ASD E2, A-B5.2c, SAM 4) p2E . Fe (ASD C-E2-2, SAM 4-4) ASD Commentary (ASD C-E3) refers to the 1986 version of the AISC-LRFD code for the calculation of Fe . The 1993 version of the AISC-LRFD code is the same as the 1986 version in this respect. Fe is calculated in the program as follows: • For Rectangular, I, Box, and Pipe sections: é 2 ù p EC w 1 ê + GJ ú Fe = 2 ê (K l ) ú I 22 + I 33 ë zz û (LRFD A-E3-5) • For T-sections and Double-angles: æ F + Fez Fe = çç e22 2H è 4 Fe22 Fez H ù ö é ÷ ÷ ê1 - 1 - ( F + F ) 2 ú ø êë e 22 ez úû (LRFD A-E3-6) ù ú úû (LRFD A-E3-6) é 4 Fe33 Fez H ù ú ê1 - 1 ( Fe33 + Fez ) 2 úû êë (ASD SAM C-C4-1) • For Channels: æ F + Fez Fe = çç e33 2H è ö ÷ ÷ ø é 4 Fe33 Fez H ê1 - 1 ( Fe33 + Fez ) 2 êë • For Single-angle sections with equal legs: æ F + Fez Fe = çç e33 2H è ö ÷ ÷ ø • For Single-angle sections with unequal legs, Fe is calculated as the minimum real root of the following cubic equation (ASD SAM C-C4-2, LRFD A-E3-7): 78 Calculation of Allowable Stresses Chapter IV Check/Design for AISC-ASD89 ( Fe - Fe33 )( Fe - Fe22 )( Fe -Fez ) - Fe2 ( Fe -Fe22 ) x 02 r02 - Fe2 ( Fe - Fe33 ) y 02 r02 =0, where, x 0 , y0 are the coordinates of the shear center with respect to the centroid, x 0 = 0 for double-angle and T-shaped members (y-axis of symme- try), r0 = x 02 + y 02 + æ x 2 + y2 H = 1 - çç 0 2 0 è r0 Fe33 = Fe22 = I 22 + I 33 = polar radius of gyration about the shear center, Ag ö ÷, ÷ ø (LRFD A-E3-9) p2E (K 33 l 33 r33 ) 2 p2E (K 22 l 22 r22 ) 2 , (LRFD A-E3-10) , (LRFD A-E3-11) é 2 ù p EC w ú 1 , + GJ Fez = ê 2 ê (K l ) ú Ar02 z z ë û (LRFD A-E3-12) K 22 , K 33 are effective length factors in minor and major directions, K z is the effective length factor for torsional buckling, and it is taken equal to K 22 in the program, l 22 , l 33 are effective lengths in the minor and major directions, lz is the effective length for torsional buckling, and it is taken equal to l 22 . For angle sections, the principal moment of inertia and radii of gyration are used for com put ing Fe (ASD SAM 4). Also, the maxi mum value of Kl, i.e, max( K 22 l 22 , K 33 l 33 ), is used in place of K 22 l 22 or K 33 l 33 in calculating Fe22 and Fe33 in this case. Calculation of Allowable Stresses 79 CSI Steel Design Manual Allowable Stress in Bending The allowable bending stress depends on the following criteria: the geometric shape of the cross-section, the axis of bending, the compactness of the section, and a length parameter. I-sections For I-sections the length parameter is taken as the laterally unbraced length, l 22 , which is compared to a critical length, l c . The critical length is defined as ìï 76 b f 20, 000 A f l c = min í , d Fy ïî Fy Af üï ý , where ïþ (ASD F1-2) is the area of compression flange, Major Axis of Bending If l 22 is less than l c , the major allowable bending stress for Compact and Noncompact sections is taken depending on whether the section is welded or rolled and whether f y is greater than 65 ksi or not. For Compact sections: Fb 33 = 0.66 Fy if f y £ 65 ksi , (ASD F1-1) Fb 33 = 0.60 Fy if f y > 65 ksi , (ASD F1-5) For Noncompact sections: bf æ Fb 33 = ç 0.79 - 0.002 ç 2t f è ö Fy ÷ Fy , if rolled and f y £ 65 ksi, (ASD F1-3) ÷ ø æ bf Fb 33 = ç 0.79 - 0.002 ç 2tf è Fy ö ÷ F , if welded and f £ 65 ksi, (ASDF1-4) y y kc ÷ ø Fb 33 = 0.60 Fy if f y > 65 ksi.. (ASD F1-5) If the unbraced length l 22 is greater than l c , then for both Compact and Noncompact I-sections the allowable bending stress depends on the l 22 rT ratio. 80 Calculation of Allowable Stresses Chapter IV Check/Design for AISC-ASD89 For l 22 £ rT 102, 000 C b , Fy Fb 33 = 0.60 Fy , (ASD F1-6) 102, 000 C b l < 22 £ Fy rT for 510, 000 C b , Fy é 2 Fy ( l 22 / rT ) 2 ù Fb 33 = ê ú Fy £ 0.60 Fy , and êë 3 1530, 000 C b úû for (ASD F1-6) l 22 510, 000 C b , > rT Fy é 170, 000 C b ù Fb 33 = ê £ 0.60 Fy , 2 ú ë ( l 22 / rT ) û (ASD F1-7) and Fb 33 is taken not to be less than that given by the following formula: Fb 33 = 12, 000 C b l 22 ( d / A f ) (ASD F1-8) £ 0.6 Fy where, rT is the radius of gyration of a section comprising the compression flange and 1 3 the compression web taken about an axis in the plane of the web, æM C b = 1.75 +1.05 çç a è Mb ö ÷ ÷ + 0.3 ø æ Ma çç è Mb 2 ö ÷ ÷ £ 2.3, where ø (ASD F1.3) M a and M b are the end moments of any unbraced segment of the member and M a is numerically less than M b ; M a M b being positive for double curvature bending and negative for single curvature bending. Also, if any moment within the segment is greater than M b , C b is taken as 1.0. Also, C b is taken as 1.0 for cantilevers and frames braced against joint translation (ASD F1.3). The program defaults C b to 1.0 if the unbraced length, l 22 , of the member is redefined by the user (i.e. it is not equal to the length of the member). The user can overwrite the value of C b for any member by specifying it. Calculation of Allowable Stresses 81 CSI Steel Design Manual The allowable bending stress for Slender sections bent about their major axis is determined in the same way as for a Noncompact section. Then the following additional considerations are taken into account. If the web is slender, then the previously computed allowable bending stress is reduced as follows: Fb¢33 = R PG R e Fb 33 , where R PG = 1.0 - 0.0005 Aw Af ( 12 + 3a - a 3 Re = (ASD G2-1) éh 760 ê Fb 33 êë t ) AA ù ú £ 1.0 , úû (ASD G2) w A 12 + 2 w Af f £ 1.0 , (hybrid girders) R e =1.0 , (non-hybrid girders) (ASD G2) (ASD G2) A w = Area of web, in 2 , A f = Area of compression flange, in 2 , a= 0.6 Fy Fb 33 £ 1.0 (ASD G2) Fb 33 = Allowable bending stress assuming the section is non-compact, and Fb¢33 = Allowable bending stress after considering web slenderness. In the above expressions, R e is taken as 1, because currently the program deals with only non-hybrid girders. If the flange is slender, then the previously computed allowable bending stress is taken to be limited as follows. Fb¢33 £ Q s (0.6 Fy ) , where Q s is defined earlier. 82 Calculation of Allowable Stresses (ASD A-B5.2a, A-B5.2d) Chapter IV Check/Design for AISC-ASD89 Minor Axis of Bending The minor direction allowable bending stress Fb 22 is taken as follows: For Compact sections: Fb 22 = 0.75 Fy if f y £ 65 ksi , (ASD F2-1) Fb 22 = 0.60 Fy if f y > 65 ksi , (ASD F2-2) For Noncompact and Slender sections: bf æ Fb 22 = ç 1.075 - 0.005 ç 2t f è ö Fy ÷ Fy , ÷ ø Fb 22 = 0.60 Fy if f y £ 65 ksi, (ASD F2-3) if f y > 65 ksi.. (ASD F2-2) Channel sections For Channel sections the length parameter is taken as the laterally unbraced length, l 22 , which is compared to a critical length, l c . The critical length is defined as ìï 76 b f 20, 000 A f l c = min í , d Fy F y îï Af üï ý , where þï (ASD F1-2) is the area of compression flange, Major Axis of Bending If l 22 is less than l c , the major allowable bending stress for Compact and Noncompact sections is taken depending on whether the section is welded or rolled and whether f y is greater than 65 ksi or not. For Compact sections: Fb 33 = 0.66 Fy if f y £ 65 ksi , (ASD F1-1) Fb 33 = 0.60 Fy if f y > 65 ksi , (ASD F1-5) For Noncompact sections: bf æ Fb 33 = ç 0.79 - 0.002 ç tf è ö Fy ÷ Fy , if rolled and f y £ 65 ksi, ÷ ø (ASD F1-3) Calculation of Allowable Stresses 83 CSI Steel Design Manual æ bf Fb 33 = ç 0.79 - 0.002 ç tf è Fy ö ÷ F , if welded and f £ 65 ksi, (ASD F1-4) y y kc ÷ ø if f y > 65 ksi.. Fb 33 = 0.60 Fy (ASD F1-5) If the unbraced length l 22 is greater than l c , then for both Compact and Noncompact Channel sections the allowable bending stress is taken as follows: Fb 33 = 12, 000 C b l 22 ( d / A f ) £ 0.6 Fy (ASD F1-8) The allowable bending stress for Slender sections bent about their major axis is determined in the same way as for a Noncompact section. Then the following additional considerations are taken into account. If the web is slender, then the previously computed allowable bending stress is reduced as follows: Fb¢33 = R e R PG Fb 33 (ASD G2-1) If the flange is slender, the previously computed allowable bending stress is taken to be limited as follows: Fb¢33 £ Q s (0.6 Fy ) (ASD A-B5.2a, A-B5.2d) The definition for rT , C b , A f , A w , R e , R PG , Q s , Fb 33 , and Fb¢33 are given earlier. Minor Axis of Bending The minor direction allowable bending stress Fb 22 is taken as follows: Fb 22 = 0.60 Fy (ASD F2-2) T-sections and Double angles For T sections and Double angles, the allowable bending stress for both major and minor axes bending is taken as, Fb = 0.60 Q s Fy . 84 Calculation of Allowable Stresses Chapter IV Check/Design for AISC-ASD89 Box Sections and Rectangular Tubes For all Box sections and Rectangular tubes, the length parameter is taken as the laterally unbraced length, l 22 , measured compared to a critical length, l c . The critical length is defined as ì b 1200 b ü l c = max í(1950 + 1200 M a /M b ) , ý F Fy þ y î (ASD F3-2) where M a and M b have the same definition as noted earlier in the formula for 1200 b in the program. C b . If l 22 is specified by the user, l c is taken as Fy Major Axis of Bending If l 22 is less than l c , the allowable bending stress in the major direction of bending is taken as: Fb 33 = 0.66 Fy (for Compact sections) (ASD F3-1) Fb 33 = 0.60 Fy (for Noncompact sections) (ASD F3-3) If l 22 exceeds l c , the allowable bending stress in the major direction of bending for both Compact and Noncompact sections is taken as: (ASD F3-3) Fb 33 = 0.60 Fy The major direction allowable bending stress for Slender sections is determined in the same way as for a Noncompact section. Then the following additional consideration is taken into account. If the web is slender, then the previously computed allowable bending stress is reduced as follows: Fb¢33 = R e R PG Fb 33 (ASD G2-1) The definition for R e , R PG , Fb 33 , and Fb¢33 are given earlier. If the flange is slender, no additional consideration is needed in computing allowable bending stress. However, effective section dimensions are calculated and the section modulus is modified according to its slenderness. Minor Axis of Bending If l 22 is less than l c , the allowable bending stress in the minor direction of bending is taken as: Calculation of Allowable Stresses 85 CSI Steel Design Manual Fb 22 = 0.66 Fy (for Compact sections) (ASD F3-1) Fb 22 = 0.60 Fy (for Noncompact and Slender sections) (ASD F3-3) If l 22 exceeds l c , the allowable bending stress in the minor direction of bending is taken, irrespective of compactness, as: (ASD F3-3) Fb 22 = 0.60 Fy Pipe Sections For Pipe sections, the allowable bending stress for both major and minor axes of bending is taken as Fb = 0.66 Fy (for Compact sections), and (ASD F3-1) Fb = 0.60 Fy (for Noncompact and Slender sections). (ASD F3-3) Round Bars The allowable stress for both the major and minor axis of bending of round bars is taken as, Fb = 0.75 Fy . (ASD F2-1) Rectangular and Square Bars The allowable stress for both the major and minor axis of bending of solid square bars is taken as, Fb = 0.75 Fy . (ASD F2-1) For solid rectangular bars bent about their major axes, the allowable stress is given by Fb = 0.60 Fy , And the allowable stress for minor axis bending of rectangular bars is taken as, Fb = 0.75 Fy . 86 Calculation of Allowable Stresses (ASD F2-1) Chapter IV Check/Design for AISC-ASD89 Single-Angle Sections The allowable flexural stresses for Single-angles are calculated based on their principal axes of bending (ASD SAM 5.3). Major Axis of Bending The allowable stress for major axis bending is the minimum considering the limit state of lateral-torsional buckling and local buckling (ASD SAM 5.1). The allowable major bending stress for Single-angles for the limit state of lateraltorsional buckling is given as follows (ASD SAM 5.1.3): é F ù Fb, major = ê0.55 - 0.10 ob ú Fob , Fy û ë if Fob £ Fy (ASD SAM 5-3a) é Fy ù Fb, major = ê0.95 - 0.50 ú Fy £ 0.66Fy , if Fob > Fy Fob ú êë û (ASD SAM 5-3b) where, Fob is the elastic lateral-torsional buckling stress as calculated below. The elastic lateral-torsional buckling stress, Fob , for equal-leg angles is taken as Fob = C b 28,250 , lt (ASD SAM 5-5) and for unequal-leg angles Fob is calculated as Fob = 143,100 C b I min S major é b 2 + 0.052( lt r ) 2 + b ù , w w min û l ë 2 (ASD SAM 5-6) where, t = min(t w , t f ) , l = max ( l 22 , l 33 ) , I min = minor principal moment of inertia, I max = major principal moment of inertia, S major = major section modulus for compression at the tip of one leg, Calculation of Allowable Stresses 87 CSI Steel Design Manual rmin = radius of gyration for minor principal axis, é 1 bw = ê ë I max ò A ù z( w 2 + z 2 ) dA ú - 2z 0 , û (ASD SAM 5.3.2) z = coordinate along the major principal axis, w = coordinate along the minor principal axis, and z 0 = coordinate of the shear center along the major principal axis with respect to the centroid. b w is a special section property for angles. It is positive for short leg in compression, negative for long leg in compression, and zero for equal-leg angles (ASD SAM 5.3.2). However, for conservative design in the program, it is always taken as negative for unequal-leg angles. In the above expressions C b is calculated in the same way as is done for I sections with the exception that the upper limit of C b is taken here as 1.5 instead of 2.3. æM C b = 1.75 +1.05 çç a è Mb ö ÷ ÷ + 0.3 ø æ Ma çç è Mb 2 ö ÷ ÷ £ 1.5 ø (ASD F1.3, SAM 5.2.2) The allowable major bending stress for Single-angles for the limit state of local buckling is given as follows (ASD SAM 5.1.1): Fb, major = 0.66 Fy , if Fb, major = 0.60 Fy , if Fb, major = Q (0.60 Fy ) , if 65 Fy < b 65 , £ t Fy (ASD SAM 5-1a) b 76 , £ t Fy (ASD SAM 5-1b) 76 b , > t Fy (ASD SAM 5-1c) where, t = thickness of the leg under consideration, b = length of the leg under consideration, and Q = slenderness reduction factor for local buckling. 88 Calculation of Allowable Stresses (ASD A-B5-2, SAM 4) Chapter IV Check/Design for AISC-ASD89 In calculating the allowable bending stress for Single-angles for the limit state of local buckling, the allowable stresses are calculated considering the fact that either of the two tips can be under compression. The minimum allowable stress is considered. Minor Axis of Bending The allowable minor bending stress for Single-angles is given as follows (ASD SAM 5.1.1, 5.3.1b, 5.3.2b): Fb,minor = 0.66 Fy , if Fb,minor = 0.60 Fy , if Fb,minor = Q (0.60 Fy ) , if 65 Fy < 65 b , £ t Fy (ASD SAM 5-1a) b 76 , £ t Fy (ASD SAM 5-1b) 76 b , > t Fy (ASD SAM 5-1c) In calculating the allowable bending stress for Single-angles it is assumed that the sign of the moment is such that both the tips are under compression. The minimum allowable stress is considered. General Sections For General sections the allowable bending stress for both major and minor axes bending is taken as, Fb = 0.60 Fy . Allowable Stress in Shear The shear stress is calculated along the geometric axes for all sections. For I, Box, Channel, T, Double angle, Pipe, Circular and Rectangular sections, the principal axes coincide with their geometric axes. For Single-angle sections, principal axes do not coincide with the geometric axes. Major Axis of Bending The allowable shear stress for all sections except I, Box and Channel sections is taken in the program as: Calculation of Allowable Stresses 89 CSI Steel Design Manual Fv = 0.40 Fy (ASD F4-1, SAM 3-1) The allowable shear stress for major direction shears in I-shapes, boxes and channels is evaluated as follows: Fv = 0.40 Fy , Fv = if Cv Fy £ 0.40 Fy , 2.89 if 380 h , and £ tw Fy (ASD F4-1) h £ 260 . tw (ASD F4-2) 380 < Fy where, ì 45, 000 k v , 2 ï ï Fy ( h t w ) Cv = í ï 190 k v , ï h t w Fy î 5.34 ì , 2 ï 4.00 + a h ( ) ï kv = í 4.00 ï5.34 + , 2 ï a h ( ) î tw = a = if k h ³ 56,250 v , tw Fy if k h < 56,250 v , tw Fy if a £1, h if a >1 , h (ASD F4) (ASD F4) Thickness of the web, Clear distance between transverse stiffeners, in. Currently it is taken conservatively as the length, l 22 , of the member in the pro- gram, h = Clear distance between flanges at the section, in. Minor Axis of Bending The allowable shear stress for minor direction shears is taken as: Fv = 0.40 Fy 90 Calculation of Allowable Stresses (ASD F4-1, SAM 3-1) Chapter IV Check/Design for AISC-ASD89 Calculation of Stress Ratios In the calculation of the axial and bending stress capacity ratios, first, for each station along the length of the member, the actual stresses are calculated for each load combination. Then the corresponding allowable stresses are calculated. Then, the capacity ratios are calculated at each station for each member under the influence of each of the design load combinations. The controlling capacity ratio is then obtained, along with the associated station and load combination. A capacity ratio greater than 1.0 indicates an overstress. During the design, the effect of the presence of bolts or welds is not considered. Also, the joints are not designed. Axial and Bending Stresses With the computed allowable axial and bending stress values and the factored axial and bending member stresses at each station, an interaction stress ratio is produced for each of the load combinations as follows (ASD H1, H2, SAM 6): • If f a is compressive and f a Fa > 0.15, the combined stress ratio is given by the larger of fa C m 33 f b 33 C m 22 f b 22 , and (ASD H1-1, SAM 6.1) + + Fa æ fa ö fa ö æ çç 1 ÷ Fb 33 çç 1 ÷ Fb 22 F' e33 ÷ F' e22 ÷ è è ø ø fa Q (0.60 Fy ) + f b 33 f + b 22 , where Fb 33 Fb 22 (ASD H1-2, SAM 6.1) f a , f b 33 , f b 22 , Fa , Fb 33 , and Fb 22 are defined earlier in this chapter, C m 33 and C m 22 are coefficients representing distribution of moment along the member length. Calculation of Stress Ratios 91 CSI Steel Design Manual 1.00 , if length is overwritten, ì ï 1.00 , if tension member, ï 0.85 , if sway frame, ï ï M Cm = í 0.6 - 0.4 a , if nonsway, no transverse loading, ï M b ï 0.85 , if nonsway, trans. load, end restrained, ï ï 1.00 , if nonsway, trans. load, end unrestrained. î (ASD H1) For sway frame C m = 0.85 , for nonsway frame without transverse load C m = 0.6 - 0.4 M a M b , for nonsway frame with transverse load and end restrained compression member C m = 0.85 , and for nonsway frame with transverse load and end unrestrained compression member C m =1.00 (ASD H1), where M a M b is the ratio of the smaller to the larger moment at the ends of the member, M a M b being positive for double curvature bending and negative for single curvature bending. When M b is zero, C m is taken as 1.0. The program defaults C m to 1.0 if the unbraced length factor, l, of the member is redefined by either the user or the program, i.e., if the unbraced length is not equal to the length of the member. The user can overwrite the value of C m for any member. C m assumes two values, C m 22 and C m 33 , associated with the major and minor directions. Fe¢ is given by Fe¢ = 12 p 2 E . 23 ( Kl / r ) 2 (ASD H1) A factor of 4/3 is applied on Fe¢ and 0.6 Fy if the load combination includes any wind load or seismic load (ASD H1, ASD A5.2). • If f a is compressive and f a Fa £ 0.15 , a relatively simplified formula is used for the combined stress ratio. fa f f + b 33 + b 22 Fa Fb 33 Fb 22 (ASD H1-3, SAM 6.1) • If f a is tensile or zero, the combined stress ratio is given by the larger of fa f f + b 33 + b 22 , and Fa Fb 33 Fb 22 92 Calculation of Stress Ratios (ASD H2-1, SAM 6.2) Chapter IV Check/Design for AISC-ASD89 f b 33 f + b 22 , where Fb 33 Fb 22 f a , f b 33 , f b 22 , Fa , Fb 33 , and Fb 22 are defined earlier in this chapter. However, either Fb 33 or Fb 22 need not be less than 0.6 Fy in the first equation (ASD H2-1). The second equation considers flexural buckling without any beneficial effect from axial compression. For circular and pipe sections, an SRSS combination is first made of the two bending components before adding the axial load component, instead of the simple addition implied by the above formulae. For Single-angle sections, the combined stress ratio is calculated based on the properties about the principal axis (ASD SAM 5.3, 6.1.5). For I, Box, Channel, T, Double-angle, Pipe, Circular and Rectangular sections, the principal axes coincide with their geometric axes. For Single-angle sections, principal axes are determined in the program. For general sections no effort is made to determine the principal directions. When designing for combinations involving earthquake and wind loads, allowable stresses are increased by a factor of 4/3 of the regular allowable value (ASD A5.2). Shear Stresses From the allowable shear stress values and the factored shear stress values at each station, shear stress ratios for major and minor directions are computed for each of the load combinations as follows: fv2 , Fv and fv3 . Fv For Single-angle sections, the shear stress ratio is calculated for directions along the geometric axis. For all other sections the shear stress is calculated along the principle axes which coincide with the geometric axes. When designing for combinations involving earthquake and wind loads, allowable shear stresses are increased by a factor of 4/3 of the regular allowable value (ASD A5.2). Calculation of Stress Ratios 93 C h a p t e r XIII Design Output Overview The program creates design output in three different major formats: graphical display, tabular output, and member specific detailed design information. The graphical display of steel design output includes input and output design information. Input design information includes design section labels, K-factors, live load reduction factors, and other design parameters. The output design information includes axial and bending interaction ratios and shear stress ratios. All graphical output can be printed. The tabular output can be saved in a file or printed. The tabular output includes most of the information which can be displayed. This is generated for added convenience to the designer. The member-specific detailed design information shows details of the calculation from the designer’s point of view. It shows the design section dimensions, material properties, design and allowable stresses or factored and nominal strengths, and some intermediate results for all the load combinations at all the design sections of a specific frame member. Overview 311 CSI Steel Design Manual In the following sections, some of the typical graphical display, tabular output, and member-specific detailed design information are described. Some of the design information is specific to the chosen steel design codes which are available in the program and is only described where required. The AISC-ASD89 design code is described in the latter part of this chapter. For all other codes, the design outputs are similar. Graphical Display of Design Output The graphical output can be produced either as color screen display or in grayscaled printed form. Moreover, the active screen display can be sent directly to the printer. The graphical display of design output includes input and output design information. Input design information, for the AISC-ASD89 code, includes • Design section labels, • K-factors for major and minor direction of buckling, • Unbraced Length Ratios, • C m -factors, • C b -factors, • Live Load Reduction Factors, • d s -factors, • d b -factors, • design type, • allowable stresses in axial, bending, and shear. The output design information which can be displayed is • Color coded P-M interaction ratios with or without values, and • Color coded shear stress ratios. The graphical displays can be accessed from the Design menu. For example, the color coded P-M interaction ratios with values can be displayed by selecting the Display Design Info... from the Design menu. This will pop up a dialog box called Display Design Results. Then the user should switch on the Design Output option button (default) and select P-M Ratios Colors & Values in the drop-down box. Then clicking the OK button will show the interaction ratios in the active window. 312 Graphical Display of Design Output Chapter XIII Design Output The graphics can be displayed in either 3D or 2D mode. The program standard view transformations are available for all steel design input and output displays. For switching between 3D or 2D view of graphical displays, there are several buttons on the main toolbar. Alternatively, the view can be set by choosing Set 3D View... from the View menu. The graphical display in an active window can be printed in gray scaled black and white from the program program. To send the graphical output directly to the printer, click on the Print Graphics button in the File menu. A screen capture of the active window can also be made by following the standard procedure provided by the Windows operating system. Tabular Display of Design Output The tabular design output can be sent directly either to a printer or to a file. The printed form of tabular output is the same as that produced for the file output with the exception that for the printed output font size is adjusted. The tabular design output includes input and output design information which depends on the design code of choice. For the AISC-ASD89 code, the tabular output includes the following. All tables have formal headings and are self-explanatory, so further description of these tables is not given. Input design information includes the following: • Load Combination Multipliers – Combination name, – Load types, and – Load factors. • Steel Stress Check Element Information (code dependent) – Frame ID, – Design Section ID, – K-factors for major and minor direction of buckling, – Unbraced Length Ratios, – C m -factors, – C b -factors, and – Live Load Reduction Factors. Tabular Display of Design Output 313 CSI Steel Design Manual • Steel Moment Magnification Factors (code dependent) – Frame ID, – Section ID, – Framing Type, – d b -factors, and – d s -factors. The output design information includes the following: • Steel Stress Check Output (code dependent) – Frame ID, – Section location, – Controlling load combination ID for P-M interaction, – Tension or compression indication, – Axial and bending interaction ratio, – Controlling load combination ID for major and minor shear forces, and – Shear stress ratios. The tabular output can be accessed by selecting Print Design Tables... from the File menu. This will pop up a dialog box. Then the user can specify the design quantities for which the results are to be tabulated. By default, the output will be sent to the printer. If the user wants the output stream to be redirected to a file, he/she can check the Print to File box. This will provide a default filename. The default filename can be edited. Alternatively, a file list can be obtained by clicking the File Name button to chose a file from. Then clicking the OK button will direct the tabular output to the requested stream ¾ the file or the printer. Member Specific Information The member specific design information shows the details of the calculation from the designer’s point of view. It provides an access to the geometry and material data, other input data, design section dimensions, design and allowable stresses, reinforcement details, and some of the intermediate results for a member. The design detail information can be displayed for a specific load combination and for a specific station of a frame member. 314 Member Specific Information Chapter XIII Design Output The detailed design information can be accessed by right clicking on the desired frame member. This will pop up a dialog box called Steel Stress Check Information which includes the following tabulated information for the specific member. – Frame ID, – Section ID, – Load combination ID, – Station location, – Axial and bending interaction ratio, and – Shear stress ratio along two axes. Additional information can be accessed by clicking on the ReDesign and Details buttons in the dialog box. Additional information that is available by clicking on the ReDesign button is as follows: • Design Factors (code dependent) – Effective length factors, K, for major and minor direction of buckling, – Unbraced Length Ratios, – C m -factors, – C b -factors, – Live Load Reduction Factors, – d s -factors, and – d b -factors. • Element Section ID • Element Framing Type • Overwriting allowable stresses Additional information that is available by clicking on the Details button is given below. • Frame, Section, Station, and Load Combination IDs, • Section geometric information and graphical representation, • Material properties of steel, • Moment factors, • Design and allowable stresses for axial force and biaxial moments, and • Design and allowable stresses for shear. Member Specific Information 315 CSI Steel Design Manual Design of Steel Structures, Part 1.1 : General Rules and Rules for Buildings, ENV 1993-1-1 : 1992, European Committee for Standardization, Brussels, Belgium, 1992. CISC, 1995 Handbook of Steel Construction, CAN/CSA-S16.1-94, 6th Edition, Canadian Institute of Steel Construction, Willowdale, Ontario, Canada, 1995. CSI, 2005a SAP2000 Getting Started, Computers and Structures, Inc., Berkeley, California, 2005. CSI, 2005b Welcome to ETABS,, Computers and Structures, Inc., Berkeley, California, 2005. CSI, 2005c CSI Analysis Reference Manual, Computers and Structures, Inc., Berkeley, California, 2005. ICBO, 1997 Uniform Building Code, 1997, International Conference of Building Officials, Whittier, California, 1997. D. W. White and J. F. Hajjar, 1991 “Application of Second-Order Elastic Analysis in LRFD: Research to Practice,” Engineering Journal, American Institute of Steel Construction, Inc., Vol. 28, No. 4, 1991. 318
Source Exif Data:
File Type : PDF File Type Extension : pdf MIME Type : application/pdf PDF Version : 1.6 Linearized : No Author : Administrator Create Date : 2011:06:07 12:46:57Z Modify Date : 2016:10:27 14:22:43-07:00 Has XFA : No XMP Toolkit : Adobe XMP Core 4.2.1-c043 52.372728, 2009/01/18-15:08:04 Format : application/pdf Creator : Administrator Title : SFD-OlderCodes.vp Creator Tool : Corel Ventura 10.0 Metadata Date : 2016:10:27 14:22:43-07:00 Producer : Corel PDF Engine Version 10.397 Document ID : uuid:a2377a16-bd21-4332-acbe-b1dfe72452a2 Instance ID : uuid:10151620-4a72-447c-8204-cfa3f193a98e Page Layout : SinglePage Page Count : 106EXIF Metadata provided by EXIF.tools