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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 . . . . . . . . . . . . . . . . .
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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 .
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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
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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
֍
֍ 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
֍
֍ 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
֍ 19
. - 12
. u
֍
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
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