SCD AISC 360 10
User Manual: SCD-AISC-360-10
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Steel Connection Design Manual
AISC 360-10
Steel Connection
Design Manual
AISC 360-10
For ETABS® 2016
ISO ETA122815M61 Rev. 0
Proudly developed in the United States of America
December 2015
Copyright
Copyright Computers & Structures, Inc., 1978-2015
All rights reserved.
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Structures, Inc.
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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)
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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.
Contents
1
2
3
Introduction
1.1
Load Combinations
1-2
1.2
Stress Check
1-2
Design Algorithms
2.1
Demand/Capacity Ratios
2-1
2.2
Design Load Combinations
2-2
2.3
Supported Connection Types
2-3
2.4
Design Checks
2-3
2.5
Choice of Units
2-6
Steel Frame Design Using ANSI/AISC 360-10
3.1
Notations
3-1
3.2
Design Loading Combinations
3-4
3.3
Design Check Calculations
3-5
3.3.1
Strength of Bolt Group
3-5
3.3.2
Shear Yield Strength
3-5
i
Steel Concrete Design AISC 360-10
3.3.3
Sher Rupture Strength
3-6
3.3.4
Block Shear Rupture Strength
3-6
3.3.5
Design Weld Strength
3-6
3.3.6
WebPlate Rupture Strength
3-7
3.3.7
Critical Flexural Stress
3-7
3.3.8
Flexural Rupture Strength
3-7
3.3.9
Local Buckling of Plate
3-8
3.3.10
Flexural Yielding of Coped Section
3-8
3.3.11
Local Web Buckling of Coped Section
3-9
3.3.12
Beam Design Flexural Strength
3-10
3.3.13
Slip Resistance
3-10
Bibliography
ii
Chapter 1
Introduction
The design/check of steel connections is seamlessly integrated within the program. Initiation of the design process, along with control of various design parameters, is accomplished using the Design menu. Model and analysis data,
such as material properties and member forces, are recovered directly from the
model database, and are used in the design process in accordance with the user
defined or default design settings. As with all design applications, the user
should carefully review all of the user options and default settings to ensure
that the design process is consistent with the user’s expectations.
1.1
Load Combinations
The design is based on a set of user-specified loading combinations. However,
the program provides default load combinations based on the design code. If
the default load combinations are acceptable, no definition of additional load
combinations is required.
1.2
Stress Check
Steel connection design consists of calculating the connection forces or
stresses, and then comparing those calculated values with acceptable limits.
1-1
Steel Connection Design AISC 360-10
That comparison produces a demand/capacity ratio, which typically should not
exceed a value of unity if code requirements are to be satisfied.
Program output can be presented graphically on the model or in calculation
sheets prepared for each connection. For each presentation method, the output
is in a format that allows the engineer to quickly study the stress conditions that
exist in the connection, and in the event the connection is not adequate, aid the
engineer in taking appropriate remedial measures.
This manual is dedicated to the use of the AISC 360-10 design code. This option covers the “ANSI/AISC 360-10 Specification for Structural Steel Buildings” (AISC 2010a, b).
The implementation covers loading and load combinations from “ASCE/SEI
7-10 Minimum Design Loads for Buildings and Other Structures” (ASCE
2010), and also special requirements from “IBC 2012 International Building
Code” (IBC 2012). Only LRFD (Load and Resistance Factor Design) is currently included in this implementation. The strengths are calculated in the nominal levels. The phi (LRFD) factor is applied during calculation of demand/capacity ratios only. The design code is written in kip-inch units. All the
associated equations and requirements have been implemented in the program
in kip-in units. The program has been enabled with unit conversion capability.
This allows the users to enjoy the flexibility of choosing any set of consistent
units during creating and editing models, exporting and importing the model
components, and reviewing the design results.
1-2
Stress Check
Chapter 2
Design Algorithms
This chapter provides an overview of the basic assumptions, design preconditions, and some of the design parameters that affect the design of steel connections.
2.1
Demand/Capacity Ratios
Determination of the controlling demand/capacity (D/C) ratios for each steel
connection indicates the acceptability of the connection for the given loading
conditions. The steps for calculating the D/C ratios are as follows:
The factored forces are determined for each connection location.
The nominal strengths and controlling material thicknesses are calculated
for various criteria based on the equations provided later in this manual.
Factored forces and material thicknesses are compared to nominal
strengths and limiting thicknesses to determine D/C ratios. In either case,
design codes typically require that the ratios not exceed a value of unity. A
capacity ratio greater than unity indicates a connection that has exceeded a
limit state.
2-1
Steel Connection Design AISC 360-10
2.2
Design Load Combinations
The design load combinations are the various combinations of the prescribed
load cases for which the structure needs to be checked. The program creates a
number of default design load combinations for steel frame design. Users can
add their own design combinations as well as modify or delete the program
default design load combinations. An unlimited number of design load combinations can be specified.
To define a design load combination, simply specify one or more load cases,
each with its own scale factor. The scale factors are applied to the forces and
moments from the load cases to form the factored design forces and moments
for each design load combination.
For normal loading conditions involving static dead load (DL), live load (LL),
roof live load (RL), snow load (SL), wind load (WL), earthquake load (EL),
notional load (NL), and dynamic response spectrum load (EL), the program
has built-in default design combinations for the design code. These are based
on the code recommendations.
The default design combinations assume all load cases declared as dead or live to
be additive. However, each load case declared as wind, earthquake, or
response spectrum cases, is assumed to be non-additive with other loads and produces multiple lateral combinations. Also static wind, earthquake and
notional load responses produce separate design combinations with the sense (positive or negative) reversed. The notional load patterns are added to load combinations involving gravity loads only. The user is free to modify the default design
preferences to include the notional loads for combinations involving lateral loads.
For other loading conditions involving moving load, time history, pattern live
load, separate consideration of roof live load, snow load, and the like, the user
must define the design load combinations in lieu of or in addition to the default
design load combinations. If notional loads are to be combined with other load
combinations involving wind or earthquake loads, the design load combinations need to be defined in lieu of or in addition to the default design load combinations.
For multi-valued design combinations, such as those involving response spectrum, time history, moving loads and envelopes, where any correspondence be-
2-2
Design Load Combinations
Chapter 2 Design Algorithms
tween forces is lost, the program automatically produces sub-combinations
using the maxima/minima values of the interacting forces. Separate combinations with negative factors for response spectrum load cases are not required
because the program automatically takes the minima to be the negative of the
maxima response when preparing the sub-combinations described previously.
The program allows live load reduction factors to be applied to the member
forces of the reducible live load case on a member-by-member basis to reduce
the contribution of the live load to the factored responses.
2.3
Supported Connection Types
The program currently handles steel base plates, as well as the following connection types.
Shear Connections
Beam to Column Flange (major axis)
Beam to Column Web (minor axis)
Beam to Beam (beam coped top)
Beam to Beam (beam coped top and bottom)
Moment Connections
Beam to Column Flange (major axis)
Beam to Column Web (minor axis)
2.4
Design Checks
The design checks performed for each of the connection types are listed below
and described in detail in the next chapter.
Beam to Column Flange Moment (Major Axis)
Beam design flexural strength
Strength of bolt group
Supported Connection Types
2-3
Steel Connection Design AISC 360-10
Beam to Column Flange Moment (Major Axis)
Shear yielding of web plate
Shear rupture of web plate
Block shear rupture strength of web plate
Design strength of weld
Web plate rupture strength at weld
Shear yielding of beam web
Shear rupture strength of beam web
Panel zone shear strength
Local flange bending
Local web yielding
Web crippling
Beam to Column Web Moment (Minor Axis)
Beam design flexural strength
Strength of bolt group
Shear yielding of web plate
Shear rupture of web plate
Block shear rupture strength of web plate
Design strength of weld
Weld strength at tension flange
Shear yielding of beam web
Beam to Column Flange Shear (Major Axis)
Bolt strength in single shear
Bolt bearing on web plate
Shear yielding of web plate
Shear rupture of web plate
2-4
Design Checks
Chapter 2 Design Algorithms
Beam to Column Flange Shear (Major Axis)
Block shear rupture strength of web plate
Design strength of weld
Bold bearing on beam web
Beam to Column Web Shear (Minor Axis)
Strength of bolt group
Maximum plate thickness for plate yielding before bolt
shear/bearing
Shear yielding of web plate
Critical flexural stress
Shear rupture of web plate
Block shear rupture strength of web plate
Flexure rupture of plate
Local buckling of plate
Strength of column web at weld
Beam to Beam Coped at Top
Bolt strength in single shear
Bolt bearing on web plate
Shear yielding of web plate
Shear rupture of web plate
Block shear rupture of strength of web plate
Design strength of weld
Bolt bearing on beam web
Block shear rupture strength of beam web
Flexural yielding of coped section
Local web buckling on coped section
Design Checks
2-5
Steel Connection Design AISC 360-10
Beam to Beam Coped at Top
Shear rupture of girder web
Beam to Beam Coped Top and Bottom
Bolt strength in single shear
Bolt bearing on web plate
Shear yielding of web plate
Shear rupture of web plate
Block shear rupture of strength of web plate
Design strength of weld
Bolt bearing on beam web
Shear yielding of beam web
Shear rupture of beam web
Block shear rupture strength of beam web
Flexural yielding of coped section
Local web buckling on coped section
Shear rupture of girder web
2.5
Choice of Units
English as well as SI and MKS metric units can be used for input. 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. However, any system of units can be used to define and design a structure in the program.
The Display Unit preferences allow the user to specify the units.
2-6
Choice of Units
Chapter 3
Design Using ANSI/AISC 360-10
This chapter provides a detailed description of the algorithms used by the program in the design/check of steel connections in accordance with “ANSI/AISC
360-10 — Specifications for Structural Steel Building” (AISC 2010a, b). The
implementation covers load combinations from “ASCE/SEI 7-10,” which is
described in the section “Design Loading Combinations” in this chapter. The
loading based on “ASCE/SEI 7-10” has been described in a separate document
entitled “CSI Lateral Load Manual” (CSI 2013). References also are made to
IBC 2012 in this document.
For referring to pertinent sections of the corresponding code, a unique prefix is
assigned for each code.
3.1
•
Reference to the ANSI/AISC 360-10 code is identified with the prefix
“AISC.”
•
Reference to the ASCE/SEI 7-10 code is identified with the prefix
“ASCE.”
•
Reference to the IBC 2012 code is identified with the prefix “IBC.”
Notations
The various notations used in this chapter are described herein.
3-1
Steel Connection Design AISC 360-10
3-2
A
Cross-sectional area, in2
Ab
Nominal bolt area, in2
Ag
Gross area, in2
Agv
Gross area subject to shear, in2
Ant
Net area subject to tension, in2
Anv
Net area subject to shear, in2
Ap
Plate cross-sectional area, in2
D
Number of sixteenths-of-an-inch for a weld size, in
FEXX
Classification strength of weld metal, ksi
Fcr
Critical stress, ksi
Ft
Nominal tensile strength of a bolt, ksi
Fu
Specified minimum tensile strength of steel, ksi
Fv
Nominal shear strength of a bolt, ksi
Ixx
Moment of inertia of a section about the x-axis, in4
L
Height of a plate, in
Leh
Horizontal edge distance, in
Lev
Vertical edge distance, in
Mn
Nominal flexural strength, kip-in
Q
Full reduction factor for slender compression elements
Rn
Nominal resistance or strength, kips
Snet
Net elastic section modulus, in3
Sx
Elastic section modulus about the x-axis, in3
Notations
Chapter 3 - Design using ANSI/AISC 360-10
Z
Plastic section modulus, in3
a
Distance from a bolt centerline to edge of the fitting, in
c
Cope length, in
d
Nominal fastener diameter, in
d
Overall member depth, in
dc
Cope depth, in
dct
Top flange cope depth, in
dcb
Bottom flange cope depth, in
db
Hole diameter, in
fd
Adjustment factor for beams coped at both flanges
ho
Remaining web depth of coped beam, in
k
Plate buckling coefficient for beams coped at top only
n
Number of bolts in a vertical row
s
Bolt spacing, in
t
Thickness, in
tw
Web thickness, in
λ
Slenderness parameter
φ
Resistance factor
φFbc
Design buckling stress for coped beams, ksi
φRn
Design strength, kips
Notations
3-3
Steel Connection Design AISC 360-10
3.2
Design Loading Combinations
The structure is to be designed so that its design strength equals or exceeds the
effects of factored loads stipulated by the applicable design code. The default
design combinations are the various combinations of the already defined load
cases, such as dead load (DL), live load (LL), roof live load (RL), snow load
(SL), wind load (WL), and horizontal earthquake load (EL).
AISC 360-10 refers to the applicable building code for the loads and load combinations to be considered in the design, and to ASCE 7-10 in the absence of
such a building code. Hence, the default design combinations used in the current version are the ones stipulated in ASCE 7-10:
For design in accordance with LRFD provisions:
1.4 DL
1.2 DL + 1.6 LL + 0.5RL
1.2 DL + 1.0 LL + 1.6RL
(ASCE 2.3.2-1)
(ASCE 2.3.2-2)
(ASCE 2.3.2-3)
1.2 DL + 1.6 LL + 0.5 SL
1.2 DL + 1.0 LL + 1.6 SL
(ASCE 2.3.2-2)
(ASCE 2.3.2-3)
0.9 DL ± 1.0WL
1.2 DL + 1.6 RL± 0.5WL
1.2 DL + 1.0LL+ 0.5RL± 1.0WL
(ASCE 2.3.2-6)
(ASCE 2.3.2-3)
(ASCE 2.3.2-4)
1.2 DL + 1.6 SL± 0.5 WL
1.2 DL + 1.0LL+ 0.5SL± 1.0 WL
(ASCE 2.3.2-3)
(ASCE 2.3.2-4)
0.9 DL ± 1.0 EL
1.2 DL + 1.0 LL+ 0.2SL± 1.0EL
(ASCE 2.3.2-7)
(ASCE 2.3.2-5)
The combinations described herein are the default loading combinations only.
They can be deleted or edited as required by the design code or engineer-ofrecord.
The program allows live load reduction factors to be applied to the member
forces of the reducible live load case on a member-by-member basis to reduce
the contribution of the live load to the factored responses.
3-4
Design Loading Combinations
Chapter 3 - Design using ANSI/AISC 360-10
3.3
Design Check Calculations
The following sections provide details of the calculations performed for each
of the design checks performed for the various connection types.
3.3.1 Strength of Bolt Group
The strength of the bolt group is determined as the minimum of the bolt
strength in single shear and bolt bearing strength.
3.3.1.1 Bolt Strength in Single Shear
ϕ𝑅𝑅𝑛𝑛 = ϕ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝐴𝐴𝑏𝑏
(AISC J3-1)
ϕ = 0.75
The nominal shear strength of the bolt, Fnv, is taken from Table J3.2. Ab is the
bolt area and n is the total number of bolts.
3.3.1.2 Bolt Bearing Strength
The bolt bearing on the web plate is calculated as follows.
ϕ𝑅𝑅𝑛𝑛 = ϕ[min�𝑟𝑟𝑛𝑛1 , 𝑟𝑟𝑛𝑛(max) � + (𝑛𝑛 − 1)min(𝑟𝑟𝑛𝑛2 , 𝑟𝑟𝑛𝑛(max) )
where,
ϕ = 0.75
𝑟𝑟𝑛𝑛1 = 1.2𝑙𝑙𝑐𝑐1 𝑡𝑡𝐹𝐹𝑢𝑢
𝑟𝑟𝑛𝑛2 = 1.2𝑙𝑙𝑐𝑐 𝑡𝑡𝐹𝐹𝑢𝑢
𝑟𝑟𝑛𝑛(𝑚𝑚𝑚𝑚𝑚𝑚) = 2.4𝑑𝑑𝑑𝑑𝐹𝐹𝑢𝑢
𝑙𝑙𝑐𝑐1 = 𝐿𝐿𝑒𝑒𝑒𝑒 −
𝑙𝑙𝑐𝑐 = 𝑠𝑠 − 𝑑𝑑ℎ
𝑑𝑑ℎ
2
3.3.2 Shear Yield Strength
The shear yielding of the material is calculated as follows.
Design Check Calculations
3-5
Steel Connection Design AISC 360-10
ϕ𝑅𝑅𝑛𝑛 = ϕ0.6𝐹𝐹𝑦𝑦 𝐴𝐴𝑔𝑔𝑔𝑔
(AISC J4-3)
ϕ=1
𝐴𝐴𝑔𝑔𝑔𝑔 = 𝐿𝐿𝐿𝐿
3.3.3 Shear Rupture Strength
The shear rupture strength is calculated as follows.
ϕ𝑅𝑅𝑛𝑛 = ϕ0.6𝐹𝐹𝑦𝑦 𝐴𝐴𝑛𝑛𝑛𝑛
ϕ = 0.75
𝐴𝐴𝑛𝑛𝑛𝑛 = �𝐿𝐿 − 𝑛𝑛 �𝑑𝑑ℎ +
(AISC J4-4)
1
�� 𝑡𝑡
16
3.3.4 Block Shear Rupture Strength
The block shear rupture strength is calculated as follows.
ϕ𝑅𝑅𝑛𝑛 = ϕ[𝐹𝐹𝑢𝑢 𝐴𝐴𝑛𝑛𝑛𝑛 + min�0.6𝐹𝐹𝑦𝑦 𝐴𝐴𝑔𝑔𝑔𝑔 , 0.6𝐹𝐹𝑢𝑢 𝐴𝐴𝑛𝑛𝑛𝑛 �
ϕ = 0.75
1
2
𝐴𝐴𝑛𝑛𝑛𝑛 = �𝐿𝐿𝑒𝑒ℎ − �𝑑𝑑ℎ +
1
�� 𝑡𝑡
16
2𝑛𝑛−1
�𝑑𝑑ℎ
2
𝐴𝐴𝑛𝑛𝑛𝑛 = �{(𝑛𝑛 − 1)𝑠𝑠 + 𝐿𝐿𝑒𝑒𝑒𝑒 } − �
𝐴𝐴𝑔𝑔𝑔𝑔 = {(𝑛𝑛 − 1)𝑠𝑠 + 𝐿𝐿𝑒𝑒𝑒𝑒 }𝑡𝑡
+
(AISC J4-5)
1
��� 𝑡𝑡
16
3.3.5 Design Weld Strength
The design strength of a double-sided fillet weld on a shear plate is calculated
as follows.
ϕ𝑅𝑅𝑛𝑛 =
φ0.6𝐹𝐹𝐸𝐸𝐸𝐸𝐸𝐸 𝐷𝐷2𝐿𝐿
22.627
ϕ = 0.75
3-6
Design Check Calculations
(AISC Manual pg. 8-8)
Chapter 3 - Design using ANSI/AISC 360-10
3.3.6 Web Plate Rupture Strength
The web plate rupture strength is calculated by determining the minimum base
metal thickness that will match the available shear rupture strength of the base
metal, to the available shear rupture strength of the weld(s). The minimum base
metal thickness is calculated as follows.
𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 =
𝐹𝐹𝐸𝐸𝐸𝐸𝐸𝐸 𝐷𝐷
22.62𝐹𝐹𝑢𝑢
(AISC Manual pg. 9-5)
3.3.7 Critical Flexural Stress
The critical flexural stress is calculated as:
ϕ𝑀𝑀𝑛𝑛 = ϕ𝐹𝐹𝑐𝑐𝑐𝑐 𝑍𝑍𝑥𝑥
where,
ϕ𝐹𝐹𝑐𝑐𝑐𝑐 = �(ϕ𝐹𝐹𝑦𝑦 )2 − 3𝑓𝑓𝑣𝑣 2
ϕ = 0.9
𝑉𝑉
𝑓𝑓𝑣𝑣 = 𝐴𝐴𝑢𝑢
𝑝𝑝
𝐴𝐴𝑝𝑝 = 𝑡𝑡𝑡𝑡
𝑍𝑍𝑥𝑥 =
𝑡𝑡𝐿𝐿2
4
3.3.8 Flexural Rupture Strength
The flexural rupture strength of a section is calculated as follows.
ϕ𝑀𝑀𝑛𝑛 = ϕ𝐹𝐹𝑢𝑢 𝑍𝑍𝑛𝑛𝑛𝑛𝑛𝑛
ϕ = 0.75
𝑍𝑍𝑛𝑛𝑛𝑛𝑛𝑛 =
𝑡𝑡𝐿𝐿2
�1
4
−
(AISC Manual pg. 9-6)
𝑑𝑑ℎ +
3
1
16
�
Design Check Calculations
3-7
Steel Connection Design AISC 360-10
3.3.9 Local Buckling of Plate
The local buckling of a plate is checked by calculating the capacity of the section as follows.
ϕ𝑀𝑀𝑛𝑛 = ϕ𝐹𝐹𝑐𝑐𝑐𝑐 𝑆𝑆𝑛𝑛𝑛𝑛𝑛𝑛
(AISC Manual pg. 9-7)
where,
ϕ = 0.9
𝑆𝑆𝑛𝑛𝑛𝑛𝑛𝑛 =
𝑡𝑡𝐿𝐿2
6
𝐹𝐹𝑐𝑐𝑐𝑐 = 𝐹𝐹𝑦𝑦 𝑄𝑄
The value of Q depends on the value of λ, where
𝑄𝑄 = 1 𝑓𝑓𝑓𝑓𝑓𝑓 𝜆𝜆 ≤ 0.7
𝑄𝑄 = 1.34 − 0.486𝜆𝜆
𝜆𝜆 =
�𝐿𝐿�𝐹𝐹𝑦𝑦 �
𝐿𝐿 2
𝑎𝑎
10𝑡𝑡�475+280� �
3.3.10 Flexural Yielding of Coped Section
Flexure of the coped section is checked by calculating the flexural capacity as
follows.
ϕ𝑀𝑀𝑛𝑛 = ϕ𝐹𝐹𝑦𝑦 𝑆𝑆𝑛𝑛𝑛𝑛𝑛𝑛
ϕ = 0.9
(AISC Manual Part 9)
where, Snet is the net elastic section modulus of the section. For beams coped at
the top and bottom,
𝑆𝑆𝑛𝑛𝑛𝑛𝑛𝑛 =
𝑡𝑡𝑤𝑤 ℎ𝑜𝑜 2
6
𝑆𝑆𝑛𝑛𝑛𝑛𝑛𝑛 =
𝐼𝐼𝑥𝑥𝑥𝑥
𝑦𝑦𝑥𝑥
For beams coped at the top only,
3-8
Design Check Calculations
Chapter 3 - Design using ANSI/AISC 360-10
where,
ℎ𝑜𝑜 2 𝑡𝑡𝑤𝑤 +𝑡𝑡𝑓𝑓 2 �𝑏𝑏𝑓𝑓 −𝑡𝑡𝑤𝑤 �
𝑦𝑦𝑥𝑥 = ℎ𝑜𝑜 − (
1
2𝐴𝐴
)
3
𝐼𝐼𝑥𝑥𝑥𝑥 = � � �𝑡𝑡𝑤𝑤 𝑦𝑦𝑥𝑥 3 + 𝑏𝑏𝑓𝑓 (ℎ𝑜𝑜 − 𝑦𝑦𝑥𝑥 )3 − �𝑏𝑏𝑓𝑓 − 𝑡𝑡𝑤𝑤 ��ℎ𝑜𝑜 − 𝑦𝑦𝑥𝑥 − 𝑡𝑡𝑓𝑓 � �
3
3.3.11 Local Web Buckling of Coped Section
The local web buckling strength of coped sections is calculated as follows.
ϕ𝑅𝑅𝑛𝑛 =
𝜙𝜙𝐹𝐹𝑏𝑏𝑏𝑏 𝑆𝑆𝑛𝑛𝑛𝑛𝑛𝑛
𝑒𝑒
(AISC Manual Part 9)
where Snet is calculated as in 3.3.10 and φFbc is calculated as follows. For a
beam section coped top and bottom:
ϕ𝐹𝐹𝑏𝑏𝑏𝑏
50840𝑡𝑡𝑤𝑤 2 𝑓𝑓𝑑𝑑
=
𝑐𝑐ℎ𝑜𝑜
𝑓𝑓𝑑𝑑 = 3.5 −
7.5𝑑𝑑𝑐𝑐
𝑑𝑑
For a beam section coped at the top only:
𝑡𝑡𝑤𝑤 2
ϕ𝐹𝐹𝑏𝑏𝑏𝑏 = φ26,210 � � 𝑓𝑓𝑓𝑓
ℎ𝑜𝑜
ϕ = 0.9
where f and k are determined as follows.
𝑐𝑐
𝑐𝑐
𝑓𝑓 = 2 � � 𝑓𝑓𝑓𝑓𝑓𝑓 ≤ 1.0
𝑑𝑑
𝑑𝑑
𝑐𝑐
𝑐𝑐
𝑓𝑓 = 1 + � � 𝑓𝑓𝑓𝑓𝑓𝑓 > 1.0
𝑑𝑑
𝑑𝑑
𝑘𝑘 = 2.2 �
𝑘𝑘 = 2.2 �
ℎ𝑜𝑜
𝑐𝑐
� 𝑓𝑓𝑓𝑓𝑓𝑓 ≤ 1.0
𝑐𝑐
ℎ𝑜𝑜
ℎ𝑜𝑜
𝑐𝑐
� 𝑓𝑓𝑓𝑓𝑓𝑓 > 1.0
𝑐𝑐
ℎ𝑜𝑜
Design Check Calculations
3-9
Steel Connection Design AISC 360-10
3.3.12 Beam Design Flexural Strength
The beam design flexural capacity is calculated as follows.
ϕ𝑀𝑀𝑛𝑛 = ϕ𝐹𝐹𝑢𝑢 𝑆𝑆𝑥𝑥
(AISC F13-1)
3.3.13 Slip Resistance
The serviceability limit state of slip is checked using the slip resistance calculated as follows.
ϕ𝑅𝑅𝑛𝑛 = ϕ𝜇𝜇𝐷𝐷𝑢𝑢 ℎ𝑓𝑓 𝑇𝑇𝑏𝑏 𝑛𝑛𝑠𝑠
where,
(AISC J3-8b)
ϕ = 1 𝑓𝑓𝑓𝑓𝑓𝑓 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 ℎ𝑜𝑜𝑜𝑜𝑜𝑜
0.85 𝑓𝑓𝑓𝑓𝑓𝑓 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 ℎ𝑜𝑜𝑜𝑜𝑜𝑜
𝐷𝐷𝑢𝑢 = 1.13
ℎ𝑓𝑓 = 1
The value of µ is taken from Appendix A, Table 1 and the value of Tb is taken
from Appendix A, Table 2.
3 - 10
Design Check Calculations
Bibliography
AISC, 2010a. ANSI/AISC 360-10: An American National Standard – Specification for Structural Steel Building, American Institute of Steel Construction. One East Wacker Drive, Suite 700, Chicago, Illinois, 60601.
June 22.
AISC, 2010b. Commentary on the Specification for Structural Steel Buildings,
American Institute of Steel Construction. One East Wacker Drive, Suite
700, Chicago, Illinois, 60601. June 22.
ASCE, 2010. SEI/ASCE 7-10. Minimum Design Loads for Buildings and Other
Structures. ASCE Standard. American Society of Civil Engineers.
CSI, 2013. CSI Lateral Load Manual. Computers and Structures, Inc., 1995
University Avenue, Berkeley, California, 94704.
IBC, 2012. International Building Code, International Code Council, 4051 West
Flossmoor Road, Country Club Hills, Illinois, 60478. January.
Wilson, E. L., 1965, "Structural Analysis of Axisymmetric Solids," AIAA
Journal 3, 2269–2274.
Bibliography - 1
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