SFD-AS-4100-1998

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ISO SAP022811M21 Rev. 0 Version 15

Berkeley, California, USA February 2011

Steel Frame

Design Manual

Australian 4100-1998

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Copyright

The CSI Logo®, SAP2000®, and ETABS® are registered trademarks of Computers and Structures, Inc. SAFETM and Watch & LearnTM are trademarks of Computers and

Structures, Inc.

The computer programs SAP2000® and ETABS® and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest with Computers and Structures, Inc. Unlicensed use of these programs or reproduction of documentation in any form, without prior written authorization from Computers and 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 and Structures, Inc.

1995 University Avenue

Berkeley, California 94704 USA Phone: (510) 649-2200

FAX: (510) 649-2299

e-mail: [email protected] (for general questions)

e-mail: [email protected] (for technical support questions) web: www.csiberkeley.com

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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.

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i

Shear

Check

3-58

4 Design Output

4.1 Display Design Information on the Model 4-2

4.2 Display Design Information in Tables 4-5

4.3 Display Detailed Member Specific Information 4-8

4.4 Save or Print Design Information as Tables 4-13

4.5 Error and Warning Messages 4-15

Appendix A Supported Design Codes Bibliography

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1 - 1

Chapter 1 Introduction

The design/check of steel frames is seamlessly integrated within the program. Initiation of the design process, along with control of various design parame-ters, is accomplished using the Design menu.

Automated design at the object level is available for any one of a number of user-selected design codes, as long as the structures have first been modeled and analyzed by the program. Model and analysis data, such as material prop-erties 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 re-view all of the user options and default settings to ensure that the design proc-ess is consistent with the user’s expectations.

The design is based on a set of user-specified loading combinations. However, the program provides default load combinations for each supported design code. If the default load combinations are acceptable, no definition of addi-tional load combinations is required. The Direct Analysis Method requires that a notional load, N = 0.002Yi , where Yi is the gravity load acting at level i, be applied to account for the destabilizing effects associated with the initial imper-fections and other conditions that may induce sway not explicitly modeled in the structure. The user must be aware that notional loads must be defined and assigned by the user. Currently, the software creates design combinations that include notional loads and gravity loads only. If the user needs notional loads

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1 - 2 Organization

that include combinations containing lateral loads, the user must define such combinations manually. The automation of default load combinations, includ-ing notional loads, is currently limited to gravity loads only. Design load com-binations of notional loads acting together with lateral loads currently are NOT automated by the software.

Steel frame design/check consists of calculating the flexural, axial, and shear forces or stresses at several locations along the length of a member, and then comparing those calculated values with acceptable limits. That comparison produces a demand/capacity ratio, which typically should not exceed a value of one if code requirements are to be satisfied. The program follows the same re-view procedures when it is checking a user-specified shape or when checking a shape selected by the program from a predefined list. The program does not do the connection design. However, it calculates the design basis forces for con-nection design.

Program output can be presented graphically on the model, in tables for both input and output data, or in calculation sheets prepared for each member. For each presentation method, the output is in a format that allows the engineer to quickly study the stress conditions that exist in the structure, and in the event the member is not adequate, aid the engineer in taking appropriate remedial measures, including altering the design member without re-running the entire analysis.

The program supports a wide range of steel frame design codes, including many national building codes. Appendix A provides a list of supported steel frame design codes. However, this manual is dedicated to the use of the menu option "AS 4100-1998." This option covers the “AS 4100-1998 Australian Standard Steel Structures” (SA 1998). The implementation covers loading and load combinations from "AS/NZS 1170.0:2002 Australian/New Zealand Standard, Part 0 : General Principals” (SA/SNZ 2002).

Currently, the software does not automate the following:

 Notional loads combinations that include lateral wind and quake loads  The validity of the analysis method. The user must verify the suitability of

the specified analysis method used under the User Options described in the preceding sections. The code requires, for instance, that the Second Order Elastic Analysis Method be used when a ratio of the second order moments

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Chapter 1 Introduction

Organization 1 - 3

to the first order moments exceeds 1.4. This check currently must be per-formed by the user.

 P-Δ analysis. Since many different codes are supported by the software and not all require a P-Δ analysis, the user must specify that a P-Δ analysis be performed during the analysis phase so that the proper member forces are available for use in the design phase.

The design codes supported under “AS 4100-1998” are written in Newton-millimeter units. All the associated equations and requirements have been im-plemented in the program in Newton-millimeter 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 de-sign results.

1.1 Organization

This manual is designed to help you quickly become productive using the AS 4100-1998 steel frame design option. Chapter 2 addresses prerequisites related to modeling and analysis for a successful design in accordance with 4100-1998. Chapter 3 provides detailed descriptions of the specific requirements as implemented in 4100-1998. Chapter 4 concludes by illustrating some of the display and output options. The appendix identifies the code supposed in SAP2000.

1.2

Chapter 2 Modeling, Analysis and Design Prerequisites

This chapter provides an overview of the basic assumptions, design precondi-tions, and some of the design parameters that affect the design of steel frames. For referring to pertinent sections of the corresponding code, a unique prefix is assigned for each code.

• Reference to the AS 4100-1998 code is identified with the prefix "AS." • Reference to the AS/NZS 1170.0:2002 code is identified with the prefix

"AS/NZS."

2.1 Check and Design Capability

The program has the ability to check adequacy of a section (shape) in accor-dance with the requirements of the selected design code. Also the program can automatically choose (i.e., design) the optimal (i.e., least weight) sections from a predefined list that satisfies the design requirements.

To check adequacy of a section, the program checks the demand/capacity ("D/C") ratios at a predefined number of stations for each design load combina-tion. It calculates the envelope of the D/C ratios. It also checks the other re-quirements on a pass or fail basis. If the capacity ratio remains less than or equal to the D/C ratio limit, which is a number close to 1.0, and if the section

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2 - 2 Analysis Sections vs. Design Sections

passes all the special requirements, the section is considered to be adequate, else the section is considered to be failed. The D/C ratio limit is taken as 0.95 by default. However, this value can be overwritten in the Preferences (Chapter 3).

To choose (design) the optional section from a predefined list, the program first orders the list of sections in increasing order of weight per unit length. Then it starts checking each section from the ordered list, starting with the one with the least weight. The procedure for checking each section in this list for adequacy is exactly the same as described in the preceding paragraph. The program will evaluate each section in the list until it finds the least weight section that passes the code checks. If no section in the list is acceptable, the program will use the heaviest section but flag it as being overstressed.

To check adequacy of an individual section, the user must assign the section using the Assign menu. In that case, both the analysis and design sections will be changed.

To choose the optimal section, the user must first define a list of steel sections, the Auto Select sections list. The user must next assign this list, in the same manner as any other section assignment, to the frame members to be opti-mized. The program will use the median section by weight when doing the ini-tial analysis. Click the Define menu > Frame Sections command to access the Frame Properties form where the Auto Select sections list may be defined.

2.2 Analysis Sections vs. Design Sections

Analysis sections are those section properties used to analyze the model when the Analyze menu > Run Analysis command is clicked. The design section is whatever section is used in the steel frame design. It is possible for the last used analysis section and the current design section to be different. For exam-ple, an analysis may be run using a W18X35 beam, and then in the design, it may be found that a W16X31 beam worked. In that case, the last used analysis section is the W18X35 and the current design section is the W16X31. Before the design process is complete, verify that the last used analysis section and the current design section are the same. The Design menu > Steel Frame Design > Verify Analysis vs. Design Section command is useful for this task.

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Chapter 2 Design Algorithms

Design and Check Stations 2 - 3

The program keeps track of the analysis section and the design section sepa-rately. Note the following about analysis and design sections:

 Assigning a frame section property using the Assign menu assigns the sec-tion as both the analysis secsec-tion and the design secsec-tion.

 Running an analysis using the Analyze menu > Run Analysis command always sets the analysis section to be the same as the current design sec-tion.

 Assigning an Auto Select section list to a frame object initially sets the analysis and design section to be the section in the list with the median weight.

 Unlocking a model deletes the design results, but it does not delete or change the design section.

 Altering the Design Combinations in any way deletes the design results, but does not delete or change the design section.

 Altering any of the steel frame design preferences deletes the design re-sults, but does not delete or change the design section.

2.3 Design and Check Stations

For each design combination, steel frame members (beams, columns, and braces) are designed (optimized) or checked at a number of locations (stations) along the length of the object. The stations are located at equally spaced seg-ments along the clear length of the object. By default, at least three stations will be located in a column or brace member, and the stations in a beam will be spaced at most 0.5 meter apart (2 feet if the model has been created in US units). The user can overwrite the number of stations in an object before the analysis is made using the Assign menu. The user can refine the design along the length of a member by requesting more stations.

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2 - 4 Demand/Capacity Ratios

2.4 Demand/Capacity Ratios

Determination of the controlling D/C ratios for each steel frame member indi-cates the acceptability of the member for the given loading conditions. The steps for calculating the D/C ratios are as follows:

 The factored forces are calculated for axial, flexural, and shear at each de-fined station for each design combination. The bending moments are calcu-lated about the principal axes. For I-Shape, Box, Channel, T-Shape, Dou-ble-Angle, Pipe, Circular, and Rectangular sections, the principal axes co-incide with the geometric axes. For Single-Angle sections, the design con-siders 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 forces are calculated for directions along the geometric axes. For all other sections, the program calculates the shear forces along the geometric and principal axes.

 The nominal capacities are calculated for compression, tension, bending and shear based on the equations provided later in this manual. For flexure, the nominal capacities are calculated based on the principal axes of bend-ing. For the I-Shape, Box, Channel, Circular, Pipe, T-Shape, 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.

The nominal capacities for shear is calculated along the geometric axes for all sections. For I-Shape, Box, Channel, T-Shape, 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.

 Factored forces are compared to nominal capacities to determine D/C ra-tios. In either case, design codes typically require that the ratios not exceed a value of one. A D/C ratio greater than one indicates a member that has exceeded a limit state.

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Design Load Combinations 2 - 5

2.5 Design Load Combinations

The design load combinations are the various combinations of the prescribed analysis 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 de-fault design load combinations. An unlimited number of design load combina-tions can be specified.

To define a design load combination, simply specify one or more analysis cases, each with its own scale factor. The scale factors are applied to the forces and moments from the analysis 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), wind load (WL), earthquake load (EL), notional load (NL), and dynamic re-sponse spectrum load (EL), the program has built-in default design combina-tions for the design code. These are based on the code recommendacombina-tions. The default design combinations assume all static load response cases declared as dead or live to be additive. However, each static 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 cases are added to load combinations involving gravity loads only.

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 combina-tions should be defined in lieu of or in addition to the default design load com-binations.

For multi-valued design combinations, such as those involving response spec-trum, time history, moving loads and envelopes, where any correspondence between forces is lost, the program automatically produces sub-combinations using the maxima/minima values of the interacting forces. Separate

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2 - 6 Notional Load Patterns

tions with negative factors for response spectrum analysis cases are not required because the program automatically takes the minima to be the nega-tive 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.

2.6 Notional Load Patterns

Notional loads are lateral loads that are applied at each framing level and are specified as a percentage of the gravity loads applied at that level. They are in-tended to account for the destabilizing effects of out-of-plumbness, geometric imperfections, inelasticity in structural members, and any other effects that could induce sway and that are not explicitly considered in the analysis.

The program allows the user to create a Notional Load pattern as a percentage of the previously defined gravity load pattern to be applied in one of the global lateral directions: X or Y. The user can define more than one notional load pat-tern associated with one gravity load by considering different factors and dif-ferent directions. In the AS 4100-1998 code, the notional loads are typically suggested to be 0.2% (or 0.002) (AS 3.2.4), a factor referred to as the notional load coefficient in this document.

The notional load patterns should be considered in combination with appropri-ate factors, appropriappropri-ate directions, and appropriappropri-ate senses. The code needs the notional loads to be considered only in gravity load combinations (ASC 3.2.4). The program does not create the notional load pattern automatically. However, if a notional load pattern is defined by the user, it is automatically included in the default design load combinations involving gravity loads only.

Currently, the notional loads are not automatically included in the default de-sign load combinations that include lateral loads. However, the user is free to modify the default design load combinations to include the notional loads with appropriate factors and in appropriate load combinations.

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Second Order P-Delta Effects 2 - 7

2.7 Second Order P-Delta Effects

Modern design provisions are based on the principle that the member forces are calculated by a second-order elastic analysis, where the equilibrium is satisfied on the deformed geometry of the structure. The effects of the loads acting on the deformed geometry of the structure are known as the second-order or the P-Delta effects.

The P-Delta effects come from two sources: global lateral translation of the frame and the local deformation of members within the frame.

Consider the frame object shown in Figure 2-1, which is extracted from a story level of a larger structure. The overall global translation of this frame object is indicated by . The local deformation of the member is shown as . The total second order P-Delta effects on this frame object are those caused by both  and .



Original position of frame element shown by vertical line

Position of frame element as a result of global lateral translation, , shown by dashed line

Final deflected position of the frame element that includes the global lateral translation, , and the local deformation of the element, 



P



Original position of frame element shown by vertical line

Position of frame element as a result of global lateral translation, , shown by dashed line

Final deflected position of the frame element that includes the global lateral translation, , and the local deformation of the element, 



P

Figure 2-1 P- and P- effects

The program has an option to consider P-Delta effects in the analysis. When you consider P-Delta effects in the analysis, the program does a good job of

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2 - 8 Second Order P-Delta Effects

capturing the effect due to the  deformation (P- effect) shown in Figure

2-1, but it does not typically capture the effect of the  deformation (P-

effect), unless, in the model, the frame object is broken into multiple elements over its length.

In design codes, required strengths are usually required to be determined using a second-order analysis that considers both P- and P- effects. Approximate second-order analysis procedures based on amplification of responses from first-order analysis for calculating the required flexural strengths are common in current design codes and have the following general form:





 

 

CAP b nt s lt

M M M (AS 4.4.2.2, App. E, App. F)

where, CAP

M = Required flexural design capacities

nt

M = Required flexural capacities from first-order analysis of the

member assuming there is no translation of the frame (i.e., asso-ciated with the  deformation in Figure 2-1)

lt

M = Required flexural capacities from first-order analysis of the member as a result of lateral translation of the frame only (i.e., associated with the  deformation in Figure 2-1)

_s = Unitless amplification factor multiplying M_lt

_b = Unitless amplification factor multiplying



M_nt _sM_lt



In the AS 4100-1998 code, a rigorous second order analysis (AS 4.4.1.2(b)) or the amplification of first order analysis results to estimate the effect of second order effects (AS 4.4.1.2(a)) is required. The program has the capability of performing both. In the first case, the required strengths are determined directly from the analysis results without any amplification factor s (i.e., s is equal to 1). However, these amplification factors can always be overwritten by the user on a member-by-member basis, if desired, using the overwrite option.

To properly capture the P- effect in a finite element analysis, each element, especially column elements, must be broken into multiple finite elements, which is not really desired for other reasons. Although a single element per

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Member Unsupported Lengths 2 - 9

member can capture the P- effect to some extent, the program considers that inadequate. The program thus uses the b factor even if the analysis considers the P- effects. This is a conservative approach.

Thus, in general, the steel frame design feature requires consideration of P-Delta effects in the analysis before the check/design is performed. Although one element per line object is generally adequate to capture the P- effect, it is recommended to use more than one element per line object for the cases where both P- and P- effects are to be considered. However, explicit manual break-ing of the member into elements has other consequences related to member end moments and unbraced segment end moment. It is recommended that the members be broken internally by the program. In this way, the member is recognized as one unit, end of the members are identified properly, and P- and P- effects are captured better.

2.8 Member Unsupported Lengths

The column unsupported lengths are required to account for column slender-ness effects for flexural buckling and for lateral-torsional buckling. The pro-gram automatically determines the unsupported length ratios, which are speci-fied as a fraction of the frame object length. Those ratios times the frame ob-ject lengths give the unbraced lengths for the member. Those ratios also can be overwritten by the user on a member-by-member basis, if desired, using the de-sign overwrite option.

The unsupported length for minor direction bending or for lateral-torsional buckling also can be defined more precisely by using precise bracing points in the Lateral Bracing option on the Steel Frame Design menu. This allows the user to define the lateral bracing of the top, bottom, or both flanges. The brac-ing can be a point brace, or continuous bracbrac-ing is considered enough for flex-ural buckling in the minor direction. The unbraced length of the compression flange is determined based on the current moment diagram to determine the lateral-torsional buckling length, l_LTB. This exact method of bracing definition does not allow the user to define unbraced lengths for major direction bending. Two unsupported lengths, l33 and l22, as shown in Figure 2-2 are to be consid-ered for flexural buckling. These are the lengths between support points of the

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2 - 10 Member Unsupported Lengths

member in the corresponding directions. The length l₃₃ corresponds to instabil-ity about the 3-3 axis (major axis), and l22 corresponds to instability about the 2-2 axis (minor axis). The length l_LTB not shown in the figure, is also used for lateral-torsional buckling caused by major direction bending (i.e., about the 3-3 axis).

In determining the values for l₂₂ and l₃₃ of the members, 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 member support points and evaluates the correspond-ing unsupported length.

Figure 2-2 Unsupported lengths l₃₃ and l₂₂

It is possible for the unsupported length of a frame object to be evaluated by the program as greater than the corresponding member length. For example, assume a column has a beam framing into it in one direction, but not the other, at a floor level. In that case, the column is assumed to be supported in one di-rection only at that story level, and its unsupported length in the other didi-rection will exceed the story height.

By default, the unsupported length for lateral-torsional buckling, lLTB, is taken to be equal to the l22 factor. Similar to l22 and l33, lLTB can be overwritten.

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Effective Length Factor (ke) 2 - 11

If the unsupported length is defined using the precise bracing point definition and if it is also overwritten in the overwrites, the value used in the design overwrites prevails. If the unsupported length is defined using the precise brac-ing point definition and if it is not overwritten in the overwrites, the value used in the bracing point definition governs. If the unsupported length is defined us-ing neither the bracus-ing point definition nor an overwrite, the program calcu-lated value will be used.

2.9 Effective Length Factor (k

_e

)

The effective length method for calculating member axial compressive strength has been used in various forms in several stability based design codes. The method originates from calculating effective buckling lengths, l_e, and is based on elastic/inelastic stability theory. The effective buckling length is used to cal-culate an axial compressive strength, N_c, through an empirical column curve that accounts for geometric imperfections, distributed yielding, and residual stresses present in the cross-section.

There are two types of ke-factors in the AS 4100-1998 code. The first type of -factor

e

k is used for calculating the Euler axial capacity assuming that all of the beam-column joints are held in place, i.e., no lateral translation is allowed. The resulting axial capacity is used in calculation of the _b factor. This

-factor e

k is named as k in the code. This _eb k factor is always less than 1 and _eb

is not calculated. By default the program uses the value of 1 for k ._eb The pro-gram allows the user to overwrite k on a member-by-member basis. _eb

The other ke-factor is used for calculating the Euler axial capacity assuming that all the beam-column joints are free to sway, i.e., lateral translation is al-lowed. This ke-factor is named as kes in the code. This kes is always greater than 1 if the frame is a sway frame. The program calculates the k factor _es

automatically based on sway condition. The program also allows the user to overwrite k factors on a member-by-member basis. The same _es k factor is _es

supposed to be used in calculation of the _s factor. However the program does not calculate _s factors and relies on the overwritten values.

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2 - 12 Effective Length Factor (ke)

Both k and _eb k have two values: one for major direction and the other for _es

minor direction, k_eb_minor, k_eb_major, k_es_minor, k_es_major.

-factors es

k are supposed to be obtained from figures given in the code (AS Figure 4.6.3.3(b)). However in absence of the exact mathematical form, either explicit or implicit, the program calculates the k_es-factor from its basic princi-ple, which is described here. The resulting k matches very closely with the _es

figure given in the code (AS Figure 4.6.3.3(b)). The same method is used for AISC codes.

The k_es-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 frame for which the k_es-factor calcula-tion is relatively complex. For the purpose of calculating k_es-factor, the ob-jects are identified as columns, beam and braces. All frame obob-jects parallel to the Z -axis are classified as columns. All objects parallel to the X - Y plane are classified as beams. The remainders are considered to be braces.

The beams and braces are assigned k_es-factor of unity. In the calculation of the -factor

es

k for a column object, the program first makes the following four stiffness summations for each joint in the structural model:

   _ _  



c c cx c x E I S L b b bx b x E I S L    _ _  



c c cy c y E I S L    _ _  



b b b y b y E I S L    _ _  



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

22 22

EI L and EI₃₃ L₃₃ 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:

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Effective Length Factor (ke) 2 - 13

22 22 22 b I c I I S S G  22 22 22 b J c J J S S G  33 33 33 b I c I I S S G  33 33 33 b J c J J

S

G



If a rotational release exists at a particular end (and direction) of an object, the corresponding value of G is set to 10.0. If all degrees of freedom for a particu-lar 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 are known for a particular direction, the column}J es

k -factors for the

corresponding direction is calculated by solving the following relationship for :    tan ) ( 6 36 2    J I J I G G G G

from which k_es = /. This relationship is the mathematical formulation for

the evaluation of k -factors for moment-resisting frames assuming sidesway _es

to be uninhibited. For other structures, such as braced frame structures, the es

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 es

k -factor algorithm:

 An object that has a pin at the joint under consideration will not enter the stiffness summations calculated above. An object that has a pin at the far end from the joint under consideration will contribute only 50% of the cal-culated EI value. Also, beam members that have no column member at the far end from the joint under consideration, such as cantilevers, will not en-ter the stiffness summation.

 If there are no beams framing into a particular direction of a column mem-ber, 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 correspond-_es

ing to that direction is set equal to unity.

 If rotational releases exist at both ends of an object for a particular direc-tion, the corresponding k_es-factor is set to unity.

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2 - 14 Effect of Breaking a Member into Multiple Elements

 The automated k_es-factor calculation procedure can occasionally generate artificially high k -factors, specifically under circumstances involving _es

skewed beams, fixed support conditions, and under other conditions where the program may have difficulty recognizing that the members are laterally supported and k_es-factors of unity are to be used.

 All k -factors produced by the program can be overwritten by the user. _es

These values should be reviewed and any unacceptable values should be replaced.

 The beams and braces are assigned k_es-factors of unity.

eb

k -factors are supposed to be obtained from figures given in the code (AS Figure 4.6.3.3(a)). However in absence of the exact mathematical form, the program calculates the k_eb-factor from its basic principle. This is similar to the determination of the k_es-factor, except that the k_eb-factor for the correspond-ing direction is calculated by solvcorrespond-ing the followcorrespond-ing relationship for :









1 2 ₁ tan 2 ₁ ₀ 4 2 tan 2          _  _     J J J G G G G where, . eb k   

If the member is assigned with a framing type of sway frame, k_eb is used for _b calculation, and k_es is used for N_c calculation. If the member is assigned with a framing type of Braced frame, k_eb is used for both _b and N_c calculation.

2.10 Effect of Breaking a Member into Multiple Elements

The preferred method is to model a beam, column or brace member as one sin-gle element. However, the user can request that the program break a member internally at framing intersections and at specified intervals. In this way, accu-racy in modeling can be maintained at the same time that design/check specifi-cations can be applied accurately. There is special emphasis on the end forces (moments in particular) for many different aspects of beam, column, and brace

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Effect of Breaking a Member into Multiple Elements 2 - 15

design. If the member is manually meshed (broken) into segments, maintaining the integrity of the design algorithm becomes difficult.

Manually breaking a column member into several elements can affect many things during design in the program.

1. The unbraced length: The unbraced length is really the unsupported length between braces. If no intermediate brace is present in the member, the un-braced length is typically calculated automatically by the program from the top of the flange of the beam framing the column at the bottom to the bot-tom of the flange of the beam framing the column at the top. The aubot-tomati- automati-cally calculated length factor typiautomati-cally becomes less than 1. If there are in-termediate bracing points, the user should overwrite the unbraced length factor in the program. The user should choose the critical (larger) one. Even if the user breaks the element, the program typically picks up the un-braced length correctly, provided that there is no intermediate bracing point.

2. ke-factor: Even if the user breaks the member into pieces, the program typi-cally can pick up the ke-factors correctly. However, sometimes it can not. The user should note the ke-factors. All segments of the member should have the same ke-factor and that factor should be calculated based on the entire member. If the calculated ke-factor is not reasonable, the user can overwrite the ke-factors for all the segments.

3. Cmfactor: The Cmfactor should be based on the end moments of unbraced lengths of each member and should not be based on the end moments of the segment (AS 4.4.2.2). The program already calculates the Cm factors based on the end moments of unbraced lengths of each member. If the member is broken, the program calculated Cmfactor is conservative. If this conservative value is acceptable, no action is required by the user. If it is not acceptable, the user can calculate the Cmfactor manually for the critical combination and overwrite its value for that segment.

4. mfactor: The mfactor should be based on the end moments of unbraced lengths of each segment and should not be based on the end moments of the member (AS 5.6.1.1). The program already calculates the m factors based on the end moments of unbraced lengths of each segment. If the bro-ken segments do not represent the brace-to-brace unsupported length, the program calculated m factor is conservative. If this conservative value is

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2 - 16 Supported Framing Types

acceptable, no action is required by the user. If it is not acceptable, the user can calculate the m factor manually for the critical combination and over-write its value for that segment.

5. bfactor: This factor amplifies the factored moments for the P- effect (AS 4.2.1.2, App. F). In its expression, there are the Cm factor and the Euler Buckling capacity Nomb. If the user keeps the unbraced length ratios (l33 and

l22) and the ke-factors (ke,33 and ke,22) correct, the bfactor would be correct. If the axial force is small, the b factor can be 1 and have no effect with re-spect to modeling the single segment or multi-segment element.

6. s factor: The program does not calculate the s factor. The program assumes that the user turns on the P- feature. In such cases, s can be taken as equal to 1. That means that modeling with one or with multiple segments has no effect on this factor.

If the user models a column with a single element and makes sure that the

l-factors and ke-factors are correct, the effect of band swill be picked up cor-rectly. The factors Cm and m will be picked up correctly if there is no interme-diate bracing point. The calculated Cm and m factors will be slightly conserva-tive if there are intermediate bracing points.

If the user models a column with multiple elements and makes sure that

l-factors and ke-factor are correct, the effect of b and s will be picked up correctly. The factors Cm and m will be picked up correctly if the member is broken at the bracing points. The calculated Cm and m factors will be conserva-tive if the member is not broken at the bracing points.

2.11 Supported Framing Types

The code (AS 4100-1998) recognizes the following types of framing systems.

Framing Type References

Sway Frame AS 4.4.2.2

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Frame Design Procedure Overwrites 2 - 17

2.12 Frame Design Procedure Overwrites

The structural model may contain frame elements made of several structural materials: steel, concrete, aluminum, cold-formed steel and other materials. The program supports separate design procedures for each material type. By default the program determines the design procedure from the material of the frame member.

The program allows the user to turn the design of specific members off and on by selecting No Design or Default from material. Overwriting the design pro-cedure can be accessed from the Design menu > Overwrite Frame Design Procedure command.

ETABS supports both regular steel frame design and composite beam design. The determination of design procedure is different. If the material is concrete, the design procedure is concrete. If the material is steel, the default design pro-cedure can be steel frame design or composite beam design. If the section is of steel material, and the member satisfies a host of other criteria, such as the member is horizontal (beam), it supports a filled deck or slab, it is an I-shaped member, it is hinged at both ends and so on, then the default design procedure is taken as composite beam design; otherwise, the default design procedure is taken as steel frame design. ETABS allows the user to overwrite a steel mem-ber frame design procedure to steel frame design, composite beam design, de-fault, or no design. Change the design procedure by selecting the member(s) and clicking the Design menu > Overwrite Frame Design Procedure com-mand. A change in design will be successful only if the design procedure is valid for that member, i.e., the program will not allow the user to change the design procedure for a steel frame object to concrete frame design.

2.13 Steel Frame Design Process

The following sequence describes a typical steel frame design process for a new structure. Note that although the sequence of steps you follow may vary, the basic process probably will be essentially the same.

1. Use the Design menu > Steel Frame Design > View/Revise Overwrites command to choose the steel frame design code and to review other steel

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2 - 18 Steel Frame Design Process

frame design preferences and revise them if necessary. Note that default values are provided for all design preferences, so it is unnecessary to define any preferences unless you want to change some of the default values. 2. Create the model.

3. Run the analysis using the Analyze menu > Run Analysis command. 4. Assign steel frame overwrites, if needed, using the Design menu > Steel

Frame Design > View/Revise Overwrites command. Note that frame members must be selected before using this command, and that overwrites may be assigned before or after the analysis is run.

5. Designate design groups, if desired, using the Design menu > Steel Frame Design > Select Design Group command. Note that some groups must al-ready have been created by selecting objects and going to the Assign menu.

6. To use design combinations other than the defaults created by the program, click the Design menu > Steel Frame Design > Select Design Combo command. Note that design combos must already have been created using the Define menu.

7. Designate displacement targets for various analysis cases using the Design menu > Steel Frame Design > Set Displacement Targets command. 8. Set time period targets for various modes using the Design menu > Steel

Frame Design > Set Time Period Targets command.

9. Click the Design menu > Steel Frame Design > Start Design/Check of Structure command to run the steel frame design.

10. Review the steel frame design results by doing one of the following: a. Click the Design menu > Steel Frame Design > Display Design Info

command to display design input and output information on the model. b. Right click on a frame object while the design results are displayed on

it to enter the interactive design mode and interactively design the frame member. Note that while in this mode, overwrites can be revised and the results of the new design displayed immediately. If

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Steel Frame Design Process 2 - 19

design results are not currently displayed (and the design has been run), click the Design menu > Steel Frame Design > Interactive Steel Frame Design command and then right click a frame object to enter the interactive design mode for the member.

11. Use the File menu > Print Tables command to print steel frame design data. If frame objects are selected before using this command, data is printed for the selected objects only.

12. Use the Display menu > Show Tables command to display steel frame de-sign data in a spreadsheet-type tabular format. If frame objects are selected before using the command, data is displayed for the selected objects only. 13. Use the Design menu > Steel Frame Design > Change Design Section

command to change the design section properties for selected frame ob-jects.

14. Click the Design menu > Steel Frame Design > Start Design/Check of Structure command to rerun the design with the new section properties. Review the results using the procedures described in Item 10.

15. Rerun the analysis using the Analyze menu > Run Analysis command. Note that the section properties used for the analysis are the last specified design section properties.

16. Compare displacements with displacement targets, or the resulting periods with period targets, if appropriate.

17. Click the Design menu > Steel Frame Design > Start Design/Check of Structure command to rerun the design with the new analysis results. Re-view the results using the previous steps.

18. Repeat the processes in steps 13 through 17 as many times as necessary. Note that steel frame design is an iterative process, and that the analysis and design will typically be rerun multiple times to complete a design. 19. Click the Design menu > Steel Frame Design > Verify Analysis vs

De-sign Section command to verify that all of the final design sections are the same as the last used analysis sections.

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2 - 20 Interactive Steel Frame Design

Again, it is important to note that design is an iterative process. The sections used in the original analysis are not likely to be the same as those obtained at the end of the design process. Always run the analysis using the frame sections from the final design, and then run a design check using the forces obtained from that analysis.

2.14 Interactive Steel Frame Design

The Interactive Steel Frame Design command is a powerful mode that allows the user to review the design results for any steel frame design and interac-tively revise the design assumptions and immediately review the revised re-sults.

Note that a design must have been run for the interactive design mode to be available. With the design results displayed, right click on a frame object to display the Steel Stress Check Information form for the member. Click on the Overwrites button to display the Design Overwrites form, where the member section or other design parameters may be changed. Clicking OK on this form results in an immediate updating of the results displayed on the Steel Stress Check Information form.

2.15 Automated Iterative Design

If Auto Select sections have been assigned to frame objects, ETABS can auto-matically perform the iterative steel frame design process. To initiate the proc-ess, first use the Options menu > Preferences > Steel Frame Design com-mand and set the maximum number of auto iterations to the maximum number of design iterations the program is to run automatically. Next, run the analysis. Then, making sure that no objects are selected, use the Design menu > Steel Frame Design > Start Design/Check of Structure command to begin the de-sign of the structure.

The program will then start the cycle of (1) performing the design, (2) compar-ing the last-used Analysis Sections with the Design Sections, (3) settcompar-ing the Analysis Sections equal to the Design Sections, and (4) rerunning the analysis. This cycle will continue until one of the following conditions has been met:

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Choice of Units 2 - 21

 The Design Sections and the last-used Analysis Sections are the same.  The number of iterations performed is equal to the number of iterations

specified for the maximum number on the Preferences form. Currently, this feature is absent in SAP2000.

2.16 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 pre-sented in the subsequent chapters correspond to that specific system of units unless otherwise noted. For example, the ACI code is published in inch-pound-second units. By default, all equations and descriptions presented in the "De-sign Process" appendix correspond to inch-pound-second units. However, any system of units can be used to define and design a structure in the program.

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3 - 1

Chapter 3 Steel Frame Design Using AS 4100-1998

This chapter provides a detailed description of the algorithms used by the pro-gram in the design/check of structures in accordance with "AS 4100-1998 Aus-tralian Standard Steel Structures" (SA, 1998). The implementation covers load combinations from "AS/NZS 1170.0:2002 Australian/New Zealand Stan-dard Structural Design Actions, Part 0: General Principle” (SA/SNZ, 2002a), which are described in section 3.4 Design Loading Combinations in this chap-ter. The wind loading based on "AS/NZS 1170.2:2002 Australian/New Zealand Standard Structural Design Actions Part 2: Wind Actions” (SA/SNZ, 2002b). The earthquake loading based on “AS 1170.04-2007 Australian Standard Structural Design Actions Part A; Earthquake Actions in Australia” (SA, 2007) has been described in a separate document entitled “CSI Lateral Load Manual” (CSI 2007).

 Reference to the AS 4100-1998 code is identified with the prefix “AS.”  Reference to the AS/NZS 1170.0:2002 code is identified with the prefix

“AS/NZS.”

3.1 Notations

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Steel Frame Design Manual AS 4100-1998

3 - 2 Notations

A Area of cross-section, mm2

Ag Gross area of a cross-section, mm

2

An Net area of a cross-section, mm

2

A

_w Gross sectional area of a web, mm2

b

_f Width of flange, mm

b_w Web depth, mm

d Depth of a section, mm

d_e Effective outside diameter of a circular hollow section, mm

d_f Distance between flange centroids, mm

dp Clear transverse dimension of a web panel, or Depth of deepest web panel in a length, mm

d1 Clear depth between flanges ignoring fillets or welds, mm

d2 Twice the clear distance from the neutral axes to the com-pression flange, mm

E Young’s modulus of elasticity, MPa

e Eccentricity, mm

F Action in general, force or load, N

f_u Tensile strength used in design, MPa

f_y Yield stress used in design, MPa

G Shear modulus of elasticity, MPa, or Nominal dead load

I Second moment of area of a cross-section, mm4

I_cy Second moment of area of compression flange about the sec-tion minor principal y-axis, mm4

I_w Warping constant for a cross-section, mm6

I_x I about the cross-section major principal x-axis, mm4

Iy I about the cross-section minor principal y-axis, mm

4

J Torsion constant for a cross-section, mm4

k_e Member effective length factor

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Chapter 3 Steel Frame Design Using AS 4100-1998

Notations 3 - 3

k_l Load height effective length factor

k_r Effective length factor for restraint against lateral rotation

l Span, or member length, or segment or sub-segment length, mm

l22, l33 Laterally unbraced length of member for major and minor axes bending, mm

le/r Geometrical slenderness ratio

M_b Nominal member moment capacity, N-mm

M_bx M_b about major principal x-axis, N-mm

Mcx Lesser of Mix and Mox, N-mm

M_i Nominal in-plane member moment capacity, N-mm

Mix Mi about major principal axis, N-mm

M_iy Mi about minor principal axis, N-mm

Mo Reference elastic buckling moment for a flexural member, N-mm

M_oa Amended elastic buckling moment for a member subjected to bending, N-mm

M_ob Elastic buckling moment determined using an elastic buck-ling analysis, N-mm

Moo Reference elastic buckling moment obtained using le = l, N-mm

Mos Mob for a segment, fully restrained at both ends, unrestrained against lateral rotation and loaded at shear centre, N-mm

Mox Nominal out-of-plane member moment capacity about major principal x-axis, N-mm

M_rx M_s about major principal x-axis reduced by axial force, N-mm

Mry Msabout minor principal y-axis reduced by axial force, N-mm

M_s Nominal section moment capacity, N-mm

Msx Msabout major principal x-axis, N-mm

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3 - 4 Notations

M_tx Lesser of M_rx and M_ox, N-mm

M* Design bending moment, N-mm

N_c Nominal member capacity in compression, N

N_cy Nc for member buckling about minor principal y-axis, N

N_om Elastic flexural buckling load of a member, N

N_omb N_om for a braced member, N

Noms Nom for a sway member, N

Ns Nominal section capacity of a compression member, or

Nominal section capacity for axial load, N

Nt Nominal section capacity in tension, N

N* Design axial force, tensile or compressive, N

Q Nominal live load

r Radius of gyration, mm

ry Radius of gyration about minor principle axis, mm

S Plastic section modulus, mm3

t Flat thickness, or wall thickness of a circular hollow section, mm

t_f Thickness of a flange, mm

tp Thickness of a plate, mm

t_w Thickness of a web, mm

V_b Nominal shear buckling capacity of a web, N

V_u Nominal shear capacity of a web with a uniform shear stress distribution, N

V_v Nominal shear capacity of a web, N

Vvm Nominal web shear capacity in the presence of bending mo-ment, N

V_w Nominal shear yield capacity of a web, N

V* Design shear force, N

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Notations 3 - 5

Z Elastic section modulus, mm3

Zc Ze for a compact section, mm

3

Ze Effective section modulus, mm

3

_b Compression member section constant

c Compression member slenderness reduction factor _m Moment modification factor for bending

l, lc, mc Factors for bending defined in Appendix H of AS 4100 s Slenderness reduction factor

_st Reduction factor for members of varying cross-section

v Shear buckling coefficient for a web

_e Modifying factor to account for conditions at the far ends of beam members

_m Ratio of smaller to larger bending moment at the ends of a member

ξ _{Compression member factor defined in AS Clause 6.3.3}

 Compression member imperfection factor (AS 6.3.3)

 Slenderness ratio

_e Plate element slenderness

ep Plate element plasticity slenderness limit _ey Plate element yield slenderness limit

n Modified compression member slenderness _s Section slenderness

sp Section plasticity slenderness limit _sy Section yield slenderness limit

 Poisson’s ratio, 0.25

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3 - 6 Design Preferences

3.2 Design Preferences

The steel frame design preferences are basic assignments that apply to all of the steel frame members. Tables 3-1 list steel frame design preferences for "AS 4100-1998." Default values are provided for all preference items. Thus, it is not necessary to specify or change any of the preferences. However, at least review the default values to ensure they are acceptable. Some of the preference items also are available as member-specific Overwrite items. The overwrites are de-scribed in the next section. Overwritten values take precedence over the prefer-ences.

To view design preferences, select the Design menu > Steel Frame Design > View/Revise Preferences command. The Preferences form will display. The preference options are displayed in a two-column spreadsheet on that form. The left column of the spreadsheet displays the Preference item name. The right column of the spreadsheet displays the preference item value.

To change a preference item, left click the desired Preference item in the left or right column of the spreadsheet. This activates a drop-down list or highlights the current preference value. If the drop-down list displays, select a new value. If the cell is highlighted, type in the desired value. The preference value will update accordingly. Values in the drdown lists provide the available op-tions. The Preference items are presented in Table 3-1.

Table 3-1: Steel Frame Design Preferences

Item Possible Values Default Value Description

Design Code Design codes available in the current version

AS4100-1998 The selected design code. Subsequent design is based on this selected code. The default values shown below appear when the AS4100-1989 is selected as the Design Code.

Multi-Response Case Design Envelopes, Step-by-Step, Last Step, Envelopes – All, Step-by-Step All

Envelopes Indicates how results for multivalued cases (Time history, Nonlinear static or Multi-step static) are considered in the design. - Envelope - considers enveloping values for Time History and Multi-step static and last step values for Non-linear static. - Step-by-Step - considers step by step values for Time History and Multi-step static and last step values for Nonlinear static. - Last Step - considers last values for Time History, Multi-step static and Nonlinear static. - Envelope - All - considers enveloping values for Time History, Multi-step static and Nonlinear static. - Step-by-Step - All - considers step by step values for Time History, Multi-step static and Nonlinear static. Step-by-Step and Step-by-Step - All default to the corresponding Envelope if more then one multi-valued case is present in the combo.

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Design Preferences 3 - 7 Table 3-1: Steel Frame Design Preferences

Item Possible Values Default Value Description

Framing Type Sway, Braced Sway Frame This item is used for ductility considerations in the design.

Structural Analysis Method General 2nd Order, Amplified 1st Order General 2nd Order

Indicates the analysis method used to check/design the steel members. The design module does not verify the acceptability of the selected analysis method. See sections 4.1, 4.3, 4.4.1.2, and Appendix E of "AS 4100:1998" code for details. The user is expected to verify the acceptability of the selected method. The user is expected to set the appropriate notional loads..

Steel Type Hot Rolled, Hot Finished, Cold Formed, Stress Relieved, Lightly Welded, Heavily Welded

Hot Rolled Indicates the residual stress level in the structural section. This affects plasticity limit and yield limit of plate element slenderness values. Eventually this can affect moment capacity and axial compression capacity through modifica-tion on Ze and Aeff. "Hot Rolled" and "Hot Finished" are

used synonymously in this program. "Cold Formed" is meant as cold-formed and not stress-relieved. "Stress Relieved" is meant as cold-formed and stress-relieved. Welded H and I sections are assumed to be fabricated from flame-cut plates. See sections 5.2.2, 6.2.4, 6.3.3, and Tables 5.2, 6.2.4, 6.3.3(1), and 6.3.3(2) of "AS 4100:1998" code for details.

Capacity Factor

Phi (Bending) 1.0 0.9

Capacity factor for strength limit state. See section 3.4 and Table 3.4 of “AS 4100 1998” for details.

Capacity Factor

Phi (Compression) 1.0 0.9

Capacity Factor, Phi (Tension Yield-ing)

1.0 0.9 Capacity factor for strength limit state. See section 3.4 and _{Table 3.4 of “AS 4100 1998” for details.} Capacity Factor

Phi (Tension-Fracture)

1.0 0.9 Capacity factor for strength limit state. See section 3.4 and Table 3.4 of “AS 4100 1998” for details.

Capacity Factor

Phi (Shear) 1.0 0.9

Consider Deflection?

Yes, No No Toggle to consider the deflection limit (Yes) or to not consider the deflection limit (No) in design.

DL Limit, L/  0 120 Deflection limit for dead load. Inputting 120 means that the limit is L/120. Inputting zero means no check will be made of this item.

Super DL+LL Limit, L/

 0 120 Deflection limit for superimposed dead plus live load. Inputting 120 means that the limit is L/120. Inputting zero means no check will be made of this item.

Live Load Limit, L/  0 360 Deflection limit for superimposed live load. Inputting 360 means that the limit is L/360. Inputting zero means no check will be made of this item.

SFD-AS-4100-1998

Steel Frame

Design Manual

Australian 4100-1998

Copyright

DISCLAIMER

Contents

Shear

Check

Chapter 1

Introduction

1.1

Organization

1.2

Recommended Reading/Practice

Chapter 2

Modeling, Analysis and Design Prerequisites

2.1

Check and Design Capability

2.2

Analysis Sections vs. Design Sections

2.3

Design and Check Stations

2.4

Demand/Capacity Ratios

2.5

Design Load Combinations

2.6

Notional Load Patterns

2.7

Second Order P-Delta Effects













2.8

Member Unsupported Lengths

2.9

Effective Length Factor (k

)

















S

S

G











2.10

Effect of Breaking a Member into Multiple Elements

2.11

Supported Framing Types

2.12

Frame Design Procedure Overwrites

2.13

Steel Frame Design Process

2.14

Interactive Steel Frame Design

2.15

Automated Iterative Design

2.16

Choice of Units

Chapter 3

Steel Frame Design Using AS 4100-1998

3.1

Notations

A

b

3.2

Design Preferences