Structural analysis

The Direct Analysis Method Fastrak Building Designer

Direct Analysis Method Guide Page 1

A Simple Guide to the Direct Analysis

Method

How to implement the Direct Analysis Method using

modern software

CSC Inc., May 2010

Prepared by Jason R Ericksen, SE

Technical Manager,

CSC Inc.



Disclaimer

A Simple Guide to the Direct Analysis Method. How to implement the Direct Analysis

Method using Modern Software.

Although CSC Inc. takes great care to ensure that any data, information, advice or

recommendations it may give either in this publication or elsewhere are accurate, no liability

or responsibility of any kind, including liability for negligence, howsoever and from

whatsoever cause arising from or related to their use, is accepted by CSC Inc., its servants or

agents.



Figure 1: Complex buildings with sloping members, hard-to-define floors, and non-

orthogonal framing are commonplace today. [Screenshot from Fastrak Building

Designer. Model courtesy of Fisher Engineering.]



SUMMARY OF THE FULL PAPER FOLLOWS. TO JUMP TO THE

FULL PAPER BEGINNING ON PAGE 8 CLICK HERE

In the 2005 AISC Specification for Structural Steel Buildings, AISC introduced significant

changes to the stability design requirements. Clear requirements for stability design and

three straight-forward methods of satisfying those requirements have been introduced. One

of these, the direct analysis method, is the premier method and the focus of this paper. The

direct analysis method is the most advantageous because it is not limited in its application,

applies to all buildings, and is the most general and accurate approach provided.

AISC STABILITY ANALYSIS AND DESIGN REQUIREMENTS

The design of all structures for stability must consider:

1. flexural, shear, and axial deformations of members

2. all component and connection deformation that contribute to the lateral displacement of the

structure

3. second-order effects (both P- and P- )

4. geometric imperfections

5. member stiffness reductions due to residual stresses

The first three requirements are covered by the structural analysis and the first two are

included in nearly all analysis packages. As noted above, three methods to account for #4

and #5 (including provisions relating to #3) are presented in the specification. The Direct

Analysis Method is the preferred method.

DIRECT ANALYSIS METHOD

The direct analysis method is found in Appendix 7 of the 2005 Specification, but will move

to Chapter C as the default method in the 2010 AISC Specification. The basics of the direct

analysis method include the following:

Second-Order analysis: A second-order analysis which considers both P- and P-

effects is required. This can be accomplished through a rigorous second-order

analysis or by using the approximate method presented in the specification.

Initial imperfections: The effects of initial imperfections of the structure geometry are

considered either by applying notional loads or directly modeling the imperfections in

the geometry of the model.

Inelasticity: The axial and flexural stiffnesses of members that contribute to the

stability of the structure are required to be reduced to account for inelastic behavior in

the members.

Effective Length Factor: One major benefit of the direct analysis method is that

K=1.0! No more calculating K when determining the nominal strength of columns.



HOW TO: SECOND ORDER ANALYSIS

Loads applied to a structure will act on the „real‟ shape of the structure, including initial

imperfections and deflections caused by lateral loads. This introduces flexure into axially

loaded members, where the magnitude of the flexure is dependent on the axial load (the‟P‟)

and the deformed shape (the „ ‟ or „ ‟). This causes second-order (nonlinear) behavior

known as the P-Delta effect. An analysis considering this effect is required.

The second-order analysis can either be a rigorous analysis or the approximate amplified

first-order method presented in the specification. The amplified first-order method certainly

works well for some buildings, generally those that are simple, regular structures. However,

to allow for the greatest range of structure geometry with the highest degree of accuracy in

determining internal forces, the best course of action is to take advantage of a rigorous

second-order analysis.

It would be difficult to apply the approximate methods to the structure in Figure 2. Even

smaller projects, with relatively small budgets, often have complex framing requirements that

will benefit from a rigorous second-order analysis.

Figure 2: Complex buildings make it difficult to apply approximate second- order analysis

methods. Today, even relatively small projects often have complex framing.

[Screenshot from Fastrak Building Designer. Model courtesy of Scott Wilson.]

HOW TO: NOTIONAL LOADS

To account for the effect of initial imperfections, the specification allows the designer to

directly model the imperfections within the model. The set of initial displacements modeled

need to consider displacements due to loading and anticipated buckling modes of the

structure. Modeling these displacements can be complicated, therefore the alternative of

applying notional loads is often best.



Notional loads are horizontal forces added to the structure to account for the effects of

geometric imperfections. Figure 3 Figure 3 below illustrates a simple version of the concept.

The notional load (Ni) is 0.2% of the total factored gravity load (Yi) and applied at each level.

Figure 3: Notional Loads

The value Yi is the total factored gravity load in each load combination on each level.

Therefore, the value of the notional loads will change from combination to combination.

AISC requires that the notional loads be distributed in plan on each level in the same manner

as the gravity load. This would indicate you could apply a single notional load (at each level

for each load combination) at the location of the resultant of the total factored gravity loads.

Depending on how the loads are distributed on the structure, calculating the location of the

resultant can become complicated. The following suggested method is more straight-

forward and easy to automate within computer software.

Calculate the total factored gravity load transferred to each column at each level.

Calculate the corresponding magnitude of the notional load for each appropriate load

combination.

Apply the notional load as a point load at each column at each level.

The point loads represent the notional load effect on each column. By applying the loads to

all columns and including all framing in the model, the effect of leaning columns is directly

included as part of the analysis. This method correctly distributes the notional loads in the

same manner as the total factored gravity load and through the 3D analysis allows the effects

of those loads to be distributed accurately to the lateral framing.

AISC requires the notional loads be applied in the direction that adds to the destabilizing

effects. For gravity load combinations you will generally have to apply the notional loads in

two orthogonal directions in both the positive and negative sense. You can apply the notional

loads in the same direction on all levels. For lateral load combinations, the notional loads are

applied in the same direction as the resultant of all lateral loads.



HOW TO: STIFFNESS REDUCTION

To account for inelastic behavior, a reduction in the axial and flexural stiffness of all

members that contribute to the lateral stability of the structure is required. This includes

members that deliver the lateral loads to the vertical lateral framing such as collectors,

chords, and horizontal bracing. In addition, it is permitted to apply the reduction to all

members in the model. Reducing only the lateral members can create artificial distortion of

the structure and result in unintended redistribution of forces.

The stiffness reduction should also be applied to members of other materials, unless a greater

reduction is required by governing codes and specifications. This also will help prevent an

unintended redistribution for forces to the members of other materials, since they had not

been reduced.

The requirements of the direct analysis method are intended for determination of required

strengths and they are not intended for serviceability checks. Therefore, when checking the

lateral drift of the structure under wind loads, for example, the stiffness reductions need not

be applied!

CONCLUSIONS

In the 2010 AISC Specification the direct analysis method will become the default method

and move from Appendix 7 to Chapter C within the body of the code itself. It is clear that if

you are not familiar with the features of this method at present you will need to be so in the

future. Hopefully, this paper will elucidate these in the context of the use of modern

structural engineering software. However, there are a number of questions for which you

should seek answers.

There are several options for how the direct analysis method is executed within a software

package, for example, the type of second-order analysis.

What effects on the results does the particular method create (if any)?

Is the method limited in its application?

If the approximate (B1,B2) method is used, how are the limitations overcome?

It is important to know the answers to these questions before you begin designing with the

software. I think the overriding question to answer is, Do any of the answers to these

questions result in a limit on the types of buildings you can design using the software

package?

Understanding the requirements of the direct analysis method and how the tools you use

implement those methods is key to successful design.



A Simple Guide to the Direct Analysis Method

How to implement the Direct Analysis Method using modern

software

INTRODUCTION

In the 2005 AISC Specification for Structural Steel Buildings, AISC introduced significant

changes to the stability design requirements. Clear requirements for stability design and

three straight-forward methods of satisfying those requirements have been introduced. One

of these, the direct analysis method, is the premier method and the focus of this paper. The

direct analysis method is the most advantageous because it is not limited in its application,

applies to all buildings, and is the most general and accurate approach provided.

The direct analysis method includes requirements for a second-order analysis, application of

notional loads, and member stiffness reductions. Use of the direct analysis method means

several things to design engineers.

K = 1.0

Straight-forward design requirements, including how to perform the structural

analysis.

Improved results with less potential for error, especially when modern software is

used.

To take advantage of these benefits, decisions must be made about how to implement the

method. For example, the most appropriate second-order analysis for the project must be

selected. Approximate methods are adequate in many cases. However, consistently using a

more general approach will allow the same method to be used for all projects for consistently

accurate results. Other details such as how to apply notional loads to the model regarding

magnitude, direction, and distribution and to which members to apply a stiffness reduction

are also important decisions.

The requirements of the specification are summarized in the first two sections of this paper.

A „how to‟ guide for implementing the direct analysis method forms the remainder. The

discussion will provide information vital to making the proper decisions while implementing

the direct analysis method to get the best possible results. The information will allow you to

refine your current design process and help you evaluate what your software tools are doing

for you.

STABILITY ANALYSIS AND DESIGN REQUIREMENTS

Chapter C of the AISC Specification covers stability design requirements. According to part

C1.1 the design of all steel structures for stability must consider:



1. flexural, shear, and axial deformations of members

2. all component and connection deformation that contribute to the lateral

displacement of the structure

3. second-order effects (both P- and P- )

4. geometric imperfections

5. member stiffness reductions due to inelasticity

The first three requirements are covered by structural analysis (typically done within a

software package). The first two items are included in nearly all structural analysis packages.

There are many types of second-order analyses (item #3) including both direct and

approximate methods. The method used varies with the software package.

Three methods to account for #4 and #5 (including provisions relating to #3) are presented in

the specification. The effective length method and the first-order analysis method are limited

to structures with low to moderate second-order effects. The third method, the direct analysis

method, is not limited and applies to all steel structures. In fact, it is the required method for

structures with large second-order effects.

The direct analysis method is described below. The other limited approaches will not be

discussed in this paper.

THE DIRECT ANALYSIS METHOD

The direct analysis method is found in Appendix 7 of the 2005 Specification, but will move

to Chapter C as the default method in the 2010 AISC Specification. (In a corresponding

move, the alternate methods mentioned above will move to appendices.) As noted

previously, the direct analysis method is not limited in its application, applies to all buildings,

and is the most general and accurate approach given in the AISC Specification. The basics of

the direct analysis method include the following:

Second-Order analysis: A second-order analysis which considers both P- and P-

effects is required. This can be accomplished through a rigorous second-order

analysis or by using the approximate method presented in the specification.

Initial imperfections: The effects of initial imperfections of the structure geometry are

considered either by applying notional loads or directly modeling the imperfections in

the geometry of the model. Notional loads are lateral loads that are applied at each

framing level and are proportional to the total gravity load for each load combination.

Inelasticity: The axial and flexural stiffnesses of members that contribute to the

stability of the structure are required to be reduced. The reduction primarily accounts

for the effects of residual stresses in rolled sections that lead to inelastic softening

before the members reach their design strength.

Effective Length Factor: One major benefit of the direct analysis method is that

K=1.0! No more calculating K when determining the nominal strength of columns.

K can be taken as 1.0 because the effects for which it was meant to compensate have



already been accounted for in the method. It should be noted that a K value less than

one can be used if it is justified by analysis.

The following sections of the paper present more details on the requirements and suggestions

for implementing them within your design process.

HOW TO: SECOND-ORDER ANALYSIS

The 2005 Specification is not the first time AISC has required a second order analysis. The

requirement can be traced back to the 1989 ASD specification, if not earlier. However, the

requirement is now much more prominent within the specification. Chapter C requires that

second-order effects be considered for al steel buildings that accounts for both P- and P-

effects.

SECOND-ORDER EFFECTS

Loads applied to a structure will act on the „real‟ shape of the structure, including initial

imperfections and deflections caused by lateral loads. This introduces flexure into axially

loaded members, where the magnitude of the flexure is dependent on the axial load (the‟P‟)

and the deformed shape (the „ ‟ or „ ‟). This causes second-order (nonlinear) behavior

known as the P-Delta effect. There are two P-Delta effects;

P- is a structure effect in which axial loads in columns act on the displacement of the

ends of the member - the story displacements,

P- a member effect in which axial loads act on the displacement between the ends of

the member.

Both of these effects are illustrated in Figure Figure 4 below on the left where represents

the frame deflection and represents the deflection along the length of the member itself.

The second-order response of the building is compared to an elastic first-order response in

the figure on the right.



Figure 4: Second-Order Effects

SECOND-ORDER WITH THE DIRECT ANALYSIS METHOD

In addition to the general requirement of a second-order analysis, the direct analysis method

has several more specific requirements. For example, there is a difference in how the

analysis is executed based on the design method being used.

LRFD: The analysis is performed using LRFD load combinations.

ASD: The analysis is performed using 1.6 times the ASD load combinations and the

results of the analysis are then divided by 1.6 to get required strengths.

Second-order effects on the structure are non-linear and the analysis must be carried out

under strength-level loading. This means the analysis must be carried out using load

combinations. Load cases cannot be analyzed separately then superimposed in a load

combination. The results are not the same.

The LRFD load combinations are at strength level. However, when ASD is used, the 1.6

factor is required to get strength-level load combinations (or an adequate approximation) to

use in the analysis. In Figure Figure 5 below, the curve represents the non-linear building

response. In Step 1, the ASD load combination applied loads, wASD, are multiplied by 1.6.

In step 2 the resulting model is analyzed with the amplified loads to yield a set of forces on

the members, 1.6RASD. This set of forces is then divided by 1.6 in Step 3 to yield the

required strengths, RASD. It is clear that the required strengths, RASD, are greater than the set

of forces that results from the analysis under ASD load combinations directly, rASD.



Figure 5: ASD Load Combination amplification

Note that the approximate B1, B2 method of second-order already includes the 1.6 factor.

AMPLIFIED FIRST-ORDER ANALYSIS

You can either perform a direct second-order analysis or use the approximate amplified first-

order method presented in the AISC specification (commonly known as the B1-B2 method).

The details of applying this method are not presented in this paper. The method has many

valid applications and has been used successfully for years, typically for regular buildings

with simple lateral framing. However, there are some limitations of the method worth

pointing out.

Different factors are applied to moments due to lateral translation of the structure (B2)

and moments with the structure restrained against translation (B1). For a structure

with regular gravity and lateral framing and uniform loading, these effects might be

easy to separate (gravity causes no translation and lateral loads cause translation), but

for real structures, the separation is not quite so straight-forward. For example, non-

symmetric gravity loading can cause translation within the structure. In cases like this

and many others, engineering judgment is required to correctly assign moments to the

two categories.

The B2 factors can vary at a joint (one value from the story above and one from

below) therefore the distribution of moments to the members at that joint can easily

become complex and require engineering judgment.

Structures with complex geometry can make calculating the factors difficult.

Structures with complex lateral framing (such as non-orthogonal frames or a

combination of braced frames and moment frames), sloping beams and columns, or

Step 1

Step 2

Step 3

Required Strength

Applied Loads

1.6RASD



where floor levels are not readily identifiable can make the method complex and

tedious if not inaccurate.

It is recommended in the AISC Commentary to use a more rigorous approach when

B1 > 1.2. Therefore, the application of this method may be limited. It should be

noted that a value of 1.2 is a significant amplification.

B2 is calculated for the entire story. If the structure has a localized area of relative

instability, this method could potentially miss this behavior.

Given these limits, the range of structures where the approximate method yields accurate

results is limited. For example, how does one calculate B1 and B2 for the project illustrated

below?

Figure 2: Screenshot from Fastrak Buildings Designer. Model Courtesy of Scott Wilson

Engineering judgment is often required for this method and therefore, generally speaking,

more suited to hand calculations since engineering judgment is difficult to program into a

software package. If the tools are available, the more general (and often more accurate)

rigorous analysis has several benefits.

GENERAL SECOND-ORDER ANALYSIS

Sophisticated analysis tools with rigorous second-order analysis methods are now readily

available to design engineers, making practical the use of the more accurate analyses. A

direct second-order analysis frees the engineer of the limitations of the approximate method



and often gives a more accurate determination of internal forces and strength level

deformations. A rigorous analysis is based on the actual stiffness of the framing and

therefore any localized instabilities and the corresponding effects on the surrounding framing

will be captured.

An engineer should have a thorough understanding of any analysis tool that he uses. The

more sophisticated analyses often require a slightly more sophisticated model. More thought

is often required while constructing the model to ensure an accurate analysis and provide

stability throughout the second-order analysis.

HOW TO: NOTIONAL LOADS

To account for the effect of initial imperfections, the specification allows the designer to

directly model the imperfections within the model. The set of initial displacements modeled

need to consider displacements due to loading and anticipated buckling modes of the

structure. One consequence of this requirement is that the out-of-plumbness of the columns

and the out-of-straightness of each member must be modeled. This must be done in a way to

capture the most destabilizing effect on the structure, which means at least four different sets

of displacements applied in the four principal directions at each level, with a corresponding

set of member out-of-straightness selected to add to the effect of the out-of-plumbness.

This method can quickly become difficult and may require several separate models. In

addition, if sharing project information through BIM, maintaining a single model with the

„real‟ geometry has many advantages. Therefore, generally the best alternative is to add

notional loads to the structure as specified by AISC.

Notional loads are horizontal forces added to the structure to account for the effects of

geometric imperfections. Figure 3 below illustrates a simple version of the concept. The

notional loads (Ni) are calculated as a portion of the gravity loads (Yi) and applied at each

level. The guidance included below will help you to calculate the magnitude of the notional

loads, decide where to place them on the model and in which direction(s).

Figure 3: Notional Loads



MAGNITUDE

The notional load, Ni, is 0.2% of the total factored gravity load at each level, Yi, and can be

written as:

Ni = 0.002Yi

Note that the value 0.002 is equal to 1/500 which is the maximum tolerance for out-of-

plumbness in steel structures as indicated in the AISC Code of Standard Practice (see Figure

6). Note that a smaller value can be used if the actual out-of-plumbness of the structure is

known.

Figure 6: AISC Code of Standard Practice Tolerance for Column Out-of-Plumbness

Gravity loads are defined in the AISC code as “Load such as that produced by dead and live

loads, acting in the downward direction.” The value Yi is the total factored gravity load in

each load combination. Therefore, the value of the notional loads will change from

combination to combination. Also, the total factored gravity load includes all gravity loads

on a level, not just those loads that are vertically supported by lateral framing members.

Therefore the effect of leaning columns is included in the notional loads.

When using ASD with a direct second-order analysis, the total gravity load (and therefore the

notional loads) is multiplied by 1.6. This is the same factor discussed earlier that is required

for the second-order analysis with ASD. The loads are not multiplied by 1.6 twice.



WHEN TO APPLY

Notional loads are required to be added to all load combinations. For combinations including

lateral loads, the notional loads are added to the other lateral loads. However, when the ratio

of second-order deflection to the first-order deflection ( 2/ 1) is less than 1.51, the notional

loads only need to be added to gravity only combinations.

DISTRIBUTION

Now that you have the magnitude of the notional loads for each level and load combinations,

you have to decide where on plan to apply them to the structure. AISC requires that they be

distributed on each level in the same manner as the gravity load. This would indicate you

could apply a single notional load (at each level for each load combination) at the location of

the resultant of the total factored gravity loads, otherwise known as the center of gravity. The

direction of the loads will be discussed in the next section.

If the gravity loads are distributed uniformly (in plan) on the level, it is easy to calculate

where the notional load should be placed. Assuming the lateral framing is symmetric, it is

easy to determine what portion of the notional loads each frame resists. See Figure 7 below.

Figure 7: Notional Load for Uniform Loading and Symmetric Lateral Framing

As areas with different gravity loads are introduced to the structure (such as a heavy storage

area) the calculation of the center of gravity becomes more complicated. You would more

likely add a notional point load at the center of gravity of each loading area. If there are only

a few loading conditions and your lateral framing is still simple, the distribution of the

notional loads to the frame is still manageable. See Figure Figure 8 below.

1 The limit of 1.5 applies to structures that have been analyzed using the nominal (unreduced)

stiffness of lateral members. If reduced stiffness is used, the limit is 1.7.



Figure 8: Multiple loading areas with Symmetric Lateral Framing

As soon as a bit more complexity is added to the lateral framing, the distribution of the

notional loads to the framing becomes more complicated. See Figure 9 below.

Figure 9: Multiple loading areas and Asymmetric Lateral Framing

In a real building there are multiple loads on the levels and usually unsymmetrical framing.

This makes placing and distributing the notional loads more and more complex. See Figure

Figure 10.



Figure 10: 'Real' Building with complex loading and Lateral Framing

These more complex situations obviously lend themselves to computer analysis. The

following suggested method works well with and without computer software, assuming you

are able to accurately distribute the notional loads to the lateral framing by hand.

Calculate the total factored gravity load transferred to each column at each level.

Calculate the corresponding magnitude of the notional load for each appropriate load

combination.

Apply the notional load as a point load at each column at each level. See Figure for a

sample set of notional loads.

Include the set of notional loads in each appropriate load combination.

Perform a 3D analysis of the structure for the load combinations. Consider all

framing, both lateral and gravity, in the analysis.

The point loads represent the notional load effect on each column. By applying the loads

to all columns and including all framing in the model, the effect of leaning columns is

directly included as part of the analysis. This method correctly distributes the notional

loads in the same manner as the total factored gravity load and through the 3D analysis

allows the effects of those loads to be distributed accurately to the lateral framing. This



method can be easily automated and included as part of the structural analysis.

Figure 11: Suggested Method for Notional Loads

DIRECTION

Now we have a good method for calculating and applying notional loads in the proper

location in the model. The next step is to determine in which direction or directions to apply

them. The requirement in the AISC Specification is to apply the notional loads in the

direction that adds to the destabilizing effects.

For gravity load combinations you will generally not know which direction is critical and

different directions will be critical for different members within the framing. Therefore you

will have to apply the notional loads in two orthogonal directions in both the positive and

negative sense. (See Figure Figure 12) You can apply the notional loads in the same

direction on all levels. Therefore, you will now have four load combinations for each gravity

load combination each with the notional loads applied in a different direction.



Figure 12: Notional Load Direction for Gravity Load Combinations

For lateral load combinations (when notional loads are required) the notional loads are

applied in the direction that adds to the destabilizing effects. This would be in the same

direction as the resultant of all lateral loads. So if you are adding notional loads to a wind

load case where the wind loads are applied in the +X direction, the notional loads would also

be placed in that direction. If you have a combination of X and Y wind loads (as is often

required by ASCE 7), then you would apply the notional loads in the resultant direction of

the wind loads. See Figure 1Figure 3 for an illustration of simple examples.

Figure 13: Notional Load Direction for Wind Load Combinations



HOW TO: STIFFNESS REDUCTION

To account for inelastic behavior, a reduction in the axial and flexural stiffness of all

members that contribute to the lateral stability of the structure is applied. See the

Commentary in the AISC Specification for more discussion on the types of behavior

accounted for by the reduction. The effective stiffness, noted by an *, are calculated as

follows:

Axial Stiffness: EA* = 0.8EA

Flexural Stiffness: EI = 0.8 bEI

For Pr/Py≤ 0.5; b = 1.0

For Pr/Py > 0.5; b = 4( Pr/Py*(1- Pr/Py))

Where; = 1.0 (LRFD), = 1.6 (ASD)

The flexural stiffness is multiplied by a factor, b (less than or equal to one), which is

dependent on the value of the axial load in the member. To avoid the iteration required to

calculate this factor, the specification allows the designer to use a value of b = 1.0, if an

additional set of notional loads equal to Ni = 0.001Yi are included. In addition, analyses

including other materials become more straight-forward since b does not need to be

calculated for those members.

MEMBERS TO REDUCE

Members that contribute to the lateral stability of the structure must have the stiffness

reduction applied. This includes members that deliver the lateral loads to the vertical lateral

framing such as collectors, chords, and horizontal bracing. In addition, it is permitted to

apply the reduction to all members in the model.

Reducing only the lateral members can create artificial distortion of the structure and result in

unintended redistribution of forces. For example, Figure 1Figure 4 shows the undeformed

shape of the sample framing. The sample consists of a moment frame on the right side with a

leaning column on the left. If only the lateral members are reduced, the relative shortening of

the moment frame columns under vertical loads will be greater than that of the gravity

column. The (exaggerated) deformed shape shown in Figure 1Figure 5 will result. This

could cause vertical load to shed to the gravity column, leaving the axial load in the lateral

framing underestimated. Reducing all members in the model will keep the relative

deflections closer and the redistribution of forces to a minimum.



Figure 14: Sample Framing - Undeformed Shape

Figure 15: Sample Framing - Deformed Shape

The stiffness reduction should also be applied to members of other materials, unless a greater

reduction is required by governing codes and specifications. This also will help prevent an

unintended redistribution for forces to the members of other materials, since they had not

been reduced.

SERVICEABILITY

The requirements of the direct analysis method are intended for determination of required

strengths and they are not intended for serviceability checks. Therefore when checking the

lateral drift of the structure under wind loads, for example, the stiffness reductions need not

be applied! Similarly, the effects of notional loads need not be included in drift checks

either.



b

As discussed above, b requires iteration to determine its value. b applies to members whose

flexural stiffness contributes to the stability of the structure and has significant compressive

load. Based on these criteria, there are several cases where you can reasonable set b = 1.0 as

a starting point for the iteration process.

Beams in moment frames since they generally have low axial load or braced frames

since the flexural stiffness does not contribute to the overall stability.

Braces since the flexural stiffness does not contribute to the overall stability.

Columns in braced frames since the flexural stiffness does not contribute to the

overall stability.

By taking the slightly conservative approach of assuming b is 1.0 and increasing the notional

loads as described above, even these decision points can be avoided.

CONCLUSIONS

The current AISC Specification (2005) includes the direct analysis method. The next AISC

specification comes out in 2010, most likely late in the summer. One significant change is

that the direct analysis method will become the default method and move from Appendix 7 to

Chapter C within the body of the code itself. It is clear that if you are not familiar with the

features of this method at present you will need to be so in the future. Hopefully, this paper

has elucidated these in the context of the use of modern structural engineering software.

However, there might need to be a number of questions for which you should seek answers.

There are several options for how the direct analysis method is executed within a software

package. An example would be selecting the type of second-order analysis that will be used.

What effects on the results does the particular method create (if any)?

Is the method limited in its application?

If the approximate (B1, B2) method is used, how are the limitations overcome?

Does the second-order analysis include both P- and P- ?

It is important to know the answers to these questions before you begin designing with the

software. Other details you should understand are:

Are the notional loads calculated automatically and if so how are they applied and in

what direction?

What members have a stiffness reduction and what effect does this have on the

distribution of forces in your model?



I think the overriding question to answer is, Do any of the answers to these questions result

in a limit on the types of buildings you can design using the software package?

Understanding the requirements of the direct analysis method and how the tools you use

implement this method is key to the whole process – but I don‟t have to tell you that.



ABOUT THE AUTHOR

Jason Ericksen is the Technical Manager for CSC Inc.

Jason manages the technical support for Fastrak Building

Designer and TEDDS for CSC in the United States. He

also helps ensure that customer requirements are

communicated effectively through our support team and

onto the software development team.

He‟s been a licensed structural engineer in Illinois for more

than 10 years. Before joining CSC in 2008, Jason was the

Director of the Steel Solutions Center at the American

Institute of Steel construction. In this role, Jason was in

charge of making sure that all engineering questions about

the design and construction of structural steel buildings were

answered correctly. Jason has delivered many technical

seminars on various subjects, including the Direct Analysis

Method, as a representative of AISC.

Jason can be reached at:

[email protected]

Toll free: 877-710-2053

FASTRAK BUILDING DESIGNER

Fastrak Building Designer is design modeling software focusing on the analysis and design

of structural steel buildings and is produced by CSC. Fastrak implements the direct analysis

method fully, using a rigorous second-order analysis that accounts for both P-Δ and P-δ

effects. CSC chose this method because it gives the user access to the most powerful

analysis and design solutions. It allows for the widest range of building structures with

accurate and reliable results. The recommendations of this paper are followed by Fastrak. In

fact, many of the suggestions were found to be best practice while developing the direct

analysis method within Fastrak.

For detailed information on how Fastrak Building Designer from CSC implements the direct

method, see our paper titled “Do You Know What Your Design Software is Up To?”

available from the CSC website. www.cscworld.com

CSC is the global leader in the provision of quality software, training, consultancy and

technical support to many thousands of structural engineers throughout the world.

http://www.cscworld.com/

Documents

Structural analysis