RAM Frame AISC 360 Stability Analysis and Design

For a broader explanation of the Direct Analysis methods in RAM Frame, including a step-by-step procedure, please refer to the following article:

AISC 360 Direct Analysis method in RAM Structural System

General

Chapter C of the AISC specification (2005 and later) covers stability analysis and design.  This document discusses how the requirements are met in RAM Frame.  For additional information, refer to the technical notes of the manual pdf file, RAMFrameSteelPostprocessor.pdf, starting with section 3.2.1. (To access the manual go to Start - Programs - Bentley Engineering - RAM Structural System - Manuals or click Help - Manual within the Steel Standard Provisions mode of RAM Frame).

Effective Length Factor

The effective length factor in the steel post processor is assumed to be 1.0 for beams and columns. Brace effective length factors default to 1.0 but can be assigned a different value (ie K = 0.5 for X bracing). Due to this assumption, only analysis and design methods that are not a function of the effective length (K = 1.0) can be used in RAM Frame. The Direct Analysis Method allows this assumption and is the preferred method because there are no restrictions on when it can be used.

Direct Analysis Method

AISC Appendix 7 covers the Direct Analysis Method. The AISC commentary is very informative and it is clear that this is the preferred method. The design-analysis constraints have four basic requirements:

• 2nd order analysis (such as an iterative 2nd order analysis or amplified 1st order analysis), including both P-Δ and P-δ
• Notional loads
• Reduced flexural stiffness
• Reduced axial stiffness

Most of the analysis parameters for the Direct Analysis Method are set in RAM Frame Analysis – Criteria – General. In this dialog box, you can toggle the parameter for reduced stiffness (A-7-2 and A-7-3) and select whether or not you want P-Delta included in the analysis. The general requirements of the appendix require that all component and connection deformations contribute to the lateral displacement of the structure. For this reason, we recommend ignoring rigid end zones in the analysis.

To meet the second order analysis requirements, the amplified first-order elastic analysis can be used if B1 and B2 are selected in RAM Frame Steel – Criteria – B1 and B2 Factors. B2 accounts for big P-Delta effects. In lieu of using B2, big P-Delta effects can be considered in the analysis if P-Delta is enabled in RAM Frame Analysis– Criteria – General. Please note, P-Delta in the analysis does not consider small P-delta effects. Therefore, B1 should always be selected in the steel post-processor when required by the specification. You are never required to use P-Delta in the analysis and B2 in the steel post-processor simultaneously. These two different options are for the same requirement.

Reduced flexural and axial stiffness should be selected in all instances when using the Direct Analysis Method. The parameter tau_b is a function of the member required compressive capacity and yield strength. The program does not automatically calculate tau_b and must be specified. Tau_b is permitted to be 1.0 when alphaPr/Py is less than or equal to 0.5. Otherwise a smaller value is required. In lieu of using a smaller value of tau_b when required, a value of 1.0 can be specified but the notional load factors must then be increased from 0.002 to 0.003. Since the value of alphaPr/Py is not known until after an analysis is performed – and may require iterative analyses to converge on the value – it is recommended that initially tau_b be set to 1.0 and that the lower value (0.002) be used for the notional loads. Generally this combination will be acceptable, but if not, the AISC 360 Direct Analysis Validation report will give a warning that either the notional loads must be increased (using 0.003) or a smaller value of tau_b should be specified. A third option may be to slightly increase the size of those columns for which the initially calculated value of alphaPr/Py is greater than 0.5 such that the calculated value of becomes less than 0.5, which then eliminates the need to either use a smaller value of tau_b or larger notional loads. If increased notional loads are used they should be analyzed and included in the load combinations in the steel-post processor per Appendix 7.

There are some limitations of Direct Analysis Method in RAM Frame. In particular, some building configurations cause problems for P-Delta in the analysis and/or for the calculation of B2. Problems with P-Delta in the analysis generally present themselves as instabilities in the finite element analysis. This is discussed further in the P-Delta technote (See Also section below). Occasionally with B2 enabled, members for a particular diaphragm(s) will fail with a Pnt>Pe2 error in the steel post-processor. It is possible that this is a real failure and there are excessive displacements, but often the error is thrown for load combinations where the displacements are reasonable. The underlying problem stems from the calculation of Pe2. Some load combinations produce displacements and small, non-zero shears. When such a condition occurs, Pe2 will also be a small non-zero number leading to negative B2 value which triggers the Pnt>Pe2 error. When this occurs, turn off B2 and make sure there is adequate strength in your members. Make sure your displacements are reasonable. Often the combination creating the error would not control the design of the member. If you are able to make this determination, you might be able to bypass the error by unselecting the problem combination in your load combinations. Please keep in mind that this would exclude the combination for all members. If both P-Delta in the analysis and B2 cause problems, you may need to account for second order effects by hand.

Other Methods

Any method that requires the effective length of the member to exceed 1.0 is not permitted while using the AISC 360 code in Ram Frame. Also, AISC 360 C2.2 requires that the Direct Analysis Method be used when the ratio of second-order drift to first-order drift exceeds 1.5. C2.2a and C2.2b can be used in the steel post-processor under certain conditions.

AISC C2.2a(4) permits K = 1.0 for braced frames or when the ratio of second-order to first-order drift is less than or equal to 1.1. Second order effects (B1 plus B2 or P-Delta) and notional loads based on a factor of .002 must be included but the reduced stiffness requirements in the Direct Analysis method need not be followed.  AISC2.2a may be the prefered methodology for braced frames.

AISC C2.2a(2) requires the analysis to be carried out under 1.6 times the ASD load combinations and divided by 1.6 to obtain the required results. This presumes that an iterative method of P-delta is used. However, RAM Frame uses the Geometric Stiffness method for the P-delta analysis which does not require that the analysis be carried out this way for ASD. However, to accurately capture the P-delta effects the P-delta analysis should be performed using ultimate (factored) masses (using an ultimate Scale Factor) if the Mass Loads are used or by using ultimate gravity loads (using ultimate Scale Factors on the Dead and Live Loads) if Gravity Loads are used, as specified in the RAM Frame – Analysis General Criteria, even if ASD is going to be specified as the design code.

AISC C2.2b permits members to be designed for the first-order required strengths when all members satisfy Eq. C2-7. If you are permitted to follow this method, P-Delta (or B2) is not required to be considered. In addition the reduced flexural/axial stiffness requirements are not necessary. However, you must still consider notional loads and B1. The factor for notional loads will exceed the options in the AISC generator and you will need to create user defined notional load cases with the appropriate factor per Eq. C2-8.

See Also

Structural Product TechNotes And FAQs

AISC 360 Direct Analysis method in RAM Structural System

RAM Frame P-Delta

Structural eSeminars