**Note: This is an updated and expanded wiki based on the requirements of ASCE 7-16 and AISC 360-16. The wiki previously was based on older versions of those documents.**

**18 July 2022: Corrections made in Step 4 for structures in Seismic Design Category B and Seismic Design Category D, see highlighted text.**

**27 June 2023: Clarification on Notional Loads for ASD, in Steps 2 and 7.**

**Overview**

The RAM Structural System contains several powerful features to assist in the analysis and design of steel members in conformance with the International Building Code. That code specifies that designs conform to the requirements of ASCE 7 and AISC 360. This document provides a detailed outline of the steps to take to obtain valid designs. The references in the document are based on the requirements of ASCE 7-16 and AISC 360-16 which are referenced by IBC 2018 and IBC 2021.

ASCE 7 gives requirements for the determination of loads and load combinations, and limits on the resulting drifts and stability. AISC 360 gives requirements for the analysis and design of steel structures. One method of obtaining a valid analysis is referred to as the Direct Analysis Method and is given in Chapter C of AISC 360-16. It is generally preferred to employ the Direct Analysis Method for moment frames in the RAM Structural System. In fact, for the AISC 360 codes the program assumes K=1, which means it assumes that moment frames are going to be designed using the Direct Analysis Method; the program doesn’t support the use of the Effective Length Method for moment frames. On the other hand, it is recommended that the Direct Analysis Method *not* be used for Braced Frames unless Appendix 7 Section 7.2.1(b) explicitly forbids the use of the Effective Length Method when the ratio of second-order drift to first-order drift is greater than 1.5 (this is very unusual for a braced frame); the Effective Length Method, given in Appendix 7.2 *Effective Length Method*, is preferred for braced frames. This recommendation is made because it is easier to apply the requirements of the Effective Length Method than those of the Direct Analysis Method to braced frames, since K is almost always equal to one for braced frames anyway.

The program has implemented a robust and practical approach to the Direct Analysis Method. This document is intended for use when the Direct Analysis Method is to be employed, not when the Effective Length Method is to be employed.

It is important to recognize that the Direct Analysis Method is not a single prescribed analysis but is rather a methodology consisting of a set of requirements that affect criteria, member stiffness, analysis methodology, loads and load combinations. The general steps outlined below are not unique to RAM Frame but would be required in order to obtain valid designs with any software.

This document is not intended to be a comprehensive outline of all necessary actions and criteria settings, such as diaphragm settings, flange bracing, reduced beam sections (RBS) if applicable, joints, etc. Its purpose is to outline one possible workflow, highlighting productivity-enhancing features available to aid in producing designs that conform to the requirements of the code.

After the model has been created and the gravity designs performed in RAM Steel, perform the following steps in RAM Frame.

**Step 1 Create the Wind and Seismic Load Cases for Drift**

Create the Wind and Seismic Loads for the drift analysis using the **Loads – Load Cases** command. It is recommended that the labels given to these load cases clearly identify that these are the drift load cases.

For the Seismic load cases when using the seismic load generator:

- Select
*Drift*for the*Provisions for*option. - Select the
*+ And -*options for eccentricity. - R values are given in Table 12.2-1 of ASCE 7.
- For T
_{a}per Eq. (12.8-7) a value for C_{t}of 0.028 is generally appropriate for steel moment frames. Note that the alternate equation, T_{a}= 0.1N, given by Eq. (12.8-8) is also permitted, with some limitations. - For the fundamental period, T, select
*Use Calculated T*(unless there is a reason that you need or want to use some other value).

For the Wind load cases, select *Use Calculated n* for *Natural Frequency* and at this time do not select the option *Exempted from Torsional Cases 2 and 4 per Appendix D* (unless you are certain that it is; it will be determined in a later step):

It is also recommended, although not necessary, to create an Eigen Solution Dynamic load case so that the building mode shapes are available for viewing. If not explicitly created the program will internally create the eigen solution dynamic load case in order to calculate the building periods, necessary for the generation of the wind and seismic story forces, but the mode shapes will not be available for viewing. Therefore, it is recommended that the eigen solution load case be explicitly created.

**Step 2 Specify the Criteria for Analysis**

Select the P-Delta criteria using the **Criteria – General** command. Generally, the most preferred option is the *Use Gravity Loads* option. The scale factors should be those associated with the load combination most likely to govern for the lateral columns. For example, since the seismic or wind loads are likely to control the designs, the strength design combination 4 of Section 2.3.1 or combination 6 of Section 2.3.6 are likely to control. In those combinations the factor on Dead Load is 1.2 and the factor on Live Load is either 0.5 or 1.0, as specified by Exception 1. These factors on P-Delta will be conservative for the uplift combinations 5 and 7, but P-Delta isn’t an issue for those combinations anyway. Conservatively, the factors of 1.2 and 1.6 per combination 2 could be used, guaranteeing that the worst P-Delta condition is covered for all combinations. Note that these values should be ultimate factors even if ASD will be used in design of the members; AISC 360-16 Section C1 requires that "*All load-dependent effects shall be calculated at a level of loading corresponding to LRFD load combinations or 1.6 time ASD load combinations.*". To conform to this requirement when ASD is to be used for design, enter ASD factors multiplied by 1.6; typically these would be 1.6 for Dead and (1.6)(0.75) = 1.2 for Live, Roof, and Snow.

Note that these are not the factors that will be used in the load combinations for design, these are merely the factors used to calculate the ultimate gravity loads used in the P-Delta analysis technique used by the program.

[A note regarding the option to Use Mass Loads: Mass loads are generally only indicative of Dead Loads, but the effects of Live Load and Roof Load must also be accounted for in the P-delta analysis. This means that if that option is selected, the Scale Factor must scale up the Mass Load to a level commensurate with the Dead, Live, and Roof loads. For example, if the Dead Load and Live Load are equal, the scale factor would need to be 2.0 so that both are accounted for, and then that scale factor would need to be *further* increased by the LRFD combination factors or 1.6 for ASD. A Scale Factor of 1.0 would most certainly be unconservative. For simplicity it is recommended that the Use Gravity Loads option be used instead.]

At this point do not select the *Use Reduced Stiffness for Steel Members* option for *AISC 360 Direct Analysis Method*. In the calculation of building periods and story drifts the unreduced stiffnesses should be used. The analysis using the reduced stiffnesses is only applicable to the member forces used for member design. The reason for this is that the reduced stiffnesses do not represent the real stiffness of the building, they are used to exaggerate the member forces used for design; this is a way of approximating the local effects of both member out-of-straightness and residual stresses. If all of the members were aligned such that their out-of-straightness and their residual stresses caused the building to sway in the same direction, then the analysis with reduced stiffness would be the correct one for calculating frequencies, drifts, etc. However, throughout the building they are randomly aligned, more or less cancelling each other out so that at the global level they have little impact on the frequencies, drifts, etc., of the entire structure. Again, the use of the reduced stiffness is an attempt to capture local (member) conditions, not global (structure) conditions. So, to get the correct building periods and story drifts the reduced stiffnesses should not be used at this time.

As necessary, specify all other pertinent criteria items in the Criteria menu, assign pertinent properties using the commands in the Assign menu, and verify and specify the appropriate values and options for loads and masses in the Loads menu.

**Step 3 Analyze**

Analyze the structure using the **Process – Analyze** command, selecting the gravity-, seismic drift-, wind drift-, and eigen solution load cases.

Note that if the initial sizes assigned to the frames are too small the structure will be unstable, and the P-Delta analysis will fail and/or the eigen solution analysis will not converge. Make sure that reasonable initial sizes have been assigned before the analysis is performed. Note that if sizes are not assigned to the moment frame members in the Modeler before the beams and columns are designed in the Steel Beam and Steel Column modules, the program will automatically select and assign beam and column sizes for the frame members that satisfy only the gravity load combinations when designs are performed in the Steel Beam and Steel Column modules; these sizes may be too small for either the P-delta analysis or the eigen analysis to successfully complete.

Review the *Loads and Applied Forces* report for accuracy and reasonableness. Verify that the specified criteria and input values are correct.

It is highly recommended that you view the deflected shapes and mode shapes. This will help identify some modeling errors or indicate a structure that is not well-defined.

View the deflected shapes using the **Process – Results – Deflected Shapes** command. Select the option to *Animate*.

View the mode shapes using the **Process – Results – Mode Shapes** command. Select the option to *Animate*. With Mode 1 selected, begin the animation by selecting the *Apply* button. To view each of the other mode shapes select the Mode Number and select the *Apply* button. In a regular, well-proportioned structure with orthogonal frames the first mode shape will usually be a translational mode, in either the X- or Y-direction, the second mode will usually be a translational mode in the orthogonal direction to the first mode, and the third mode will usually be a rotational mode. That is not always the case, so if not, be sure you understand why not (e.g., the frames are very significantly stiffer in one axis than the other).

If any diaphragms have been defined as Semi-rigid, and if extreme out-of-plane displacements of the diaphragm appear when the mode shapes are displayed, this probably indicates that the diaphragm properties or options need to be modified to eliminate these diaphragm modes (that almost certainly don’t exist in reality); the discussion of this problem is beyond the scope of this wiki.

Review the *Periods and Modes* report. If the *%Mass* values listed under *Modal Effective Mass Factors* for Mode 1 for X-Dir, Y-Dir, and Rotation are all 0.00, this indicates that some individual member/element (such as an individual beam, an out-of-plane wall or column, or a diaphragm), rather than the structural frames, is producing the first mode results. If not corrected, the program will erroneously use this period in the generation of wind and seismic forces. The exception to this is that if all diaphragms are Semirigid the Torsion values in that report will be 0.0; this doesn't indicate an error if the X- and Y-direction values are non-zero.

Make any necessary model changes (e.g., fixities, diaphragm thickness and properties, etc.) to correct the error conditions that may have been exposed by looking at these results, and reanalyze if necessary.

If it has not already been done, assign Frame Numbers to the various frames using the **Assign – Frame ****Numbers** command. This will be helpful when viewing some reports.

**Step 4 Check for Structural Irregularities**

Horizontal Structural Irregularities are defined in Table 12.3-1 and Vertical Structural Irregularities are defined in Table 12.3-2 of ASCE 7. Horizontal Structural Irregularities 2 through 5 can be determined by inspection or with simple calculations. Horizontal Structural Irregularities 1a and 1b are more complicated and will be discussed below. Vertical Structural Irregularities generally require some computation. Several reports are available that can assist in these calculations.

In some cases the existence of an Irregularity requires an increase in the member design forces, and some Irregularities are prohibited in structures assigned to Seismic Design Categories C, D, E, and F, requiring a change in the configuration of the structural framing. A detailed discussion of Irregularities is beyond the scope of this wiki, but two webinars on the topic are available on-demand: *Identifying Structural Irregularities (Part 1)* and *Dealing with Structural Irregularities (Part 2)*. These webinars show how the RAM Structural System analysis and reports can be used to identify structural irregularities, and how to satisfy the requirements when they exist:

Identifying and Dealing with Structural Irregularities: Part 1 and Part 2

One type of structural irregularity, Torsional Irregularity, has particular impact on the analysis and design process, and will be discussed in more detail here. ASCE 7 Table 12.3-1 defines Torsional Irregularity to exist when the drift at one end of the structure is greater than 1.2 times the average drift of the two ends, and it defines Extreme Torsional Irregularity to exist when the drift at one end of the structure is greater than 1.4 times the average drift of the two ends. A report for this can be obtained using the **Process – Results – Drift – At Control Points** command by inputting the coordinates for key locations on the plan, typically at the center of mass (those coordinates, *Xm* and *Ym*, can be found in the *Story Mass Data* section of the *Criteria, Mass and Exposure Data* report) and at the four corners. At the end of the *Drift* report there is a section titled *Torsional Irregularity Data*; the last column lists the worst case at each level, in each axis, of the maximum drift divided by the average drift (the second to last column lists the ratio of the drifts at each end; that value is used by some international codes, but can be ignored here).

If at any level the value is greater than 1.2, the structure is Torsionally Irregular (Horizontal Irregularity Type 1a); if at any level the value is greater than 1.4, the structure is Extreme Torsionally Irregular (Horizontal Irregularity Type 1b). This has an impact on what you need to do next, as given in Section 12.3.3.1 *Prohibited Horizontal and Vertical Irregularities for Seismic Design Categories D through F*, and Section 12.8.4.2 *Accidental Torsion*:

- If the structure is in Seismic Design Category D, E, or F E or F and has an Extreme Torsional Irregularity (Type 1b), the structural configuration is not permitted and must be revised by changing member sizes or adding additional frames. Repeat Steps 3 and 4 until the structure is no longer Extreme Torsionally Irregular.

- If the structure is in Seismic Design Category B and has torsional irregularity Type 1b, or if the structure is in Seismic Design Category C or D and has either torsional irregularity Type 1a or Type 1b, or if the structure is in Seismic Design Category D, E, or F E or F and has torsional irregularity Type 1a (as noted above Type 1b is not permitted for those structures), the accidental torsion must be amplified by Ax given by Eq. (12.8-14). Note that in that equation, δ
_{max}/δ_{avg}is the value taken from the report. Since this amplifier may be different for each story it will be necessary to specify eccentricities at each story: Select the**Loads – Masses**command, select the option to*Use Specified Values*, and multiply the*Eccen X*and*Eccen Y*values in the table by the appropriate Ax for that story and direction. Be aware that if this option is selected, masses listed here will not automatically be updated if the model is subsequently modified in any way that would affect masses; in that case it may be necessary to temporarily select the*Use Calculated Values*and*Recalculate*to get updated values. (For simplicity you could keep the option to*Use Calculated Values*, amplify the*5% Eccentricity*values – which are applied to all stories – by the largest value of Ax, and select the Recalculate button; this is likely to be conservative.) Then reanalyze the gravity-, seismic drift-, wind drift-, and eigen solution load cases. Tip: Rather than penalizing the structure by amplifying the accidental torsion this way, consider adding or moving frames and/or modifying stiffnesses in a way that eliminates the torsional irregularity.

- If the structure is in Seismic Design Category B and has torsional irregularity Type 1b, the accidental torsional moment must be included in the analysis, but need not be amplified by Ax.

- Otherwise (not torsionally irregular, or in Seismic Design Category B and only Type 1a), Section 12.8.4.2 indicates that it is not necessary to include the accidental torsional moment. Select the
**Loads – Load Cases**command, and for seismic load cases set the*Eccentricity*selection to*None*, and for the wind load cases select the option*Exempted from Torsional Cases 2 and 4 per Appendix D*. Then reanalyze the gravity-, seismic drift-, wind drift-, and eigen solution load cases.

Note: it is possible that the structure is torsionally irregular in one axis but not the other; the above checks are performed for each axis independently.

**Step 5 Check Drift**

ASCE 7 Section 12.12.1 *Story Drift Limit* limits the seismic design story drift, Δ, to the appropriate Δ_{a} value listed in Table 12.12-1, except that for moment frames in Seismic Design Categories D through F the design story drift, Δ, shall not exceed Δ_{a}/r. Note that the Δ_{a} values listed in the table are story drifts (e.g., 0.020h_{sx}), and that the coefficients (e.g., 0.020) are the story drift ratios (which is simply the story drift divided by the story height, h_{sx}). ASCE 7 Section 12.8.6 indicates that for structures assigned to Seismic Design Category C, D, E, or F, if the structure has either torsional irregularity Type 1a or Type 1b, the limits apply to drift at any point around the perimeter of the structure; elsewise the limits apply to the drift at the point of center of mass and it is not necessary to investigate drift at extreme points. Drift values can be obtained using the **Process – Results – Drift at a Point** command and clicking on any point on a floor plan or the **Process – Results – Drift at Control Points** command by inputting the coordinates of key locations on the plan, typically the centers of mass or the four corners, as explained. The resulting Drift report lists the displacements, story drifts, and drift ratios. These deflections are the elastic deflections, or δ_{xe} defined in Section 12.8.6. The design deflections are then given by Eq. (12.8-15):

C_{d} is the Deflection Amplification Factor given in Table 12.2-1 and I_{e} is the seismic Importance Factor given in Section 11.5.1.

Rather than factoring the elastic deflections in this way, calculating story drifts, and then comparing against the allowable story drift values in Table 12.12-1, a practical approach is to take the applicable coefficient (the story drift ratio) value from Table 12.12-1 and modify it so that it can be compared directly with the drift ratio values listed in the *Drift* report:

Maximum Allowable Elastic Drift Ratio = (Coefficient)(I_{e})/C_{d}

For example, a building four stories tall or less in Occupancy Category II has an Allowable Story Drift of 0.025h_{sx}, which means that the allowable story drift ratio is 0.025, C_{d} = 5.5 for a steel special moment frame, and I_{e} = 1.00 for Occupancy Category II. The Maximum Allowable Drift Ratio can then be computed as:

Maximum Allowable Elastic Drift Ratio = (Coefficient)(I_{e})/C_{d}

= 0.025(1.00)/5.5 = 0.00455 for this example

This limiting value can then be compared directly with the *Drift Ratio* values listed for the seismic cases in the *Drift* report:

Note: If the option to include P-Delta in the **Criteria – General** command was not selected for the analysis, the reported drifts won’t include any contribution due to P-Delta, you must amplify the drift values by the factor of 1.0 / (1.0 - θ) using the value θ calculated for each story unless θ is less than 0.1, as indicated in ASCE 7 Section 12.8.7 *P-Delta Effects*. Again, to simplify the process you could calculate a modified (reduced) Maximum Allowable Elastic Drift Ratio for each story using θ calculated for each story:

Maximum Allowable Elastic Drift Ratio = (Coefficient)(I_{e})(1.0 – θ)/C_{d}

These limits can then be compared directly against the elastic drift values listed in the report, using the limit appropriate for a given story. For simplicity it is recommended to use the P-Delta option in the program rather than using this approximate method.

Limits on Wind drift can similarly be compared against the values listed for the Wind load cases (no explicit limits for wind drift are given in ASCE 7).

If the drift ratios exceed the allowable, the member sizes should be adjusted or new frames added as necessary and Steps 3, 4, and 5 repeated until satisfactory drift ratios are obtained. Note that if these changes might change the status of the Torsional Irregularity or the amplifier on the accidental torsion, you will need to reset the Load Cases to generate all of the seismic and wind load cases (i.e., consider +/- Ecc for seismic and not exempt from Torsional Cases for wind), and you will need to reset the Diaphragm Masses to use the 5% Eccentricity.

Tip: Although increasing the beam size may be more effective in some cases than increasing the column size in reducing drift, it may result in joints that fail the strong column / weak beam seismic requirements of AISC 341. Furthermore, larger columns may also have the advantage of eliminating the requirement for web plates or stiffeners, which can be very expensive. These checks will be formally performed with all of the proper load cases and settings in a later step, but approximate results with the current settings can be obtained at any time by going to the **Steel – Standard Provisions** mode and **Steel – Seismic Provisions** mode and invoking the **Process – Member Code Check** and **Process – Joint Code Check** commands. With this in mind, weigh the advantages of increasing column sizes vs. beam sizes in the effort to reduce drift.

**Step 6 Stability Coefficient**

Calculate and determine the acceptability of the Stability Coefficient. Section 12.8.7 specifies a maximum allowable stability coefficient, θ_{max}, given by Eq. (12.8-17). To determine conformance to this requirement, the *ASCE 7 Stability Coefficients* report lists the values of θ and θ_{max} at each story for each seismic load case. This report is available using the **Reports – ASCE 7 Stability Coefficients** command. Specify C_{d} (given in Table 12.2-1) for each direction; the ratio of shear demand to shear capacity for the story, β, which can be conservatively taken as 1.0; and the Seismic Importance Factor, I_{e}, given in Section 11.5.1. The *Factors for Px* are those from the seismic design combination, except no factor need exceed 1.0:

Section 12.8.7 indicates that when the analysis includes the P-Delta effects, the value of θ/(1+θ), rather than θ, may be compared against θ_{max}. The report gives both values, but if P-Delta was included in the analysis use the θ/(1+θ) values:

If the Stability Coefficient exceeds the maximum allowable, θ_{max}, at any level for any seismic load combination, the member sizes must be adjusted or new frames added as necessary, and Steps 3 through 6 repeated until satisfactory stability coefficient values are obtained. Note: if β was conservatively assumed to be 1.0, it may be worth the effort to calculate a more precise value of β in order to get a more correct (larger) value of θ_{max}. The shear demand (the story shears) can be obtained from the *Building Story Shear* report. The Commentary to ASCE 7 defines the shear capacity as the "shear in the story that occurs simultaneously with the attainment of the development of first significant yield of the overall structure." As explained in the Commentary this can be determined by iteratively increasing the applied story forces until the first significant yield occurs at a given story (i.e., the demand on any frame member exceeds its capacity). The story shear on this story is then the value to be used in the calculation of β. This process would need to be continued until the story shear was similarly determined when first yield occurs for each story. The Commentary provides a simplified alternative: determine the worst interaction equation value for any frame member at a given level and use that interaction value for β. This can be done by looking at the *Member Code Check* reports for steel members or the *Concrete Column Design* or *Concrete Beam Design* reports for concrete members. Note that if the shear interaction is larger than the Axial/Moment interaction, the larger value should be used.

Section 12.8.7 also indicates that when the stability coefficient, θ, is less than or equal to 0.10, it is not necessary to include P-Delta effects in the analysis. Note that this is only true for the analysis used to calculate drifts; the Direct Analysis Method requires (despite what ASCE 7 says) that P-Delta effects be included in the analysis if the design equations of AISC 360 are to be used. Therefore, for simplicity it is suggested that P-Delta always be included in the analysis.

**Step 7 Create Load Cases and Perform Analysis for Member Design**

The wind and seismic load cases created previously were for the purpose of checking drifts and stability, with the analysis based on the full member stiffnesses, not the reduced stiffness required for the Direct Analysis Method. It is now necessary to create new wind and seismic load cases that can be used for member design. Because the stiffness reduction required for the Direct Analysis Method would change the calculated building periods, it is necessary to assign the building periods using those previously calculated, rather than allowing the program to use these new calculated periods, in the generation of the wind and seismic loads. The building period used in the calculation of the story forces should be the building period based on the unreduced stiffness, not on the reduced stiffness required by the Direct Analysis Method for analysis for member design. The period for the structure with the unreduced stiffness can be obtained from the *Loads and Applied Forces* report:

In the **Loads – Load Cases** command, add a new set of Seismic load cases. Select “*Member Forces*” for the *Provisions for* option, select *Use T* for T for the* Structure Period*, and input the building periods obtained from the *Loads and Applied Forces* report. If the existence of a Torsional Irregularity requires that both plus- and minus eccentricity be considered as discussed in Step 4, select the *+And- *option for *Eccentricity*, otherwise select *None*:

[Note: For Seismic Design Category A it is not necessary to create this Seismic Load case. For Seismic Design Category A the Provisions for Member Forces will give the same results as the Provisions for Drift (the base shear is not a function of the period, T), so the results from that analysis can be used in the subsequent steps.]

In the **Loads – Load Cases** command, add a new set of Wind load cases. Select *Use n* for the *Natural Frequency* and input the building frequencies. These can be obtained from the Loads and Applied Forces report for the Wind load case (and are the inverse of the building periods obtained from the Loads and Applied Forces report for the Seismic load case):

In the **Loads – Load Cases** command create the AISC 360 Notional Load cases. For now, specify 0.002 for the *Fraction of Gravity Loads*. The validity of this value will be verified in a later step:

Note that this Notional load is appropriate for either LRFD or ASD; because of the method of analysis used by the RAM Structural System it is not necessary to amplify the Notional Load by the alpha (1.6) factor. AISC 360 Section C2.1(d) requires that for ASD design the second-order analysis be carried out under 1.6 times the ASD load combinations; in the RAM Structural System this requirement is satisfied by applying 1.6 factors to the loads used for the P-delta analysis as explained in Step 2, above. Section C2.1(d) then goes on to say that the results shall be divided by 1.6 to obtain the required strengths of components; this is based on the assumption that the analysis is an iterative analysis. Because the RAM Structural System uses the Geometric Stiffness method rather than an iterative method of 2nd-order analysis, amplifying the loads by 1.6, including the notional loads, and then dividing the results by 1.6 is not necessary. Therefore, using a notional load of 0.002 times the gravity load is appropriate for both LRFD and ASD in the RAM Structural System. [Note that this interpretation and implementation of AISC 360 Chapter C has been affirmed by AISC Committee on Specifications Task Committee 3, the committee responsible for the provisions of the Direct Analysis Method.]

In the **Criteria – General **command, select the option to *Use Reduced Stiffness for Steel Members*:

At this time select the option to set t_{b} = 1.0. The validity of this decision will be verified in a later step, in the *AISC 360 Direct Analysis Validation* report, and the appropriate action will be indicated.

Perform the Analysis. Select the Dead, Live, and Roof load cases and the new Seismic, Wind and Notional load cases, but do not select the original seismic drift or wind drift load cases.

Caveat: AISC 360-16 Section C2.1(b) makes a distinction between including P-Δ and P-δ effects in the analysis and including them in the member forces. The purpose of including them in the analysis is to capture any system or local instabilities caused by them, exacerbated by the interplay between them. The purpose of including them in the member forces is so that the members are designed for the higher forces created by those effects. The Specification always requires that members are designed for the higher forces; this is correctly accomplished in the program by selecting the *P-Delta* option or by selecting the *B2* option for the P-Δ effects, and by selecting the *B1* option for the P-δ effects. The Specification also always requires that P-Δ effects be included in the analysis, but only sometimes requires that P-δ be included in the analysis (when the conditions described in Section C2.1(b) are not satisfied). Most structures satisfy those conditions, so most structures don’t require the inclusion of P-δ effects in the analysis. The RAM Structural System includes the P-Δ effects but does not include the P-δ effects in the analysis, it does not perform the iterative analysis required for P-δ. This is only a potential problem if the structure does not satisfy the conditions of Section C2.1(b). You can get a sense of the magnitude of the problem by looking at the values calculated for B1 for the various members (performed in Step 9); these values are often 1.0, and if so it is unlikely that the inclusion of the P-δ effects in the analysis would have more than minimal impact on the stability of the structure or member. If both B1 and B2 are reasonable values it is highly unlikely that there are instabilities in the structure, and it is unlikely that a structure that satisfies ASCE 7’s Stability Coefficient limits and drift limits will have large values of B1 and B2. In short, the lack of consideration of the P-δ effects in the analysis performed by RAM Structural System is acceptable per the Specification for most structures, and is only likely to be a problem in the most extreme case of a structure that is unstable or nearly so, but you need to use your engineering judgement on this.

**Step 8 Specify Code, Load Combinations and Criteria for Design**

Go to the **Steel – Standard Provisions** module.

Select the desired AISC 360 steel design code.

In the Load Combination Generation dialog select the *Code for Combinations*. Generally, the *IBC 2018 / ASCE 7-16* ASD or LRFD selection is appropriate.

- The Live Load factor f1 is defined in IBC 2018 Section 1605.2 to be either 1.0 or 0.5; this is the same requirement as is given in ASCE 7 Section 2.3.1 Exception 1.
- The Snow Factor f2 is defined in IBC 2018 Section 1605.2 for LRFD combinations to be either 0.7 or 0.2; in ASCE 7 Section 2.3.6 it is merely listed as 0.2. The Snow Factor f2 is defined in IBC 2018 Section 1605.3.1 for ASD combinations to be either 0.75 or, in Exception 2 to be either 0.2 or 0.0; in ASCE 7 Section 2.4.5 it is merely listed as 0.75.
- The value of
*S*can be obtained from the_{DS}*Loads and Applied Forces*report and is used for the Vertical Seismic Load Effect as defined in Section 12.4.2.2. - The redundancy factor, ρ, is defined in Section 12.3.4.2.
- In Seismic Design Categories A, B, and C its value is 1.0.
- In Seismic Design Categories D, E, and F its value is either 1.0 or 1.3; 1.3 may conservatively be used. In some cases, determining this value may require creating and running separate models to investigate the effect of removing elements.

- For
*Notional Loads*the option to*Consider with Combinations containing only gravity loads*should be selected if the largest ratio of second-order drift vs. first-order drift is less than 1.7, otherwise the option to*Consider with all Combinations in direction of lateral load*should be selected. At this time, unless that ratio is known, select the option to*Consider with Combinations containing only gravity loads*. The validity of this decision will be verified in a later step, in the*AISC 360 Direct Analysis Validation*report, and the appropriate action will be indicated.:

Wind drift and seismic drift load cases, if any, should be deselected before the load combinations are generated to avoid generating unnecessary combinations.

Generate the combinations.

Select the **Criteria – B1 and B2 Factors** command. To account for the P-δ effects, select the *Apply B1 Factors* option. To account for the P-Δ effects, the B_{2} factors can be used in lieu of the P-Delta analysis (the value of R_{M} is 1.0 for braced frames and calculated from Eq. (A-8-8) for moment frames), but if the P-Delta option has been selected for the analysis it is not necessary to also apply the B_{2} factors (it is not necessary to select the *Apply B2 Factors* option):

There may be specific requirements for your structure not discussed here; specify all necessary criteria items in the Criteria menu, and override the criteria on a member-by-member basis if necessary, using the assign commands in the Assign menu. It is not necessary to specify or assign K-factors. When the Direct Analysis method is used, the effective length factor, K, can be 1.0 for all members. That is the value used automatically by RAM Frame when AISC 360 is selected as the design code, and need not be specified in the Criteria.

**Step 9 Perform AISC 360 Standard Provisions Member and Joint Checks**

Perform a Code Check on the members using the **Process – Member Code Check** command.

Review the *AISC 360 Direct Analysis Validation Report* using the **Reports – AISC 360 Direct Analysis Validation** command. This report is extremely useful for verifying the validity of the options and choices selected in the analysis and design:

That report lists the maximum B_{2} factor, which is a measure of the ratio of second-order drift to first-order drift. If this factor is greater than 1.7 and the option to only include Notional Loads in the gravity-only combinations was selected, an error message will be given in the *NOTIONAL LOADS* section indicating that Notional Loads must be included with all combinations. It will be necessary to regenerate the load combinations with this option selected (although it is possible that if the member sizes are increased for some other reason, this error may go away).

Note the error message in red text in the REDUCED STIFFNESS section of the report shown above. In this example, analysis shows that there are four members for which t_{b} should be less than one, whereas in Step 7 the option to use t_{b} = 1.0 was selected. The program lacks the ability to assign t_{b} on a member-by-member basis, but listed below are three options for rectifying this invalid analysis:

Option 1: Increase the size of the members for which the required t_{b} is less than 1.0, until the required t_{b} is equal to 1.0. Only the member with the smallest required t_{b} is identified on the report but in some cases it can be deduced which are the other members that are likewise required to use a smaller t_{b}. Note that if some members have failed the Code Check just performed, upsizing those members to sizes that adequately pass the code check may eliminate the condition whereby some members require a t_{b} less than 1.0. This option may be advantageous if there are only a few members whose size needs to be increased over that otherwise required, although it may take some trial and error to determine which members to up-size.

Option 2: In the **Criteria – General** command in **Analysis** mode, select the option to *Use t _{b}*, and specify a value equal to the smallest required t

This is conservative, however, because it penalizes all members, not just those that require a smaller t_{b}. Its only advantage is that it is easy to do. As the designs evolve it may be necessary to change the value specified here.

Option 3: In the **Loads – Load Cases** command in **Analysis** mode, modify the Notional Load cases to use 0.003, rather than 0.002, as the *Fraction of Gravity Load*. In the generation of the combinations, specify that the Notional Loads are to be included in all combinations. This may be conservative because the 0.002Yi portion of these notional loads may not need to be applied to all combinations, but the 0.001Yi portion must be. Again, this penalizes all members, not just those that require a smaller t_{b}, but it is easy to do.

In the report, text in blue indicates unnecessary (conservative and/or redundant) selections, such as “Both P-Delta and B2 factors were applied. Only one or the other is required” which would appear in the SECOND-ORDER ANALYSIS section of the report if both the P-Delta option and the B_{2} factors option were selected:

Text in red indicates erroneous selections, such as “B1 factors were not applied” which would appear if the B_{1} option was not selected:

In order to have a valid design based on the AISC 360 Direct Analysis method it is necessary to make the necessary changes to eliminate all of the error messages in red text from the report. It is also recommended that the necessary changes are made to eliminate all of the warnings listed in blue text.

Once the analysis and design options have been validated, verify the acceptability of the member sizes by looking at the on-screen code check results (failing members are shown in red) or the *Member Code Checks Summary* report, and change the sizes as necessary.** The Process – Member View/Update** command is very helpful in investigating and modifying sizes.

Similarly, perform a joint check using the **Process – Joint Code Check** command and verify the acceptability of the doubler and stiffener plate requirements. The joint symbols can be made more visible using the *Increase symbol size*s button on the toolbar. A Green ball indicates the joint is acceptable. A Red ball indicates that the joint fails, requiring a change of member sizes. A Blue ball indicates the joint requires a web plate. Blue plates indicate that the joint requires web stiffeners. Change the sizes as necessary to obtain acceptable joint designs or to eliminate doublers and stiffeners if desired. The** Process – Joint View/Update** command is very helpful in investigating and modifying sizes.

**Step 10 Perform AISC 341 Seismic Provisions Member and Joint Checks**

Go to the **Steel – Seismic Provisions** module.

Select and specify the code settings and load combination options and values, consistent with those selected in **Steel – Standard Provisions** mode. If the Notional Loads were required to be included in all combinations in **Steel – Standard Provisions** mode, include the Notional Loads in all combinations in **Steel – Seismic Provisions** mode when generating the combinations; otherwise it is not necessary to include the Notional Loads in any combinations.

Assign the frame type (e.g., Special Moment Frame) to the frames using the **Assign – Frame Type** command.

Specify all necessary criteria items in the Criteria menu and override the criteria on a member-by-member basis, if necessary, using the assign commands in the Assign menu. It is not necessary to specify or assign K-factors.

Perform a member code check using the **Process – Member Code Check** command and perform a joint code check using the **Process – Joint Code Check** command.

Modify the sizes as necessary to satisfy the seismic requirements. The **Process – Member View/Update** and the **Process – Joint View/Update** commands are very helpful in investigating and modifying sizes.

**Step 11 Iterate**

Repeat the above steps until acceptable designs are obtained. When sizes are changed, the stiffness of the frames change, which impacts drifts, distribution of forces, P-delta, etc. Since the selection of proper sizes is an iterative process with trial member sizes increasing and decreasing, it may require that some or all of the above steps be repeated. To work more productively, it may be best not to spend too much time trying to refine the sizes too much for each individual step, since a subsequent step may require significant size changes. Rather, at each step select sizes that are close but not necessarily “perfect”, especially in the early stages. The refinement of sizes should occur as the steps are iterated.

Contact Allen Adams at allen.adams@bentley.com for comments or if you want to discuss this further.