**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 7-05 and AISC 360-05 which are referenced by IBC 2009, with references to ASCE 7-10 and AISC 360-10 shown in square brackets [] if the reference is different. Specifically, references to Sections and Equations listed below refer to ASCE 7-05 unless explicitly stated otherwise.

ASCE 7 gives requirements for the determination of loads and load combinations, and 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 in AISC 360-10. It is generally preferred to employ the Direct Analysis Method for moment frames in the RAM Structural System. On the other hand, it is recommended that the Direct Analysis Method *not* be used for Braced Frames unless explicitly required by Section C2.2 of AISC 360-05 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*”, in AISC 360-10 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.

It is important to recognize that the Direct Analysis Method is not a single prescribed analysis technique, 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.

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.

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 Loads for the drift analysis using the **Loads – Load Cases** command. It is recommended that the labels given to these load cases clearly identifies 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, and select *Use Calculated T* for T for the* Structure Period* (unless there is a reason that you need or want to use some other value).

R values are given in Table 12.2-1. In the calculation of Ta per Eq. (12.8-7) a value for Ct of 0.028 is generally appropriate for steel moment frames. Also note that the alternate equation, Ta = 0.1N, given by Eq. (12.8-8) is also permitted.

For the Wind load case when using the wind load generator, select *Use Calculated n* for *Natural Frequency*:

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. Note that if the initial sizes assigned to the frames are too small the eigen solution analysis will not converge. Make sure that reasonable initial sizes have been assigned before the analysis is performed.

**Step 2**

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 combinations 4 or 5 of Section 2.3.2 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 6 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 should be ultimate factors even if ASD will be used in design of the members so that the P-Delta analysis will be performed at an ultimate level, which is necessary for the principle of superposition of load cases to be valid. Also 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.

At this point do not select the *Use Reduced Stiffness for Steel Members* option for *AISC 360*. 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.

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. Make sure that reasonable initial sizes have been assigned before the analysis is performed.

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 the structure, selecting the gravity-, seismic drift-, wind-, and eigen solution load cases.

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 mode shapes and deflected 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. 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. Review the Periods and Modes report; if the %Mass values listed for all direction components for the first mode are 0.00, this indicates that some member/element (such as an individual beam, an out-of-plane wall or column, or a diaphragm) is producing the first mode results. The model must be corrected so that these values are valid in order to obtain the correct building period results.

To view the mode shapes invoke the **Process – Results – Mode Shapes** command. With Mode Number 1 selected, begin the animation by clicking on the Start button. To end the animation, click on the Stop button. To view each of the other mode shapes select the Mode Number and repeat. 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. If any diaphragms have been defined as Semi-rigid, turn on the deck mesh view by selecting the *Display Semirigid Diaphragms* option on the *Semirigid Diaphragms* tab in the **View – Members** command. 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.

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 Seismic drift. Section 12.12.1 limits the design story drift, D, to the appropriate D_{a} value listed in Table 12.12-1, except for moment frames in Seismic Design Categories D through F the design story drift, D, shall not exceed D_{a}/r. Note that the D_{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}). 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 for up to four key locations on the plan, typically the four corners. The resulting Drift report lists the displacements, story drifts, and drift ratios. These deflections are the elastic deflections, or d_{xe} defined in Section 12.8.6. The design deflections are then given by Eq. (12.8-15):

Cd is the Deflection Amplification Factor given in Table 12.2-1 and I is the seismic Importance Factor given in Section 11.5.1 [Ie in Table 1.5-2 of ASCE 7-10].

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 the table and modify it so that it can be compared directly with the drift ratio values listed in the Drift report:

Maximum Allowable Drift Ratio = (Coefficient)(I)/Cd

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, Cd = 5.5 for a steel special moment frame, and I = 1.00 for Occupancy Category II [“Occupancy Category” is referred to as “Risk Category” in ASCE 7-10]. The Maximum Allowable Drift Ratio can then be computed as:

Maximum Allowable Drift Ratio = (Coefficient)(I)/Cd = 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 in the Drift report:

Limits on Wind drift can similarly be calculated and compared against these values 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 and 4 repeated until satisfactory drift ratios are obtained.

This report is also useful in determining the presence of torsional irregularity and the need for amplification of accidental torsional moment as required in Section 12.8.4.3. This should be checked before proceeding. If necessary, the *% Eccentricity* value (which is applied to all stories) or *Eccen X* or *Eccen Y* (for each story individually) specified in the **Loads – Masses** command can be modified to satisfy this requirement, and the model reanalyzed.

**Step 5**

Calculate and determine the acceptability of the Stability Coefficient. Section 12.8.7 specifies a maximum allowable stability coefficient, q_{max}, given by Eq. (12.8-17). To determine conformance to this requirement the ASCE 7 Stability Coefficients report lists the values of q and q_{max} at each story for each seismic load case. This report is available using the **Reports – ASCE 7 Stability Coefficients** command. Specify Cd (given in Table 12.2-1) for each direction; the ratio of shear demand to shear capacity for the story, b, which can be conservatively taken as 1.0; and the Seismic Importance Factor, I, given in Section 11.5.1 [Ie in Table 1.5-2 in ASCE 7-10]:

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

If the Stability Coefficient exceeds the maximum allowable, q_{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 5 repeated until satisfactory stability coefficient values are obtained. [Note: if b was conservatively assumed to be 1.0, it may be worth the effort to calculate a more precise value of b in order to get a more correct (larger) value of q_{max}. The shear demand (the story shears) can be obtained from the Building Story Shear report. The shear capacity of the story can be obtained by manually summing up the column shear capacities for a steel moment frame system, for example, by looking at the Member Code Check reports for each of the columns; since column shear rarely if ever controls the design of moment frame columns it will generally be found that the sum of the capacities is substantially higher than the story shear. Hence b will be very small, and q_{max}will be very large, capped by the maximum value of 0.25; this will often be the case. Shear capacities of concrete columns can similarly be obtained by looking at the column design report in RAM Concrete Column.]

Section 12.8.7 also indicates that when the stability coefficient, q, is less than or equal to that given in Eq. (12.8-16), 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 7-05 says) that P-Delta effects be included in the analysis if the design equations of AISC 360 are to be used. Therefore it is suggested that P-Delta always be included in the analysis.

**Step 6**

Set criteria, create load cases and perform analysis for member design. 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, and the appropriate action will be indicated.

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.

In the **Loads – Load Cases** command, add a new set of Seismic load cases. Select “Member Forces” for the “Provisions for” option, and select *Use T* for T for the* Structure Period*, and input the building periods:

As stated previously, it is generally felt that 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 Wind load cases. Select *Use n* for the *Natural Frequency* and input the building frequencies. These are the inverse of the building periods obtained from the Loads and Applied Forces report:

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:

In order to determine whether or not the Notional loads need to be included with all load combination or just those load combinations that include Gravity loads it is necessary to determine the ratio of second-order drift to first-order drift. To do this, temporarily turn off the P-Delta option in **Criteria – General** and perform an Analyze. Print out the story drifts using the **Process – Results – Drift at Control Points** command; this set of results is the first-order story drifts. Then re-select the P-Delta option in **Criteria – General** and perform Analyze again. Print out the story drifts; this set of results is the second-order story drifts. From the values on these two reports manually calculate the ratios of the Story Drifts, that is, the Story Drift from the second-order results divided by the Story Drift from the first-order results, for each story at each location, for each load case (note that when investigating an X-direction load case it is not necessary to calculate these ratios for the Y-direction, and vice-versa). Determine the largest of any of these ratios. Note that although it would be more thorough to perform these calculations on all of the lateral load cases it is probably not necessary to do so; it is probably adequate to merely perform these calculations on the Dead Load Notional load case, using that as the representative load case.

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.

**Step 7**

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 IBC09/ASCE7-05 ASD or LRFD selection is appropriate.

- The Live Load factor f1 is defined in IBC 2009 Section 1605.2 to be either 1.0 or 0.5; this is the same requirement as is given in ASCE 7 Section 2.3.2 Exception 1.
- The Snow Factor f2 is defined in IBC 2009 Section 1605.2 for LRFD combinations to be either 0.7 or 0.2; in ASCE 7 Section 2.3.2 it is merely listed as 0.2. The Snow Factor f2 is defined in IBC 2009 Section 1605.3 for ASD combinations to be either 0.75 or, in Exception 2 to be either 0.2 or 0.0; in ASCE 7 Section 2.4.1 it is merely listed as 0.75.
- The value of
*S*can be obtained from the Loads and Applied Forces report, and is used for the Vertical Seismic Load Effect as defined in Section 12.4.2.2._{DS} - The redundancy factor, r, is defined in Section 12.3.4. In some cases determining this value may require creating and running separate models to investigate the effect of removing elements. In ASCE 7-05 and later the value of r is either 1.0 or 1.3; 1.3 may conservatively be used in any case.
- For
*Notional Loads*the option to*Consider with Combinations containing only gravity loads*should be selected if the largest ratio of second-order drift over first-order drift from Step 6 is less than 1.5, otherwise the option to*Consider with all Combinations in direction of lateral load*should be selected:

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.

Using the **Criteria – B1 and B2 Factors** command, select the *Apply B1 Factors* option. This is to account for the small P-d effects, which are not accounted for in the analysis. The B_{2} factors can be used in lieu of the P-Delta analysis (for moment frames the value of R_{M} should be 0.85 for AISC 360-05 or calculated from Eq. (A-8-8) in AISC 360-10), but if the P-Delta option has been selected it is not necessary to also apply the B_{2} factors:

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 8**

Perform a Code Check 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:

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 seven members for which t_{b} should be less than one, whereas in Step 6 the option to use t_{b} = 1.0 was selected. There 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

_{b}listed on the report:

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*. If the notional loads were only included with the Gravity load combinations, increasing the notional loads to 0.003Yi will not have any impact on the member designs unless one of the gravity load combinations controls the design (not likely); if the notional loads were included with all combinations, increasing the notional loads to 0.003Yi will penalize all members, not just those that require a smaller t_{b}.

Also note the message in the Notional Loads section of the report shown above that says, “Verify that Notional Loads do not need to be included with all combinations”. This message will appear if the option to include notional loads only with gravity combinations is selected and the option to use B_{2} factors is not included. The verification was performed in Step 6, where the ratio of second-order drift to first-order drift was calculated. If the maximum value of that ratio is less than 1.5 it is not necessary to include the Notional Loads in all combinations. Note that if the option to use B_{2} is selected rather than the option to perform a P-Delta analysis (in which case it would not be necessary to manually calculate the ratios of second-order drift to first-order drift as directed in Step 6), the program will use the largest B_{2} value as the ratio of second-order drift to first-order drift (which is what B_{2} represents) when determining the validity of the choice to include the Notional loads only with the gravity combinations, and an error message will be given if that choice is not valid.

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 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, and change the sizes as necessary to eliminate doublers and stiffeners if desired. The** Process – Joint View/Update** command is very helpful in investigating and modifying sizes.

In **Steel – Seismic Provisions** mode:

- Select and specify the code settings and load combination options and values, consistent with those selected in
**Steel – Standard Provisions**mode. - 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 9**

Repeat the above steps until acceptable designs are obtained. 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, including the investigation of drift.

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