A Practical Approach to Using the Response Spectra Analysis Method
Webinar Q & A
Webinar Date: June 2015. Repeated September 2016.
A recording of the Bentley Success Factors webinar titled A Practical Approach to Using the Response Spectra Analysis Method can be found at: http://pages.info.bentley.com/video-details/
As Building Codes get more stringent and buildings get more complicated, an increasing number of structures must be analyzed using the Response Spectra Analysis method. Lack of experience and familiarity with the method can result in critical errors in both analysis and design. A clear understanding of the method and of the Code requirements is necessary to properly and productively design structures using dynamic Response Spectra Analysis. Response Spectra Analysis is more complicated than traditional equivalent static methods. With the proper approach and the proper tools, the effort required for Response Spectra Analysis need not be significantly more than that required using those more conventional methods.
Questions and Answers
During that webinar several questions were received. Time did not permit answering all of the questions nor of providing detailed answers. Compiled here are the questions that were received that were related to this topic, with more thorough answers.
When do we use response spectra versus the equivalent lateral force method?
Refer to Table 12.6-1 of ASCE 7-10, which indicates that you can always use the response spectra analysis method, but there are certain cases in which you cannot use the equivalent lateral force method, particularly structures with some irregularities as identified in that table.
ASCE 7-10 Section 12.9.5 states that the amplification of accidental torsional moment is not required. However, some commentary says that if the model is simply applying a torsional moment to the structure that this statement is not satisfied and Section 220.127.116.11 is still required. Does RAM simply apply a torsional moment or does it actually shift the mass when performing a response spectra analysis in determining the accidental torsion?
ASCE 7-10 Section 12.9.5 requires that the Accidental Torsion defined in Section 18.104.22.168 be applied to the Response Spectra analysis. This is defined as “… the torsional moments caused by an assumed displacement of the center of mass each way from its actual location by a distance equal to 5% of the dimension of the structure…”. This can be accomplished in one of two ways:
Calculate and apply a torsional moment equal to the horizontal story force times 5% of the building dimension. Both the positive moment associated with the +5% eccentricity and the negative moment associated with the -5% eccentricity must be created. This creates a set of static load cases that are then combined with the Response Spectra analysis results.
Offset the masses, first by +5% and then by -5%, and perform the eigen analysis and the response spectra analysis. This means that two completely separate Response Spectra analyses are performed for each direction, two in the X- and two in the Y-directions (in RAM Frame, X and Y are the horizontal axes and Z is the vertical axis; that is the convention that will be used in this document).
Section 22.214.171.124 further requires that when a Torsional Irregularity (as defined in Table 12.3-1) exists, the accidental torsion shall be amplified by Ax that is a function of the drifts at each end of the story. Section 12.9.5, however, states that that additional amplification is not necessary “where accidental torsion effects are included in the dynamic analysis model.” This means that if you use the first approach listed above you must amplify the accidental torsion per the requirements of Section 126.96.36.199 because that approach does not include the accidental torsion effects (i.e., offset masses) in the actual analysis model. However, if you use the second approach listed above you do not need to further amplify the accidental torsion because that approach does include the accidental torsion effects directly in the analysis model. The reason the amplification is not required in the latter case is because the Response Spectra analysis itself, performed at the offset mass locations, will magnify any tendency for the structure to rotate, and the design values resulting from the analysis will be amplified directly by the analysis, not artificially through an amplification factor.
RAM Frame can utilize either approach, but by default it uses the second approach. When a Response Spectra analysis is specified, two load cases are created in each direction; the eigen/ritz vector analysis and response spectra analysis for the first case are performed with the masses offset 5% in the positive direction, and then the the eigen/ritz vector analysis and response spectra analysis are repeated for the second case with the masses offset 5% in the negative direction.
Is there a way to quickly output the needed info to calculate Ax and adjust the accidental eccentricity accordingly?
For the static Equivalent Lateral Force method, and if it is desired to amplify the eccentricity for the Response Spectra load cases rather than offsetting the masses, the amplified accidental torsion eccentricity can be easily calculated. In RAM Frame, the drifts can be obtained at any point on a diaphragm, including at its extreme ends. From these values the amplification factor, Ax, can be calculated per Equation (12.8-14), and the Eccentricity value can be increased from 5% to whatever amplified value is required (Ax times 5%).
Can both static and dynamic analyses be performed in a single model in RAM Frame?
Yes, both kinds of analyses can be defined and analyzed in a single model, at the same time. There may be some situations, however, where it is necessary to analyze some load cases separately. For example, if the eccentricity for the accidental torsion needs to be amplified by Ax it will be necessary to first analyze the Response Spectra load cases with the eccentricity value set to 5%, and then to analyze the static Equivalent Lateral Forces cases with the eccentricity value set to the amplified value.
Why should the dynamic base shear be a minimum of 85% of static base shear?
This is required in ASCE 7-10 Section 188.8.131.52.
How did you calculated R/Ie?
The initial scale factor for the Response Spectra analysis results, given in Section 12.9.2, is R/Ie, where R is the Response Modification Coefficient given in ASCE 7-10 Table 12.2-1, and Ie is the Seismic Importance Factor given in Table 1.5-2.
Aren't you limited by the lesser R when analyzing the structure as a whole? Are you allowed to use a different R in each direction?
Nowhere in Section 12.9 Modal Response Spectrum Analysis does it indicate that the lesser of the two R values is to be used in both directions. It is my understanding that the scale factor used in a given direction can be calculated using the R appropriate for the type of lateral system used in that direction.
For the scaling of results, the procedure in RAM Frame is manually done or is fully automated?
The scale factor must be calculated manually and entered in the program, but the program provides reports listing the base shears that can be used to easily determine these scale factors.
What are the minimum data inputs need for response spectra since we may not have certain inputs during analysis?
You need to specify a response spectrum curve. These are generally specified by Code, or site specific curves can be specified. In the case of the RAM Structural System these can be automatically generated by specifying the code (for example, ASCE 7-10), the site class, the site characteristics (for example, Ss, S1, and TL) and the damping ratio. These are necessary, in order to define the response spectra curve. Additionally, the program allows you to indicated the directions (X-axis, Y-axis, and/or rotated) and whether or not to generate the response spectra cases to include the eccentricity cases due to accidental torsion. You can also indicate Scale Factors, which initially can be specified as the Importance Factor divided by R, but these aren’t necessary until you have compared the analysis results with the results of the equivalent lateral force method.
The Mass Participation Factors for the two horizontal directions normally can get more than 90% of the mass, but in the rotational direction it is very hard to get more than 90%. Do we need to include more mode shapes to get the torsional direction to include more than 90% of the mass?
In practice I have always included enough mode shapes so that at least 90% of the mass is obtained for both horizontal directions and for rotation. However, a careful review shows that the Code only requires that a sufficient number of modes be included to obtain at least 90% of the mass “in each of the orthogonal horizontal directions of response….” The Code does not have any requirement on the percent of mass that must be obtained for the rotational component.
Does this 90 percent mass include “missing mass” correction for ASCE 7-10?
STAAD has implemented a method for accounting for “missing mass” in the dynamic analysis, RAM Structural System has not. It is fairly rare that the requirement of 90% of the mass isn’t met with a reasonably small number of modes, and even rarer that it can’t be met using a large number of modes. See this wiki for more information on that topic: “Missing Mass” in Dynamic Analysis
When P-delta effects are considered in RAM for RSA, is P-delta analysis being used for Eigenvalue Analysis?
Yes. The P-delta method used by RAM Structural System is called the Geometric Stiffness method, and can be applied for use in a static analysis, a response spectra analysis, and an eigenvalue analysis. This is the proper approach, since the structural effects of P-delta should be considered in each of these analyses. This is one of the advantages over the iterative P-delta approach, which can only be used in a static analysis.
Do internal member axial loads influence the eigenvalue of the member?
Yes, the softening effects of the axial loads on the member stiffness is accounted for in the analysis.
There are differences in the results obtained while using the CQC method and the SRSS method. Please explain.
Despite the fact that the Response Spectra Analysis method is very calculation-intensive, it is only an approximate method. After the modal responses have been determined they must somehow be combined to produce design forces, displacements, reactions, etc. A few methods for combining these nodal results have been proposed and used, but they are not exact. The most simple approach would be to sum up the modal responses to get the design response, but this is generally considered inaccurate: it may be inconsistent in the way it handles modal response values of opposite signs and because it doesn’t consider that some modes contribute more than others. The SRSS method (Square Root of the Sum of the Squares) is an improvement and is adequate for simple structures, but still doesn’t consider that some modes contribute more than others. The CQC method (Complete Quadratic Combination) is more sophisticated in that it attempts to weight the responses of modes that are more dominant. There are even other more sophisticated methods, but CQC is most commonly used. With the speed of modern computers there is no advantage to using the SRSS method; I recommend that the CQC method always be used.
In which cases do we have to use CQC and SRSS method specifically?
You always have a choice, but CQC is a more accurate method and is recommended.
How do you introduce sign for response spectrum results?
Because the methods of combining the modal results result in the loss of the sign on the final values (they are always positive), a method of recovering those signs is desirable. Usually in a building the response is dominated by the first mode, and the signs on the results for that mode can be used to provide the signs for the combined model results. This isn’t always true, but is very often the case. In the RAM Structural System there is an option in the Criteria – General command that you can select, Consider Sign for Analysis Results. When this option is selected the program bases the signs on those of the results for the primary mode. This is generally reasonable, especially for building structures, but care should be given in using this option if one of the other modes plays a significant role such that it could cause the correct sign to be opposite. Most software has a similar capability, with the same limitations; you have to use engineering judgment.
What if moment signs are different for different modes in the same direction? Does the directional response spectrum analysis CQC method only include the modes that generate the same sign for consideration in CQC?
No, the CQC (and SRSS) method considers the contribution of all modes. Remember, each mode acts independently of each other, not in the same phase. So sometimes modes are acting in the same direction but at other times they are acting in opposite directions. The purpose of the CQC method is to capture the combined contributions in a reasonable manner.
What do the Torsional modes represent?
They are the rotational modes around the vertical axis.
Is there a choice of doing lumped mass or consistent mass?
No, the RAM Structural System only does the lumped mass approach. Analysis time is much faster and the results are nearly identical.
If the calculated period of the structure based on Eq 12.8-7 is smaller than the calculated period with the software, which one is to be used in determining Base shear?
When determining the member design forces, the base shear from the Equivalent Lateral Force method should be calculated with the period limited to the smaller of the calculated building period and that given by Eq 12.8-7. When determining the story drifts, the limit on the period given by Eq. 12.8-7 does not need to be applied. RAM Frame provides load cases and reports based on both sets of values.
Does the same approach apply to shear walls?
Yes, the requirements for implementing the response spectra analysis are the same whether the lateral system is moment frames, braced frames, shear walls, or combinations of those.
Does RAM Frame take into account the vertical component of the seismic action?
As defined in Section 184.108.40.206, the vertical seismic load effect is handled in the load combinations, by adding the term Ev = 0.2SDSD. This is appropriate whether the horizontal seismic forces were obtained using the Equivalent Lateral Force procedure or the Response Spectrum analysis.
In the Eurocode there is consideration of a vertical response spectra; RAM Frame does not incorporate this capability.
What Base Fixity would you use or is suitable for Response Spectrum Analysis? Fixed, Partially Fixed, Springs?
The same as for performing a static analysis. The response spectra analysis can appropriately handle any of those, so use what best describes the actual conditions, just as you would do for a static analysis.
If we have a column supported directly on the floor slab, do we need to consider Overstrength Factor (omega), as is required for the static method or is it enough to take the forces of the response spectra analysis as it is?
The response spectra analysis results should be treated the same as any other seismic load case results. The Overstrength Factor should be applied when required. In Section 220.127.116.11 there is an Exception indicating certain analysis methods that are exempt from the requirements of the Overstrength Factor; however, response spectra analysis is not one of those methods.
How do you incorporate the AISC 360 Direct Analysis Method procedure with response spectrum? Using a reduced nominal stiffness is going to give longer periods and lower base shears.
The Direct Analysis Method of AISC 360 requires that in the determination of member forces used in the design of steel frames you use a reduced stiffness of 0.8 applied to all stiffnesses that contribute to the stability of the structure, with an additional factor tb applied to the flexural stiffnesses of all members whose flexural stiffness contributes to the stability of the structure. The purpose of this requirement is to account for member out-of-straightness and residual stresses. This is a requirement even for the response spectra analysis. Unfortunately these stiffness reductions impact the periods that are calculated for the response spectra analysis (the calculated periods are longer when the reduced stiffnesses are used in the analysis), resulting in base shears potentially smaller than they should be. This is usually not a problem, however, because usually these lower values still need to be factored up to 85% of the base shear calculated using the Equivalent Lateral Force method (it is important that the base shear be taken from an Equivalent Lateral Force analysis that was performed using fundamental periods that were determined using the unreduced stiffnesses). So whether the response spectra results are based on reduced stiffnesses or not, they will get factored up to the same level. Then with the member forces determined from this base shear, the members will have larger design forces because of the use of the reduced stiffnesses (which is the purpose of using reduced stiffnesses). In the rare case where the base shear does not need to be factored up you will need to use engineering judgment on factoring the results for member design.
Please clarify what you said about P-Delta analysis being incompatible with Response Spectrum analysis.
A commonly used method for accounting for P-Delta effects is the iterative analysis approach. However, Response Spectrum analysis is not an iterative analysis. So the two are incompatible; I am not aware of any way of performing an iterative P-Delta while also performing the Response Spectra analysis. As a result, when programs use the iterative P-Delta method they can’t do any P-Delta analysis with the response spectra analysis (the P-Delta analysis is turned off), so the response spectra analysis results do not include any P-Delta effects. But Section 12.9.6 requires that they be included, and refers to Section 12.8.6. So if the analysis does not include P-Delta explicitly you must multiply all member forces and displacements by 1/(1-theta).
RAM Frame uses a different methodology for calculating P-Delta effects, the Geometric Stiffness method. This method is not iterative, and so can be used with a response spectrum analysis. As a result, P-Delta effects are include with the response spectrum analysis, and it is not necessary to multiply the results by 1/(1-theta).
The above discussion is in reference to the so-called “P-large delta”. The “P-small delta” effects also need to be accounted for. Again this is often done as part of the iterative analysis, but since that is incompatible with the response spectrum analysis it must be accounted for some other way. One way that this can be done is by applying a modifier to the moments such as the B1 factor of AISC 360-10 Appendix 8. RAM Frame does this.
How are the stability coefficients checked when using Modal Response Spectrum Analysis?
This has reference to Section 12.8.7. Once the scale factors have been appropriately specified, I would use the results from the Response Spectra analysis the same as I would for any other seismic load case. D is the story drift and Vx is the story shear from the Response Spectrum analysis, and Px, Ie, hsx and Cd are independent of the type of analysis used. Because the stability coefficient is a function of D/Vx I would not expect there to be much difference between the coefficient using the Equivalent Lateral Force procedure values and that using the Response Spectrum analysis values unless the vertical distribution of story shears is very different between the two methods.
If the building is in Seismic Design Category A, B or C, should the Equivalent Lateral Force procedure and the Response Spectrum analysis both be performed?
No, it is not necessary to perform a Response Spectrum analysis for structures in Category A, B or C. Section 11.7 indicates that structures in Category A only needs to conform to Section 1.4, and Table 12.6-1 indicates that the Equivalent Lateral Force procedure is always permitted for structures in Category B and C.
What is the difference between time history and response spectrum analysis?
A time history analysis provides the load conditions at each time step, and the results are member forces and displacements at each time step. The response spectra analysis method is a numerically intensive but approximate method that calculates the responses for each mode and then combines those modal results to produce a set of results representing the worst condition.
Which would be better - response spectra or time history analysis for getting base shear distribution?
Response Spectra is much more practical, and much more widely used than time history analysis. It is also faster. Time history analysis generally requires that several design earthquakes be analyzed, and the results from these multiple runs be somehow extrapolated, combined or interpreted before they can be used for design. Then the structure must be designed at each time step to determine which time step gives the heaviest design. Unless there is some compelling reason to use the time history method, the response spectra method is recommended.
When should the Seismic Response History (time history) procedure be used?
It can be used any time, but it is never exclusively required. Table 12.6-1 lists the conditions under which the Equivalent Lateral Force procedure is acceptable (which is the case for most structures), and indicates that for those structures not conforming to those conditions either a Modal Response Spectrum Analysis or a Seismic Response History Procedure must be performed; the engineer may choose between either method.
How are tension-only members modeled for response spectrum analysis?
This is a difficult question, and I don’t know of any method that works complete correctly. Tension-only analysis requires an iterative analysis (it is a nonlinear analysis), but Response Spectra analysis is a linear analysis. There are a few possibilities: If you know which braces will be in compression for the analysis in a given axis, don’t include them in the model. This isn’t exactly correct because in some modes a brace may be in tension while in other modes the brace may be in compression. However, if the brace would be in compression in the fundamental mode it is probably reasonable to remove it from the model.
Another approach is to assign one-half of the actual area to each tension-only brace. Then in the eigen analysis the correct periods and mode shapes will be obtained because the correct overall stiffness would be correct. However, the axial force in each brace will be one-half of what it should be, and half the braces will be in tension and half in compression. For those braces in tension, design the brace for twice the tension force (since in the model both tension and compression braces were included in the analysis but only half of them can actually resist the seismic forces in a given direction). For those braces in compression, recognize that if the earthquake acts in the opposite direction those brace forces will be tension forces, and design for twice that tension force. This assumes that there are an equal number of braces each way such as in an X-braced configuration. Note that in this analysis the design forces in the columns and beams are not necessarily correct because the pairs of tension and compression braces distributes the forces to the framing members differently than would only the tension braces.
How do you use the dynamic forces for foundation design? Will the sign considered be sufficient to perform the analysis of foundation correctly?
When a response spectra analysis is performed the signs on the results are lost (because the SRSS and CQC methods always produce positive result values). Foundation designs based on these positive values may result in incorrect designs for spread footings, and most certainly for continuous footings. If the option to Consider Sign is selected (as described elsewhere in this wiki), the results should then be suitable for footing design. It should be easy to see if the option to Consider Sign is applying the wrong sign, it will be obvious if you look at the footing loads and see load acting in a direction not expected.
Is response spectrum analysis suitable for oil and gas structures too?
Yes, it is.
How can I apply RSA to bridges? Which tool will you recommend?
For advanced analysis of bridges, Bentley offers an excellent program called RM Bridge. See this website for more information: Bridge Design, Analysis and Construction Software.
Can an optimization be done for steel take off?
For gravity members the program optimizes sizes. However, for frame members the user must assign the sizes to be used; the program does not perform an optimization on frame member sizes. In either case, a Takeoff report is available listing sizes, quantities and weight.
What code is used for response spectrum analysis? What are the requirements for the Eurocodes?
The basic methodology of performing a response spectrum analysis is the same regardless of the building code. However, the various building codes each have their own requirements regarding the definition of the response spectra curve, when the response spectra analysis method is required, and how to modify and use the results. In the webinar I focused on the specific requirements of ASCE 7-10, but the general approach would be very similar for other codes as well.
There are many similarities between ASCE 7 and EN 1998, the Eurocode requirements for the design of structures for earthquake resistance. Several of the more significant requirements of that document are referenced here:
The design response spectrum has nearly the identical shape, the parameters that define each segment are slightly different. See EN 1998-1:2004 Clause 18.104.22.168.
Table 4.1 lists the conditions for which modal response spectra analysis is required. If the structure is not Regular in elevation, the method is required. See Clause 22.214.171.124. Also see Clause 126.96.36.199.1 which indicates when the Lateral Force method of analysis can be used (otherwise, modal response spectra analysis or a nonlinear analysis is required).
Inclusion of an eccentricity of the masses is required in Clause 4.3.2 (5%, same as ASCE 7) and Clause 188.8.131.52.3.
Clause 184.108.40.206 gives the requirements for performing the Modal Response Spectrum Analysis.
Clause 220.127.116.11.1(3) requires that the effective modal mass includes at least 90% of the total mass.
Clause 18.104.22.168.2 indicates when SRSS (square root of sum of squares) method may be used, and when CQC (complete quadratic combination) must be used.
In the webinar there is considerable discussion regarding the calculation of the scale factor, but EN 1998 takes a different approach with a material-dependent behaviour factor, q, in the response spectra equations rather than scaling the results of the analysis.
Clause 22.214.171.124 specifies the use of a reduction factor v (referred to as a Scale Factor in the webinar) for scaling the drifts.
Please advise the procedure to follow for AS 1170.4 (Australian EQ code).
Dynamic analysis is covered in Section 7 of AS 1170.4. The response spectra curve is defined in Section 7.2(a) – this curve can be generated in RAM Structural System. Section 7.4.2 requires that 90% of the mass be participating. Section 7.4.3 requires that the modal results be combined “by a recognized method”, of which CQC is one. Section 126.96.36.199 requires that the effects of accident torsion be accounted for, which the RAM Structural System can do by adjusting the mass locations. Furthermore, Section 188.8.131.52 indicates that the design values must include the P-delta effects. I can find no mention of further scaling the results to match the equivalent lateral load analysis. The RAM Structural System is well-suited for performing the analysis and design required by the Australian standards.
Are the National Building Code of Canada 2010 requirements implemented in RAM Frame?
Not all of those requirements are explicitly implemented but can easily be accommodated similar to what was shown in the webinar for ASCE 7. The approach is very similar. The requirements for the Dynamic Analysis Procedure are listed in NBCC Article 184.108.40.206.
Article 220.127.116.11(7) gives the parameters that define the response spectra curve. This curve is available in RAM Frame.
Article 18.104.22.168(7) defines the initial scale factor as IE/(RdRo).
Article 22.214.171.124(8) indicates that except as required in Article 126.96.36.199(9), if the resulting base shear is less than 80% of that obtained from the Equivalent Static Force Procedure, the base shear must be scaled up to be at least 80% of that value.
Article 188.8.131.52(9) indicates that if the structure is irregular (see Article 184.108.40.206), if the resulting base shear is less than 100% of that obtained from the Equivalent Static Force Procedure, the base shear must be scaled up to be at least 100% of that value.
Article 220.127.116.11(6) lists an additional factor that may need to be applied.
Article 18.104.22.168(4) requires the consideration of the accidental torsional moments, for which the masses are to be offset by either 5% or 10%.
Article 22.214.171.124(11) allows the use of the actual structural period (not limited to Ta) in the determination of the Equivalent Static Force Procedure base shear used to determine the scaling of deflections
In the Philippines, our local code is patterned after UBC 97. Is there a dialog in RAM Frame for the UBC 97 code?
Yes, UBC 97 is one of the options.
STAAD Questions and Answers
There were several questions specific to STAAD that would require responses longer than could be accommodated here. Information on STAAD is available elsewhere on Bentley Communities. See this wiki for information on the implementation of the response spectra method in STAAD: STAAD Response Spectrum Questions. If answers to your question are not already there, post the question there and a STAAD expert will respond.
Recordings of past STAAD webinars is available here: http://pages.info.bentley.com/videos/
Information on STAAD training courses is available here: https://www.bentley.com/en/learn/for-users/training-programs
Does STAAD have similar capabilities? Is the method for performing response spectra analysis in STAAD similar to this RAM example? Which one is more accurate for RSA?
STAAD also has the ability to perform a response spectra analysis. The generally methodology that I explained in the webinar is essentially the same for any program, including STAAD. Of course the menu structures and report formatting will vary between programs, but the process and workflow would be very similar. I expect that both programs give virtually the same results.
What is the difference between STAAD and RAM if both can do the same?
Both programs have their strengths, so it depends on what is being analyzed and designed. The RAM Structural System is specifically for building structures. This allows for faster modeling and more specialized analysis, design, and reporting. Generally the RAM Structural System is preferred for buildings. STAAD has a wider selection of building codes, some of which aren’t available in the RAM Structural System. It is also general purpose, suitable for any structure, building, plant, tank or frame of virtually any configuration. With the Structural Enterprise License, a bundled license of STAAD and the RAM line of products, you can have both:
Can we import STAAD results in RAM?
Analysis results cannot be imported, but using the ISM/Structural Synchronizer capability, models can be shared between the two programs. See this wiki for more information: Integrated Structural Model (ISM).