In June 2015, Bentley hosted a Bentley Success Factors webinar titled A Practical Approach to Using the Response Spectra Analysis Method. A recording of that webinar can be found at: http://pages.info.bentley.com/video-details/
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, with more thorough answers.
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 12.8.4.3 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 12.8.4.2 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 12.8.4.3 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 12.8.4.3 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.
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.
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.
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.
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 12.4.2.2, 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.
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 12.4.3.1 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.
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.
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.
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.
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 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 3.2.2.5.
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 4.2.3.3. Also see Clause 4.3.3.2.1 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 4.3.3.3.3.
Clause 4.3.3.3 gives the requirements for performing the Modal Response Spectrum Analysis.
Clause 4.3.3.3.1(3) requires that the effective modal mass includes at least 90% of the total mass.
Clause 4.3.3.3.2 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 4.4.3.2 specifies the use of a reduction factor v (referred to as a Scale Factor in the webinar) for scaling the drifts.
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 4.1.8.12.
Article 4.1.8.4(7) gives the parameters that define the response spectra curve. This curve is available in RAM Frame.
Article 4.1.8.12(7) defines the initial scale factor as IE/(RdRo).
Article 4.1.8.12(8) indicates that except as required in Article 4.1.8.12(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 4.1.8.12(9) indicates that if the structure is irregular (see Article 4.1.8.7), 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 4.1.8.12(6) lists an additional factor that may need to be applied.
Article 4.1.8.12(4) requires the consideration of the accidental torsional moments, for which the masses are to be offset by either 5% or 10%.
Article 4.1.8.12(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