Response Spectrum

The Response Spectrum analysis tool is part of the seismic module add-in and is used to determine the design forces on a structural due to seismic loading. This part of the seismic module allows building to be analysed using a Response Spectrum analysis. The seismic module also includes an analysis of building structures using the Lateral Force method. Since the Lateral Force method is based on equivalent static forces, it does not depend upon a mode shape analysis, so it is used through MasterFrame directly rather than through the dynamic analysis. The Response Spectrum analysis uses a code defined elastic response spectrum to model the effective peak ground accelerations.

The Response Spectrum analysis can be carried out in accordance with Eurocode 8, the International Building Code IBC 2012, the Uniform Building Code UBC 1997, or alternatively for a user defined response spectrum. In each case the response spectra relate to horizontal ground movements only; no vertical ground accelerations are included. The method employed in the software is suitable for use where vertical ground accelerations are less than 2.5 m/s². Vertical acceleration is not likely to exceed this value where the horizontal accelerations are less that 2.7 m/s². The IStructE guide "Manual for the seismic design of steel and concrete buildings to Eurocode 8" notes that in most cases, vertical accelerations may be considered to be adequately accounted for in the partial factors on gravity loads. However, vertical accelerations to seismic events must be covered in the following cases:

Horizontal or nearly horizontal members with spans of 20m or greater

Horizontal or nearly horizontal cantilever components of span 5m or more

Prestressed components of any length or orientation

Transfer beams supporting columns

Base isolated structures

The software is not suitable for use with ground conditions not covered by those given in Eurocode EC8. It is also not suitable for use with structures which require analysis by either a analysis  by 'push-over' non-linear methods, or requiring a full non-linear time-history analysis.

On first entering the Response Spectrum Analysis tab, the initial screen layout is as show below.

To add a seismic Response Spectrum Load Case, click on the  icon. Multiple seismic load cases can be created, to allow for the analysis with different parameters. Each of the seismic load cases can then be added to the Masterframe analysis. Each load case is named automatically.

Force axes input

The response spectrum analysis requires the model to be analysed under forces acting in two perpendicular horizontal directions. These should align with the principal horizontal axes of the structure to be analysed. The theta input allows for the rotation of the force axes to be rotated to align with the structural axes of the structure.

Note: if the structure to be analysed does not have two clearly defined primary horizontal axes, the Response Spectrum Analysis method may not be appropriate. Further reference should be made to the relevant design code.

Modal Combination Method

The response of the structure to the applied seismic loading is composed of contributions from al the modes shapes. However, since the modal maxima do not necessarily occur concurrently, the results are combined using a statistical method.  The software presents two methods to achieve this, the square root sum of the squares and the complete quadratic combination. The square root sum of the squares method is satisfactory unless there are modes used in the analysis whose periods have less than a 10% difference, in which case the CQC method should be used.

The Response Spectrum Analysis is based on a multi-modal analysis. This type of analysis is the standard method used in EC8 and caters for both regular and irregular structures. However, where a structure has a high level of irregularity, either in plan or elevation, a non-linear analysis, which is beyond the scope of the software, may be required. Reference should be made to the relevant code for guidance on the applicability of the modal analysis method.

Design Code

The Design code is selected using the drop down menu. The three included seismic codes are EC8, IBC 2012 and UBC 1997. It is also possible to input a user defined Spectrum. Depending on the code selected the inputs below the code drop down will change to reflect the inputs required in that code.

Eurocode 8

When Eurocode 8 is selected, the input area is as shown below.

The required inputs to the Eurocode design are as follows:

ERS Type - The Elastic Response Spectrum Type based. For UK sites, Type 2 is recommended, but reference should be made to published document PD 6698.

Ground Type - Ground Type A-E as defined in Table NA1 of the UK National Annex to BS EN 1998-1-1.

Importance - the Importance Class for building classification

Design Spectrum - this option modifies the Elastic Response Spectrum to give the horizontal design spectra, for use with the behaviour modification factor q.

q - the behaviour factor. This is a structure dependent parameter, based on the structure ductility, used to reduce the seismic design forces.

Damping - the viscous damping ratio of the structure, expressed as a percentage.

agr - the reference peak ground acceleration on rock. This parameter is modified to given the design ground acceleration ag.

IBC 2012

With the IBC selected, the screen layout as is shown below.

For details of the required inputs, refer to the International Building Code 2012.

UBC 1997

With the UBC selected, the screen layout is as shown below.

For further information on the required inputs, refer to the Universal Building Code 1997.

User Defined Spectrum

The user defined spectrum allows the user to input a design response spectrum. The screen layout is shown below.

Note: The graphs of the design spectra for each design code incorporate the ground accelerations ag in the calculation of the vertical axis.

Analysis

Once the required design code has been selected, the analysis is run by clicking on the

Results

The Response Spectrum analysis is based on a multi-modal analysis where the effects of the seismic actions are calculated mode by mode and then combined to give the analysis results. The nodal displacement and rotations of this multi-modal analysis as displayed in the right hand pane. The bottom pane gives additional information relating to the results, where the results show the total mass in the model and the total mass mobilised in the analysis, along with the resultant forces in the x- and z-axes. In addition the results indicate the angel the largest resultant forces makes with the x-axis. The resultant forces are also displayed graphically. The seismic analysis includes forces applied to the model in perpendicular axes, and the results can be displayed for these perpendicular u- and v- axes.

Since the analysis is based on perpendicular forces applied in the primary axes directions of the structure, the u- and v-axis forces should be perpendicular. If these forces are not perpendicular, this may indicate that the structure is not suitable for analysis using the Response Factor method and may need to be analysed using a more advanced time-history analysis, which is outside the scope of the software.

Attaching seismic analysis results to a Static Load case in Masterframe

Once the required Response Spectrum analyses have been completed, the resulting system of equivalent nodal forces required to produce the nodal deflections and member end forces that result from the seismic analysis can be added into a MasterFrame static analysis. This is done within MasterFrame.

To apply a set of equivalent static seismic forces to a load case within MasterFrame, go to Loads>Dynamic and Seismic Loads>Seismic Loads. This will open the Dynamic and Seismic Loads pane on the right hand side of the screen. To add a set of Seismic forces to a load case, select the required loadcase from the drop down menu. To then add the seismic loads, check the "Apply Seismic Loading" checkbox. The radio buttons for the become active. For a response spectrum analysis, select the "Dynamic response spectrum" radio button. The Dynamic Response Spectrum Method will now be shown in the right hand pane. The screen layout is shown below.

To select the Response Spectrum load case, use the Load Case drop down.

The load factor to apply to the u- and v-components of the equivalent lateral forces derived from the design response spectrum are input in the Component Factors inputs. Where buildings are regular in plan and bracing elements for each lateral direction are independent, the Eurocode permits seismic actions in each direction to be considered to act independently and so the analysis may consider the u- and v-components separately. Where the Code rules on regularity and/or bracing independence do not apply, the seismic loads in each axis should be combined. For further information on combining the load components, reference should be made to the Code or another relevant reference.

For guidance on combining seismic loads with permanent and variable loads, refer to the relevant section of the Code or other published guidance material.

Once seismic loads have been added to a Masterframe load case, when the analysis is selected, the Analysis Type and License window will indicate that the seismic loads have been added to the relevant loadcases. A typical example is shown below, with seismic loads added to loadcase 1.