Introduction to seismic analysis and design

Tekla Structural Designer
2021
Tekla Structural Designer

Introduction to seismic analysis and design

Definitions

The actual method applied to a specific beam will depend upon whether it is required to support sensitive finishes.

Various terms used in Tekla Structural Designer's seismic processes are described below:

Code Spectra

The spectra specified in a country's loading and design codes for use in ELF and RSA analysis.

Site Specific Spectra

User defined spectra for ELF and RSA which are required for locations which use another country's loading and design codes where the code spectra are not relevant.

Base Shear Combination

Also referred to as the Effective Seismic Weight Combination (ASCE 7/UBC) or the Seismic Inertia Combination (Eurocode). This combination is used for modal analysis, and in the calculation of base shears, during the Seismic Analysis Process. This combination is created and modified by the Seismic Wizard only.

RSA Seismic Combinations

These combinations are created by the Combination Generator at the end of the Seismic Wizard, but can also be modified in the standard Combination dialog. They consist of 3 kinds of loadcases: Static, RSA Seismic and RSA Torsion. The Base Shear Combination is not included in this category of combination.

Static Loadcase

Standard loadcases, e.g. "Self weight - excluding slabs", "Dead", etc., and derived cases for NHF/EHF, but no patterns.

RSA Seismic Loadcase

Two loadcases, i.e. "Seismic Dir1" and "Seismic Dir2", which cannot be edited. These are created at the end of the Seismic Wizard. being derived from information supplied in the Seismic Wizard and the results of the modal analysis. No actual loads are available for graphical display.

RSA Torsion Loadcase

These cases can be generated by the Seismic Wizard and are regenerated whenever RSA Seismic Combinations are modified.

Fundamental Period (T)

Separately for Dir 1 & Dir 2, this is either defined in the Seismic Wizard, (user value or calculated), or determined in the modal analysis for the Base Shear Combination.

Level Seismic Weight

For each relevant level, this is the sum of the vertical forces in nodes on that level, for the Base Shear Combination.

Effective Seismic Weight

This is the sum of the level seismic weights for all relevant levels for the Base Shear Combination.

Seismic Base Shear

The base shear is calculated separately for Dir 1 & Dir 2, for the Base Shear Combination.

Note: In Tekla Structural Designer the base shear is displayed when you Review story shear tabular results for Cumulative Story Shear

Square root of Summation of Square (SRSS)

The SRSS formula for combining modes in RSA is as follows:

SRSS_formula.png

λ = Absolute value of combined "response"

λk = "response" value for Relevant Mode k

n = Number of Relevant Modes

Complete Quadratic Combination (CQC)

The CQC formula for combining modes in RSA is as follows:

CQC_formula.png

λ = Absolute value of combined "response"

λi = "response" value for Relevant Mode i

λj = "response" value for Relevant Mode j

n = Number of Relevant Modes

ρij = Cross modal coefficient for i & j

Cross Modal Coefficient

This co-efficient is used in the CQC method for combining modes in RSA.

Cross_modal_coefficient.png

ζ = modal damping ratio

IBC/ASCE assumed = 5% (ASCE Figs 22-1 to 6)

EC8 assumed = 5% where q accounts for the damping in various materials being different to 5% (EC8 Cl 3.2.2.5)

IS codes the user can define the level of damping and this is accounted for in the above equation.

β = Frequency ratio = ωi / ωj

ωi = Frequency for Relevant Mode i

ωj = Frequency for Relevant Mode j

Overview

All seismic codes work in a similar manner from the loading view point with relatively minor differences in terminology and methodology.

It is worth noting at the start that seismic analysis determines a set of forces for which it is expected (statistically) that if those forces are designed for and other design precautions taken (additional seismic design) then in the event of an earthquake the structure may well suffer extensive damage but will not collapse and for some categories of building should actually remain serviceable.

In Tekla Structural Designer a seismic wizard gathers all the information together to setup the requirements for a seismic analysis.

From this information a number of things are determined:

  • If working to ASCE 7 - the seismic design category (SDC) for the building - giving amongst other things the permissible type of analysis
  • The Base Shear Combination to determine the seismic base shear in the building
  • The natural frequencies of the building in two horizontal directions
  • The combination of the gravity and other lateral forces with the seismic loadcases

Earthquakes load a building by a random cyclic acceleration and deceleration of the foundations. These are in both horizontal directions (Dir1 and Dir2) but can also be in a vertical direction too. This ground acceleration excites the building in its natural and higher frequencies.

As a result if the building is:

  • In an area of low seismic acceleration, low in height and poses limited risk to life then a gross approximation can be used in analysis - assuming a % of gravity loading is applied horizontally to the building to represent the earthquake (US codes 1%, Australian codes 10%).
  • In an area of moderate to low seismic acceleration, medium to low in height and does not house a significant number of people - the predominant mode excited is the 1st mode. An equivalent lateral force (ELF) approximation can be used that applies static horizontal loading distributed up the building to mimic the shape of the 1st mode of vibration in a static analysis.
  • Anything else, in an area of high acceleration, tall in height and could be holding many people or be critical post-earthquake then a "more representative" analysis method of Response Spectrum Analysis (RSA) should be used. This analysis is based upon a modal analysis considering all mode shapes in the two horizontal directions in which typically 90% of the structure's mass is mobilized.

The results from the chosen method of seismic analysis are used in combination with other gravity and lateral loadcases to design both normal members and those members in seismic force resisting systems (SFRS). These latter members need additional design and detailing rules to ensure they resist the seismic forces that they subjected to during an earthquake. If working to ASCE 7, the extent of these rules are determined by the SDC noted above (the higher the demand, the ‘better’ the SFRS that will be required).

Note: The additional design and detailing requirements of “seismic” design are only supported in Tekla Structural Designer for the ACI/AISC and the Indian Head Codes.

Seismic Wizard

In Tekla Structural Designer the Seismic Wizard sets up the information required for either ELF or RSA seismic analysis - the main input parameters being:

  • Ground acceleration - strength of the earthquake
  • The Importance Level (or Importance Class) of the building - the use to which the building is being put - typically
    • I= very minor, farm and temporary buildings,
    • II= general buildings occupied by people,
    • III = buildings occupied by a large number of people
    • IV = critical buildings with a post-disaster function eg hospitals, police stations, fire stations and buildings along access route to them)
  • The ground conditions upon which the building is founded (typically Hard Rock, Rock, Shallow soil, Deep Soil, Very Soft Soil)
  • Building height - for low buildings the first mode is totally dominant in taller buildings other modes become significant
  • Plan and vertical irregularities in the building

From this input the Seismic Wizard determines the seismic design category for ASCE 7, and also the elastic design response spectrum to be used for the building.

Additionally the Wizard sets up the Base Shear Combination - the combination of loads likely to be acting on the building when the earthquake strikes.

Vertical and Horizontal Irregularities

There are typically 5 types of horizontal irregularity and 5 types of vertical irregularity - all are defined to pick up structures that have lateral framing systems and shapes in plan that will preclude the structure naturally developing a simple first mode of vibration. Since this is a basic assumption of ELF - the presence of these irregularities may preclude the use of ELF.

Vertical Loads

Note: There is no explicit analysis or consideration of a vertical spectrum in either the ELF or RSA analysis methods in Tekla Structural Designer.

The treatment of seismic vertical load effects in Tekla Structural Designer is code dependent:

ASCE 7

Vertical seismic load effect

The vertical seismic load effect, Ev is defined in ASCE 7-22 clause 12.4.2 as follows:
  

E = Eh + Ev

or

E = Eh - Ev

where

E = seismic load effect

Eh = horizontal seismic load effect

Ev = vertical seismic load effect

Ev is determined from clause 12.4.2.2 as:

Ev = 0.2 x SDS x D

where

SDS = design spectral response acceleration parameter at short periods

D = effect of dead load

In Tekla Structural Designer, when it is to be applied, Ev is calculated when the seismic combinations are generated. The calculation is the same irrespective of the ASCE 7 code year being worked to. Whether it is applied or not depends on on the Seismic Design Category:
  • For structures assigned to Seismic Design Category A, Ev is not applied.
  • For structures assigned to Seismic Design Category B an 'Include vertical seismic load effect' checkbox is provided on the Basic Information page of the seismic wizard. By unselecting the checkbox Ev will taken as zero.
  • For structures assigned to Seismic Design Categories C, D, E or F; Ev is automatically applied.
When Ev is applied, it is accounted for by an adjustment to the dead load factors in the seismic combinations. This adjustment is illustrated in the following examples.
Example 1 - adjustment of dead load factors in the ASD seismic combination 1.0D + 0.7v + 0.7h when SDS = 26.67 % g
Original combination including vertical seismic load effect 1.0D + 0.7Ev + 0.7Eh

Substituting for Ev

1.0D + 0.7(0.2 x SDS x D) + 0.7Eh

Which can be rearranged to

(1.0 + 0.7(0.2 x SDS))D + 0.7Eh

Substituting for SDS = 0.2667

(1.0 + 0.7(0.2 x 0.2667))D + 0.7Eh

Which simplifies to

1.037D + 0.7Eh

Hence the adjusted factors displayed for this combination in Tekla Structural Designer:

Example 2 - adjustment of dead load factors in the ASD seismic combination 0.6D - 0.7v + 0.7h when SDS = 26.67 % g
Original combination including vertical seismic load effect

0.6D - 0.7v + 0.7Eh

Substituting for Ev

0.6D - 0.7(0.2 x SDS x D) + 0.7Eh

Which can be rearranged to

(0.6 - 0.7(0.2 x SDS))D + 0.7Eh

Substituting for SDS = 0.2667

(0.6 - 0.7(0.2 x 0.2667))D + 0.7Eh

Which simplifies to

0.563D + 0.7Eh

Hence the adjusted factors displayed for this combination in Tekla Structural Designer:

Vertical spectra

The commentary to ASCE 7-22 states:

  

For most structures, the effect of vertical ground motions is not analyzed explicitly; it is implicitly included by adjusting the load factors (up and down) for permanent dead loads, as specified in Section 12.4. Certain conditions requiring more detailed analysis of vertical response are defined in Chapters 13 and 15 for nonstructural components and nonbuilding structures, respectively.

Consequently, there is no explicit analysis or consideration of a vertical spectrum in either the ELF or RSA analysis methods in Tekla Structural Designer.

Horizontal cantilevers

Horizontal cantilevers have broadly similar requirements in each of the ASCE 7 versions. For ASCE 7-22 the requirement is stated in clause 12.4.4 as follows:
  

12.4.4 Minimum Upward Force for Horizontal Cantilevers for Seismic Design Categories D through F

For a structure assigned to Seismic Design Category D, E, or F, horizontal cantilever structural members shall be designed for a supplemental basic load combination consisting of a minimum net upward force of 0.2 times the dead load for strength design, or 0.14 times the dead load for allowable stress design.

Tekla Structural Designer does not do this automatically and so it is up to the user to deal with it with separate combinations.

UBC

Vertical seismic load effect

The method of application for UBC is the same as that for ASCE 7 - the calculated vertical seismic load effect being automatically applied to either amplify, or in combinations where the dead load is being considered as beneficial, to reduce the dead load strength factors in the seismic combinations. The only difference being that for UBC the vertical seismic load effect factor is calculated as follows:

  • 0.5 x Ca x I x Dead loads for strength design

  • 0.0 for allowable stress design

EC8

Vertical component of seismic action

The vertical component of the seismic action is considered in clause 4.3.3.5.2 which states:
  

(l) If avg is greater than 0.25 g (2.5 m/s2) the vertical component of the seismic action, as defined in 3.2.2.3, should be taken into account in the cases listed below:

  • for horizontal or nearly horizontal structural members spanning 20m or more;

  • for horizontal or nearly horizontal cantilever components longer than 5m;

  • for horizontal or nearly horizontal pre-stressed components;

  • for beams supporting columns;

  • in base-isolated structures.

The above cases are not dealt with explicitly in Tekla Structural Designer.

IS1893 (Part 1)

Design vertical earthquake effects

Design vertical earthquake effects are considered in IS1893 (Part 1) : 2016 section 6.3.3.

In amendment no.2 November 2020, clause 6.3.3.1 b) states:
  

Effects due to vertical earthquake shaking shall be considered for the safety of buildings, embankments, bridges and dams or their components, including in the following cases:

a) structure located in Seismic Zone IV or V,

b) structure has vertical or plan irregularities,

c) structure is rested on soft soil,

d) structures with long spans, which cause amplification of oscillations due to their flexibility,

e) structure has large overhangs of structural members or sub-systems,

f) prestressed structures, and

g) structures with prestressed members.

When both horizontal and vertical seismic forces are to be taken into account, section 6.3.4 then goes on to describe how earthquake load components may be combined to account for three directional earthquake ground shaking.

Clause 6.3.4.1 states:
  

When responses from the three earthquake components are to be considered, the responses due to each component may be combined using the assumption that when the maximum response from one component occurs, the responses from the other two components are 30 percent each of their maximum. All possible combinations of three components (ELX, ELY and ELZ) including variations in sign (plus or minus) shall be considered. Thus, the structure should be designed for the following sets of combinations of earthquake load effects:

1. +/- ELX +/- 0.3 ELY +/- 0.3 ELZ

2. +/- ELY +/- 0.3 ELZ +/- 0.3 ELX and

3. +/- ELZ +/- 0.3 ELX +/- 0.3 ELY

where X and Y are orthogonal plan directions and Z vertical direction.

Currently neither section 6.3.3 or 6.3.4 are automatically catered for in Tekla Structural Designer, the user would therefore have to consider these manually if required.

Vertical spectra

Clause 6.4.6 states:

  

The design seismic acceleration spectral value Av shall be taken as: (2/3 x Z/2) x 2.5 / (R / I) for buildings

The above clause is not currently considered in Tekla Structural Designer.

Torsion

When a structure's center of mass at a level does not align with the position of the center of rigidity then torsion is introduced in the structure at that level when an earthquake excites the structure. To account for this, there are three types of torsion potentially applied to levels with rigid or semi-rigid diaphragms during a seismic analysis:

  • Inherent torsion - in a 3D analysis when the center of mass and center of rigidity at a level do not align, this is taken account of automatically
  • Accidental torsion - to allow for the uncertainty in position of loads in a structure, an additional eccentricity of usually 5% of the structure's width in all relevant directions - this is accounted for with a torsion loadcase in the analysis
  • Amplified accidental torsion - structures with certain SDCs and certain horizontal irregularities require an amplified accidental torsion to allow for extra effects. For this to be calculated the following conditions must all apply:
    • Seismic Code is ASCE 7
    • SDC is C, D, E or F
    • Either Plan irregularities 1a or 1b apply

    Assuming the above conditions all exist, calculations are performed to determine if amplified accidental torsion is required. As part of these calculations the following are determined at each relevant level from the deflections of the seismic lateral and torsion loadcases (in each permutation of positive and negative directions):

    • δmax = maximum horizontal displacement for all column/wall nodes on that level
    • δmin = minimum horizontal displacement for all column/wall nodes on that level*
    • δavg = (δmax + δmin)/2
    • Ax = min( 3.0, max(Ax, (δmax / (1.2 ×δavg))2 )) where Ax is the value for this level for the torsional loadcase
    Note: * The δmin value currently output in the Seismic Design Report is NOT the minimum value used in the above calculation for δavg. (It is instead the numerical minimum for all permutations, i.e. the largest negative value).

    At the end of these calculations, for each relevant level with Ax > 1.0 the accidental torsion loads on each level are multiplied by Ax only when the ratio dmax / davg > 1.2 or 1.4.

    The analysis results are automatically updated if the accidental torsion loads are amplified.

    When (and only when) the accidental torsion loads have been amplified, this is confirmed by the output of additional tables in the Seismic Design Report which give the displacement and calculated Ax values for each direction and level.

Tip: Torsional irregularity and amplification must always be checked for. A suggested method for this is presented here: Workflow to check for torsional irregularity and amplification

Modal Analysis

Using the Base Shear Combination, a modal analysis is run for two purposes:

  • the natural frequencies of the building in two directions are determined to assist with the calculation of the seismic base shear that in turn is used to determine the distribution of applied loads up the building for an ELF analysis
  • the frequencies and mode shapes of the building are determined that need to be included in an RSA analysis so that typically 90% of the mass in the building is mobilized during the RSA analysis

% of Gravity Load Method

The % of gravity load method is used as a means of a gross approximation of the earthquake and is only used in situations where seismic effects are considered to be low. This loadcase is combined with the relevant load factor with other gravity and lateral loadcases to determine the design forces and moments to be considered in conventional design.

Note: This method is not applicable when working to Eurocodes.

Equivalent Lateral Force Method

The ELF method assumes that the first mode shape is the predominant response of the structure to the earthquake.

Based on the natural frequency and the Base Shear Combination, a total base shear on the structure is determined and this is then set up as a series of forces up the structure at each level (in the shape of an inverted triangle) and these deflect the structure in an approximation to the shape of the first mode.

The resulting seismic loadcases are combined with the correct combination factors with the other gravity and lateral loadcases in the seismic combinations to give the design forces and moments which are used in both the conventional design of all steel and concrete members, and the seismic design of any steel or concrete members that have been identified as part of a seismic force resisting system.

Response Spectrum Analysis Method

The RSA method uses a set of vibration modes that together ensure that the mass participation is typically 90% in the structure in a particular direction.

The response of the structure is the combination of many modes that correspond to the "harmonics". For each mode, a response is read from the design spectrum, based on the modal frequency and the modal mass, and they are then combined to provide an estimate of the total response of the structure.

Combination methods include the following:

  • Square root of Summation of Square (SRSS)
  • Complete Quadratic Combination (CQC) - a method that is an improvement on SRSS for closely spaced modes

As a result of the combination methods (SRSS and CQC), the resulting seismic loadcases are without sign and so they are applied with the correct combination factors both + and - around the "static" results of the other gravity and lateral loadcases in the seismic combinations to give the design forces and moments which are used in both the conventional design of all steel and concrete members, and the seismic design of any steel or concrete members that have been identified as part of a seismic force resisting system.

Response Spectrum Analysis Processes

RSA Seismic Analysis (1st or 2nd order) is run as a stand-alone analysis from the Analyze ribbon tab, or as part of one of the Design (RSA) processes available from the Design ribbon tab. In the latter case the use of 1st order or 2nd order is set for the static analysis is set via Design Settings > Analysis.

The RSA seismic analysis process consists of the following steps:

Step Process Description
1 Model Validation

Run to detect any design issues which might exist.

This is similar to standard model validation but also checks:

  • Base Shear Combination must exist
  • At least one RSA Seismic Combination must exist including at least one RSA Seismic Loadcase.
2 Modal Analysis A 1st order modal analysis for the Seismic Inertia Combination only, which returns the standard results for that analysis type, but also the fundamental periods for directions 1 & 2.
3 Pre-Analysis for Seismic

Performs calculations for RSA Torsion Loadcases.

The seismic weight and seismic torque are both calculated at this stage.

4 Static Analysis 1st Order Linear or 2nd Order Linear analysis is performed for all RSA Seismic Combinations and all their relevant loadcases, i.e. this includes Static Loadcases, but does not include RSA Seismic and RSA Torsion Loadcases.
5 RSA Analysis A set of results is generated for a sub-set of vibration modes for each RSA Seismic Loadcase.
6 Accidental Torsion Analysis Analysis of any RSA Torsion Loadcases that exist.
Note: If running one of the Design (RSA) processes, an extra member design step is added to the end of the above list.

Seismic Drift

Seismic drift is assessed on a floor to floor horizontal deflection basis and there are limits for acceptability of a structure.

When working to the ASCE 7 code, the engineer can directly define the shear demand / capacity ratio (beta) for columns and walls. The default value of 1.0 could be over-conservative. This option is located in the “Seismic” group of member properties, and can be set separately for 'Direction 1' and 'Direction 2' and for each stack/panel, as shown in the picture below.
  • The setting is applicable to all years of the ASCE 7 code and has the following default and limits: Default = 1; Min = 0.001; Max = 10.

The building's overall seismic drift status is displayed in the Design branch of the Status Tree in the Project Workspace.

Full details for all columns are presented in a table accessed from the Review ribbon.

These details can be included in printed output by adding the Analysis>Seismic Drift chapter to your model report.

Design Coefficients and Factors (ASCE 7/UBC)

Typically three factors are determined based on the lateral force resisting systems in the structure and which account approximately for the inelastic response that occurs during the earthquake which is not accounted for directly in the analysis.
  • The response modification coefficient which affects the seismic base shear.

  • The overstrength factor accounts for the reinforcement steel yielding overstrength and is utilized in the concrete beam and column capacity calculations.

  • The deflection amplification factor which is used in the calculation of seismic drift.

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