Earthquake Analyses in Ansys Workbench

ANSYS Tutorial: Earthquake analyses in workbench  Do you want to perform earthquake earthquake analyses according according to design codes codes or just just in order  to verify your structure? The current article describes in great detail two different approaches; the static (response specter) and the transient approach

Introduction: Earthquake analyses can be performed by applying different procedures. The most  popular procedure is the Response Spectrum analysis (RS-analysis). The RS-analysis RS-analysis is cheap to use in terms of numerical costs as it is based on modal results. Hoe!er" the spectrum solution can only sho positi!e results" i.e. positi!e stresses and strains" as it only records the ma#imum amplitudes for each mode and the superposition of these results in turn ill gi!e the positi!e results. $nother procedure is to perform a full transient analysis of the earthquake. Such analyses are computational e#pensi!e. Hoe!er" they ill gi!e results based on the dynamic equation of equilibrium and hence both positi!e (tensile) and negati!e (compressi!e) stress results ill be reported for the full length of the earthquake. %n this tutorial a shell structure ill be used to sho ho such analysis can be run in $&S'S orkbench. orkbench.

igure !: Shell structure used as an example in the earthquake analyses

Response Spectrum Analysis: There are to steps in running a response spectrum analysis in $&S'S. irst e run a modal analysis hich ill gi!e use the modes*eigen!alues of the structure. Secondly e run the Response Spectrum analysis hich does the folloing+ • •

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,alculates the participation factor for each of the structures frequencies ind the ma#imum accelerations from the gi!en Response Specter (for each mode) Scales the modal displacements found in the modal analysis to physical mode shapes based on acceleration" participation factors and circular frequencies. inally superpose these modal results to the final result using i.e. the SRSS method.

Step 1 - Modal analysis+ The odal analysis ill gi!e us the eigenfrequencies o f the structure. e are going to run a response spectrum analysis here the ground acceleration is applied in the y-direction. Hence" e need to make sure that the effecti!e mass in the y-direction is higher than / 0 of the total mass as most codes use this as a requirement for the RS analysis. e check this in solution information and for this case e see that by requesting 12 modes e ill ha!e 1//0 participating mass in the ydirection. oreo!er it is seen that 3 of the modes (mode 1 and 4) are contributing ith 52 0 of the effecti!e mass and consequently is can be e#pected that the earthquake response ill be dominated by these modes. %n the subsequent RS-analysis e ill only use the

first 4 modes as input as these modes participate ith 30 of the effecti!e mass in ydirection.

igure ": Details of the modal analysis can be found in the Solution Information

Step 2: RS analysis+ The RS-analysis uses the modal results obtained abo!e as input for calculation of the earthquake response. To include the response specter data containing the relation beteen structural acceleration and the structures frequencies e insert the tool 6RS $cceleration7 (see Fiure !) and include earthquake data as a table (frequency 8H9: !s. acceleration 8m*s3:). $ graphical presentation of these data can be seen in igure 5 a). urther e decide the direction of the earthquake to be the y-direction and define the combinational method in $nalysis Settings to be SRSS. The response specter analysis can no be run. The results of the normal stress in y-direction are presented in  igure ;. &ote that the results are all positi!e in a RS-analysis. The reason for this ill be discussed in the folloing part here e aim to gi!e a short description of ho a RS-analysis is  performed

igure #$ Set up of the RS-analysis

igure %$ ormal stress in !-direction" ote that there are only positi#e results in RS analysis

Step $ % Discussion of RS results: To demonstrate ho the results are obtained in a RSanalysis e ill do a stepise procedure here e manually calculate the modal contributions and combine these. To do so e ill first look at the contributions of each mode and then e ill see ho these results end up i.e. in the result gi!en in igure ;. 1. To e!entually get the same result as in the RS-analysis (igure ;) e ill include the contribution of the 4 first modes as as done in the RS-analysis. rom the modal analysis e ill ha!e the folloing 4 normal stress results as shon 3. $s a comparison e first present the normal stress results for each of the 4 modes obtained from the modal analysis (see igure 2). These are non-physical results as they are calculated from the modal displacements. Hoe!er" although the absolute !alues are

rong the relati!e stress !alues ithin the structure are correct for each mode as they are  based on the modal shapes. Hence" these results are used as a base for the RS-analysis.

igure &$ ormal stress results obtained in the modal analysis from the first & modes

$" 'he non-physical results presented abo#e need to be scaled to obtain the structures response from the earthquake" 'his is done in the RS-analysis by multiplyin( each of the modal results )ith a mode coefficient" 'he mode coefficient is calculated as )here i represents the mode number* is the spectral acceleration* is the participation factor and is the circular frequency" +ll of these parameters for each mode can be found in the  solution information for the response spectrum analysis" 'he physical results for each mode can then be plotted usin( a ,ser Defined Result scaled )ith the mode coefficient" 'he normal stress in y-direction - for each mode - after this operation is performed is then

igure '$ Scaled modal results (i#in( the maximum amplitude contribution for each mode

;. The results for each mode gi!en in igure 4 are the amplitude ma#imums as the structure ob!iously is !ibrating. That said it is also ob!ious that the results could be multiplied ith 6-17 as the counter-phase are S?@ATE combinations are some of the most popular. %n igure B some of the scaled modal results from a corner node (probe result) are combined manually using the SRSS method. This is done by first e#tracting a scaled result from each mode and then combined using the SRSS method. The SRSS results

from the RS-analysis are also presented so it can be seen that e ill get the same !alue.  ence )e ha#e sho)n ho) the RS-analysis is )orkin( . &ote that by using the combinational methods the sign con!entions are lost. $lthough e don7t ha!e the option in the orkbench RS analysis to use the $bsolute method" e ha!e manually combined the pro!e !alues ith this method as ell to illustrate that using different combinational strategies ill yield different results although the modal data is the same.

igure $ .robe results: RS-analysis results are compared )ith a manually superposition of the scaled modal results to sho) )hat is (oin( on in the back(round of the RSanalysis"

Transient Earthquake Analysis: The response specter (RS) analysis has a great ad!antage in fast solution times" but also has to ob!ious drabacks. irst of all the methods of combining the scaled modal results ill alays lead to final results hich are all positi!e. The second draback is that the analysis must be linear. $ transient analysis does not ha!e these limitations" but on the other side it is more costly in terms of solution times. urther" to run the earthquake analysis transient" it is necessary to artificially create the time-acceleration data in such a ay that these data are compatible ith the smoothed response specter in the frequency plane. This criterion is illustrated in igure 5 here in igure 5 a) the smoothed response specter in the frequency plane is the blue line (Siss standard- S%$ 341) hile the red line is the compatible artificial earthquake as the acceleration for each frequency are in the same order as the smoothed data. hen these artificial data are ourier transformed to the time-plane (igure 5 b) e ha!e time-acceleration data hich e can use in a transient analysis.

igure $ /ompatible specters in a0 the frequency plane b0 time plane

The set-up of the transient analysis is shon in igure . The ground acceleration data !s. time (see igure 5 b) is found in a te#t file and is read into $&S'S using a command script. %n this analysis e ha!e run a linear analysis to be able to compare the results to the RS-analysis. Hoe!er" by using this procedure e could ha!e run the analysis as a non-linear analysis as ell (inclusion of non-linear contacts" materials and large deformational geometry).

igure *$ +pplyin( compatible (round acceleration data on the structure

The result of the structure can be e#tracted throughout the analysis. %.e. the normal stress in y-direction after 4.32 8s: and 3/.;5 8s: are shon in igure 1/.

igure !+$  Results of normal stress in y-direction after &"2 3s4 and 25"67 3s4

The probe !alues of the different result sets presented in the RS-analysis are compared to the transient analysis in igure 11-igure 1C. %t is seen that the SRSS results does not gi!e the e#actly same results as the transient analysis although the probe !alues are in the same range. %n fact the transient data and the RS-analysis ill ne!er gi!e the e #actly same results as the compatible response specter data per definition cannot be e#actly the same (the RS-specter is smooth) and because the superposition of the modal data does not take into account the difference in phase angles beteen the modes.  &ote that the ma#imum #-displacements ob!iously ha!e a higher frequency than hat it is seen from the y-displacements. The cause of this is that y-displacements are mainly caused by the first mode ith the loest frequency (found in the modal analysis results) hereas the ma#imum #-displacements also ha!e significant contributions from modes at higher frequencies.

igure !!$  ormal stress in y-direction from the probe location 8see 9i(ure 0" 'he red line (i#e the SRSS #alue from the RS-analysis

igure !": !-displacement from the probe location 8see 9i(ure 0" 'he red line (i#e the SRSS #alue from the RS-analysis

igure !#$  ;-displacement from the probe location 8see 9i(ure 0" ' he red line (i#e the SRSS #alue from the RS-analysis and the (reen line is the absolute #alue from the RSanalysis 8found by manually combinin( the modes0