ansys tutorial - earthquake analyses in workbench
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ansys tutorialTRANSCRIPT
ANSYS Tutorial: Earthquake analyses in workbench
Do you want to perform earthquake analyses according to design codes or 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 is
cheap to use in terms of numerical costs as it is based on modal results. Hoe!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. Hoe!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
igure !: Shell structure used as an example in the earthquake analyses
Response Spectrum Analysis:
There are to 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 folloing+
• Calculates the participation factor for each of the structures frequencies
• Find the maximum accelerations from the given 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.
• Finally superpose these modal results to the nal result using i.e. the SRSS method.
Step 1 - Modal analysis + The ,odal analysis ill gi!e us the eigenfrequencies of 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 / 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 01 modes e ill ha!e 0/ participating mass in the y-
/ 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 3 modes as input as these modes participate ith 2/ of the effecti!e mass in y-
direction.
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 beteen structural acceleration and the structures frequencies e insert the
tool 5RS $cceleration6 (see Figure 3) and include earthquake data as a table (frequency
7H89 !s. acceleration 7m*s29). $ graphical presentation of these data can be seen in igure
4 a).
urther e decide the direction of the earthquake to be the y-direction and define the
combinational method in $nalysis Settings to be SRSS. The response specter analysis can
no be run.
The results of the normal stress in y-direction are presented in igure :. &ote that the
results are all positi!e in a RS-analysis. The reason for this ill be discussed in the
folloing part here e aim to gi!e a short description of ho a RS-analysis is
performed
igure %$ 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 RS-
analysis e ill do a stepise 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 :.
0. To e!entually get the same result as in the RS-analysis (igure :) e ill include the
contribution of the 3 first modes as as done in the RS-analysis. rom the modal analysis
e ill ha!e the folloing 3 normal stress results as shon
2. $s a comparison e first present the normal stress results for each of the 3 modes
are calculated from the modal displacements. Hoe!er" although the absolute !alues are
rong the relati!e stress !alues ithin the structure are correct for each mode as they are
based on the modal shapes. Hence" these results are used as a base for the RS-analysis.
igure &$ 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 3 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 5-06 as the counter-phase are ;ust as !alid results. Hoe!er" in some
manner e ill ha!e to combine the modal results to get a final result but as e don6t
kno the phase angles beteen the modes (these cannot be found in a modal analysis" for
this it is necessary to run a full transient analysis)" the superposition can only be an
attempt to estimate the correct earthquake response. There are se!eral different methods
hich can be used to combine the modes here SRSS" <=< and $>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 don6t 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 RS-
analysis"
Transient Earthquake Analysis:
The response specter (RS) analysis has a great ad!antage in fast solution times" but also
has to ob!ious drabacks. irst of all the methods of combining the scaled modal
results ill alays lead to final results hich are all positi!e. The second draback 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 4 here in igure 4 a) the
smoothed response specter in the frequency plane is the blue line (Siss standard- S%$
230) 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 4 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 shon in igure . The ground acceleration data !s. time
analysis e ha!e run a linear analysis to be able to compare the results to the RS-analysis.
Hoe!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-
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 00-igure 0C. %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 beteen 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 loest 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
Figure 13: X-displacement from the probe location (see Figure 7). The red line give
the SRSS value from the RS-analysis and the green line is the absolute value from
the RS-analysis (found by manually combining the modes)
Do you want to perform earthquake analyses according to design codes or 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 is
cheap to use in terms of numerical costs as it is based on modal results. Hoe!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. Hoe!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
igure !: Shell structure used as an example in the earthquake analyses
Response Spectrum Analysis:
There are to 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 folloing+
• Calculates the participation factor for each of the structures frequencies
• Find the maximum accelerations from the given 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.
• Finally superpose these modal results to the nal result using i.e. the SRSS method.
Step 1 - Modal analysis + The ,odal analysis ill gi!e us the eigenfrequencies of 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 / 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 01 modes e ill ha!e 0/ participating mass in the y-
/ 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 3 modes as input as these modes participate ith 2/ of the effecti!e mass in y-
direction.
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 beteen structural acceleration and the structures frequencies e insert the
tool 5RS $cceleration6 (see Figure 3) and include earthquake data as a table (frequency
7H89 !s. acceleration 7m*s29). $ graphical presentation of these data can be seen in igure
4 a).
urther e decide the direction of the earthquake to be the y-direction and define the
combinational method in $nalysis Settings to be SRSS. The response specter analysis can
no be run.
The results of the normal stress in y-direction are presented in igure :. &ote that the
results are all positi!e in a RS-analysis. The reason for this ill be discussed in the
folloing part here e aim to gi!e a short description of ho a RS-analysis is
performed
igure %$ 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 RS-
analysis e ill do a stepise 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 :.
0. To e!entually get the same result as in the RS-analysis (igure :) e ill include the
contribution of the 3 first modes as as done in the RS-analysis. rom the modal analysis
e ill ha!e the folloing 3 normal stress results as shon
2. $s a comparison e first present the normal stress results for each of the 3 modes
are calculated from the modal displacements. Hoe!er" although the absolute !alues are
rong the relati!e stress !alues ithin the structure are correct for each mode as they are
based on the modal shapes. Hence" these results are used as a base for the RS-analysis.
igure &$ 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 3 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 5-06 as the counter-phase are ;ust as !alid results. Hoe!er" in some
manner e ill ha!e to combine the modal results to get a final result but as e don6t
kno the phase angles beteen the modes (these cannot be found in a modal analysis" for
this it is necessary to run a full transient analysis)" the superposition can only be an
attempt to estimate the correct earthquake response. There are se!eral different methods
hich can be used to combine the modes here SRSS" <=< and $>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 don6t 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 RS-
analysis"
Transient Earthquake Analysis:
The response specter (RS) analysis has a great ad!antage in fast solution times" but also
has to ob!ious drabacks. irst of all the methods of combining the scaled modal
results ill alays lead to final results hich are all positi!e. The second draback 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 4 here in igure 4 a) the
smoothed response specter in the frequency plane is the blue line (Siss standard- S%$
230) 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 4 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 shon in igure . The ground acceleration data !s. time
analysis e ha!e run a linear analysis to be able to compare the results to the RS-analysis.
Hoe!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-
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 00-igure 0C. %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 beteen 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 loest 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
Figure 13: X-displacement from the probe location (see Figure 7). The red line give
the SRSS value from the RS-analysis and the green line is the absolute value from
the RS-analysis (found by manually combining the modes)