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Module 06: Response Spectrum Analysis

1 © 2016 ANSYS, Inc. September 29, 2016

ANSYS Mechanical Linear and Nonlinear Dynamics

​

Release 17.0

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Module 06 Topics

© 2016 ANSYS, Inc.

September 29, 2016

2

  1. What is Response Spectrum Analysis?
  2. Generating the Response Spectrum
  3. Types of Analyses
  4. Single Point Response Spectrum

Analysis

  1. Mode Combination Methods
  2. Rigid Response
  3. Missing Mass Response
  4. Multi-Point Response Spectrum Analysis
  5. Recommendations

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A. What is Response Spectrum Analysis?

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September 29, 2016

  • A response spectrum analysis is mainly used in place of a time-history analysis to determine the response of structures to random or time- dependent loading conditions such as:
  • earthquakes,
  • wind loads,
  • ocean wave loads,
  • jet engine thrust,
  • rocket motor vibrations, and so on.

3

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... What is Response Spectrum Analysis?

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September 29, 2016

4

  • The most accurate solution would be to run a large, long transient analysis.
    • Here, “large” means many DOF, and “long” means many time points.
    • In most cases, this approach would take too much time and compute resources.
  • Instead of solving the (1) large model and (2) long transient together, it can be desirable to approximate the maximum response quickly by using the results of a modal analysis and a known input spectrum to calculate displacements and stresses in the model.
  • The input spectrum is a graph of “spectral value” versus “frequency” that captures the intensity and frequency content of the input time-history loads.

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... What is Response Spectrum Analysis?

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September 29, 2016

  • Idea: solve the (1) large model and (2) long transient separately and combine the results.

Large model

Long transient

Large model Mode extraction

↓

Mode shapes

Small model Long transient

↓

Response spectrum

Combined solution Fast, approximate

Full solution Slow, accurate

Large model

Long transient

5

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B. Generating the Response Spectrum

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September 29, 2016

  • Response Spectrum:
    • A response spectrum is a plot of the maximum response of linear one-DOF systems to a given time-history input.
    • The abscissa of the plot is the natural frequencies of the systems, the ordinate is the maximum response:
      • Displacement
      • Velocity
      • Acceleration.

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... Generating the Response Spectrum

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September 29, 2016

  • The generation of the response spectrum will usually be done for you, but the

process can be described as follows:

•

•

  1. Subject a small model to the transient loading. smallest is 1 DOF oscillator (k, c, m)
  2. Track the response over time (disp, velo, or accel).

note the maximum absolute amplitude over time

m

k

c

k m

ω ≈

e.g., for oscillator with frequency ω = 30 Hz

max absolute value over time

S = 95 m/s2

7

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... Generating the Response Spectrum

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September 29, 2016

  1. Repeat for oscillator with different frequency (same damping).
  2. Plot the max response over time as a function of frequency.

ω = 30 Hz, S = 95 m/s2

ω = 50 Hz, S = 138 m/s2

ω = 70 Hz, S = 86 m/s2

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... Generating the Response Spectrum

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September 29, 2016

  • Note that the damping is included in the response spectrum.
  • Additional spectra can be generated for other damping values.

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... Generating the Response Spectrum

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September 29, 2016

  • Using many oscillators results in a more detailed curve.
    • The graph is typically plotted in log-log scale.
    • This also allows us to generate the spectrum only once and reuse it for any model.
  • For efficiency, one analysis is done on an array of many oscillators.
    • the same damping is used for all oscillators

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... Generating the Response Spectrum

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  • We can easily convert between acceleration, velocity, and displacement spectra

by multiplying or dividing by the frequency.

– remember to convert frequency units; ω rad/s = 2πf Hz

a

= S /(2πf )2

Sd = Sv /(2πf )

a

v d

= S /(2πf )

S = S (2πf )

v

a d

= S (2πf )

S = S (2πf )2

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C. Types of Analyses

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  • There are two types of Response Spectrum Analysis available:
    • Single-Point Response Spectrum (SPRS) • Multi-Point Response Spectrum (MPRS)

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D. Single Point Response Spectrum (SPRS) Analysis

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  • The structure is excited by a spectrum of:
    • known direction and frequency components,
    • acting uniformly on all support points.
  • Application examples:
    • Nuclear power plant buildings and components, for seismic loading
    • Airborne Electronic equipment for shock loading
    • Commercial buildings in earthquake zones
  • The structure is linear (i.e., constant stiffness and mass).

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stresses in a particular direction.

​

mode

​

frequency

​

mode shape

​

participation factor

​

​

1

ω1

{φ}1

​

γ1

​

​

2

ω2

{φ}2

​

γ2

​

​

3

ω3

{φ}3

​

γ3

​

​

​

…

​

…

​

…

​

​

…

​

​

( )

D

M

T

i

i

i

i

γ = {φ} [M ]{ }

−ω [ ]+ [K ]

{φ} = {0}

2

... Participation Factor, γ

  • Recall from the Modal Analysis Chapter:
    • The participation factor γ is a measure of the response of the structure at a given natural frequency.
    • γ represents how much each mode will contribute to the deflections and

Modal Analysis

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... Spectrum Values, S

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September 29, 2016

​

mode

​

frequency

​

mode shape

spectrum value

participation factor

​

​

1

ω1

{φ}1

S1

γ1

​

​

2

ω2

{φ}2

S2

γ2

​

​

3

ω3

{φ}3

S3

γ3

​

​

​

…

​

…

​

…

​

…

​

…

​

​

  • For each ω, the spectrum value S can be determined by a simple look-up from the response-spectrum table.
  • Log-log interpolation is done for modal frequencies

between spectrum points.

  • No extrapolation is done for frequencies outside of the spectrum range; i.e. the value at the closest point is used.

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... Mode Coefficients, A

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  • The mode coefficient Ai is defined as the amplification factor that is multiplied by the eigenvector to give the actual displacement in each mode.
  • Ai can be determined from the participation factors and the spectrum values,

depending on the type of spectrum input.

  • Recall: participation factors measure the amount of mass moving in each direction for a unit displacement.

​

mode

​

frequency

​

mode shape

spectrum value

participation factor

mode coefficient

​

1

ω1

{φ}1

S1

γ1

A1

​

2

ω2

{φ}2

S2

γ2

A2

​

3

ω3

{φ}3

S3

γ3

A3

​

​

​

​

​

​

​

​

…

…

…

…

…

…

displacement velocity acceleration

i i

i

i i

i i

ω2

ω

S γ S γ

A =

Ai = Siγi Ai =

displacement velocity acceleration

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... Response, R

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  • The response (displacement, velocity or acceleration) for each mode can then be computed from the frequency, mode coefficient, and mode shape.
  • If there is more than one significant mode, the response for each mode must be

combined using some method.

​

mode

​

frequency

​

mode shape

​

spectrum value

participation factor

mode coefficient

​

response

1

ω1

{φ}1

S1

γ1

A1

{R}1

2

ω2

{φ}2

S2

γ2

A2

{R}2

3

ω3

{φ}3

S3

γ3

A3

{R}3

​

…

​

…

​

…

​

​

…

​

​

…

​

…

​

…

for displacement response for velocity response

for acceleration response

2

i i i i

{R}i

{R}i

ω A {φ}

= Ai {φ}i

= ωi Ai {φ}i

{R} =

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E. Mode Combination Methods

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  • The response spectrum analysis calculates the maximum displacement/stress response in the structure (i.e., individual maximum modal responses of the system).
  • It is not directly known how much of these maxima will combine to give an actual total response (i.e., phasing of the modes).
  • It is unlikely that all the modal maxima will act simultaneously and be of the

same sign.

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… Mode Combination Methods

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  1. Square Root of the Sum of the Squares (SRSS) Method

​

​

  • Complete Quadratic Combination (CQC) method

​

​

  • Rosenblueth (ROSE) method

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… Square Root of the Sum of the Squares (SRSS) Method

© 2016 ANSYS, Inc.

September 29, 2016

  • One straightforward method for calculating the combined response is to find the square root of the sum of the squares (SRSS).
  • For modes with sufficiently separated frequencies, the SRSS is approximately the probable maximum value of response
  • SRSS is also known as the Goodman-Rosenblueth-Newmark rule

∑

=

N

i

{R}

{R}= {R} + {

i =1

2

2

N

2

2

1 2

R} + + {R}

​

mode

​

frequency

​

mode shape

spectrum value

participation factor

mode coefficient

​

response

1

ω1

{φ}1

S1

γ1

A1

{R}1

2

ω2

{φ}2

S2

γ2

A2

{R}2

3

ω3

{φ}3

S3

γ3

A3

{R}3

​

​

​

​

​

​

​

20

…

…

…

…

…

…

…

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… Square Root of the Sum of the Squares (SRSS) Method

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  • There are circumstances in which this SRSS rule must be modified:
    1. Accounting for modes with closely-spaced natural

frequencies.

    • Adjusting for modes with partially- or fully-rigid responses.
    • Including high-frequency mode effects without extracting

all modes.

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… Sufficiently-Spaced Modes

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  • If modes are sufficiently spaced, the modes are uncorrelated.

ω1 ω2 ω3 ω4 ω5 ω6 ω7 ω8

​

  • It is valid to combine the responses using the SRSS method.

N

i

{R}

{R}=

∑

i =1

2

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… Closely-Spaced Modes (Correlated)

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method

is not

  • If modes with closely-spaced frequencies exist, the SRSS

applicable.

  • Modes with closely spaced frequencies become correlated.

ω1

ω2 ω3

ω4 ω5 ω6

ω7 ω8

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… Closely-Spaced Modes (Correlated)

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  • The definition of modes with closely spaced frequencies is a function of the

critical damping ratio:

  • For critical damping ratios ≤ 2%
    • modes are considered closely spaced if the frequencies are within 10% of each

other

      • Example, for fi < fj , fi and fj are closely-spaced if fj ≤ 1.1 fi
  • For critical damping ratios > 2%
    • modes are considered closely spaced if the frequencies are within five times the critical damping ratio of each other
      • Example: for fi < fj and 5% damping, fi and fj are closely-spaced if fj ≤ 1.25 fi
      • Example: for fi < fj and 10% damping, fi and fj are closely-spaced if fj ≤ 1.5 fi

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… Closely-Spaced Modes (Correlated)

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September 29, 2016

  • Idea: come up with a coefficient (ε) to determine the amount of correlation

between modes.

0.0 ≤ ε ≤ 1.0

ε = 0:

ε = 1:

0.0 < ε < 1.0:

uncorrelated

fully correlated

partially correlated

  • Two methods of combination can be used:
  1. Complete Quadratic Combination (CQC) method
  2. Rosenblueth (ROSE) method
  • Each method has a formula for the correlation coefficient, ε, which
  1. is based on the frequency and damping of modes i and j
  2. is designed to vary between 1 (fully correlated) and 0 (uncorrelated)

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… Mode Combination Methods

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2. Complete Quadratic Combination (CQC) method

3. Rosenblueth (ROSE) method

1

⎟

⎟

⎠

⎞ 2

⎜

⎜

⎝

⎛

N N

j

i

∑ ∑ ij i =1 j =i

{R}=

kε {R} {R}

2

1. Square Root of the Sum of Squares (SRSS) Method

1

2

⎞

⎝ i =1 ⎠

i

{R}= ⎛⎜ ∑N {R} ⎟

1

⎠

⎞ 2

⎛

N N

⎝ i =1 j =1

{R}= ⎜⎜ ∑ ∑εij {R}i {R}j ⎟⎟

Additional guidance on choosing a mode combination method will be provided in the “Recommendations” section.

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F. Rigid Response

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  • Spectral Regions
    • There are two frequencies that can often be identified on a response spectrum:
      • fSP (frequency at peak response: Spectral Peak)
      • fZPA (frequency at rigid response: Zero Period Acceleration)

mid frequency

high frequency

low frequency

fSP

frequency at peak response

(spectral peak)

fZPA

frequency at rigid response

(zero period acceleration)

ZPA

u

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... Spectral Regions

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  1. Low frequency (below fSP)
    • periodic region
    • modes generally uncorrelated (periodic) unless closely spaced
  2. Mid frequency (between fSP and fZPA)
    • transition from periodic to rigid
    • modes have periodic component and rigid component
  3. High Frequency (above fZPA)
    • rigid region
    • modes correlated with input frequency and, therefore, also with themselves

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... Spectral Regions

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low frequency

  • The responses are uncorrelated (unless closely spaced) and can be combined using the SRSS, CQC, or ROSE methods.

1

⎟

⎠

⎞ 2

⎜

⎜

⎛

N N

⎝ i =1 j =1

j ⎟

i

∑ ∑ ij p p

p

{R }=

ε {R } {R }

Low-Frequency Range

  • In the low-frequency range, the periodic responses predominate.

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... Spectral Regions

High-Frequency Range

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September 29, 2016

  • In the high-frequency range, the rigid responses predominate.

N

  • The responses are fully correlated (with the input frequency and consequently

with themselves) and can therefore be combined algebraically, as follows:

{Rr }= ∑{Rr }i

i =1

high frequency

30

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... Spectral Regions

Mid-Frequency Range

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  • In the mid-frequency range, the modal responses consist of
    • periodic components, and
    • rigid components.

mid frequency

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... Spectral Regions

Mid-Frequency Range

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  • Idea: come up with a coefficient (α) to split the response into a periodic component and a rigid component.

0.0 ≤ α ≤ 1.0

α = 0:

α = 1:

0.0 < α < 1.0:

periodic rigid

part periodic, part rigid

  • Methods to Calculate α:
    1. Lindley-Yow method
    2. Gupta method

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… Lindley-Yow method

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  • Lindley-Yow method, α = α(Sa)
  • The rigid response coefficient, α,
    • attains a minimum value at Sa,max
    • increases for decreasing Sa
    • attains a maximum value of 1 at Sa = ZPA
    • is set to zero where Sa < ZPA

ai

i

S

α = ZPA

α=0

α=1

ZPA

ZPA: acceleration at zero period

Sai: acceleration at the ith frequency

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… Gupta method

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  • Gupta method, α = α(f)
  • The rigid response coefficient, α,
    • attains a minimum value of 0 at f ≤ f1
    • increases linearly in log-log space between f1 and f2
    • attains a maximum value of 1 at f ≥ f2

fZPA

f1 f2

⎪

⎪⎩

⎪

⎧

2

1

2 1

2

1

1

0

3

for

for f ≤ f ≤ f

for

⎨ln( f / f )

ln( f / f )

f

f =

fi ≥ f2

i

i 1

fi ≤ f1

i

= ( f1 + 2 fZPA )

v,max

Sa,max

α =

2πS

α=0

α=1

ZPA

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Rigid Response

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  • Gupta method

– Affects all modes with f > f1.

  • Lindley-Yow method
  • Affects all modes with Sa ≥ ZPA.
  • Should not be used on modes with f < fSP.

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Rigid Response Calculations

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  • The individual modal responses are calculated as before.
    • With rigid response turned on, these modes are not combined directly.
    • The responses will be split into periodic and rigid components.

​

mode

​

frequency

spectrum value

​

response

​

​

​

1

ω1

S1

{R}1

​

​

​

2

ω2

S2

{R}2

​

​

​

3

ω3

S3

{R}3

​

​

​

​

…

​

…

​

…

​

…

​

​

​

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… Rigid Response Calculations

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  • The rigid response coefficient is calculated

according to the method selected.

​

mode

​

frequency

​

spectrum value

​

response

​

rigid response coefficient

​

​

1

ω1

S1

{R}1

α1

​

​

2

ω2

S2

{R}2

α2

​

​

3

ω3

S3

{R}3

α3

​

​

​

…

​

…

​

…

​

…

​

​

…

​

​

Lindley - Yow :

i

i

i

ln( f / f )

/ f1 )

ln( f

S

ai

2 1

0.0 ≤ αi ≤ 1.0

Gupta : α =

α = ZPA

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… Rigid Response Calculations

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  • The periodic and rigid components are calculated from the rigid response

coefficient.

  • As before, the response for each mode must be combined using some method.

Now, the periodic modes and rigid modes will be treated separately.

​

mode

​

frequency

​

spectrum value

​

response

​

rigid response coefficient

​

periodic component

rigid compone nt

1

ω1

S1

{R}1

α1

{Rp}1

{Rr}1

2

ω2

S2

{R}2

α2

{Rp}2

{Rr}2

3

ω3

S3

{R}3

α3

{Rp}3

{Rr}3

​

…

​

…

​

…

​

…

​

​

…

​

…

​

…

periodic component rigid component

2

i i

i

p

R

{Rr }i α{R}ii

{R } = 1−α { }

=

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… Rigid Response Calculations

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  • Example: rigid response components using Gupta method.

ω1

ω2

ω3 ω4 ω5 ω6

​

mode

​

frequency

​

response

rigid response coefficient

periodic component

​

rigid component

1

0.5

{R}1

0.0

{R}1

{0}

2

1.4

{R}2

0.0

{R}2

{0}

3

3.6

{R}3

0.18

0.98 {R}3

0.18 {R}3

4

6.4

{R}4

0.61

0.79 {R}4

0.61 {R}4

5

12

{R}5

1.0

{0}

{R}5

6

25

{R}6

1.0

{0}

{R}6

periodic

transition

​

​

rigid

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… Rigid Response Calculations

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September 29, 2016

​

mode

​

frequency

​

spectrum value

​

response

rigid response coefficient

​

periodic component

​

rigid component

1

ω1

S1

{R}1

α1

{Rp}1

{Rr}1

2

ω2

S2

{R}2

α2

{Rp}2

{Rr}2

3

ω3

S3

{R}3

α3

{Rp}3

{Rr}3

​

…

​

…

​

…

​

…

​

…

​

…

​

…

{ }

1

  • The periodic modes are combined according to the desired combination rule

(SRSS, CQC, or ROSE).

– Recall: CQC or ROSE are used if closely spaced modes are present.

SRSS CQC ROSE

⎟

⎟

⎠

1

⎞ 2

⎜

⎜

⎛

⎟

⎟

⎠

1

⎞ 2

⎜

⎜

⎝

⎛

2 ⎞ 2

⎛

N N

⎝ i =1 j =1

p

i j

∑ ∑ ij p

p

N N

i =1 j =1

p

i j

∑ ∑ ij p

p

N

⎝ i =1

i

∑ p

p

{R }=

{R }=

R ⎟

⎠

{R }= ⎜

ε {R } {R }

kε {R } {R }

40

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… Rigid Response Calculations

  • The rigid modes are summed algebraically.

{Rr }= ∑{Rr }i

i =1

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September 29, 2016

​

mode

​

frequency

​

spectrum value

​

response

​

rigid response coefficient

​

periodic component

​

rigid component

1

ω1

S1

{R}1

α1

{Rp}1

{Rr}1

2

ω2

S2

{R}2

α2

{Rp}2

{Rr}2

3

ω3

S3

{R}3

α3

{Rp}3

{Rr}3

​

​

…

​

​

…

​

​

…

​

​

…

​

​

…

​

​

…

​

​

…

N

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​

mode

​

frequency

​

spectrum value

​

response

rigid response coefficient

periodic component

​

rigid component

1

ω1

S1

{R}1

α1

{Rp}1

{Rr}1

2

ω2

S2

{R}2

α2

{Rp}2

{Rr}2

3

ω3

S3

{R}3

α3

{Rp}3

{Rr}3

​

…

​

​

…

​

​

…

​

​

…

​

​

…

​

​

…

​

​

…

2 2

r p

t

R } + {R }

{R }= {

… Rigid Response Calculations

​

  • The combined periodic and combined rigid modes are finally combined to give the total response.

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G. Missing Mass Response

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eff ,i i

T

i

i

D M

= γ2

γ = {φ} [M ]{ }

  • Recall: printed in the modal output file is the effective mass.
  • Generally, we cannot practically extract all possible modes to account for 100% of the mass of the structure.
    • Many structures may have important natural vibration modes at frequencies higher than the ZPA frequency, fZPA.

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Missing Mass Response

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mid frequency

high frequency

low frequency

R1

R2 R3

R4 R5 R6

R7 R8

R9

R10

R11

  • So far, we have addressed the low-, mid-, and high-frequency ranges of the spectrum.

– We could have many modes extend far beyond fZPA.

ZPA

Neglected modes

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… Missing Mass Response

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  • Idea: if we can figure out how much mass is missing from the modal analysis,

then we don’t have to extract all modes above fZPA.

  • Its effect can be lumped into an additional response

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… Missing Mass Response Calculation

​

  • Recall, above fZPA, the acceleration response is rigid (in-phase), so it can be fairly

accurately represented by a static acceleration analysis.

    • We can calculate what the total inertia force should be above fZPA.

{FT }= −[M ]{D}SZPA

    • We can also calculate the inertia force contributed by each mode.

{F }= −[M ]{φ} γ S

j j j ZPA

​

    • The sum of inertia force contributed by all modes is simply

∑

N

j j ZPA

j

{F }= −

j =1

N

∑

j =1

[M ]{φ} γ S

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  • The “missing mass response” is the static shape due to the missing inertia forces.
  • The missing mass response is a pseudo-static response to an acceleration base

excitation.

{

N

j j

N

M T

⎜

⎜

⎝ ⎠

⎛ ⎞

{F }= [M ]

{F }= {F }−

∑

j =1

∑ j j =1

φ} γ − {D}⎟⎟SZPA

M M

−1

{R }= [K ] {F }

… Missing Mass Response Calculation

​

  • The “missing” inertia force must simply be the difference between the total inertia force and the sum of modal inertia forces.

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  • If rigid response is included, then the missing mass is added to the rigid response.
  • The total response is then calculated by combining the periodic and rigid

components.

N

{Rr }= ∑{Rr }i + {RM }

i =1

2

2

r

p

{R } + {R }

{R}=

… Missing Mass Response Calculation

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H. Multi-Point Response Spectrum (MPRS) Analysis

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  • In multi-point response spectrum analysis, different constrained points can be subjected to different spectra
  • Up to 100 different excitations are allowed.

​

  • The structure is linear (i.e. constant stiffness

and mass).

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… Multi-Point Response Spectrum

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  • Each spectrum is treated individually first, so all of the previous information on single-point response spectrum applies
  • closely spaced modes (SRSS, CQC, ROSE)
  • rigid response (Lindley-Yow, Gupta)
  • missing mass
  • Finally, the response of the structure is obtained by combining the responses to each spectrum using the SRSS method.
  • where

{RMPRS} is the total response of the MPRS analysis

{RSPRS}1 is the total response of the SPRS analysis for spectrum 1

{RSPRS}2 is the total response of the SPRS analysis for spectrum 2

etc

2

50

2

1 2

SPRS

SPRS

R

{R } + { } +

{RMPRS }=

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I. Recommendations

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  • Set up a response spectrum analysis in the schematic by linking a modal system to a

response spectrum system at the solution level.

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Recommended Solution Procedure

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  • The recommended solution method is generally specified by your design code.
    • combination method
    • rigid response method
    • missing mass effects
  • Alternatively, the best solution method can be determined by
    • extracting the modes to be used for combination and
    • comparing them to the response spectrum

ω1 ω2 ω3

ω4 ω5 ω6

ω7 ω8

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Recommended Solution Procedure

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  • Modes only in low-frequency region
    • SRSS (or CQC/ROSE for closely spaced modes).
    • No rigid response effects. No missing mass effects.
  • Modes only in mid- to high-frequency region
    • SRSS (or CQC/ROSE for closely spaced modes).
    • Rigid response by Lindley or Gupta method. Missing mass on.
  • Modes in all frequency regions
    • SRSS (or CQC/ROSE for closely spaced modes).
    • Rigid response by Gupta method. Missing mass on.

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Analysis Settings

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  • Points to Remember
    • The excitation is applied in the form of a response spectrum:
      • displacement,
      • velocity, or
      • acceleration units.
    • The excitation must be applied at fixed degrees of freedom.
    • The response spectrum is calculated based on modal responses. A modal

analysis is therefore a prerequisite.

    • If response strains or stresses are of interest, then the calculation of modal strains and stresses must be performed in the modal analysis.

– This will happen automatically when the Modal and Response Spectrum analysis systems are linked in the Project Schematic as shown previously; however, depending on the sequence of events leading up to combined solution of the linked systems, you may end up having to solve the Modal analysis twice. This situation can be prevented by setting “Future Analysis” to “MSUP Analyses” in the Analysis Settings Details of the Modal system before its first solution.

  • The results are in terms of the maximum response.

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… Analysis Settings

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  • Analysis Settings > Options
  • Number of Modes To Use:
    • It is recommended to include the modes whose frequencies span 1.5 times the maximum frequency defined in the input response spectrum.

​

  1. Spectrum Type:
    • Single Point
    • Multiple Points

​

  • Modes Combination Type:
    • SRSS method (more conservative),
    • CQC method
    • ROSE method

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… Analysis Settings

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  • Analysis Settings > Output Controls

​

    • By default, only displacement responses are calculated.
    • To include velocity and/or acceleration responses, set their respective Output Controls to Yes.

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… Loads and Supports

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  • Supported boundary condition types include:
  • fixed support,
  • displacement,
  • remote displacement, and
  • body-to-ground spring.
  • For a Single Point spectrum type, input excitation spectrums are applied to all boundary condition types defined in the model.
  • For Multiple Points however, each input excitation spectrum is associated to only one boundary condition type.

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… Loads and Supports

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  • Three types of input excitation spectrum are supported:
  • displacement input excitation (RS Displacement),
  • velocity input excitation (RS Velocity), and
  • acceleration input excitation (RS Acceleration).
  • For each spectrum value, there is one corresponding frequency.

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… Loads and Supports

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  • Missing Mass effect:
    • If set to YES, includes contribution of high frequency modes in the total response calculation.
    • Only applicable to RS Acceleration excitation.
    • ZPA (Zero Period Acceleration) needs to be defined.

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… Loads and Supports

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  • Rigid Response Effect:
    • Specify option to include or not include rigid responses to the total response calculation by setting Rigid Response Effect to Yes or No.
    • The rigid responses normally occur in the frequency range that is lower than that of

missing mass responses, but is higher than that of periodic responses.

​

RS Acceleration RS Velocity RS Displacement

Gupta: requires f1 and f2

Lindley: requires ZPA

60

Gupta: requires f1 and f2

Gupta: requires f1 and f2

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… Results

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  • Applicable Deformation results are Total, Directional (X,Y,Z), Directional Velocity, and Directional Acceleration.

​

​

  • If strain/stress are requested, applicable results are normal strain and stress,

shear strain and stress, and equivalent stress.

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… Results

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  • To review reaction results, Force Reaction and Moment Reaction probes can be scoped to any boundary condition that was used to apply the base excitation.
  • Should be used carefully

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Workshop 06.1: Suspension Bridge

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Module 06: Response Spectrum Analysis

END

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