Dynamic Analysis

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Dynamic Analysis Tips, Techniques, etc. New and
Review
Michael H. Swanger Georgia Tech CASE
Center GTSUG 2004 June 9-12, 2004 Boston, MA
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Topics

• Lumped vs Consistent Mass Joint Constraints
• Number of Joints
• Number of Modes
• Transient Seismic Loads Joint Loads
• 4. Number of Time Points Transient Analysis
• Transient Seismic Loads Joint Loads
• 5. Modal Combinations
• CQC vs Everything Else
• 6. Static Load Response Spectrum Mode
  Combination Results
• Member Forces and Section Forces

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1. Lumped vs Consistent Mass Joint Constraints
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INERTIA OF JOINTS LUMPEDMember Lumped Mass

• Translational Inertia
• Moment of Inertia Bending DOFs
• Torsional Moment of Inertia

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(No Transcript)
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1. Joint Constraints Lumped vs Consistent Mass
5 Stories, 30 Bays X, 20 Bays Z 3906 Joints, 9505
Members, Bandwidth 111 Joints
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1. Lumped vs Consistent Mass Joint Constraints
INERTIA OF JOINTS LUMPED/CONSISTENT EIGENVALUE
PARAMETERS SOLVE USING GTLANCZOS NUMBER OF
MODES 100 PRINT MAXIMUM INITIAL STRESS
LOADING OFF END EIGENVALUE PARAMETERS DYNAMIC
ANALYSIS EIGENVALUES
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1. Lumped vs Consistent Mass Joint Constraints

• Consistent Mass vs Lumped Mass
• Increases number of arithmetic operations.
• Increases memory requirements.
• Use of joint constraints joint ties and rigid
  bodies
• in Versions 27 and earlier forces mass assembly
  to
• be consistent.
• Version 28 joint constraints honors INERTIA OF
• JOINTS LUMPED, but throws away off-diagonal
• mass matrix terms.

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1. Lumped vs Consistent Mass Joint Constraints

• Some Tips When Using Joint Constraints in
• Pre-Version 28 Dynamic Analysis
• Dont use the INERTIA OF JOINTS LUMPED/
• CONSISTENT command.
• Specify all inertia as joint inertia INERTIA OF
  JOINTS
• WEIGHT/MASS, INERTIA OF JOINTS FROM LOAD
• commands DEAD LOAD JOINTS, DEAD LOAD JOINTS,
• GTMenu -gt Old Gravity Load.
• This strategy starts with a diagonal mass matrix,
  but
• REMEMBER, joint constraint transformations will
• expand the number of terms in the mass matrix.

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2. Number of Joints
Additional Mass 5 k/ft
Fx, Fy, Mz
Plane Frame Pinned Supports Lumped Mass Damping
0.05 All Modes
El Centro -- Y
El Centro -- X
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2. Number of Joints
INERTIA OF JOINTS LUMPED UNITS KIPS FEET MEMBER
ADDED INERTIA WEIGHT EXISTING 3 TRANS X Y
GLOBAL UNIF FR W 5 LA 0 LB 1 UNITS KIPS
INCHES DYNAMIC ANALYSIS EIGENVALUES TRANSIENT
LOAD 'X' SUPPORT ACCELERATION TRANSLATION X
FILE 'ELCENTRO' INTEGRATE FROM 0.0 TO 25.0 AT
0.005 END TRANSIENT LOAD TRANSIENT LOAD
'Y' SUPPORT ACCELERATION TRANSLATION Y FILE
'ELCENTRO' INTEGRATE FROM 0.0 TO 25.0 AT
0.005 END TRANSIENT LOAD DAMPING RATIOS 0.0500
100 PERFORM TRANSIENT ANALYSIS COMPUTE TRANSIENT
FORCES MEMBER 1 LIST TRANSIENT MAX FORCES MEMBER 1
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2. Number of Joints
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2. Number of Joints

• Need sufficient number of translation DOFs
  (number of joints)
• to capture the significant displacements in the
  direction(s) of the
• applied loads.
• Apply the dynamic load as a static load (joint
  loads). You need
• enough joints so that you can see the static
  displacement in the
• form of joint translation displacements.
• 3. Remember that each additional node increases
  the number
• of frequencies and mode shapes that must be
  computed.

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2. Number of Joints
3906 Joints 23,436 DOFs
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3. Number of Modes Transient Seismic Loads
285 Joints, 1678 DOFs Damping 0, All Modes
Support Accel El Centro
El Centro DT 0.02 Seconds
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3. Number of Modes Transient Seismic Loads
INERTIA OF JOINTS LUMPED EIGENVALUE PARAMETERS
SOLVE USING GTLANCZOS NUMBER OF MODES 300
PRINT MAX END DYNAMIC ANALYSIS EIGENVALUE UNITS
INCHES KIPS CYCLES SECONDS TRANSIENT LOAD
'EQY' 'Global Y Seismic Load' SUPPORT
ACCELERATION TRANSLATION Y FILE 'ELCENTRO'
INTEGRATE FROM 0.0 TO 25.0 AT 0.01 END
TRANSIENT LOAD
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3. Number of Modes Transient Seismic Loads
90 global Y mass participation
32 Modes ACTIVATE MODES ALL BUT 7 9 11 TO
20 22 24 TO 26 29 TO 31 34 35 37 41 42 44 TO -
61 63 64 66 TO 72 74 75 77 78 80 TO 87 89 TO 93
97 TO 103 106 108 TO 121 123 - TO 126 128 TO
300 PERFORM TRANSIENT ANALYSIS COMPUTE TRANSIENT
FORCES MEMBER 'C21' UNITS INCHES KIPS LIST TRANS
MAX ACCEL JOINT 's272' LIST TRANS MAX DISPL JOINT
's272' LIST TRANS MAX FORCES MEMBER 'C21
All Modes (300) 99 global Y mass
participation ACTIVATE MODES ALL PERFORM
TRANSIENT ANALYSIS COMPUTE TRANSIENT FORCES
MEMBER 'C21' UNITS INCHES KIPS LIST TRANS MAX
ACCEL JOINT 's272' LIST TRANS MAX DISPL JOINT
's272' LIST TRANS MAX FORCES MEMBER 'C21'
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3. Number of Modes Transient Seismic Loads
Number of modes OK if addition of remaining
modes Does not change the results by more than
10 (ASCE 4-98, Section 3.2.2.2f)
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3. Number of Modes Transient Seismic Loads

• The number of modes used in the transient
  solution for seismic loads must be able to
  capture sufficient mass participation usually
  90 -- in the direction of the seismic load.
• 90 mass participation generally produces an
  adequate solution that changes less than 10 if
  the remaining number of modes are used.

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3. Number of Modes Transient Joint Loads
100sin25(2P)t kips (joint s77) Time step
0.001 seconds
285 Joints, 1678 DOFs
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3. Number of ModesTransient Joint Loads
INERTIA OF JOINTS LUMPED EIGENVALUE PARAMETERS
SOLVE USING GTLANCZOS NUMBER OF MODES 300
PRINT MAX END DYNAMIC ANALYSIS EIGENVALUE
Integration 10 load cycles, 40 time
pts/cycle UNITS FEET KIPS CYCLES
SECONDS TRANSIENT LOAD 'JLY' JOINT 's77'
FORCE Y FUNCTION SINE AMPLITUDE 100.0 FREQUENCY
25.0 INTEGRATE FROM 0.00 TO 0.40 AT 0.001 END
TRANSIENT LOAD PERFORM TRANSIENT
ANALYSIS COMPUTE TRANSIENT FORCES
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3. Number of ModesTransient Joint Loads
90 global Y mass participation
ACTIVATE MODES ALL BUT 7 9 11 TO 20 22 24 TO
26 29 TO 31 34 35 37 41 42 44 TO 61 63 64 66
TO 72 74 75 77 78 80 TO 87 89 TO 93 97 TO 103
106 108 TO 121 123 - TO 126 128 TO 300
PERFORM TRANSIENT ANALYSIS COMPUTE TRANSIENT
FORCES MEMBER 'C21' UNITS INCHES KIPS LIST TRANS
MAX ACCEL JOINT 's77' LIST TRANS MAX DISPL JOINT
's77' LIST TRANS MAX FORCES MEMBER 'C21
All Modes (300) 99 global Y mass
participation ACTIVATE MODES ALL PERFORM
TRANSIENT ANALYSIS COMPUTE TRANSIENT FORCES
MEMBER 'C21' UNITS INCHES KIPS LIST TRANS MAX
ACCEL JOINT 's77' LIST TRANS MAX DISPL JOINT
's77' LIST TRANS MAX FORCES MEMBER 'C21'
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3. Number of ModesTransient Joint Loads
EIGENVALUE PARAMETERS NUMBER OF MODES
400 END DYNAMIC ANALYSIS EIGENVALUE
400 Modes. Still 99 mass participation
ACTIVATE MODES ALL PERFORM TRANSIENT
ANALYSIS COMPUTE TRANSIENT FORCES MEMBER
'C21' UNITS INCHES KIPS LIST TRANS MAX ACCEL
JOINT 's77' LIST TRANS MAX DISPL JOINT 's77' LIST
TRANS MAX FORCES MEMBER 'C21'
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3. Number of ModesTransient Joint Loads
90 Global Y Mass Participation 32 modes
99 Global Y Mass Participation 300 Modes
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3. Number of ModesTransient Joint Loads
90 Global Y Mass Participation 32 modes
99 Global Y Mass Participation 300 Modes
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3. Number of ModesTransient Joint Loads
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3. Number of ModesTransient Joint Loads

• Sufficient number of modes are needed to capture
  displacement DOF(s) corresponding to the joint
  load DOFs.
• ASCE 4-98, Section 3.2.2.2f
• Alternatively, the number of modes included in
  the
• analysis shall be sufficient to insure that
  inclusion of
• the remaining modes does not result in more than
• 10 increase in total responses of interest.
• All modes having a displacement component
  corresponding to the applied joint load DOF(s)
  will contribute something to the response
  regardless of mass participation. It is load
  participation,, i.e. modal load, that is
  important

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3. Number of ModesTransient Joint Loads

• The contributing modes need to be of high
  quality. So be careful about skimping on the
  number of DOFs. And remember that you need at
  least twice as many DOFs as the number of modes
  that you need to compute.

Mode 127, 106 Hz
Mode 256, 222 Hz
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4. Number of Time PointsTransient Seismic Loads
285 Joints, 1678 DOFs

• Dt 0.01 seconds
• Dt 0.005 seconds
• Dt 0.002 seconds
• 99 Global Y Mass Participation 300 Modes

Support Accel El Centro
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4. Number of Time PointsTransient Seismic Loads
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4. Number of Time PointsTransient Seismic Loads
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4. Number of Time PointsTransient Seismic Loads

• 1. ASCE 4-98, Section 3.2.2.1c
• An acceptable rule is that the Dt used be small
  enough such
• that the use of 1/2Dt does not change the
  response by more
• than 10.
• Normally, Dt (shortest T of interest)/12
  seconds.
• For seismic loads, Dt (1/33 Hz)/12 0.0025
  seconds,
• assuming that 33 Hz is a reasonable ZPA cutoff
  frequency.

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4. Number of Time PointsTransient Seismic Loads
Dt must capture extreme points of both these
functions
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4. Number of Time PointsTransient Joint Loads
100sin25(2P)t kips (joint s77)

• Dt 0.01 seconds
• Dt 0.005 seconds
• Dt 0.002 seconds
• Dt 0.001 seconds
• 300 Modes

285 Joints, 1678 DOFs
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4. Number of Time PointsTransient Joint Loads
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4. Number of Time PointsTransient Joint Loads

• The 10 rule for adequate size of time step
  applies equally
• well to all loading types, single-frequency
  joint loads as well
• as ground accelerations.
• A pretty good estimate of time step size for
  single frequency
• joint loads is
• Dt (1/12)(1/(loading frequency -- Hz))
• Dt 1/(25 Hz)1/12 0.003 seconds
• A better and safer first estimate is
• Dt 1/1.5(12)(loading frequency) 0.002
  seconds

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4. Number of Time PointsTransient Joint Loads
Dt must capture extreme points of both these
functions
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5. Modal Combinations CQC vs Everything Else
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5. Modal Combinations CQC vs Everything Else
10316
RS - X
Damping 0.3, All Modes
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5. Modal Combinations CQC vs Everything Else
INERTIA OF JOINTS LUMPED EIGENVALUE PARAMETERS
SOLVE USING GTLANCZOS NUMBER OF MODES
100 END DYNAMIC ANALYSIS EIGENVALUES ACTIVE
MODES 1 TO 5 99 mass participation in
horizontal directions LIST DYNAMIC PARTICIPATION
FACTORS RESPONSE SPECTRUM LOAD 'DLE_X' 'DLE
horizontal spectrum in X direction' SUPPORT
ACCELERATION TRANSLATION X 1.000 FILE
'dle-h' END DAMPING RATIOS 0.3 100 PERFORM
RESPONSE SPECTRUM ANALYIS COMPUTE RESPONSE
SPECTRUM DISPLACEMENTS FORCES MODE COMBINATIONS
ALL OUTPUT MODAL COMBINATIONS LIST RESPONSE
SPECTRUM FORCES MODE COMBINATIONS ALL MEMBER 10316
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5. Modal Combinations CQC vs Everything Else
NORMALIZED PARTICIPATION FACTORS OF X
DIRECTION MASS PARTICIPATING
----------------------------------- MODE
PERCENT MODE PERCENT MODE PERCENT
MODE PERCENT MODE PERCENT MODE
PERCENT 1 5.017229 2 13.44735
3 0.6814709E-01 4 73.66347 5
7.745363 6 0.0000000E00 . . . TOTAL
PERCENTAGE OF X DIRECTION MASS PARTICIPATING
99.942
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5. Modal Combinations CQC vs Everything Else
LIST RESPONSE SPECTRUM FORCES MODE COMB CQC RMS
MEMBER 10316
RESULTS OF LATEST ANALYSES
ACTIVE UNITS
M MN DEG DEGC SEC

LOADING - DLE_X DLE
horizontal spectrum in X direction


MEMBER FORCES MEMBER JOINT
RESPONSE /----------FORCE------//--------MOMENT-
--------------/ TYPE
AXIAL BENDING-Z
10316 10305 MODE 1 -1.024857
-141.3777
MODE 2 2.463083
149.6922 MODE 3
0.1364790 11.84382
MODE 4 0.6384398
43.17134
MODE 5 -0.2965805E-01
-53.89271 RMS
2.746675
217.4945 ABS SUM
4.292517 399.9778
PRMS 3.678584
307.4772
CQC 1.943536
13.34483 NRC GRP
3.553971 307.0560
NRC TPM 3.553971
307.0560
NRC DSM 4.085470
373.5420
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5. Modal Combinations CQC vs Everything Else
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5. Modal Combinations CQC vs Everything Else
MEMBER JOINT RESPONSE /----------FORCE-----
-//--------MOMENT---------------/
TYPE AXIAL
BENDING-Z 10316 10305 MODE 1
-1.024857 -141.3777
MODE 2 2.463083
149.6922
MODE 3 0.1364790
11.84382 MODE
4 0.6384398
43.17134 MODE 5
-0.2965805E-01 -53.89271
RMS 2.746675
217.4945
CQC 1.943536
13.34483
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
LIST FORCES LIST SECTION CHECK/SELECT
MEMBERS AS BEAM CHECK/SELECT MEMBERS AS COLUMN
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces

• Proceedure Adding Static and Dynamic Analyses
  Results
• Perform STIFFNESS ANALYSIS for static loads
• Perform dynamic analysis for dynamic loads
  (PERFORM
• RESPONSE SPECTRUM ANALYSIS)
• Create pseudo-static loads from dynamic analysis
  results
• CREATE PSEUDO STATIC
• Create load combinations from static and
  pseudo-static
• loads
• CREATE LOAD COMBINATION

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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Additional Mass 5 k/ft (live load)
Fx, Fy, Mz
Plane Frame Pinned Supports Lumped Mass Damping
0.05, All Modes
RS -- X
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Perform STIFFNESS ANALYSIS for static loads
Stiffness analysis for static
gravity loads DEAD LOAD 'DL' DIR -Y ALL
MEMBERS UNITS FEET LOADING 'LL' MEMBER LOADS 3
LOAD FORCE Y GLOB UNIF FR W -5.0 LA 0.0 LB
1.0 STIFFN CREATE LOAD COMBINATION 'DLLL' SPECS
'DL' 1.0 'LL' 1.0
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Perform dynamic analysis for dynamic
loads (PERFORM RESPONSE SPECTRUM ANALYSIS)
Response spectrum analysis
RESPONSE SPECTRUM LOAD 'RS-X' SUPPORT
ACCELERATION TRANSLATION X 1.0 FILE
'S.1GA51' END RESPONSE SPECTRUM LOAD DAMPING
RATIOS 0.0500 100 PERFORM RESPONSE SPECTRUM
ANALYSIS COMPUTE RESPONSE SPECTRUM DISPLACEMENTS
FORCES REACTIONS MODE COMB RMS
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Create pseudo-static loads from dynamic analysis
results CREATE PSEUDO STATIC
Create pseudo-static results from
the response spectrum results
CREATE PSEUDO STATIC LOAD 'PS-X' FROM RMS OF
LOAD 'RS-X'
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Menu Results-gtDynamic Analysis Results-gtCreate
Pseudo Static Loads
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Create load combinations that add
pseudo-static results to static analysis
results LOAD LIST ALL CREATE LOAD
COMBINATION 'DesLd1' TYPE ALG SPECS 'DLLL'
1.000000 'PS-X' 1.000000 CREATE LOAD COMBINATION
'DesLd1-' TYPE ALG SPECS 'DLLL' 1.000000
'PS-X' -1.000000
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Menu Results-gtDynamic Analysis Results-gtCREATE
Load Combinations
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Member Forces, Member 3, Load DLLL (static
load) ACTIVE UNITS FEET KIP RAD DEGF SEC
MEMBER FORCES MEMBER LOADING JOINT
/---------------------FORCE--------
-//--------MOMENT----------------/
AXIAL SHEAR-Y
BENDING-Y BENDING-Z 3
DLLL 3 7.5348096
50.3501641
113.0221458 4
-7.5348096 50.3501641
-113.0221458
Member Section Forces, Member 3, Load
DLLL ACTIVE UNITS FEET KIP RAD DEGF SEC
--------------------------------------------------
--------------- --------------------------------
------ --- MEMBER 3

--- ----------------------------------
--------------------------------
-------------------------------------
LOADING DLLL

DISTANCE /------------------- FORCE
--------------- ---//------------ MOMENT
--------/ FROM START AXIAL
Y SHEAR Z SHEAR Y BENDING
Z BENDING 0.000 FR -7.534810
-50.35017
-113.0222 1.000 -7.534810
50.35016
-113.0221
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Member Forces, Member 3, Pseodo-static Load
PS-X ACTIVE UNITS FEET KIP RAD DEGF
SEC MEMBER FORCES MEMBER LOADING
JOINT /---------------------FORCE---------
--//----MOMENT--------------------/
AXIAL SHEAR-Y
BENDING-Y BENDING-Z 3
PS-X 3 0.0000000
11.6196895
116.1968958 4
0.0000000 11.6196895
116.1968958
Member Section Forces, Member 3, Pseodo-static
Load PS-X ACTIVE UNITS FEET KIP RAD DEGF
SEC -------------------------------------------
-------------------- ---------------------------
--------------- --- MEMBER 3

--- -----------------------
----------------------------------------
------------------------------------------
LOADING PS-X

DISTANCE /------------------- FORCE
------------- ---//------ MOMENT
------------------/ FROM START
AXIAL Y SHEAR Y
BENDING Z BENDING 0.000 FR
0.2536936E-07 11.61969
116.1969 1.000
0.2536936E-07 11.61969
116.1969
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Member Forces, Member 3, Load Combinations
DesLd1 and DesLd1- ACTIVE UNITS FEET KIP
RAD DEGF SEC MEMBER FORCES MEMBER
LOADING JOINT /---------------------FORCE-----
------ ----//----MOMENT--------------------/
AXIAL
SHEAR-Y BENDING-Y
BENDING-Z 3 DesLd1 3
7.5348096 61.9698516
229.2190417 4
-7.5348096 61.9698516
3.1747500 DesLd1- 3
7.5348096 38.7304766
-3.1747500 4
-7.5348096 38.7304766
-229.2190417
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
Member Section Forces, Member 3, Load
Combinations DesLd1 and DesLd1- ACTIVE
UNITS FEET KIP RAD DEGF SEC
--------------------------------------------------
---- -------------------------------------------
------- --- MEMBER 3

--- -------------------------------
------------------------- ----------------------
--------------------------- LOADING
DesLd1
DISTANCE
/------------------- FORCE ------
-//------------------ MOMENT ------------------/
FROM START AXIAL Y
SHEAR TORSION Y BENDING
Z BENDING 0.000 FR -7.534810
-38.73048
3.174751 1.000
-7.534810 61.96985
3.174780
LOADING DesLd1-

DISTANCE /------------------- FORCE
------- --//---------------- MOMENT
------------------/ FROM START
AXIAL Y SHEAR TORSION
Y BENDING Z BENDING 0.000 FR
-7.534811 -61.96986
-229.2191 1.000
-7.534811 38.73047
-229.2190
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6. Static Load Response Spectrum Mode
Combination Results Member Forces and Section
Forces
When adding static load results and response
spectrum mode combination results, remember that
the while the static components maintain
equilibrium, the response spectrum components do
not. Therefore, the final result does not
satisfy equilibrium.