SAP2000 - Problem 6-008

C OMP UTE R S &S TRU CTU R ES

IN C.

R Software VerificationPROGRAM NAME: SAP2000REVISION NO.: 0

EXAMPLE 6-008 - 1

EXAMPLE 6-008LINK – PLASTIC WEN LINK

PROBLEM DESCRIPTION

This example uses a single degree of freedom structure to test the behavior of aplastic Wen link element. Bilinear force-deformation characteristics are definedfor the link element along with an exponent that defines the sharpness of thetransition from the initial stiffness to the yielded stiffness. A nonlinear staticanalysis is used to push the link element to a positive 10 inch displacement. Thena second nonlinear analysis case is started from the final conditions of the firstanalysis case and used to push the link element to a negative 10 inchdisplacement, a 20 inch push. The resulting link force at various deformations iscompared with the defined link force-deformation characteristics.

The SAP2000 model consists of a single joint, labeled joint 1, and one linkelement. The model is created in the XZ plane. Only the Uz degree of freedom isactive for the analysis. The plastic Wen link element is modeled as a single-jointlink element at joint 1. This means that one end of the link element is connectedto the ground and the other end is connected to joint 1. The link element isoriented such that its positive local 2 axis is parallel to the positive global Z axis.This is not the default orientation of single joint link elements so SAP2000’sadvanced local axes assignment feature for link elements is used to orient thelocal axes as desired. Only U2 degree of freedom properties are defined for thelink element.

Only the nonlinear properties of the link element are relevant for this examplebecause the only analysis cases used are nonlinear analysis cases. The stiffness ofthe link element is 100 k/in. The yield force is 50 kips. The ratio of initialstiffness to yielded stiffness is 0.1; in other words, the yielded stiffness is 10 k/in.The yielding exponent, which controls the sharpness of the transition from theinitial stiffness to the yielded stiffness, is 1.

The weight of the link is 1 kip. This is the only load acting on the link, and it isapplied as a gravity load acting in the Z direction.

Two displacement-controlled nonlinear static analysis cases are used in thisexample. They are named NLSTAT1 and NLSTAT2. NLSTAT1 starts from zeroinitial conditions and pushes the link to a positive 10 inch deformation.NLSTAT2 starts from the conditions at the end of NLSTAT1 and pushes the linkfrom a positive 10 inch deformation to a negative 10 inch deformation.


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EXAMPLE 6-008 - 2

GEOMETRY, PROPERTIES AND LOADING

LoadingSelf weight is applied as a gravity load

Active Degrees of FreedomUz only

Plastic Wen link oriented with local 2 axis in global Z direction. Self weight of link is 1 kip.

Link Properties (U2 DOF)Linear Properties

Not usedShear Distance

Not used for zero length linkNonlinear Properties

Stiffness, k = 100 k/inYield force, y = 50 kYield ratio, r = 0.1Yield exponent, e = 1

Z

X

12

1

Link local axes orientation

1

k

1

k

1r * k

yield, y

Link Deformation, d

Link

For

ce, f Yield exponent, e,

controls sharpness of transition from initial stiffness to yielded stiffness

The link force-deformation characteristics are controlled by the following equation:

f = r k d + (1 – r) y z

where

k, r and y are defined abovef = forced = deformationz = hysteretic variable where -1 <= z <= 1,

the initial value of z is zero and zevolves according to the followingdifferential equation:

0)1( >−= zdifzdy

kz

e

otherwisedy

kz =


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EXAMPLE 6-008 - 3

TECHNICAL FEATURES OF SAP2000 TESTED

Plastic Wen links Displacement-controlled nonlinear static analysis Link local axis assignments Link gravity load

RESULTS COMPARISON

Independent results are hand calculated from the defined link force-deformationcharacteristics shown in the figure on the previous page.

OutputParameter

LinkDeformation

AnalysisCase SAP2000 Independent

PercentDifference

0.20 in NLSTAT1 16.836 16.836 0%

0.80 in NLSTAT1 43.915 43.915 0%

9.60 in NLSTAT1 141.000 141.000 0%

9.60 in NLSTAT2 105.000 105.000 0%

8.60 in NLSTAT2 48.438 48.438 0%

Link force atspecified

deformationfor specifiedanalysis case

kips

-9.60 in NLSTAT2 -141.000 -141.000 0%

The figures on the following page show a plot of link deformation versus thehysteretic variable, z, and a plot of link deformation versus link force. Data isplotted for both analysis case NLSTAT1 and analysis case NLSTAT2.


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EXAMPLE 6-008 - 4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-10 -8 -6 -4 -2 0 2 4 6 8 10

Link Deformation (inches)

Hys

tere

tic

Var

iab

le Z

(u

nit

less

)

NLSTAT1

NLSTAT2

-150

-100

-50

0

50

100

150

-10 -8 -6 -4 -2 0 2 4 6 8 10

Link Deformation (inches)

Lin

k F

orc

e (k

ips)

NLSTAT1

NLSTAT2


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EXAMPLE 6-008 - 5

COMPUTER FILE: Example 6-008

CONCLUSION

The SAP2000 results show an exact comparison with the independent results.


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EXAMPLE 6-008 - 6

HAND CALCULATION


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EXAMPLE 6-008 - 7


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EXAMPLE 6-008 - 8


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EXAMPLE 6-008 - 9


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EXAMPLE 6-008 - 10


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EXAMPLE 6-008 - 11


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EXAMPLE 6-008 - 12


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EXAMPLE 6-008 - 13


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EXAMPLE 6-008 - 14


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EXAMPLE 6-008 - 15


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EXAMPLE 6-008 - 16


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EXAMPLE 6-008 - 17


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EXAMPLE 6-008 - 18

SAP2000 - Problem 6-008

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