problem 6-002

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Software Verification

PROGRAM NAME: SAP2000

REVISION NO.: 8

EXAMPLE 6-002 - 1

EXAMPLE 6-002

LINKMULTI-LINEAR ELASTIC LINK

PROBLEM DESCRIPTION

This example uses a single degree of freedom structure to test the behavior of a

multi-linear elastic (no hysteresis) link element. Multi-linear elastic force-

deformation characteristics are defined for the link element. A nonlinear staticanalysis is used to push the link element to a negative 12 inch displacement.

Then a second nonlinear load case is started from the final conditions of the first

load case and used to push the link element to a positive 12 inch displacement, a24 inch push. The link force at the end of each load case is compared with thedefined link force-deformation characteristics. In addition the entire force-

deformation history for each load case is graphically compared with the defined

link force-deformation characteristics.

The SAP2000 model consists of a two-joint multi-linear link element that is fixedat one end and free at the other end. As shown in the following figure, the link is

modeled in the XZ plane and is oriented such that its length (and thus its local 1

axis) is parallel to the global Z axis. The link element length is arbitrarily chosen

as ten inches.

The only active degree of freedom in the model is Uz. Similarly, the only degreeof freedom in the linear link element with nonzero properties is the U1 (axial)

degree of freedom.

A unit load is applied in the positive Z direction at joint 2. This load is used in

the displacement-controlled static nonlinear analysis.

GEOMETRY

k(z)

p(z)

u(z)

1

2

p(z)

Z

Y

X

Multilinear link element

with force-displacement

characteristics, k(z),

defined for the U1 degree

of freedom

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REVISION NO.: 8

EXAMPLE 6-002 - 2

LINK PROPERTIES

The link force-deformation characteristics are

defined as shown in the table to the right. This

table is plotted in the following figure. The solidline in the force-deformation plot is the data

actually included in the table. The dotted lines in

the plot show how SAP2000 extrapolates theprovided data to reach the desired deformations.

In general, for the multi-linear link, the slope

given by the last two specified points on thepositive deformation axis is extrapolated to

infinite positive deformation. Similarly, the slope

given by the last two specified points on the

negative deformation axis is extrapolated toinfinite negative deformation.

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Link Deformation (in)

Link

Force

(kips)

Deformation(in)

Force(kips)

-10 -50

-6 -30

-5 -40

-3 -40

0 0

2 40

7 50

8 30

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REVISION NO.: 8

EXAMPLE 6-002 - 3

LOAD CASE DEFINITIONS

Two displacement-controlled nonlinear static load cases are used in this example.

They are named NLSTAT1 and NLSTAT2.

NLSTAT1 starts from zero initial conditions and pushes the link out to a negative

12 inch deformation.

NLSTAT2 starts from the conditions at the end of NLSTAT1 and pushes the link

from a negative 12 inch deformation to a positive 12 inch deformation.

TECHNICAL FEATURES OF SAP2000TESTED Multi-linear links Displacement-controlled nonlinear static analysis

RESULTS COMPARISON

Independent results are obtained from the defined link force-deformation

characteristics shown in the figure on the previous page.

OutputParameter Load Case SAP2000 Independent PercentDifference

NLSTAT1 -60 -60 0%Link force atlast step

kips NLSTAT2 -50 -50 0%

The figures on the following page show the link force-deformation curves

obtained from load case NLSTAT1 and NLSTAT2. As expected, these curves

exactly match the defined force-deformation characteristics for the link.

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REVISION NO.: 8

EXAMPLE 6-002 - 4

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Deformation (in)

Force(

kips)

Force-Deformation

curve for analysis

case NLSTAT1

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Deformation (in)

Force(

kips)

Force-Deformation

curve for analysis

case NLSTAT1

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Deformation (in)

Force

(kips)

Force-Deformation

curve for analysiscase NLSTAT2

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Deformation (in)

Force

(kips)

Force-Deformation

curve for analysiscase NLSTAT2

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REVISION NO.: 8

EXAMPLE 6-002 - 5

COMPUTER FILE: Example 6-002

CONCLUSION

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

The multi linear link has no hysteretic behavior. It always loads and unloadsalong the same path.

problem 6-002

Documents

Transcript of problem 6-002