Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 6-009 - 1

EXAMPLE 6-009 LINK PLASTIC KINEMATIC LINK

PROBLEM DESCRIPTION This example uses a single degree of freedom structure to test the behavior of a plastic kinematic link element. Multi-linear force-deformation characteristics are defined for the link element for both tension and compression behavior. The force-deformation characteristics modeled for tension are different from those modeled for compression. A nonlinear static analysis is used to push the link element to a positive 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 negative 12 inch displacement, a 24 inch push. The resulting link force at various deformations is compared with the defined link force-deformation characteristics.

The SAP2000 model consists of a single joint, labeled joint 1, and one link element. The model is created in the XZ plane. Only the Uz degree of freedom is active for the analysis. The plastic kinematic link element is modeled as a single-joint link element at joint 1. This means that one end of the link element is connected to the ground and the other end is connected to joint 1. The link element is oriented such that its positive local 1 axis is parallel to the positive global Z axis. This is the default orientation of single joint link elements. Only U1 degree of freedom properties are defined for the link element.

Only the nonlinear properties of the link element are relevant for this example because the only load cases used are nonlinear load cases. The nonlinear force-deformation characteristics of the link are defined in the table and chart on the following page.

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

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 to a positive 12 inch deformation. NLSTAT2 starts from the conditions at the end of NLSTAT1 and pushes the link from a positive 12 inch deformation to a negative 12 inch deformation.

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 6-009 - 2

GEOMETRY, PROPERTIES AND LOADING

Linear PropertiesNot used

Shear Distance Not used for zero length link

Nonlinear Properties

LoadingSelf weight is applied as a gravity load

Active Degrees of FreedomUz only

Plastic kinematiclink. Self weight of link is 1 kip.

Link Properties (U1 DOF)

Z

X

1

Force (kip)Deformation (in)-55-16-50-6-40-100

5027068016

See force-deformation chart to left

PointABCDEFG-80

-60

-40

-20

0

20

40

60

80

-16 -12 -8 -4 0 4 8 12 16

Link Deformation (inch)

Link

For

ce (k

ip)

AB C

D

E

FG

HYSTERETIC BEHAVIOR OF PLASTIC KINEMATIC LINKS The hysteretic behavior for the plastic kinematic link element is described in detail in the SAP2000 Analysis Reference Manual. This section describes the hysteretic behavior as it relates to this example.

Link Deformation

Consider the link force-deformation relationship shown in the figure to the right. Segments D-E and D-C represent elastic deformation. Segments E-F, F-G, C-B and B-A represent plastic deformation. For elastic deformation, the loading and

Link

For

ce

A BC

D

EF G

X

Link Deformation

For

ce

A BC

D

EF G

X

Link

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 6-009 - 3

unloading follow the same path. For plastic deformation, the unloading follows a different path from the loading.

his is illustrated in the first figure to the right.

e second figure shown to the right.

Assume that the loading is positive and starts from zero at point D and proceeds along path D-E-F-G until it reaches point X. At point X the load reverses direction.

As the load passes through point E and proceeds to point F, point E is pulled along with the load along segment E-F such that when the load reaches point F, points E' and F are in the same location. Similarly, as the load passes through point F and proceeds to point X, points E' and F are pulled along with the load along segment F-G such that when the load reaches point X, points X, E' and F' are in the same location. Link Deformation

Link

For

ce

A BC

D

EF G

C'C

D'

X, E', F'

B'Link Deformation

Link

For

ce

A BC

D

EF G

C'C

D'

X, E', F'

B'

As point E is pulled, it pulls points C and D along a similar path to points C' and D', respectively. Similarly, as point F is pulled, it pulls point B along a similar path to point B'. T

Link Deformation

Link

For

ce

A BC

D

EF G

C'C

D'

X, E', F'

B'Link Deformation

Link

For

ce

A BC

D

EF G

C'C

D'

X, E', F'

B'

When the load reverses, it follows path X-D'-C'-B'-A and then continues out on the slope defined by B-A. This is illustrated in th

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 6-009 - 4

TECHNICAL FEATURES OF SAP2000 TESTED Plastic kinematic links Displacement-controlled nonlinear static analysis Link gravity load

RESULTS COMPARISON Independent results are hand calculated from the defined link force-deformation characteristics and hysteretic behavior.

Output Parameter

Link Deformation

Load Case SAP2000 Independent

Percent Difference

1.2 in NLSTAT1 30 30 0%

4.2 in NLSTAT1 61 61 0%

12 in NLSTAT1 76 76 0%

11.52 in NLSTAT2 64 64 0%

9.6 in NLSTAT2 10 10 0%

2.4 in NLSTAT2 -36 -36 0%

Link force at specified

deformation for specified

load case

kips

-12 in NLSTAT2 -52.25 -52.25 0%

The following figure shows a plot of the link force versus deformation results obtained from SAP2000 for load cases NLSTAT1 and NLSTAT2.

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 6-009 - 5

-60

-40

-20

0

20

40

60

80

-12 -8 -4 0 4 8 12

Deformation (inch)

Forc

e (k

ip)

NLSTAT1 NLSTAT2

COMPUTER FILE: Example 6-009

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

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 6-009 - 6

HAND CALCULATION

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 6-009 - 7

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 6-009 - 8

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 6-009 - 9

EXAMPLE 6-009Link Plastic Kinematic LinkProblem DescriptionGeometry, Properties and loadingHysteretic Behavior of Plastic Kinematic LinksTechnical Features of SAP2000 TestedResults ComparisonComputer File: Example 6-009ConclusionHand Calculation