Software Verification

PROGRAM NAME: SAP2000

EXAMPLE 3-001
PLANE – PATCH TEST WITH PRESCRIBED DISPLACEMENTS

PROBLEM DESCRIPTION
In this example, a rectangular plate with irregularly shaped elements is subjected
to prescribed displacements at the edges that theoretically impose a constant
stress field over the model. The geometry, properties and loading are as
described in MacNeal and Harder 1985. The plane stress element is used in
SAP2000 and the membrane stress components resulting from the prescribed
displacements are compared with hand-calculated results.

The Ux and Uy degrees of freedom are active for the analysis. All other degrees
of freedom are inactive. Joints 1, 2, 7 and 8 are restrained for translation in the X
and Y directions. The prescribed displacements are applied to the restrained
degrees of freedom of those joints.

The plane section is modeled using the plane stress element. Separate models are
used to test the model with and without the incompatible bending modes option.

GEOMETRY AND PROPERTIES

0.24"
Joint Coordinates (inches)
Joint X Y Z
2 8
4 1 0 0 0
4 6 2 0 0.12 0
3 0.04 0.02 0
0.12"

1 5
3 4 0.08 0.08 0
Y 5 0.18 0.03 0
3 2 5
Z 1 7 6 0.16 0.08 0
7 0.24 0 0
1 - Joint number 8 0.24 0.12 0
X
1 - Area object number
Material Properties Section Properties
E = 1,000,000 lb/in2 Thickness = 0.001 in
ν = 0.25

EXAMPLE 3-001 - 1
 Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 2

LOADING
The loading is provided in the form of prescribed edge displacements Ux and Uy,
which are imposed on joints 1, 2, 7 and 8. Those displacements are defined by
the following equations.

y x
x y
Ux  2, Uy  2
1000 1000

The following table shows the applied displacements calculated from the
preceding equations for each of the edge joints. These displacements are applied
in a load case named Membrane.

X Y Ux Uy
Joint (in) (in) (in) (in)

1 0 0 0 0

2 0 0.12 0.00006 0.00012

7 0.24 0 0.00024 0.00012

8 0.24 0.12 0.00030 0.00024

TECHNICAL FEATURES OF SAP2000 TESTED

RESULTS COMPARISON
The independent results are based on Equation 2 on page 6 in Timoshenko and
Goodier 1951. Additional independent results are published in MacNeal and
Harder 1985.

EXAMPLE 3-001 - 2
 Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 2

With Incompatible Bending Modes

Percent
Stress Component SAP2000 Independent Difference
Direct stress σxx lb/in2 1333 1333 0%
Direct stress σyy lb/in2 1333 1333 0%
Shear stress σxy lb/in2 400 400 0%

Without Incompatible Bending Modes

Percent
Stress Component SAP2000 Independent Difference
Direct stress σxx lb/in2 1333 1333 0%
Direct stress σyy lb/in2 1333 1333 0%
Shear stress σxy lb/in2 400 400 0%

COMPUTER FILES: Example 3-001-incomp, Example 3-001-comp

CONCLUSION
The SAP2000 results show an exact comparison with the independent results
both with and without the incompatible bending modes option..

EXAMPLE 3-001 - 3
 Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 2

HAND CALCULATION

EXAMPLE 3-001 - 4
Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 2

EXAMPLE 3-001 - 5