Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 1-010 - 1

EXAMPLE 1-010 FRAME - END OFFSETS

EXAMPLE DESCRIPTION This example uses a cantilever beam to test the SAP2000 end offsets. In SAP2000, end offsets may be non-rigid, partially rigid, or fully rigid. The rigidity of the offset is specified by a rigid zone factor. This factor specifies the fraction of the end offset length, measured from the frame element end, that is assumed to be infinitely rigid. The remainder of the end offset, if any, is assumed to have the same flexibility as the beam.

Four models are created in this example. The first has no end offset, the second through fourth have an end offset with 0%, 50% and 100% rigidity, respectively. For each model the vertical displacement at the free end of the cantilever is compared with independent hand calculated results.

Important Note: Bending and shear deformations are included in the analyses for this example.

GEOMETRY, PROPERTIES AND LOADING

12' Material Properties

End Offsets

E = 4,320 k/in2 = 0.2G= 1,800 k/in2

Model A: a = 0, no end offsetModel B: a = 6" end offset, 0% rigidModel C: a = 6" end offset, 50% rigidModel D: a = 6" end offset, 100% rigid

Section Propertiesb = 12 ind = 18 inA = 216 in2I = 5,832 in4Av = 180 in2 (shear area)

Z

XY

a10k

C

CEnd offset

Section C-C

18"

12"

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 1-010 - 2

TECHNICAL FEATURES OF SAP2000 TESTED The use of end offsets in frames, including

Non-rigid offsets Partially rigid offsets Fully rigid offsets

The effect of end offsets on the frame static analysis results RESULTS COMPARISON

Independent results are hand calculated using the unit load method described on page 244 in Cook and Young 1985.

Model

Rigid Zone

Factor Output

Parameter SAP2000 Independent Percent

Difference

A N.A. Uz (free end) in -0.39951 -0.39951 0%

B 0.0 Uz (free end) in -0.39951 -0.39951 0%

C 0.5 Uz (free end) in -0.37523 -0.37523 0%

D 1.0 Uz (free end) in -0.35197 -0.35197 0%

COMPUTER FILE: Example 1-010a, Example 1-010b, Example 1-010c, Example 1-010d

CONCLUSION The SAP2000 results match exactly with the independent results.

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0

EXAMPLE 1-010 - 3

HAND CALCULATION

EXAMPLE 1-010Frame - End OffsetsExample DescriptionGeometry, Properties and LoadingTechnical Features of SAP2000 TestedResults ComparisonComputer File: Example 1-010a, Example 1-010b, Example 1-010c, Example 1-010dConclusionHand Calculation