Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-003 FRAME - DISTRIBUTED AND CONCENTRATED MOMENTS EXAMPLE DESCRIPTION This example tests distributed and concentrated moments assigned to frame objects, by applying torsional moments on a shaft. In SAP2000, you can apply distributed (uniform, trapezoidal and triangular) and concentrated moments to frame objects. In this example a 1-inch-diameter circular shaft, fixed at one end, is loaded with various types of torsional moments in two different load cases. The resulting torsional reaction at the fixed end and the rotation at two joints along the shaft are compared with independent, hand calculated results. GEOMETRY, PROPERTIES AND LOADING 10" 5" Z
1 1
2"
1"
2
3 4 3 4 Geometry
2 X 1 k-in/in
2" 5
2 k-in Load Case 1
1.5 k-in/in 2 k-in Load Case 2
Material Properties E = 28,990 k/in2 v = 0.3 G = 11,150
Section Properties J = 0.09817 in4
Load Cases Load Case 1: 1 k-in/in uniform distributed torsion on frame element 2 and 2 k-in torsion on the joint 4 end of frame object 3 Load Case 2: Triangular distributed torsion with a maximum value of 1.5 k-in/in on frame element 1 and 2 k-in torsion on the joint 5 end of frame object 4
EXAMPLE 1-003 - 1
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
TECHNICAL FEATURES OF SAP2000 TESTED The application of Distributed moments (uniform, trapezoidal, triangular) to frame objects Concentrated moments to frame objects RESULTS COMPARISON The independent results are based on hand calculations using equation 8.1.3 on page 284 in Cook and Young 1985. Load Case
1
2
Output Parameters
SAP2000
Independent
Percent Difference
Mx(jt. 1) k-in
-4.0
-4.0
0%
Rx (jt. 3) rad.
0.02375
0. 02375
0%
Rx (jt. 5) rad.
0.02558
0. 02558
0%
Mx(jt. 1) k-in
-5.75
-5.75
0%
Rx (jt. 3) rad.
0.02421
0. 02421
0%
Rx (jt.5) rad.
0.02969
0. 02969
0%
COMPUTER FILE: Example 1-003 CONCLUSION The SAP2000 results show an exact match with the independent solution.
EXAMPLE 1-003 - 2
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
HAND CALCULATION
EXAMPLE 1-003 - 3
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-003 - 4