Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 1
EXAMPLE 1-016 FRAME - TENSION STIFFENING USING P-DELTA ANALYSIS EXAMPLE DESCRIPTION The SAP2000 tension stiffening calculation using P-Delta analysis is verified in this example using a tie rod (beam) with a large axial force. In this example a simply supported, 3-inch-square, steel beam has a large axial force and a small transverse uniform load. The deflection in the direction of the transverse load (global Z direction) is reduced because of the stiffening effect of the tension force. The values of the midpoint deflection and bending moment with and without tension stiffening are calculated and compared with independent results derived using formulas presented in Timoshenko 1956. Two different methods are used to apply the tension stiffening. In one method, a P-Delta force equal to the specified tension is assigned directly to the beam. The beam is then analyzed in a linear static load case with the transverse loading applied. In the second method, the tension is applied to the beam in a nonlinear static load case that is specified to consider P-Delta effects. The beam is then analyzed in a separate linear static load case with the transverse loading applied. This second load case is specified to use the stiffness at the end of the static nonlinear case. The beam is modeled with two objects so that there is a midpoint node where displacements are reported. Several models are created using different discretizations of the frame objects Important Note: Shear deformations are ignored in the analysis by setting the frame property modification factor for shear area to zero. GEOMETRY, PROPERTIES AND LOADING 0.002 k/in
Z Y
1 X
2 150"
3 150"
300"
20.25 k
Material Properties E = 30,000 k/in2 Section Properties b = 3 in d = 3 in I = 6.75 in4
EXAMPLE 1-016 - 1