Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-015 FRAME - STEADY STATE HARMONIC LOADS EXAMPLE DESCRIPTION Steady state and periodic time history analysis are verified in this example using a fixed-end beam that is subjected to a uniformly distributed load varying harmonically with respect to time. The maximum midpoint deflections from the SAP2000 analyses are compared with independent results published in Paz 1985. The example is solved using two different calculation methods. They are undamped steady state analysis; and periodic time history analysis. For the steady state analysis, the frequency of the forcing function is used as input into SAP2000. For the time-history analysis, one complete cycle of the sine wave loading function, discretized at 100 equal intervals, is used as input, and, for consistency with Paz 1985, five modes are used in the time history analysis. The fixed end beam is modeled with two objects so that there is a midpoint node where displacements are reported. Each of the objects is internally meshed in SAP2000 into 120 elements each one inch long. Because the line mass in the SAP2000 analysis is lumped at the nodes, this discretization of the beam provides a good approximation of the uniform mass assumed in the example. Important Note: Only bending deformations are considered in this analysis. Shear deformations are ignored by setting the frame property modification factor for shear area to zero. Axial and torsional modes are excluded by excluding the Ux and Rx degrees of freedom from the analysis. GEOMETRY , PROPERTIES AND LOADING
Material Properties E = 3,000,000 lb/in2 Mass per unit length = 0.1 lb-sec2/in2
200sin(300t)
Z
X
1
2 120"
3 120"
240"
Section Properties b = 12 in d = 10 in I = 1,000 in4
EXAMPLE 1-015 - 1