VM243

VM243
Cantilever Beam with Triangular Loading Defined by Function

Overview

Reference:	F. P. Beer and E. J. Johnston, Jr., Mechanics of Materials, McGraw-Hill, New York, NY, 1981, pp. 356, 366, 397, 613
Analysis Type(s):	Static
Element Type(s):	PLANE183
Input Listing:	vm243.dat

Test Case

Figure 414: Cantilever Beam with Triangular Loading

Material Properties

Geometric Properties

E = 30E6

s = 1

L = 10

w(x = 0) = 1

w(x = L) = 0

linear variation between them

Analysis Assumptions and Modeling Notes

Two models are used to test the method of creating a functional load. In the first case, the loading function P(x) is applied using the functional loading to create a load corresponding to P(x) = (x/L) In the second case, the loading is applied using the established two value linear loading. According to beam theory, the equation for maximum displacement of this loading is:

This result is then compared against the results

Results Comparison

	Target	Mechanical APDL	Ratio
Displacement (max), tabular loading	0.367E-3	0.370E-3	1.01
Displacement (max), two value linear loading	0.367E-3	0.370E-3	1.01