VM2

VM2
Beam Stresses and Deflections

Overview

Reference:	S. Timoshenko, Strength of Material, Part I, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 98, problem 4.
Analysis Type(s):	Static Analysis (ANTYPE = 0)
Element Type(s):	3D 2 Node Beam (BEAM188)
Input Listing:	vm2.dat

Test Case

A standard 30" WF beam, with a cross-sectional area A, is supported as shown below and loaded on the overhangs by a uniformly distributed load w. Determine the maximum bending stress σ in the middle portion of the beam and the deflection δ at the middle of the beam.

Figure 2: Beam with Cross Section Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

= 20 ft = 240 in.

a = 10 ft = 120 in.

h = 30 in.

A = 50.65 in²

I_z = 7892 in⁴

w = 10000 lb/ft = (10000/12) lb/in

Analysis Assumptions and Modeling Notes

An I-section beam is modeled. The width, depth, and thickness of the flanges are chosen to obtain the required area and moment of inertia values. Consistent length units (inches) are used. A half-model could also have been used because of symmetry.

Results Comparison

	Target	Mechanical APDL	Ratio
Stress, psi	-11400.000	-11440.746	1.004
Deflection, in	0.182	0.182	1.003

occurs at the bottom flange of the beam

Figure 3: Displaced Geometry Display