VM-LSDYNA-SOLVE-023

VM-LSDYNA-SOLVE-023
I-Shape Beam Deflection Under Uniformly Distributed Loads

Overview

Reference:	Timoshenko, S.P. (1995). Strength of materials: Part I: Elementary theory and problems. (3rd ed.). D. Van Nostrand Co. p.10.
Analysis Type(s):	Implicit Analysis
Element Type(s):	Beam (I-shape cross section)

Test Case

A standard 30 in WF beam with a cross-sectional area A, is supported as shown in Figure 90 and loaded on the overhangs by a uniformly distributed load w. Determine the deflection 𝛅 at the middle of the beam.

This problem is also presented in test case VM2 in the Mechanical APDL Verification Manual.

Figure 90: Problem Sketch

Material Properties	Geometric Properties	Loading
E = 3e7 psi	L = 240 in a = 120 in h = 30 in A = 50.65 in² I_z = 7892 in⁴	w = 10000 / 12 = 833.33 lb/in

Material Properties

Geometric Properties

E = 3e7 psi

L = 240 in

a = 120 in

h = 30 in

A = 50.65 in²

I_z = 7892 in⁴

w = 10000 / 12 = 833.33 lb/in

Analysis Assumptions and Modeling Notes

The beam is modeled with beam element elform 2 with an I-shaped cross section (SECTION_01). The geometric parameters for the I-shape cross section are defined as D1 = 15, D2 = 1.0484, D3 = 30.0968, and D4 = 0.6856481. The orientations of the beam elements are defined in the *ELEMENT_BEAM_ORIENTATION card. *LOAD_NODE_POINT is used to apply equal load at each node of the beam overhangs. An implicit analysis is performed to obtain beam deflection.

Figure 91: Representative Finite Element Model

Equal load is applied to the seven nodes at the two beam overhangs as shown in Figure 92. The load applied at each node = w x a/7.

Figure 92: Loading in the LSDYNA Model

Results Comparison

Figure 93: Deflected Beam from the LS-DYNA Analysis

Results	Target	LS-DYNA Solver	Error (%)
Deflection at middle point (in)	0.182	0.1825	0.27