Linear Stress Analysis: Cantilever I Beam

This tutorial demonstrates the basic concepts and workflow for linear FE (Finite Element) structural analyses in Simcenter STAR-CCM+.

The case under study is a cantilevered I beam loaded at its free end. The displacements that result from loading are assumed to be small, so that the load-displacement relationship remains linear. For simplicity, the beam is assumed weightless.

In this tutorial, you compare the numerical solution, obtained with 3D solid hexahedral elements in Simcenter STAR-CCM+, with the analytical solution given by Euler-Bernoulli beam theory. This theory is valid for slender beams with L h > 10 .

The mathematical model is schematized below.

Geometry Material Properties (Ferretic Steel)/Load
Flange thickness t f = 8.5 m m Load | F | = 800 N
Web thickness t w = 5.6 m m Young's Modulus E = 2 10 5 M P a
Beam height h = 200 m m Poisson Ratio ν = 0.3
Beam length L = 4000 m m Density ρ = 7500 k g / m 3
Flange length b = 100 m m
For this problem, Bernoulli-Euler's beam theory gives the values of the deflection at the free end, and the maximum value of the stress tensor component σ z z , as:
δ y , max = F L 3 3 E I x 4.63 m m σ z z , max = M I x h 2 17.3 M P a
(5264)
where Ix=Ay2A1845.6104mm4 is the moment of inertia about the x axis, M is the bending moment, and all the remaining quantities are listed in the table above.