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 .
The mathematical model is schematized below.


Geometry | Material Properties (Ferretic Steel)/Load | ||
---|---|---|---|
Flange thickness | Load | ||
Web thickness | Young's Modulus | ||
Beam height | Poisson Ratio | ||
Beam length | Density | ||
Flange length |
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
, as:
(5264)
where
is the moment of inertia about the x axis,
is the bending moment, and all the remaining quantities are listed in the table above.