Lateral Torsional Buckling Analysis of a Steel Beam - Mathematical and Matlab Coding Software

This assignment has to be a report version by using hand calculations or Mathematical and Matlab coding software and the Abaqus model for analyzing if needed. As long as, answer all the 4 questions clearly will be fine. Finally, the Images, graphs, and code must be attached.

When a concentrated load is applied on a simply supported I-beam, the top flange of beam is in compression, and the bottom flange is in tension. If the beam is not laterally supported (i.e., perpendicular to the plane of bending), it will experience a lateral deflection of the compression flange as the load increases. The lateral deflection of the compression flange is restrained by the beam web and tension flange, but for an open section the twisting mode is more flexible, hence the beam both twists and deflects laterally in a failure mode known as lateral-torsional buckling [1]. Here is an example of a real torsional buckling test [2].

As a first step, the student is asked to choose the proper size of a simply supported I-beam that can fail in a lateral torsional mode under a concentrated load at mid-span, and conduct an elastoplastic FEA analysis with proper material properties on this beam. The student is then asked to extend the work to different sizes of simply supported I-beams.

-For elastoplastic analysis, applying concentrated loads might lead to stress concentrations leading to high local deformations. In that case, the student should investigate apply the load in alternate ways such as using contact, as a distributed load, or as a concentrated load on a reference point rigidly attached to a small area of the beam.

-The boundary conditions at the supports have a large effect on the solution. The requirement of: “simply supported” is only concerned with the in-plane stability. Out-of-plane stability should be considered and appropriate out-of-plane boundary conditions and their effect on the solution should be discussed.

1. Describe the setup of the model such as dimensions of the beam, boundary conditions and the loading conditions.

2. Describe and the major steps you have to model the buckling behavior of the beam.

3. The calculation of theoretical flexural buckling capacity according to CAN/CSA-S16.

4. Compare and comment on the difference between the theoretical and FEA results.