Determine the deflection of a cantilever beam at the free end; determine the stress at the midpoint of the beam.
Problem description:
The model consists in a 480 in. beam fixed at one end and free at the other; the section oh the beam is a square, 30 x 30 in. The beam is made of steel, E = 30e6 psi, nu = 0.3.
The free end is subjected to a load of 50 000 lb in the Y direction.
Expected results:
The following results are expected to be obtained:
- von Mises stress at midpoint 5333 psi;
- Y deflection at the free end 0.9102 in.
Solving in Abaqus/CAE:
The first thing I would like to do before solving this is to change all the units to the metric system; it is not that I don't like it but it doesn't have much meaning to me. Therefore we have the dimensions of the beam 0.762 x 0.762 x 12.192 m; Young's modulus is 206.84 GPa; the load is 222.411 kN.
The expected values are 36.77 MPa and 23.1 mm.
The geometry looks like this:
In order to get a precise value of the stress at the middle of the beam we have to make a partition of the beam:
The mesh of the assembly:
The loads applied:
Results:
Value of the stress at the middle section =
The deflection plot:
The maximum deflection is at the free end and it is .
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