Static Stress Analysis of Beams of different cross-section

Aim: To perform static stress analysis on beams of different cross-section and choose best one out of them.

Introduction:

Beam is a structural element that primarily resists loads applied laterally to the beam's axis. It's mode of deflection is primarily by bending. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beam and that produces internal stress, strain and deflection of beam. Beams are characterized by their manner of support, profile (i.e. shape of cross-section), equilibrium conditions. length and their material.

In this study cantilever beams(i.e. beams that are rigidly fixed from one end) of 400mm length and of rectangular, I and C shaped cross-section are examined using static stress analysis in solidworks. The material used for beams is alloy steel.
The beams are modeled by sketching the cross-section and then extruding it.

The models of the beams and their dimensions are as shown below,

Rectangular section beam:

I section beam:

C section beam:

From the model, one can conclude that maximum material would be used in rectangular shaped beam and minimum in C shaped beam and that means cost of rectangular shaped beam would be high and that for C shaped beam would be low.

Analysis setup:

A new study is created for static stress analysis in solidworks simulation. The material is choosen as alloy steel for the beam. Fixed constrain is applied to one end of the beam and force of 1500N is applied to smaller face of the beam. Mesh size of 10mm is used for the meshing and simulation is run.

The beams setuped with force and constains are as shown below:

Rectangular section beam:

I section beam:

C section beam:

Results:

Rectangular section beam:

I section beam:

C section beam:

Result comparison:

Sr. No.	Beam Section	Von-mises Stress(MPa)	Displacement(mm)	Strain	Factor of Safety
1	Rectangular	7.354	0.031	0.000026	84.36
2	I-shaped	19.299	0.085	0.0000723	32.14
3	C-shaped	36.764	0.301	0.0001219	16.87

Conclusion:

From the results, it can be seen that the stress, strain and displacement are minimum in the rectangular shaped beams but the the factor of safety is unnecessarily high and it would be uneconomical to manufacture such beam. On the other hand, C shaped beam would be cheaper but the factor os safetly is relatively low and as far as safetly is concerned this is not recommended.
I-shaped beam is thus recommended beacause it has factor of safelty with relatively lower cost than rectangular shaped beam.