Structural Analysis of Beams for Engineering Students

Structural Analysis of Beams: This tutorial paper illustrates the traditional hand calculation methods of structural analysis to determine the shear force and bending moment diagrams for statically determinate beams of differing support conditions and loading.

Case (i) start with a simple beam case to illustrate the general approach:

Bending Moment Diagram (BMD):

Shear Forces Along Beam :

Bending Moments Along Beam

Bending Moment Diagram (BMD):

Discussion: The parabolic shape of the BM is due to the UDL on the cantilever span. The shear force
diagram shape equals the gradient of the BM diagram. For point loads, the resultant bending moments is triangular in shape with a constant gradient on the shapes sides, hence there will a constant shear force value along that length of the beam. For UDLs, the BM profile is parabolic and the shape gradient is constantly changing along the length of the span under consideration, giving a varying shear force value. Refer to the associated shear force diagram for this case. For combined load types, the associated SFD and BMD shapes can be superimposed.

Case (iii) Beam with reverse loading

Shear Forces Along Beam :

Shear Force Diagram (SFD):

Discussion: note the parts of the SFD diagram where the shear force value is constant over a length
of the span. By inspection, this will inform the shape of the BMD noting that the gradient of the BMD
equals the shear force. Both end cantilever spans have a constant SF whilst over the length of the
main central span the SF is varying. This informs a straight line BMD profile at the end spans and a
parabolic shape over the central span.

Concluding Remarks

This tutorial paper is intended to assist engineering students with their understanding of beam analysis and the development of shear force and bending moment diagrams. A traditional hand calculation approach that is based upon visualising the beam in discrete sections and balancing the shears and moments is presented. A range of beam configurations and loading actions has been considered.