5-Shear force and bending moment diagrams PDF

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Shear force and bending moment diagrams

In most practical situations beams are subjected to a combination of concentrated loads and uniformly distributed loads (u.d.l). In this session we will first of all study the effect of uniformly distributed loads, and then we will consider the effect of combined loads, i.e. both concentrated and uniformly distributed loads. Example 1

A uniform beam AB is 4 m long and simply supported at each end. It carries a uniformly distributed load of 5 kNm–1 throughout its entire length. Construct shear force and bending moment diagrams for the beam, showing bending moment calculations at 1 m intervals along the beam.

Remember – write down your principles and work from there…

Example 2 A uniform beam AB is 5 m long and simply supported at each end. It carries a uniformly distributed load of 8 kN m–1 over its entire length and a concentrated load of 50 kN acting vertically downwards at 2 m from A. Sketch shear force and bending moment diagrams for the beam showing bending moment calculations at 1 m intervals along the beam.

Example 3

A uniform beam is 6 m long and carries a uniformly distributed load of 10 kN m–1 over its entire length. It is simply supported at its left-hand end and at a point 5 m from its left-hand end. It carries concentrated loads as shown below. Sketch shear force and bending moment diagrams for the beam showing bending moment values at 1 m intervals along the beam.

Further problems 1. A beam is 5 m long and is simply supported at each end. It carries a uniformly distributed load of 10 kN m–1 along its entire length and it also carries concentrated loads of 20 kN and 40 kN vertically downwards at 2 m and 4 m respectively from the left-hand support. Sketch shear force and bending moment diagrams for the beam, showing bending moment calculations at 1 m intervals along the beam. State the magnitude and position of the maximum bending moment.

2. A beam is 10 m long and is simply supported at its left-hand end (A) and at point B which is 8 m from its left-hand end. It carries a uniformly distributed load of 20 kN m–1 along its entire length. It also carries concentrated loads as shown below.

Complete the following tasks: (i) Sketch shear force and bending moment diagrams for the beam. (ii) State position and magnitude of maximum bending moment.

Solution area: Solution diagrams – example 1

There are some key points to consider from your diagrams and the solution above… Note – the maximum bending moment occurs where the SF diagram crosses the x axis. Also the BM diagram is constructed with a smooth curve connecting plotted points. Solution diagrams – example 2

Solution diagrams – example 3...