The cantilever AB shown in Fig. P.3.8 carries a uniformly distributed load of 5 kN/m and a concentrated load of 15 kN at its free end. Construct the shear force and bending moment diagrams for the beam.

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Accepted Answer

The support reactions for the beam have been calculated in S.2.10(b). However, in this case, if forces and moments to the right of any section are considered, the calculation of the support reactions is unnecessary.

Shear force
At any section a distance x, say, from B the shear force is given by

[latex] S_{ AB }=-15-5 x [/latex]

Then, when [latex] x=0, S_{ AB }=-15 kN ext { and when } x=10 m , S_{ AB }=-65 kN [/latex]; the distribution is linear as shown in Fig. S.3.8(b).

Bending moment
The bending moment is given by

[latex] M_{ AB }=-15 x-5 x\left(\frac{x}{2} ight)=-15 x-\frac{5 x^{2}}{2} [/latex]

When [latex] x=0, M_{ AB }=0 ext { and when } x=10 m , M_{ AB }=-400 kNm [/latex]. The distribution, shown in Fig. S.3.8(c), is parabolic and does not have a turning value between A and B.

Question 3.8: The cantilever AB shown in Fig. P.3.8 carries a uniformly di...

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