A cantilever beam projects 1.5 m from its support and carries a uniformly distributed load of 16 kN/m over its whole length together with a load of 30 kN at 0.75 m from the support. The outer end rests on a prop which compresses 0.12 mmfor every kN of compressive load. If the value of EI for the beam is $2000 kNm ^{2}$ , determine the reaction in the prop.
Ans. 23.4 kN.

Question

A cantilever beam projects 1.5 m from its support and carries a uniformly distributed load of 16 kN/m over its whole length together with a load of 30 kN at 0.75 m from the support. The outer end rests on a prop which compresses 0.12 mmfor every kN of compressive load. If the value of EI for the beam is [latex]2000 kNm ^{2}[/latex], determine the reaction in the prop.
Ans. 23.4 kN.

Accepted Answer

Using the moment-area method and referring to Fig. S.13.29, Eq. (13.10),

[latex]x_{ B }\left(\frac{ d v}{ d x} ight)_{ B }-x_{ A }\left(\frac{ d v}{ d x} ight)_{ A }-\left(v_{ B }-v_{ A } ight)=\int_{ A }^{ B } \frac{M}{E I} x d x[/latex] (13.10)

with the origin for x at B, becomes

[latex]v_{ B }=0.12 imes 10^{-3} R_{ B }=\left(\frac{1}{E I} ight)\left[\int_{0}^{0.75}\left(R_{ B } x-\frac{16 x^{2}}{2} ight) x d x+\int_{0.75}^{1.5}\left(R_{ B } x-\frac{16 x^{2}}{2}-30(x-0.75) ight) x d x ight][/latex]

i.e.

[latex]E I imes 0.12 imes 10^{-3} R_{ B }=\left[\frac{R_{ B } x^{3}}{3}-2 x^{4} ight]_{0}^{0.75}-30\left[\frac{x^{3}}{3}-\frac{0.75 x^{2}}{2} ight]_{0.75}^{1.5}[/latex]

which gives

[latex]R_{ B }=23.4 kN[/latex].

Question 13.P.29: A cantilever beam projects 1.5 m from its support and carrie...

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