A beam 10 m long is simply supported at its ends and carries concentrated loads of 30 kN and 50 kN at distances of 3 m, from each end. Draw the S.F. and B.M. diagram.

Question

A beam 10 m long is simply supported at its ends and carries concentrated loads of 30 kN and 50 kN at distances of 3 m, from each end. Draw the S.F. and B.M. diagram. [KU, June 2009]

Accepted Answer

The loading diagram is shown in Fig. 9 (a).

[latex]R_A+R_B=30+50=80 \mathrm{\ kN}[/latex]

Taking moments about B, we have

[latex]10 R_A=30 imes 7+50 imes 3=360[/latex]

[latex]\begin{aligned}&R_A=36 \mathrm{\ kN} \&R_B=80-36=44 \mathrm{\ kN}\end{aligned}[/latex]

S.F.D.

Span AC :

[latex]\begin{aligned}&F_x=R_A=36 \mathrm{\ kN} \&F_A=F_C=36 \mathrm{\ kN}\end{aligned}[/latex]

Span CD :

[latex]\begin{aligned}&F_x=36-30=6 \mathrm{\ kN} \&F_C=F_D=6 \mathrm{\ kN}\end{aligned}[/latex]

Span DB:

[latex]\begin{aligned}&F_x=36-30-50=-44 \mathrm{\ kN} \&F_B=-44 \mathrm{\ kN}\end{aligned}[/latex]

The S.F.D. is shown in Fig. 9 (b).

B.M.D.

Span AC :

[latex]\begin{aligned}&M_x=36 x \&M_A=0, M_C=36 imes 3=108 \mathrm{\ kN} . \mathrm{m}\end{aligned}[/latex]

Span CD :

[latex]\begin{aligned}M_x &=36 x-30(x-3) \M_D &=36 imes 7-30(7-3)=252-120=132 ext { kN.m }\end{aligned}[/latex]

Span DB :

[latex]M_B=0[/latex]

Question A2.10: A beam 10 m long is simply supported at its ends and carries...

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