Question A2.10: A beam 10 m long is simply supported at its ends and carries...
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]
The loading diagram is shown in Fig. 9 (a).
R_A+R_B=30+50=80 \mathrm{\ kN}
Taking moments about B, we have
10 R_A=30 \times 7+50 \times 3=360
\begin{aligned}&R_A=36 \mathrm{\ kN} \\&R_B=80-36=44 \mathrm{\ kN}\end{aligned}
S.F.D.
Span AC :
\begin{aligned}&F_x=R_A=36 \mathrm{\ kN} \\&F_A=F_C=36 \mathrm{\ kN}\end{aligned}
Span CD :
\begin{aligned}&F_x=36-30=6 \mathrm{\ kN} \\&F_C=F_D=6 \mathrm{\ kN}\end{aligned}
Span DB:
\begin{aligned}&F_x=36-30-50=-44 \mathrm{\ kN} \\&F_B=-44 \mathrm{\ kN}\end{aligned}
The S.F.D. is shown in Fig. 9 (b).
B.M.D.
Span AC :
\begin{aligned}&M_x=36 x \\&M_A=0, M_C=36 \times 3=108 \mathrm{\ kN} . \mathrm{m}\end{aligned}
Span CD :
\begin{aligned}M_x &=36 x-30(x-3) \\M_D &=36 \times 7-30(7-3)=252-120=132 \text { kN.m }\end{aligned}
Span DB :
M_B=0
