Question A2.19: A simply supported beam carries point loads as shown in Fig....
A simply supported beam carries point loads as shown in Fig. 19. Draw SFD and BMD. [MDU, May 2010]
The loaded beam is shown in Fig. 20 (a)
R_A+R_B=12+8+10=30 \mathrm{\ kN} \text {. }
Taking moments about B, we have
\begin{aligned}7.5 R_A &=12 \times 6.5+8 \times 4.5+10 \times 3=144 \\R_A &=19.2 \mathrm{\ kN} \\R_B &=30-19.2=10.8 \mathrm{\ kN}\end{aligned}
S.F.D.
\begin{aligned}&F_A=R_A=19.2 \mathrm{\ kN} \\&F_C=19.2-12=7.2 \mathrm{\ kN} \\&F_D=7.2-8=-0.8 \mathrm{\ kN} \\&F_E=-0.8-10=-10.8 \mathrm{\ kN} \\&F_B=-10.8 \mathrm{\ kN}\end{aligned}
The S.F.D. is shown in Fig. 20 (b).
B.M.D.
\begin{aligned}M_A &=0 \\M_C &=19.2 \times 1=19.2 \mathrm{\ kN} . \mathrm{m} \\M_D &=19.2 \times 3-12 \times 2=57.6-24=33.6 \mathrm{\ kN} . \mathrm{m} \\M_E &=19.2 \times 4.5-12 \times 3.5-8 \times 1.5=32.4 \mathrm{\ kN} . \mathrm{m} \\M_B &=0\end{aligned}
The B.M.D. is shown in Fig. 20 (c).
