Question A2.18: A simply supported beam carries point loads as shown in Fig....
A simply supported beam carries point loads as shown in Fig. 17. Draw SFD & BMD. [MDU, Dec. 2009]
The loading diagram is shown in Fig. 18 (a).
R_A+R_B=5+10+15+2=32 \mathrm{\ kN}
Taking moments about B, we have
\begin{aligned}8.5 \mathrm{R}_{\mathrm{A}} &=5 \times 6.5+10 \times 4.5+15 \times 2.5+2 \times 1=117 \\R_A &=13.7647 \mathrm{\ kN} \\R_B &=-32-13.7647=18.2353 \mathrm{\ kN}\end{aligned}
S.F.D.
\begin{aligned}F_A &=13.7647 \mathrm{\ kN} \\F_C &=13.7647-5=8.7647 \mathrm{\ kN} \\F_D &=8.7647-10=-1.2353 \mathrm{\ kN} \\F_E &=-1.2353-15=-16.2353 \mathrm{\ kN} \\F_F &=F_B=-16.2353-2=-18.2353 \mathrm{\ kN}\end{aligned}
The S.F.D. is shown in Fig. 18 (b).
B.M.D.
\begin{aligned}&M_A=0 \\&M_C=13.7647 \times 2=27.5294 \mathrm{\ kN} . \mathrm{m} \\&M_D=13.7647 \times 4-5 \times 2=45.0588 \mathrm{\ kN} . \mathrm{m} \\&M_E=13.7647 \times 6-5 \times 4-10-2=42.5882 \mathrm{\ kN} . \mathrm{m} \\&M_F=18.2353 \times 1=18.2353 \mathrm{\ kN} . \mathrm{m} \\&M_B=0\end{aligned}
The B.M.D. is shown in Fig. 18 (c).
