Question 20.P.12: One of the main girders of a bridge is the truss shown in Fi...
One of the main girders of a bridge is the truss shown in Fig. P.20.12. Loads are transmitted to the truss through cross beams attached at the lower panel points. The self-weight of the truss is 30 kN/m and it carries a live load of intensity 15 kN/m and of length greater than the span. Draw influence lines for the force in each of the members CE and DE and determine their maximum values.
When unit load is to the right of E, F_{CE} may be found by taking moments about the intersection of GC and ED produced and is then equal to 0.95R_{A}. When unit load is to the left of D, V may be found by taking moments about the intersection of GH and DE produced. Then, F_{CE} = – 2.085 R_{B}. The IL is then as shown in Fig. S.20.12(a). Further, F_{DE} = M_{C}/3 and the IL is as shown in Fig. S.20.12(b).
Then
\begin{gathered}F_{\mathrm{CE}}(\max . \text { pos })=-30\left(0.695 \times \frac{10.38}{2}\right)+45\left(0.475 \times \frac{13.62}{2}\right)=37.3 \mathrm{\ kN} \\F_{\mathrm{CE}}(\max . \text { neg })=-45\left(0.695 \times \frac{10.38}{2}\right)+30\left(0.475 \times \frac{13.62}{2}\right)=-65.3 \mathrm{\ kN} \\F_{\mathrm{DE}}=45 \times 24 \times \frac{1.78}{2}=961.2 \mathrm{\ kN}\end{gathered}
