Question 20.P.14: The Pratt truss shown in Fig. P.20.14 has a self-weight of 1...
The Pratt truss shown in Fig. P.20.14 has a self-weight of 1.2 kN/m and carries a uniformly distributed live load longer than the span of intensity 2.8 kN/m, both being applied at the upper chord joints. If the diagonal members are designed to resist tension only, determine which panels require counterbracing.
The family of influence lines for the shear force in each panel of the truss is drawn and is shown in Fig. S.20.14.
The central panel will require counterbracing.
For panel 4
\begin{aligned}S &=2.8 \times \text { area } \mathrm{n}_{3} \mathrm{pa}-1.2\left(\text { area } \mathrm{n}_{3} \mathrm{fb}-\text { area } \mathrm{n}_{3} \mathrm{pa}\right) \\&=4 \times 3.375 \frac{\left(\frac{3}{9}\right)}{2}-1.2 \times 5.625 \frac{\left(\frac{5}{9}\right)}{2} \\&=0.38\end{aligned}
Therefore panel 4 (and 6) require counterbracing.
For panel 3
S=4 \times 2.25 \frac{\left(\frac{2}{9}\right)}{2}-1.2 \times 6.75 \frac{\left(\frac{6}{9}\right)}{2}=-1.7
Therefore panel 3 and the remaining panels do not require counterbracing.
