Gere & Goodno — Axially Loaded Members: Problem 2.4-18

2.4-18 Three-bar truss \(ABC\) (see figure) is constructed of steel pipes having a cross-sectional area \(A = 3500 \text{ mm}^2\) and a modulus of elasticity \(E = 210 \text{ GPa}\). Member \(BC\) is of length \(L = 2.5 \text{ m}\), and the angle between members \(AC\) and \(AB\) is known to be \(60^\circ\). Member \(AC\) length is \(b = 0.71 L\). Loads \(P = 185 \text{ kN}\) and \(2P = 370 \text{ kN}\) act vertically and horizontally at joint \(C\), as shown. Joints \(A\) and \(B\) are pinned supports. (Use the law of sines and law of cosines to find missing dimensions and angles in the figure.) (a) Find the support reactions at joints \(A\) and \(B\). Use horizontal reaction \(B_x\) as the redundant. (b) What is the maximum permissible value of load variable \(P\) if the allowable normal stress in each truss member is \(150 \text{ MPa}\)?