Sec. 1.8 HISTORICAL REMARKS 27 compression in every member when a load P is applied at the point shown in the figure. Note: A joint is said to be a pin joint if no moment can be transmitted across it. This problem is statically determinate. 1.3. Find the vertical deflections at a, b, c of the truss in Fig. P1.2 due to a load P at point b. Assume that P is sufficiently small so that the truss remains linear elastic. Use the fact that for a single uniform bar in tension the total change in length of this bar is given by PLIAE, where P is the load in the bar, L is the bar length, A is the cross-sectional area, and E is the Young’s modulus of the material. For structural steels E is about 3 x lo’ lb/sq in, or 20.7 x lo’ kPa. Hint Use Castigliano’s theorem. 1.4. A “rigid” frame of structural steel shown in Fig. P1.4 is acted on by a horizontal force P. Find the reactions at the points of support a, and d. The a d P1.4 p--I cross-sectional area A and the bending rigidity constant
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cross-sectional area, horizontal force, local bending rigidity, local bending moment, single uniform bar