# Strengths - 5.15 Rigid bar ABCD is loaded and supported as...

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5.15 Rigid bar ABCD is loaded and supported as shown in Fig. P5.15. Bars (1) and (2) are unstressed before the load P is applied. Bar (1) is made of bronze [ E = 100 GPa] and has a cross- sectional area of 520 mm 2 . Bar (2) is made of aluminum [ E = 70 GPa] and has a cross-sectional area of 960 mm 2 . After the load P is applied, the force in bar (2) is found to be 25 kN (in tension). Determine: (a) the stresses in bars (1) and (2). (b) the vertical deflection of point A . (c) the load P . Fig. P5.15 Solution Given that the axial force in bar (2) is 25 kN (in tension), the deformation can be computed as: 2 2 2 2 2 2 2 (25,000 N)(800 mm) 0.297619 mm (960 mm )(70,000 N/mm ) F L A E δ = = = Since the pin at C is a perfect connection, the deflection of the rigid bar at C is equal to the deformation of bar (2): 2 0.297619 mm C v δ = = From a deformation diagram of the rigid bar, the vertical deflection of joint C is related to B by similar triangles: 1.6 m 0.5 m 1.6 m 3.2 0.5 m 3.2(0.297619 mm) 1.116071 mm B C B C C v v v v v = = = = = The joint at B is also a perfect connection; therefore, the downward displacement of B also

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