The pin-connected structure shown consists of a rigid bar ABCD and two axial members. Bar (1) is steel [E = 200 GPa; a =

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The Pin Connected Structure Shown Consists Of A Rigid Bar Abcd And Two Axial Members Bar 1 Is Steel E 200 Gpa A 1 (359.28 KiB) Viewed 43 times

The pin-connected structure shown consists of a rigid bar ABCD and two axial members. Bar (1) is steel [E = 200 GPa; a = 11.7 x 10-6/°C), with a cross-sectional area of A1 = 370 mm2. Bar (2) is an aluminum alloy [E = 70 Pa; a = 22.5 x 10-6/°C), with a cross- sectional area of Az = 440 mm2. The bars are unstressed when the structure is assembled. Assume a=310 mm, b=610 mm, c=680 mm, P=31 kN, and L=900 mm. After a concentrated load of P = 31 kN is applied and the temperature is increased by 25°C, determine (a) the normal stresses in bars (1) and (2). (b) the deflection of point Don the rigid bar. L A (1) a * B (2) Р b D On a piece of paper, sketch a FBD of rigid bar ABCD. Write an equilibrium equation which relates F1, the force in Bar (1), and F2, the force in Bar (2). Select the correct equation below. By convention, a tension force is positive, and a compression force is negative. Answer: a) F1 + F2 = 0 O c) F1 +0.6630 F2 = 22.9130 KN Ob) F1-F2 = 0 O d) F1+F2 = 31 kN O e) F1 -0.6630 F2 = 22.9130 KN
Part 2 On a piece of paper, sketch a deformation diagram. Based on this diagram, write a geometry-of-deformation equation in terms of deformations and 82, which are the deformations of Bars (1) and (2), respectively. From the geometry-of-deformation equation, enter the ratio, 81/82. Answer: 81/82 = i Save for Later Attempts: 0 of 3 used Submit Answer Part 3 Substitute force-temperature deformation relationships into the geometry-of-deformation equation to derive the compatibility equation. Then, find the force in Bar (1), F1, and the force in Bar (2),F2. Be sure to use the correct sign for each force. By convention, a tension force is positive and a compression force is negative. Answers: F1 = i <N F2= i Ź KN Save for Later Attempts: 0 of 3 used Submit Answer Part 4 Find on and o2, the normal stresses in members (1) and (2), respectively. By convention, a tension stress is positive, and a compression stress is negative. Answers: 0] = i MPa 02 i MPa
Part 5 Determine 81, the deformation of Bar (1). By convention, a deformation is positive for a member that elongates, and it is negative for a member that is shortened. Answer: 8 = i mm Save for Later Attempts: 0 of 3 used Submit Answer Part 6 Determine the deflection of point Don the rigid bar. In this case, report a downward deflection as a positive value, or an upward deflection as a negative value. Answer: Vp = i mm Save for Later Attempts: 0 of 3 used Submit Answer