The pin-connected structure shown in the figure consists of a rigid bar ABCD and two aluminum alloy [E = 70 GPa) bars, e

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The pin-connected structure shown in the figure consists of a rigid bar ABCD and two aluminum alloy [E = 70 GPa) bars, e

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The Pin Connected Structure Shown In The Figure Consists Of A Rigid Bar Abcd And Two Aluminum Alloy E 70 Gpa Bars E 1
The Pin Connected Structure Shown In The Figure Consists Of A Rigid Bar Abcd And Two Aluminum Alloy E 70 Gpa Bars E 1 (453.7 KiB) Viewed 162 times
The pin-connected structure shown in the figure consists of a rigid bar ABCD and two aluminum alloy [E = 70 GPa) bars, each with a cross-sectional area of 310 mm². Bar (1) has a length of Lj = 895 mm and bar (2) has a length of L2 = 980 mm. Assume dimensions of a = 490 mm, b 380 mm, and c = 650 mm. If the allowable normal stress in bars (1) and (2) must be limited to 140 MPa, determine: = (a) the maximum load P that may be applied to the rigid bar at D. (b) the deflection at D for the load determined in part (a). L (1) a L2 B (2) VV b С Хи D с P
Part 1 Construct an FBD of rigid bar ABCD and determine an equilibrium equation relating the applied load P, the internal force Fi in bar (1), and the internal force F2 in bar (2). Your equation must be consistent with the sign convention for internal axial forces discussed in Section 5.3. Choose the correct equilibrium equation below. O -Fi(a + b) – F2b + Pc = 0 O-Fi(a + b) – F2b + P = 0 O – Fi(a + b) + F2b = 0 O Fi + F2 = 0 = Save for Later Attempts: 0 of 3 used Submit Answer
Part 2 Determine geometry-of-deformation relationships. Find the ratio of us to ub, where us is the magnitude of the horizontal deflection of pin A and up is the magnitude of the horizontal deflection of pin B. Also, find the ratio of us to vp, where vp is the magnitude of the vertical deflection of point D. UA i UB UA i VD Save for Later Attempts: 0 of 3 used Submit Answer Part 3 What is the ratio of 8 to 82, where di is the magnitude of the deformation of bar (1) and 82 is the magnitude of the deformation of bar (2) 8 82 i Save for Later Attempts: 0 of 3 used Submit Answer
Part 4 Determine the compatibility equation and rearrange it find the ratio of Fi to F2, where Fi is the magnitude of the internal force in bar (1) and F2 is the magnitude of the internal force in bar (2). F F2 = i Save for Later Attempts: 0 of 3 used Submit Answer Part 5 The allowable normal stress in bars (1) and (2) must be limited to 140 MPa. Determine the allowable internal force for each bar. The allowable force is the same for both bars. Fallow = i KN Save for Later Attempts: 0 of 3 used Submit Answer Part 6 When the maximum load P is applied, determine Fi and F2, the magnitudes of the internal forces in bars (1) and (2), respectively. F = i KN F2 = i KN Save for Later Attempts: 0 of 3 used Submit Answer
Part 7 Determine the magnitude of the maximum load P that may be applied to the rigid bar at D. P= i KN Save for Later Attempts: 0 of 3 used Submit Answer Part 8 When the maximum load P is applied, determine the elongation of bar (1). dj = mm Save for Later Attempts: 0 of 3 used Submit Answer Part 2 When the maximum load P is applied, determine the magnitude of the downward deflection at D. Since the magnitude is required, enter a positive value. VD = i mm Save for Later Attempts: 0 of 3 used Submit Answer
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