SOLVE FOR THE REACTIONS OF THE TRUSS SHOWN BELOW: P 2m 2m D P 2m -2m -2m 2m Assume P = 13 KN SOLVE FOR THE AXIAL STRESSES OF MEMBERS BD, DE & FG OF THE TRUSS SHOWN ABOVE. INDICATE WHETHER IT IS TENSILE OR COMPRESSIVE STRESS.
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- Compound axial member ABC has a uniform diameter of d = 1.25 in. • Segment (1) is an aluminum [E1 = 10000 ksi] alloy. The length of segment (1) is L1 = 100 in. • Segment (2) is a copper [E2 = 17000 ksi] alloy. The length of segment (2) is L2 = 140 in. When axial force Pis applied, a strain gage attached to copper segment (2) measures a normal strain of ɛ2 = 2300 uin./in. in the longitudinal direction. What is the total elongation of member ABC? L2 (1) Aluminum B (2) Copper Answer: in, AL = iThe static indeterminacy of the structure shown below is Hinge - K I J H F E G A B DRefer to the composite body shown in Figure IV.a) Solve for the reactions at pin support at A and roller support at B. b) Determine the reactions at each connection- B,C,D.
- Compound axial member ABC has a uniform diameter of d = 1.50 in. Segment (1) is an aluminum [E1 = 10000 ksi] alloy. The length of segment (1) is L1 = 80 in. • Segment (2) is a copper [E2 = 17000 ksi] alloy. The length of segment (2) is L2 = 112 in. When axial force P is applied, a strain gage attached to copper segment (2) measures a normal strain of ɛ2 = 1700 pin./in. in longitudinal direction. What is the total elongation of member ABC? L2 (1) d Aluminum В (2) СopperThe pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 75 GPa] with a cross-sectional area of A = 790 mm2. Bar (2) is a bronze alloy [E = 108 GPa] with a cross-sectional area of A2 = 540 mm?. Assume L1= 2.5 m, L,= 3.0 m, a= 0.5 m, b= 1.7 m, and c= 1.3 m. All bars are unstressed before the load P is applied; however, there is a 3.2-mm clearance in the pin connection at A. If a load of P = 56 kN is applied at B, determine: (a) the normal stresses o1,02, in both bars (1) and (2). (b) the normal strains &1, 82, in bars (1) and (2). (c) determine the downward deflection va of point A on the rigid bar. (2) (1) L2 L1 A B D b Answers: (a) oj = i MPa, oj = i MPa. ( b) ε - HE, E2 = i HE. (c) VA = i mm.The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 72 GPa] with a cross-sectional area of A₁ = 820 mm². Bar (2) is a bronze alloy [E = 104 GPa] with a cross-sectional area of A₂ = 470 mm². Assume L₁=3 m, L₂=3.5 m, a=0.8 m, b=1.7 m, and c=1.2 m. All bars are unstressed before the load P is applied; however, there is a 4-mm clearance in the pin connection at A. If a load of P = 38 kN is applied at B, determine: (a) the normal stresses 0₁, 02, in both bars (1) and (2). (b) the normal strains £1, 2, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. (1) Answers: (a) 6₁ = (b) &₁ = (c) VA = i i L₁ B b ล с L2 MPa, 0₁ = με, εξ = i mm. D MPa. με.
- Bar FA in the pin-connected structure below is to be considered rigid and is horizontal before loads are applied to the structure. Member BC is an aluminum alloy bar with E= 75 GPa and a cross-sectional area of 1000 mm². Member DE is a steel bar with E = 200 GPa and a cross-sectional area of 500 mm². Assuming elastic behavior and adequately reinforced ends for BC and DE, determine the axial (normal) stresses in BC and DE and the deflection of point A when the 150 kN load is applied. 1.5 m 1.5 m 2.5m B 2.0 m 1.0m- 150 KNThe pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 79 GPa] with a cross-sectional area of A₁ = 700 mm². Bar (2) is a bronze alloy [E = 106 GPa] with a cross-sectional area of A₂ = 480 mm². Assume L₁=1.8 m, L₂=2.1 m, a=0.5 m, b=1.6 m, and c=0.8 m. All bars are unstressed before the load P is applied; however, there is a 3.4-mm clearance in the pin connection at A. If a load of P = 53 kN is applied at B, determine: (a) the normal stresses 01, 02, in both bars (1) and (2). (b) the normal strains 1, 2, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. (1) A Answers: (a) σ₁ = (b) 1 (c) VA = i a L₁ B b (2) L2 MPa, 0₁ = με, €2 = mm. i i D MPa. με.The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 77 GPa) with a cross-sectional area of A₁ = 790 mm². Bar (2) is a bronze alloy [E = 98 GPa] with a cross-sectional area of A2 = 550 mm². Assume L₁=2.6 m, L₂=3.3 m, a=0.8 m, b=1.4 m, and c=1.2 m. All bars are unstressed before the load P is applied; however, there is a 3-mm clearance in the pin connection at A. If a load of P = 38 kN is applied at B, determine: (a) the normal stresses 01, 02, in both bars (1) and (2). (b) the normal strains &1, 2, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. (1) Answers: (a) σ₁ = (b) ₁ = (c) VA = i i L₁ B b (2) C MPa, 0₁ = L2 με, €2 = i mm. i D MPa. με.
- The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 61 GPa] with a cross-sectional area of A₁ = 810 mm². Bar (2) is a bronze alloy [E = 103 GPa] with a cross-sectional area of A2 = 470 mm². Assume L₁=2.4 m, L₂=3.1 m, a=0.7 m, b=1.9 m, and c= 1.1 m. All bars are unstressed before the load P is applied; however, there is a 5.8-mm clearance in the pin connection at A. If a load of P = 44 kN is applied at B, determine: (a) the normal stresses 0₁, 0₂, in both bars (1) and (2). (b) the normal strains &1, 82, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. A Answers: (a) 0₁ = (STVA = a i i B 156.10 0.00256 b C MPa, 0₁ = με, €2 = mm L2 i i D 20.75 0.0002014 MPa. με.The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 74 GPa] with a cross-sectional area of A₁ = 780 mm². Bar (2) is a bronze alloy [E = 95 GPa] with a cross-sectional area of A₂ = 500 mm². Assume L₁=2.4 m, L₂=2.9 m, a=0.5 m, b=1.1 m, and c-0.8 m. All bars are unstressed before the load P is applied; however, there is a 4-mm clearance in the pin connection at A. If a load of P = 41 kN is applied at B, determine: (a) the normal stresses 0₁, 0₂, in both bars (1) and (2). (b) the normal strains &₁, E2, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. (1) Answers: (a) σ₁ = (b) E1 = (C) VA = i a i i L₁ B b L2 MPa, σ₁ = με, εν Ξ i mm. i D MPa. με.The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 69 GPa] with a cross-sectional area of A₁ = 830 mm². Bar (2) is a bronze alloy [E = 119 GPa] with a cross-sectional area of A₂ = 430 mm². Assume L₁=2.6 m, L₂=3.2 m, a=0.8 m, b=1.1 m, and c=1.2 m. All bars are unstressed before the load P is applied; however, there is a 2.1-mm clearance in the pin connection at A. If a load of P = 57 kN is applied at B, determine: (a) the normal stresses 0₁, 0₂, in both bars (1) and (2). (b) the normal strains 1, 2, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. Answers: (a) σ₁ = (b) &₁ = i (C) VA = Mi i L₁ B P b C L2 MPa, o₁ = με, €z = i mm. i D MPa. με.