The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 75 GPa] with across-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-mmclearance 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)L2L1ABDbAnswers:(a) oj =iMPa, oj =iMPa.( b) ε -HE, E2 =iHE.(c) VA =imm.

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Answered: The pin-connected structure consists of…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Steel 1 m Aluminum T 0.75 m Determine the maximum permissible value of T subject to the following conditions: tt S 80 MPa, Tal 50 MPa, and the angle of rotation of the free end is limited to 0.1 radian. For T. Hollow Solid d= 30 mm D= 40 mm %3D steel, G = 82 GPa and for aluminum, G= 28 GPa. %3D d = 30 mm %3D
A brass (? =5.6 ? 10^6 ???) and aluminum (? = 3.7 ? 10^6 ???) cylinders are bonded together at B, and are attached to fixed supports A and C. Determine (a) The torsion in AB, (b) The torsion in BC, (c) The maximum shearing stress in AB (d) The maximum shearing stress in BC.
For the two element rod shown, element (1) is steel with: E₁ = 210 GPa, A₁ = 1000 mm², L₁= 2 m, and coefficient of thermal expansion, a₁ = 12X106/°C. Element (2) is a titanium alloy with E2 = 120 GPa, A2 = 1500 mm², L2 = 1.5 m, and coefficient of thermal expansion, a₂ = 8X10-6/°C. a) Determine the axial stress ₁ and ₂ in the two rods if the temperature in both is increased by 100°C. b) Determine the deflection of point B following the temperature increase. A₁, E₁, 0₁ L₁ B UB A2, E2, 02 -L₂
The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 65GPa] with a cross-sectional area of A_{1} = 850m * m ^ 2 Bar (2) is a bronze alloy [E = 100GPa] with a cross-sectional area of A_{2} = 540m * m ^ 2 Assume L_{1} = 1.9m L_{2} = 2.2m , a = 0.5m b = 1.6n , and c = 1.3 m. All bars are unstressed before the load P is applied; however, there is a 1.6-mm clearance in the pin connection at A. If a load of P = 55 KN is applied at B, determine: (a) the normal stresses Oj, 62, in both bars (1) and (2). (b) the normal strains E1, E2, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar
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.
A two pinned end bars AB (copper) and BC (aluminum) is subjected to a horizontal force P = 90KN applied at pin B %3D as shown in the figure, determine the horizontal displacement of pin B. Aluminum: L= 1.5m, A= 1000mm2, E= 70 GPa Copper: L= 2.0m, A= 850mm², E= 120 GPa Degree: 45° Alumaum L-15m A=1000 mm E-70 GPa >P=90 kN Copper L=2.0m Aa550 mm E=120 GPa
The 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 shown consists of a rigid bar ABCD and two axial members. Bar (1) is steel [E = 200 GPa; a = 11.7x 10-6/°C], with a cross-sectional area of A1 = 370 mm2. Bar (2) is an aluminum alloy [E = 70 GPa; a = 22.5 x 10-6/°C], with a cross- sectional area of A2 = 380 mm?. The bars are unstressed when the structure is assembled. Assume a=360O mm, b=620 mm, c=730 mm, P=20 kN, and L=890 mm. After a concentrated load of P = 20 kN is applied and the temperature is increased by 35°C, determine (a) the normal stresses in bars (1) and (2). (b) the deflection of point D on the rigid bar. A (1) B (2)
One of the following values is a possible for possion ratio for steel ? a. Zero b. one c. 0.3 d 0.9
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.
The total tensile load of 160kN of a steel is to be stress at the middle portion limited to 150 N/mm2, find the diameter of the middle portion and also the length of the middle portion if the total elongation of the rod is to be 0.2mm. consider the young modulus of a steel.
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 = 820 mm². Bar (2) is a bronze alloy [E = 117 GPa] with a cross-sectional area of A₂ = 420 mm². Assume L₁=1.9 m, L₂=2.5 m, a=0.7 m, b=1.9 m, and c=1.3 m. All bars are unstressed before the load P is applied; however, there is a 1.4-mm clearance in the pin connection at A. If a load of P = 34 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 = = tel i L₁ B b L2 mm. C MPa, σ₁ = με, εξ = i i D MPa. με.

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