The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 74 GPa] with across-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=2.4m, 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 inthe 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 = iaiiL₁BbL2MPa, σ₁ =με, εν Ξ imm.iDMPa.με.

Answered: Image /qna-images/answer/7868570c-38d7-4181-903f-8e9f8b06d81e.jpg

cross-sectional area of A₁ = 780 mm². Bar (2) is a bronze alloy [E = 950 m, L2=2.9 m, a=0.5 m, b=1.1 m, and c-0.8 m. All bars are unstressed bet 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 E₁, E2, 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)x₁= a i M L₁ B P b (2) C L2 mm. C MPa, 0₁ = με, €2 = i D

cross-sectional area of A₁ = 780 mm². Bar (2) is a bronze alloy [E = 950 m, L2=2.9 m, a=0.5 m, b=1.1 m, and c-0.8 m. All bars are unstressed bet 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 E₁, E2, 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)x₁= a i M L₁ B P b (2) C L2 mm. C MPa, 0₁ = με, €2 = i D

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

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.
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
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 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)
At a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; a = 12.5 x 10-6/°F] bar with a width of 3.0 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; a = 9.6 x 10-6/°F] bar with a width of 2.0 in. and a thickness of 0.75 in. The supports at A and C are rigid. Determine (a) the lowest temperature at which the two bars contact each other. (b) the normal stress in the two bars at a temperature of 250°F. (c) the normal strain in the two bars at 250°F. (d) the change in width of the aluminum bar at a temperature of 250°F. (1) 3.0 in. 32 in. 2.0 in. B ↓ (2) 44 in. 0.04-in. gap Determine the lowest temperature, Tcontact, at which the two bars contact each other.
An aluminum alloy [E = 72 GPa; v = 0.33; a= 23.0 x 10-6/°C] plate is subjected to a tensile load P. The plate has a depth of d = 245 mm, a cross-sectional area of A = 5500 mm², and a length of L = 6.0 m. The initial longitudinal normal strain in the plate is zero. After load P is applied and the temperature of the plate has been increased by AT = 69°C, the longitudinal normal strain in the plate is found to be 3340 μc. Determine: (a) the magnitude of load P. (b) the change in plate depth Ad. L P Answer: (a) P = i (b) Δd = i KN mm
Narrow bars of aluminum are bonded to the two sides of a thick steel plate as shown. Initially, at T₁ = 70°F, all stresses are zero. Knowing that the temperature will be slowly raised to T₂ and then reduced to T₁, determine (a) the highest temperature T₂ that does not result in residual stresses, (b) the temperature T₂ that will result in a residual stress in the aluminum equal to 58 ksi. Assume aa = 12.8 x 10-6/°F for the aluminum and a = 6.5 × 10-6/°F for the steel. Further assume that the aluminum is elastoplastic with E = 10.9 × 106 psi and ay = 58 ksi. (Hint: Neglect the small stresses in the plate.) Fig. P2.121
At a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; α=α=12.5 x 10-6/°F] bar with a width of 2.5 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; α=α=9.6 x 10-6/°F] bar with a width of 1.7 in. and a thickness of 0.75 in. The supports at A and C are rigid. Assume h1=2.5 in., h2=1.7 in., L1=31 in., L2=46 in., and Δ=Δ= 0.04 in. (A) Determine the lowest temperature, Tcontact, at which the two bars contact each other. (B) Find a geometry-of-deformation relationship for the case in which the gap is closed. Express this relationship by entering the sum δ1+δ2, where δ1 is the axial deflection of Bar (1), and δ2 is the axial deflection of Bar (2). δ1+δ2= _____in. (C) Find the force in the Bar (1), F1, and the force in Bar (2), F2, at a temperature of 225oF. By convention, a tension force is positive and a compression force is negative. IN KIPS (D) Find σ1 and σ2,…
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 = 400 mm². Bar (2) is an aluminum alloy [E = 70 GPa; a = 22.5 x 10-6/°C], with a cross-sectional area of A₂ = 400 mm². The bars are unstressed when the structure is assembled. After a concentrated load of P = 36 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 D on the rigid bar. 350 mm 600 mm 900 mm (1) (2) A B 36 kN 720 mm D
Steel, Brass, and Copper rods are connected as shown in the figure. Initially, the temperature was 15 degrees Celsius and the stress on the bars is zero. Eventually, the temperature increased to 25 degrees Celsius. Determine the total deformation on the steel. Steel Brass Copper Est = 200 GPa Ebr = 100 GPa Ecu = 120 GPa %3D ast = 12(10-6)/°C abr = 21(10¬6)/°C acu = 17(10-)/°C %3D Acu = 515 mm² |Ast = 200 mm? Abr = 450 mm² %3D 300 mm- 200 mm 100 mm O -0.0058mm O 0.0165mm O -0.0165mm O 0.0058mm
The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 60 GPa] with a cross-sectional area of A1 = 870 mm?. Bar (2) is a bronze alloy [E = 92 GPa] with a cross-sectional area of Ay = 520 mm?. Assume L$=2.6 m, La=2.9 m, a=0.7 m, b= 1.3 m, and c= 1.1 m. All bars are unstressed before the load P is applied; however, there is a 3.9-mm clearance in the pin connection at A. If a load of P= 58 kN is applied at B, determine: (a) the normal stresses 01, 02, in both bars (1) and (2). (b) the normal strains € , E2, in bars (1) and (2). (c) determine the downward deflection vA of point A on the rigid bar.
In the figure shown below, determine: 1) The final temperature if the normal stress at aluminium is Oal = = -90 MPa and the initial temperature 20°C. 2) The final length of the aluminium member. Aluminum Bronze A=1800mm2 A=1500mm2 E=105GPA E=73GPA a=23.2x10-6/°C a=21.6x10-6/°C Gap=0.5mm 0.35m 0.45m