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 copper. Steel Brass Copper Est = 200 GPa 12(10-6)/°C 120 GPa Ecu 17(10-)/°C Epr 100 GPa %3D %3D ast apr = 21(10-6)/°C acu Acu = 515 mm2 200 mm? Abr = 450 mm2 Ast %3D 300 mm- 200 mm 100 mm O 0.0105mm O -0.0105mm O 0.0057mm O -0.0057mm o oo o

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 copper. Steel Brass Copper Est = 200 GPa 12(10-6)/°C 120 GPa Ecu 17(10-)/°C Epr 100 GPa %3D %3D ast apr = 21(10-6)/°C acu Acu = 515 mm2 200 mm? Abr = 450 mm2 Ast %3D 300 mm- 200 mm 100 mm O 0.0105mm O -0.0105mm O 0.0057mm O -0.0057mm o oo o

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, 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 brass. Steel Brass Copper Est = 200 GPa 12(10-)/°C apr Ebr Ecu 17(10-)/°C 120 GPa 100 GPa %3D ast = 21(10-6)/°C acu Acu = 515 mm? |Ast 200 mm2 Abr = 450 mm2 300 mm -200 mm 100 mm O -0.0109mm O 0.0241mm O -0.0241mm O 0.0109mm oooO
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,…
-6 The aluminum shell is fully bonded to the brass core and the assembly is unstressed at a temperature of 16°C. It is known thatE = 105 GPa and a = 20.9 × 10 °C for the brass core and E = 71 GPa and a = 23.8 × 10¯6°C for the aluminum shell. Considering only axial deformations, determine the stress in the aluminum when the temperature reaches 185°C. 25 mm σα MPa -63 mm
A rigid bar, AB, is pinned at point B. Two other bars, AC and AD, are connected to point A to provide support for AB. We are investigating the behavior of this system under a specific load. Key Details: Bar properties: Material: Steel with Young's modulus (Esteel) of 200 GPa and coefficient of thermal expansion (a) of 11.7 x 10^-6 /°C. Cross-sectional area: AC: 1960 mm² AD: 1250 mm² Length: AC: √2 meters (square root of 2 meters) AD: 1 meter Inclination angles: AC: θ₁ (theta 1) = 30° from horizontal AD: θ₂ (theta 2) = 20° from horizontal Load on bar AB: Idealized linearly increasing load with a maximum value of 30 kN/m at point B. Problem Objectives: Determine the internal forces (axial forces) acting within bars AC and AD due to the applied load on AB. Calculate the displacement of point A in both horizontal (dA,x) and vertical (dA,y) directions.If the bar is cooled by 10°C, what would be the: Determine the internal forces (axial forces) acting within bars AC and AD…
Problem # 2. At room temperature (20°C) a 0.5-mm gap exists between the ends of the rods shown. At a later time when the temperature has reached 140 °C, determine (a) the normal stress in the aluminum rod Ans: A -300 mm Aluminum A = 2000 mm² E = 75 GPa α = 23 x 16-6/°C 0.5 mm -250 mm Stainless steel A = 800 mm² B E = 190 GPa a = 17.3 x 10-6/°C
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 A=1800mm? E=73GPA Bronze A=1500mm2 E=105GPA a=23.2x10-6/°C a=21.6x10-6/°C Gap=0.5mm 0.35m 0.45m
The following information about the o-e curve is given for a steel alloy. E = 0.001527 at o = 300 MPa and ɛ = 0.003054 for o = 600 MPa. (a) Draw the stress-strain diagram and calculate the E for this alloy.
A mild steel flat of width 120 mm and thickness 10 mm is bent into an arc of a circle of radius 10 m by applying a pure moment 'M'. If E is 200 GPa, then magnitude of the pure moment 'M' will be
Knowing that a 0.02in gap exists when the temperature is 75°F, determine (a) the temperature at which the normal stress in the aluminum bar will be equal to -11ksi, (b) the corresponding exact length (2 decimal places in 103 inches) of the aluminum bar. 0.02 in. 14 in. Bronze A = 2.4 in² E = 15 × 106 psi a = 12 x 10-6/°F 18 in. Aluminum A = 2.8 in² E = 10.6 × 106 psi a = 12.9 x 10-6/°F
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