The rigid bar ABC is supported by a pin at Band two vertical steel rods. Initially the bar ishorizontal and the rods are stress-free. Findthe stress in each rod if the temperature rises35°C after a load W = 150 kN is applied. Thecoefficients of linear expansion are 11.7um/(m-°C) for steel and 18.9 µm/(m-°C) forbronze.BronzeL = 3 mA = 1300 mm?E = 83 GPaSteelL = 1.5 mA = 320 mm?+1m -E= 200 GPa2.5 m1.5 mWhat is the stress in the bronze rod (in MPa)?Your answerWhat is the stress in the steel rod (in MPa)?

Answered: Image /qna-images/answer/c91e5c6c-a068-4434-b7f7-dbaa53b25198.jpg

Answered: The rigid bar ABC is supported by a pin…

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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2.58 Knowing that a 0.02-in. gap exists when the temperature is 75°F, determine (a) the temperature at which the normal stress in the alu- minum bar will be equal to -11 ksi, (b) the corresponding exact length of the aluminum bar. 0.02 in. - 14 in. - Bronze A = 2.4 in² E = 15 x 106 psi a = 12 x 10-6/°F Fig. P2.58 and P2.59 18 in.. Aluminum A = 2.8 in² E = 10.6 x 106 psi a = 12.9 x 10-6/°F 300 mm 0.5 mm 250
Three aluminum rods support the rigid L-shaped bracket BCF as shown in the figure. Determine the stress in rod DE (express answer in MPa) if rod FG is cooled by 50°C. All three rods have the same cross-sectional area of 1000 mm^2. Use 73.1 GPa and 23 x 10^-6/°C for the modulus of elasticity and the coefficient of thermal expansion of aluminum, respectively.
# 2-14. Normal Strain in rods constrained by walls with misfit At its initial temperature, the bar is too long by a distance of 8 to fit into the gap between the rigid walls, which are separated by a distance L. In order to make it fit tightly, the bar is cooled to a very low temperature so that it shrinks enough to fit easily into the gap. After it is fit in the gap, the temperature of the bar is raised to a temperature AT below the initial temperature and the bar fits tight between the walls. What is the stress in the bar at this temperature AT? The bar has elastic modulus E = 35. 10³ ksi, thermal expansion coefficient a = 6.10-6 /°F and cross-sectional area A = 1 in². Use L = 10 in, 8 = 3 . 10-² in and AT = -200 °F. 0 = ksi L Initial AT=0 L Final AT
Problem 1 An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown. Axial loads are applied at the positions indicated. Aluminum Steel A=800mm2 A=1000mm2 Bronze A=700mm? 4P 2P 500mm 600mm 700mm 1. What is the maximum value of P that will not exceed the axial stress bronze of 105 MPa? 2. What is the maximum value of P that will not exceed the axial stress in aluminum of 90 MPa? 3. If P=10KN, what is the axial force to be carried by the aluminum in KN? 4. If P is 5KN, what is the axial stress of steel?
At room temperature (20°C) a 0.7-mm gap exists between the ends of the rods shown. At a later time when the temperature has reached 150°C, determine: (a.)The normal stress in the aluminum rod, (b.) The change in length of the aluminum rod. 0.7 mm 300 mm A Aluminum A =2,000 mm² E= 75 GPa α = 23 x 106/°C 250 mm B Stainless steel A = 800 mm² E = 190 GPa a = 17.3 x 10-6/°C
TWO SOLID CYLINDRICAL RODS ARE JOINED AT B AND LOADED AS SHOWN. ROD AB IS MADE OF STEEL (E = 210 GPa) AND ROD BC OF BRASS (E = 108 GPa). DETERMINE (A) THE TOTAL DEFORMATION OF THE COMPOSITE ROD ABC, (B) THE DEFLECTION OF POINT B. 40 KN 400 mm 600 mm A B C 30 mm 50 KN 50 mm
3. The rigid bar ABC is pinned at B and attached to the two vertical rods. Initially, the bar is horizontal and the vertical rods are stress-free. Determine the stress in the steel rod if the temperature of the both rods is decreased by 30°C. Neglect the weight of bar ABC. Steel L=0.9 m A 300 mm E= 200 x 10 N/m' a= 11.7 um/(m C) Aluminum L=1.2 m A = 1200 mm E = 70 x 10 N/m a= 23 pum/(m "C) Answer: Ost B 0.6 m 1.2 m
1. At a temperature of 5°C, a 3-mm gap exists between the end of polymer bar (1) and support A as shown. Bar (1) is 50 mm wide and 20 mm thick (E = 800 MPa, a = 140 x 10-6/°C). Bar (2) is 75 mm wide and 25 mm thick (E = 2.7 GPa, a = 67 x 106/°C). The supports at A and C are rigid (i.e., fixed). Determine: a) the temperature at which the normal stress in bar (2) will be equal to -3.0 MPa, and b) the lengths of the two polymer bars at this temperature. (1) 3-mm gap 50 mm 500 mm B 75 mm 400 mm (2)
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
Problem 3: Inside a steel tube, 2.4 meters long, 34 mm radius, and 1.5 mm thick, 32.5A circular bar made of aluminum with a radius of mm is inserted and these two materials arethey are linked together to form a cross section that will work. This cantilever beam obtained from end Ait is fixedly supported. This cantilever beam,A torque of T = 900 Nm from end B(torque) is applied. Stiffness modulus of steel, Strength= 77 GPa and the stiffness modulus of aluminum Gal = 26Since GPa is the rotation at point BWhat is the (torsion) angle? Calculate.
The solid shaft, made of three different materials, carries the two torques shown. (a) Calculate the maximum shear stress in each material. (b) Find the angle of rotation of the free end of the shaft. The shear moduli are 28 GPa for the aluminum, 83 GPa for steel and 35 GPa for bronze. Aluminum 100 mm -3 m- 4 kN.m Steel 75 mm -2 m 1.5 kN - m Bronze |--15m-l
Three aluminum rods support the rigid L-shaped bracket BCF as shown in the figure. Determine the stress in rod DE (express answer in MPa) if rod FG is cooled by 50°C. All three rods have the same cross-sectional area of 1000 mm^2. Use 73.1 GPa and 23 x 10^-6 /°C for the modulus of elasticity and the coefficient of thermal expansion of aluminum, respectively.

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