3. An aluminum material element experiences a state of plane stress with the magnitudes and directions of the stress components given in the figure. Please calculate the change in volume per unit volume this material element would experience when subjected to the stress state given in the image below and a temperature increase of 80°C. (Note that the dotted horizontal line and 15 degree angle are irrelevant to this problem). Aluminum Properties: Thermal Coefficient of Expansion = 24 x 10-6 mm/mm/°C, Elastic Modulus = 69 GPa, Poisson Ratio = 0.35 250 MPa 60 MPa 15° 150 MPa

3. An aluminum material element experiences a state of plane stress with the magnitudes and directions of the stress components given in the figure. Please calculate the change in volume per unit volume this material element would experience when subjected to the stress state given in the image below and a temperature increase of 80°C. (Note that the dotted horizontal line and 15 degree angle are irrelevant to this problem). Aluminum Properties: Thermal Coefficient of Expansion = 24 x 10-6 mm/mm/°C, Elastic Modulus = 69 GPa, Poisson Ratio = 0.35 250 MPa 60 MPa 15° 150 MPa

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

At a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown in the figure. Bar (1) is an aluminum alloy (E-10,000 ksi; u= 0,32; a= 12.5 x10°/°F] bar with a width of 3 in, and a thickness of 0.75 in. Bar (2) is a stainless steel |E-28,000 ksi; u=0.12; a=9.6x10°/°F] bar with a width of 2 in. and a thickness of 0.75 in. The supports at A and C are rigid. Determine the normal stress in bar (1) at a temperature of 450°F
The stress-strain diagram for a steel alloy having an original diameter of 0.5 in. and a gage length of 2 in. is given in the figure. If the specimen is loaded until it is stressed to 70 ksi, determine the approximate amount of elastic recovery and the increase in the gage length after it is unloaded. o (ksi) 80 70 60 50 40 30 20 10 e (in./in.) 0 04 0.08 0.12 0.16 0.20 0.24 0.28 0 0005 0.0010.0015 0.002 0.0025 0.0030.0035
The elastic portion of the tension stress-strain diagram for an aluminum alloy is shown in the figure. The specimen used for the test has a gauge length of 2 in. and a diameter of 0.5 in. If the applied load is 10 kip, determine the new diameter of the specimen. The shear modulus is G al =3.811032 ksi
A circular bar of magnesium alloy is 390 mm long. The stress-strain diagram for the material is shown in the figure. 70 63 56 49 O (MPa) 42 35 28 21 14 7 0.002 0.004 0.006 0.008 0.01 The bar is loaded in tension to an elongation of 2.34 mm, and then the load is removed. Hint: Use the concepts illustrated in the figures below. (Assume the curve in the figure above is linear between (0, 0) and (0.001, 28), and curves with a gradually decreasing slope otherwise.) F В E F Loading CD Loading Residual Elastic strain recovery (a) What is the permanent set of the bar (in mm)? 2.184 X mm (b) If the bar is reloaded, what is the proportional limit (in MPa)? 55 X MPa
Determine the modulus of Elasticity E for a material that has proportional stress of 100 MPa and proportional strain of 0.001. Select one: a. 1 GPa b. 100 GPa C. 0.1 MPa d. 1000 kPa
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,…
A tension test performed on a metal specimen to fracture produced the stress-strain relationship shown in Figure. Graphically determine the following (show units and all work):a. Modulus of elasticity within the linear portion.b. Yield stress at an offset strain of 0.002 in./in.c. Yield stress at an extension strain of 0.005 in/in.d. Secant modulus at a stress of 62 ksi.e. Tangent modulus at a stress of 65 ksi.
An aluminum plate is subjected to uniform stress along its boundaries, as shown in the figure. Determine the change of length of diagonal BD. 120mm 120 MPa 160mm , 100мра C 240 MPa E=80GPa ✓=0.3 G=30GPa Answer = -0.5888mm
An extruded polymer beam is subjected to a bending moment M. The length of the beam is L = 760 mm. The cross-sectional dimensions of the beam are b1 = 33 mm, d1 = 110 mm, b2 = 20 mm, d2 = 20 mm, and a = 6.5 mm. For this material, the allowable tensile bending stress is 11 MPa, and the allowable compressive bending stress is 12 MPa. Determine the largest moment M that can be applied as shown to the beam.
An extruded polymer beam is subjected to a bending moment M. The length of the beam is L = 680 mm. The cross-sectional dimensions of the beam are b, = 36 mm, d1 = 95 mm, b2 = 22 mm, d2 = 22 mm, and a = 7 mm. For this material, the allowable tensile bending stress is 11 MPa, and the allowable compressive bending stress is 13 MPa. Determine the largest moment M that can be applied as shown to the beam. b2 M d2 d1 |A В b1 Answer: M = N-m
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
Data taken from a stress-strain test for a brittle alloy are given in the table. The curve is linear between the origin and the first point. o (ksi) e (in./in.) 0 0 44.8 0.0008 54.0 0.0013 57.5 0.0017 59.5 0.0021 60.0 0.0023 Part A Determine approximately the modulus of toughness. The rupture stress is o, 30.0 ksi. Express your answer in inch-pounds per cubic inch as an integer. VAE Ivec U Submit Provide Feedback Request Answer in-lb/in³