Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
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Chapter 9, Problem 26CQ
To determine
The model of viscoelastic solid with a series spring and dashpot.
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The assembly shown consists of an aluminum shell (E,= 70 GPa, a, = 23.6 × 10-6rC) fully bonded to a steel core (Es = 200 GPa, as =
11.7 x 10-6rC) and the assembly is unstressed at a temperature of 20°C. Considering only axial deformations, determine the stress in
the aluminum when the temperature reaches 215°C.
200 mm
20 mm
Aluminum shell
Steel
50 mm
core
The stress in the aluminum is
MPa.
2. A steel bar of 5 mm is heated from 25°C to 45°C
and it is free to expand. The bar will induce
OCA) No stress
O(B) Shear stress
OC) Tensile stress
OD) Compressive stress
A steel bar is heated from room temperature to 80oC while it is free to expand. The bar will therefore be subject to:
A.
compression
B.
tension
C.
no stress
D.
shear
Chapter 9 Solutions
Materials Science And Engineering Properties
Ch. 9 - Prob. 1CQCh. 9 - Prob. 2CQCh. 9 - Prob. 3CQCh. 9 - Prob. 4CQCh. 9 - Prob. 5CQCh. 9 - Prob. 6CQCh. 9 - Prob. 7CQCh. 9 - Prob. 8CQCh. 9 - Prob. 9CQCh. 9 - Prob. 10CQ
Ch. 9 - Prob. 11CQCh. 9 - Prob. 12CQCh. 9 - Prob. 13CQCh. 9 - At temperatures above the equi-cohesive...Ch. 9 - Prob. 15CQCh. 9 - Prob. 16CQCh. 9 - Prob. 17CQCh. 9 - Prob. 18CQCh. 9 - Prob. 19CQCh. 9 - Prob. 20CQCh. 9 - Prob. 21CQCh. 9 - Prob. 22CQCh. 9 - Prob. 23CQCh. 9 - Prob. 24CQCh. 9 - Prob. 25CQCh. 9 - Prob. 26CQCh. 9 - Prob. 27CQCh. 9 - Prob. 28CQCh. 9 - Prob. 29CQCh. 9 - Prob. 30CQCh. 9 - Prob. 31CQCh. 9 - Prob. 32CQCh. 9 - Prob. 33CQCh. 9 - Prob. 34CQCh. 9 - Prob. 35CQCh. 9 - Prob. 1ETSQCh. 9 - Prob. 2ETSQCh. 9 - Prob. 3ETSQCh. 9 - Prob. 4ETSQCh. 9 - Prob. 5ETSQCh. 9 - Prob. 6ETSQCh. 9 - Prob. 7ETSQCh. 9 - Prob. 8ETSQCh. 9 - Prob. 9ETSQCh. 9 - Prob. 10ETSQCh. 9 - Prob. 11ETSQCh. 9 - Prob. 12ETSQCh. 9 - Prob. 9.1PCh. 9 - Prob. 9.2PCh. 9 - Prob. 9.3PCh. 9 - Prob. 9.4PCh. 9 - Prob. 9.5PCh. 9 - Prob. 9.6PCh. 9 - Prob. 9.7PCh. 9 - Prob. 9.8PCh. 9 - Prob. 9.9PCh. 9 - Prob. 9.10PCh. 9 - For silver at a tensile stress of 7 MPa and a...Ch. 9 - For germanium at a tensile stress of 410 MPa and a...Ch. 9 - Prob. 9.13PCh. 9 - Prob. 9.14PCh. 9 - Prob. 9.15PCh. 9 - Prob. 9.16PCh. 9 - Prob. 9.17PCh. 9 - Prob. 9.18PCh. 9 - Prob. 9.19PCh. 9 - Prob. 9.20PCh. 9 - Prob. 9.21PCh. 9 - Prob. 9.22P
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- 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 mmarrow_forwardThe brass shell (ab = 20.9 × 10-6/°C) is fully bonded to the steel core (as = 11.7 × 10-6°C). Determine the largest allowable increase in temperature if the stress in the steel core is not to exceed 47 MPa. x 5 mm 5 mm 20 mm 20 mm 5 mm -5 mm Steel core E = 200 GPa Brass shell E = 105 GPa 250 mm The largest allowable increase in temperature is °C.arrow_forwardCompare the engineering and true secant elastic moduli for the natural rubber in Example Problem 6.2 at an engineering strain of 6.0. Assume that the deformation is all elastic.arrow_forward
- The failure stress of a homogeneous steel bar having a diameter of 10 mm is 250 MPa. Using a factor of safety of 2.0, calculate the maximum load in N that the bar can support.arrow_forwardAn aluminum alloy [E = 73 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 = 250 mm, a cross-sectional area of A = 6900 mm², and a length of L = 5.9 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 = 50°C, the longitudinal normal strain in the plate is found to be 2400 με. Determine: (a) the magnitude of load P. (b) the change in plate depth Ad. L Answer: (a) P = i (b) Δd = KN mmarrow_forwardAs shown, an aluminium alloy construction BCD with a circular cross section is fixed at end B and affected by a force of 150 N at the free end D. The diameter of the cross-section a-a is 20 mm. The yield strength of the material is 80 MPa: a) Determine the stresses at point A of the a-a cross-section. As indicated in the picture, draw the stress element in Cartesian coordinates and specify the stress values.(b) Calculate the factor of safety, n for Tresca, and the von Mises yield criterion to see if the structure would yield based on the stresses at point A.(c) In the major stress area, draw the yield loci of both criteria and indicate the operational stress state & why is the Rankine failure criterion inappropriate for aluminium alloys?arrow_forward
- The material returns to its original shape when the load is removed. (A Elastic Limit B Elastic Behavior Limit c) Maximum Limit D D Proportional Limitarrow_forward-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 mmarrow_forwardAn aluminum alloy [E = 67 GPa; ν = 0.33; α = 23.0 × 10–6/°C] plate is subjected to a tensile load P. The plate has a depth of d = 225 mm, a cross-sectional area of A = 5100 mm2, and a length of L = 4.1 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 ΔT = 63°C, the longitudinal normal strain in the plate is found to be 2900 με. Determine: (a) the magnitude of load P. (b) the change in plate depth Δd.arrow_forward
- 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.arrow_forward6 A steel pipe with a 50 mm outside diameter and a 43.75 'mm inside diameter surrounds a solid brass rod 37.5 mm in diameter as shown. Both materials are joined to a rigid cover plate at each end. The assembly is free to expand longitudinally. The assembly is stress free at a temperature of 27°C. For steel, Young's modulus is 200 GN/m², and the coefficient of linear thermal expansion is 11.7x10-6 1/°C. For brass, Young's modulus is 93.33 GN/m², and the coefficient of linear thermal expansion is 1.872 x 10-5 1/°C. What is the stress in the steel tube when the temperature is raised to 121°C? brass rod (solid) 37.5 mm diameter steel tube 50 mm outside diameter 43.75 mm inside diameterarrow_forwardAn AISI 1040 hot-rolled steel [E = 207 GPa; α = 11.3×10–6/°C] bar is held between two rigid supports. The bar is stress free at a temperature of 30°C. The bar is then heated uniformly. If the yield strength of the steel is 429 MPa, determine the temperature at which yield first occurs.arrow_forward
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