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 αa ‚= 12.8 × 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

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 αa ‚= 12.8 × 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

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: The elongation of a bar in axial loading is proportional to the following except A Stress in the bar…

Q: An aluminum alloy [E = 73 GPa; v = 0.33; a= 23.0 x 10-6/°C] plate is subjected to a tensile load P.…

Q: The minimum strain at failure in tension steel having yield stress modulus E = 200 GPa, as per Limit…

Q: An aluminum alloy [E = 67 GPa; v=0.33; a = 23.0 × 10-6/°C] plate is subjected to a tensile load P.…

Q: A sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are ϵx = 0.40…

A: given data:

Q: At room temperature (200C) a 0.50mm gap exists between the ends of the rods shown. At a later time…

Q: A steel 0.6 inch×1.2 inch steel 90 m long is subjected to a 45 KN tensile load along its lenght.If…

A: Given data, Width B = 0.6 inch = 15.24 mm Thickness D = 1.2 inch = 30.48 mm Length L = 90 m = 90000…

Q: increased by 10°C. If the coefficient of thermal A metal bar of length 100 mm is inserted between…

A: Given data : Coefficient of thermal expansion (α)=12×10-6 per ∘CYoungs Modulus (E)=2×105…

Q: A test is conducted on a beam loaded by end couples. The fibres at layer CD are found to lengthen by…

A: Given data : increase in length of CD = 0.03 mm Decrease in length of AB is 0.09 mm Gauge length =…

Q: eurie the formula) d= M K wher, M- momint Ka d,

Q: 2. A steel with E = 29 000 ksi with a rectangular cross-section is bent over a rigid mandrel with R…

Q: Two cylindrical rods AB and BC are welded together at B and loaded as shown. Knowing that the…

Q: Calculate the mass of each sphere. Assume a = 4.9, b = 2.3, 0=29. y 1 R aR Titanium Answers:…

Q: (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; a = 13.8 × 10-6/°F] bar with a width of 3 in.…

Q: Two uniform spheres are positioned as shown. Determine the gravitational force F which the titanium…

Q: Find the value of strain if stress is 50 MPa and youngs modulus is 100 MPa

A: The strain can be calculated using Hookes law.

Q: The figure as shown below is a rigid bar which is supported by two rods and a pin support. If the…

Q: At an axial load of 24 kN, a 50-mm-wide by 10- mm-thick polyimide polymer bar elongates 2.5 mm while…

Q: Determine the maximum permissible value of T subject to the following conditions: tst < 80 MPa, Tal…

Q: For the following state of stress find the principal stresses.

Q: An extruded polymer beam is subjected to a bending moment M. The length of the beam is L = 620 mm.…

A: Aluminum billets are extruded by forcing them through a die at either a high or low temperature.…

Q: In the strain hardening regi happens if the stress is reme

Q: The aluminum shell is fully bonded to the brass core, and the assembly is unstressed at a…

Q: For the figure shown, increasing temperature causes compressive .stress in the steel rod

A: When there is an increase in temperature steel rod tends to expand . But due to the presence of a…

Q: A 0.375 -in. thick rectangular alloy bar is subjected to a tensile load P by pins at A and B. The…

A: Given Data Thickness of member (B) = 0.375 in Width of member (h) = 3 in Longitudinal strain (εx)…

Q: The stresses on the surface of a cast iron machine component are sx = 85 MPa, =-230 MPa, and fy =…

Q: A 2 m long axially loaded mild steel rod of 8 mm diameter exhibits the load-displacement (P - 8)…

Q: 10.1. A 0.505-in-diameter mild steel specimen was tested to failure in a tensilé tëstihg fma- chine…

A: a}

Q: 2.58 Knowing that a 0.02-in. gap exists when the temperature is 75°F, determine (a) the temperature…

Q: Calculate Young's modulus for an iron crystal when tension is applied along [2 -2 1] direction.…

A: S11 = 7.6(TPa)-1 S12 = 2.8(TPa)-1 S44 = 8.6(TPa)-1

Q: y 400 mm a 200 mm A 150 N a 10 mm В A Section a –a

Q: Two polymer bars are connected to a rigid plate at B, as shown. Bar (1) has a cross-sectional area…

A: To determine the horizontal deflection of end C relative to end A. Given, Area of bar (1), A1 =…

Q: A component made of Aluminium 6061-T651 has an edge crack with length equal to 15 mm, as shown The…

Q: The rigid bar of ABCD of negligible weight is supported hinge at A, steel rod at B and bronze rod at…

Q: When the stress is removed, the material returns to the dimension

A: Deformation : change in size or shape of an object is referred to as deformation. The absolute…

Q: Draw a typical stress-strain behaviour of steel subjected to tension. On the graph, show the modulus…

Q: 1. For each state of plane stress shown below, i.e., for configurations (a) and (b), indicate…

Q: A constantan alloy strain gauge is mounted on a gold (Young's modulus = 90GPA) cantilever that is…

A: Given data Modulus of elasticity of alloy (E) = 90 GPa Dimensions of strain gauge Thickness (t) =…

Q: A brass (? =5.6 ? 10^6 ???) and aluminum (? = 3.7 ? 10^6 ???) cylinders are bonded together at B,…

A: Note:- Hi! Thank you for the question, As per the honor code, we are allowed to answer three…

Concept explainers

Material Properties

Construction in civil engineering demands high strength, durability, and longevity. These targets can be achieved by better design and analysis, along with the correct choice of materials. Different materials have different properties and hence, they respond and performs differently under the various condition of external loadings. It is therefore a critical task of an engineer to select the right material based on the property that the material is supposed to function in real-time. When speaking about the property, there are different categories of material properties like chemical property, physical property, mechanical property, electrical property, magnetic property, thermal property, etc. These material properties form the basis of material selection in various applications.

Question

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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Introducing given data

VIEW

Step 2: Calculate highest temperature T2

VIEW

Step 3: Calculate temperature difference

VIEW

Step 4: Calculation for part b

VIEW

Solution

VIEW

Step by step

Solved in 5 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

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
Two polymer bars are connected to a rigid plate at B, as shown. Bar (1) has a cross-sectional area of 1.58 in. and an elastic modulus of 2430 ksi. Bar (2) has a cross-sectional area of 0.714 in and an elastic modulus of 4110 ksi. Assume Ly-18 in., Lz-47in, Q=6,4 kips, P-3.2 kips, and R-128 kips. Determine the horizontal deflection of end Crelative to end A. (1) Answer: uCA in.
A steel component is subjected to alternate cyclical loading. The steel follows Basquin's law for high cycle fatigue, o, x N = C, (where the stress amplitude is in MPa). Ignore the geometric detail and assume that Marin's modifying factors are all equal to 1. You are given the minimum stress ain = -213 MPa, the maximum stress omax = 213 MPa. The material data are Tensile strength oUTS = 539 MPa, Basquin's constant c, = 875 MPa, Basquin's exponent a = 0.085. a) Calculate the stress ratio R, the stress amplitude o, in MPa and the mean stress am in MPa. The answers are acceptable with a tolerance of 0.01 for R and of 1 MPa the stresses. R: MPa MPа b) Calculate the corresponding life, in 10° cycles, (tolerance of 0.1 106 cycles) N :
The lowest stress at which permanent .deformation can be measured
An element in the plane stress is having the larger principal stress (tension) as 30 MPa and it is subjected to stresses, Ox = 50 MPa, 40 MPa then what will be and Txy the value of the stress oy? (in MPa) =
6
The state of stress at a point is shown with respect to xy-plane. The state of stress at a point is shown with respect to x'y'-plane? 8 MPa y'v 60° S MPa +S MPa 10 MPa 8 MPa
If the material is graphite for which Eg = 800 ksi and vg = 0.23, determine the principal strains.
1 It is the ratio of ultimate tensile stress to the permissible stress. Plastic Shear Plastic limit Proportional limit Factor of safety Poisson's ratio
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.
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 triangular wedges are glued together as shown in the figure. The stress acting normal to the interface, o, is MPa. 100 MPa 100 MPa on 45% 100 MPa -100 MPa