Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 10.6, Problem 10.45P
To determine
The orientation θ
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For the state of a plane strain with εx, εy and γxy components: (a) construct Mohr’s circle and (b) determine the equivalent in-plane strains for an element oriented at an angle of 30° clockwise. εx = 255 × 10-6 εy = -320 × 10-6 γxy = -165 × 10-6
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Chapter 10 Solutions
Mechanics of Materials (10th Edition)
Ch. 10.3 - Prove that the sum of the normal strains in...Ch. 10.3 - The state of strain at the point on the arm has...Ch. 10.3 - The state of strain at the point on the pin leaf...Ch. 10.3 - The state of strain at the point on the pin leaf...Ch. 10.3 - The state of strain at the point on the leaf of...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Use the strain- transformation equations to...
Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Determine the equivalent state of strain on an...Ch. 10.3 - Determine the equivalent state of strain which...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Determine the equivalent state of strain, which...Ch. 10.3 - Solve Prob.103 using Mohrs circle. 103. The state...Ch. 10.3 - using Mohrs circle. 103. The state of strain at...Ch. 10.3 - Solve Prob.105 using Mohrs circle. 105. The state...Ch. 10.3 - Solve Prob.108 using Mohrs circle 108. The state...Ch. 10.3 - using Mohrs circle. 106. The state of strain at a...Ch. 10.5 - The strain at point A on the bracket has...Ch. 10.5 - Determine (a) the principal strains at A, (b) the...Ch. 10.5 - Determine (a) the principal strains at A, in the...Ch. 10.5 - The following readings are obtained for each gage:...Ch. 10.5 - The following readings are obtained for each gage:...Ch. 10.5 - The following readings are obtained for each gage:...Ch. 10.5 - The following readings are obtained from each...Ch. 10.6 - For the case of plane stress, show that Hookes law...Ch. 10.6 - to develop the strain tranformation equations....Ch. 10.6 - Determine the modulus of elasticity and Polssons...Ch. 10.6 - If it is subjected to an axial load of 15 N such...Ch. 10.6 - If it has the original dimensions shown, determine...Ch. 10.6 - If it has the original dimensions shown, determine...Ch. 10.6 - A strain gage having a length of 20 mm Is attached...Ch. 10.6 - Determine the bulk modulus for each of the...Ch. 10.6 - The strain gage is placed on the surface of the...Ch. 10.6 - Determine the associated principal stresses at the...Ch. 10.6 - Determine the applied load P. What is the shear...Ch. 10.6 - If a load of P = 3 kip is applied to the A-36...Ch. 10.6 - The cube of aluminum is subjected to the three...Ch. 10.6 - The principal strains at a point on the aluminum...Ch. 10.6 - A uniform edge load of 500 lb/in. and 350 lb/in....Ch. 10.6 - Prob. 10.45PCh. 10.6 - A single strain gage, placed in the vertical plane...Ch. 10.6 - A single strain gage, placed in the vertical plane...Ch. 10.6 - If the material is graphite for which Eg = 800 ksi...Ch. 10.6 - Determine the normal stresses x and y in the plate...Ch. 10.6 - The steel shaft has a radius of 15 mm. Determine...Ch. 10.6 - Prob. 10.51PCh. 10.6 - The A-36 steel pipe is subjected to the axial...Ch. 10.6 - Air is pumped into the steel thin-walled pressure...Ch. 10.6 - Air is pumped into the steel thin-walled pressure...Ch. 10.6 - Prob. 10.55PCh. 10.6 - The thin-walled cylindrical pressure vessel of...Ch. 10.6 - The thin-walled cylindrical pressure vessel of...Ch. 10.6 - Prob. 10.58PCh. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - A material is subjected to plane stress. 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- (a) Determine the shear strain at corner A if the plate distorts as shown by the dashed line. (b) Determine the average normal strain that occurs along the diagonal AC and DB. 5 mm 2 mm 4 mm 2 mm IB 300 mm $2 mm D A 400 mm 3 mmarrow_forwardDetermine the normal strains at the point associated with the x and y axes. Determine the shear strain at the point associated with the x and y axes. Determine the normal stresses at the point associated with the x and y axes. Determine the shear stress at the point. Determine the normal stress that acts along an axis rotated at θ= 45° counterclockwise from the positive x-axis.arrow_forwardThe state of plane strain on an element is represented by the following components: Ex =D340 x 10-6, ɛ, = , yxy Ey =D110 x 10-6, 3D180 x10-6 ху Draw Mohr's circle to represent this state of strain. Use Mohrs circle to obtain the principal strains and principal plane.arrow_forward
- Your answer is partially correct. On the free surface of an aluminum [E=10100 ksi; v = 0.35] component, the strain rosette shown was used to obtain the following normal strain data: a=-425 με, ε = -200 με, and ε & εν +575 μɛ. Determine the normal stress that acts along an axis that is rotated at an angle of 0 = 60° counterclockwise from the positive x axis. 60° 60° b a 60° x Determine the normal strains at the point associated with the x and y axes. Answers: Ex = -425 με, ε, Ξ i με.arrow_forwardThe force P applied at joint D of the square frame causes the frame to sway and form the dashed rhombus. Suppose that θ = 3.6∘arrow_forwardDetermine the average normal strain along diagonal DB, based on the original plate (blue) and the deformed shaped (dashed line): 2 mm y C 300 mm 12 mm D -400 mm A 5 mm B 3 mm 4 mm 12 mm Xarrow_forward
- Mechanics of materials Iarrow_forward2. The two wires are connected at A. If the force P causes point A to be displaced horizontally 2 mm, determine the normal strain developed in each wire. B 300 mm 20⁰ 20⁰ 300 mm A Parrow_forwardThe block is deformed into the position shown by the dashed lines. Determine the average normal strain along with line AB.arrow_forward
- The strain components, ex= 940 micro strain, ey= -360 micro strain and yxy=830micro strain are given for a point in body subjected to plane strain. Determine; a. Magnitude of the principal strains b. The direction of the principal strain axes c. The maximum in-plane shear strain. Confirm your answer by means of Mohr's circle of strain and determine the linear strain on an axis inclined at 20 degrees clockwise to the direction of eyarrow_forwardThe strain rosette shown below was used to obtain normal strain data at a point on the free surface of a 2024-T4 aluminum alloy machine part. The gage readings were Ea = +630μ, b = +450μ, and Ec = +1200μ. Determine (a) The strain components Ex, Ey, and Yay at the point. (b) The stress components o, y, and Tay at the point. Express the stresses in SI units. (c) The principal stresses and the maximum shearing stress at the point. Gage c Y 90° Gage b Gage a 45° -Xarrow_forwardFour stress elements are shown below. All members have the same value for E (Young’s Modulus) and ν (Poisson’s ratio). Rank the members from largest to smallest absolute value of the normal strain in the y direction.arrow_forward
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