Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 9.3, Problem 9.4FP
Determine the equivalent state of stress on an element at the same point that represents the maximum in-plane shear stress at the point.
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The stresses at a point in a bar are 200 N/mm2 (tensile) and 80 N/mm2 (compressive). Determine the resultant stress in magnitude and direction on a plane inclined at 60° to the axis of the major stress. Also determine the maximum intensity of shear stress in the material at the point.
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Chapter 9 Solutions
Mechanics of Materials (10th Edition)
Ch. 9.3 - In each case, the state of stress x, y, xy...Ch. 9.3 - Given the state of stress shown on the element,...Ch. 9.3 - Determine the normal stress and shear stress...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Also, find the corresponding orientation of the...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Determine the maximum principal stress at point B.Ch. 9.3 - Determine the principal stress at point C.Ch. 9.3 - Prove that the sum of the normal stresses x + y =...Ch. 9.3 - Determine the stress components acting on the...
Ch. 9.3 - Determine the stress components acting on the...Ch. 9.3 - Determine the normal stress and shear stress...Ch. 9.3 - Determine the normal stress and shear stress...Ch. 9.3 - Determine the stress components acting on the...Ch. 9.3 - Determine the stress components acting on the...Ch. 9.3 - Solve Prob.97 using the stress transformation...Ch. 9.3 - Determine the stress components acting on the...Ch. 9.3 - Solve Prob.99 using the stress transformation...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Determine the equivalent slate of stress on an...Ch. 9.3 - Determine the stress components acting on the...Ch. 9.3 - Determine (a) the principal stresses and (b) the...Ch. 9.3 - The state of stress at a point is shown on the...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - A point on a thin plate is subjected to the two...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - The stress along two planes at a point is...Ch. 9.3 - The stress acting on two planes at a point is...Ch. 9.3 - The state of stress at a point in a member is...Ch. 9.3 - The grains of wood in the board make an angle of...Ch. 9.3 - The wood beam is subjected to a load of 12 kN. If...Ch. 9.3 - The internal loadings at a section of the beam are...Ch. 9.3 - Solve Prob.925 for point B. 925. The internal...Ch. 9.3 - Solve Prob.925 for point C. 925. The internal...Ch. 9.3 - It is subjected to a torque of 12 kip in. and a...Ch. 9.3 - The bell crank is pinned at A and supported by a...Ch. 9.3 - The beam has a rectangular cross section and is...Ch. 9.3 - A paper tube is formed by rolling a cardboard...Ch. 9.3 - Solve Prob.931 for the normal stress acting...Ch. 9.3 - The 2-in.-diameter drive shaft AB on the...Ch. 9.3 - Determine the principal stresses in the...Ch. 9.3 - The internal loadings at a cross section through...Ch. 9.3 - The internal loadings at a cross section through...Ch. 9.3 - The shaft has a diameter d and is subjected to the...Ch. 9.3 - The steel pipe has an inner diameter of 2.75 in....Ch. 9.3 - Solve Prob.938 for point B, w1ich is located on...Ch. 9.3 - The wide-flange beam is subjected to the 50-kN...Ch. 9.3 - Solve Pro b. 9-40 for point B located on the web...Ch. 9.3 - The box beam is subjected to the 26-kN force that...Ch. 9.3 - Solve Prob.942 for point B. 942. The box beam is...Ch. 9.4 - Use Mohrs circle to determine the normal stress...Ch. 9.4 - Also, find the corresponding orientation of the...Ch. 9.4 - Draw Mohrs circle and determine the principal...Ch. 9.4 - Determine the principal stresses at a point on the...Ch. 9.4 - Determine the principal stresses at point A on the...Ch. 9.4 - Point A is just below the flange.Ch. 9.4 - Solve Prob.9-2 using Mohrs circle. 92. Determine...Ch. 9.4 - Solve Prob.93 using Mohrs circle. 93. Determine...Ch. 9.4 - Solve Prob.96 using Mohrs circle. 96. Determine...Ch. 9.4 - Solve Prob.911 using Mohrs circle. 911. Determine...Ch. 9.4 - Solve Prob.915 using Mohrs circle. 915. The state...Ch. 9.4 - Solve Prob.916 using Mohrs circle. 916. Determine...Ch. 9.4 - Mohrs circle for the state of stress is shown in...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine the equivalent state of stress if an...Ch. 9.4 - Draw Mohrs circle that describes each of the...Ch. 9.4 - Draw Mohrs circle trial describes each of the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Determine (a) the principal stresses and (b) the...Ch. 9.4 - Draw Mohrs circle that describes each of the...Ch. 9.4 - The grains of wood in the board make an angle of...Ch. 9.4 - The post is fixed supported at its base and a...Ch. 9.4 - Determine the principal stresses, the maximum...Ch. 9.4 - The thin-walled pipe has an inner diameter of 0.5...Ch. 9.4 - The frame supports the triangular distributed load...Ch. 9.4 - The frame supports the triangular distributed load...Ch. 9.4 - The rotor shaft of the helicopter is subjected to...Ch. 9.4 - The pedal crank for a bicycle has the cross...Ch. 9.4 - A spherical pressure vessel has an inner radius of...Ch. 9.4 - The cylindrical pressure vessel has an inner...Ch. 9.4 - Determine the normal and shear stresses at point D...Ch. 9.4 - Determine the principal stress at point D, Which...Ch. 9.4 - If the box wrench is subjected to the 50 lb force,...Ch. 9.4 - If the box wrench is subjected to the 50-lb force,...Ch. 9.4 - The post is fixed supported at its base and the...Ch. 9.5 - Draw the three Mohrs circles that describe each of...Ch. 9.5 - Draw the three Mohrs circles that describe the...Ch. 9.5 - Draw the three Mohrs circles that describe the...Ch. 9.5 - Determine the principal stresses and the absolute...Ch. 9.5 - Determine the principal stresses and the absolute...Ch. 9.5 - Determine the principal stresses and the absolute...Ch. 9.5 - Determine the principal stresses and the absolute...Ch. 9.5 - The solid shaft is subjected to a torque, bending...Ch. 9.5 - The frame is subjected to a horizontal force and...Ch. 9.5 - The bolt is fixed to its support at C. If a force...Ch. 9.5 - The bolt is fixed to its support at C. If a force...Ch. 9 - Prob. 9.1RPCh. 9 - The steel pipe has an inner diameter of 2.75 in....Ch. 9 - Determine the equivalent state of stress If an...Ch. 9 - The crane is used to support the 350-lb load....Ch. 9 - Determine the equivalent state of stress on an...Ch. 9 - The propeller shaft of the tugboat is subjected to...Ch. 9 - Determine the principal stresses in the box beam...Ch. 9 - Determine (a) the principal stresses and (b) the...Ch. 9 - Determine the stress components acting on the...
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- Determine the equivalent state of stress on an element if it is oriented 30° clockwise from the element shown. Use the stress-transformation equations. 300 MPa 950 MParrow_forwardThe state of stress at the point can also be represented in termsof the maximum in-plane shear stress.True or False?arrow_forwardThe distribution of stress in an isotropic aluminium machine component is given (in MPa) as: σ₂ = y +2z² - 6 σ₁ = x+z-6 oy σ₂ = 3x+y-13 6: T =3z² -11 xy (i) (ii) =x²-14 Tyz Txz = y² XZ x, y and z are coordinates of a point within the machine component. By taking Young's modulus, E = 70 GPa, Poisson ratio, v= 0.3 and yield stress, Y = 5 MPa, do the following for a point P located at (4, 1, 2): a) Provide the stress and strain tensors. b) Determine all the principal stresses and principal strains. c) Determine if the machine component will fail based on the failure criteria below: Tresca criterion Von Mises criterionarrow_forward
- Determine state of stress at the remaining points (P2, P3 and P4). Calculate the maximumprincipal (σ1) and maximum in-plane stress (τmax) for the remaining points (P2, P3 and P4) located at Point A.arrow_forwardDetermine the equivalent state of stress on an element at the same point oriented 60° counterclockwise with respect to the element shown. Sketch the results on the elementarrow_forwardThe plate has a thickness of 20 mm and the force P = 3 kN acts along the centerline of this thickness such that d = 150 mm. Plot the distribution of normal stress acting along section a–a.arrow_forward
- 1. Find the average normal stress. 2. Find the maximum in-plane shear stress.arrow_forwardThe wide-flange beam is subjected to the 50-kN force. Determine the principal stresses in the beam at point A located on the web at the bottom of the upper flange. Although it is not very accurate, use the shear formula to calculate the shear stress. A B₂ ➜ 10 mm- B 200 mm 12 mm 250 mm 12 mm -3 m 50 kNarrow_forwardThe shear stress is maximum on the principal plane Select one: O True O Falsearrow_forward
- Determine the shear stress at point A and point B with appropriate unitsarrow_forwardDirect stresses of 120 N/mm2 (tension) and 90 N/mm2 (compression) are applied at a particular point in an elastic material on two mutually perpendicular planes. The principal stress in the material is limited to 200 N/mm2 (tension). Calculate the allowable value of shear stress at the point on the given planes. Determine also the value of the other principal stress and the maximum value of shear stress at the point using Mohr’s Circle.arrow_forwardif the maximum and minimum principal stresses at a point are (27 Mpa) and (5 Mpa) respectively. The maximum shear stress at this point isarrow_forward
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Understanding Stress Transformation and Mohr's Circle; Author: The Efficient Engineer;https://www.youtube.com/watch?v=_DH3546mSCM;License: Standard youtube license