Mechanics Of Materials, Si Edition
9th Edition
ISBN: 9789810694364
Author: Russell C Hibbeler
Publisher: Pearson Education
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Textbook Question
Chapter 10.5, Problem 10.23P
Determine (a) the principal strains at A, (b) the maximum shear strain in the x-y plane, and (c) the absolute maximum shear strain.
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Students have asked these similar questions
1. Find the relationships between strain components in the polar coordinate and
strain components in the rectangular coordinate.
The state of strain in a plane element is Ex = -300 x 10-6 , Ey= 450 x 10-6, and
Yxy = 275 x 10-6.
(a)
Use the strain transformation equations to determine the equivalent
strain components on an element oriented at an angle of 0 = 30°
counterclockwise from the original position.
(b)
Sketch the deformed element due to these strains within the x-y
plane.
Deformed length of the elongated diagonal.
Chapter 10 Solutions
Mechanics Of Materials, Si 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 - Prob. 10.3PCh. 10.3 - Prob. 10.4PCh. 10.3 - 10-5. The state of strain at the point on the gear...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Prob. 10.8PCh. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Use the strain- transformation equations to...
Ch. 10.3 - 10–11. The state of strain on an element has...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 - Prob. 10.17PCh. 10.3 - Prob. 10.18PCh. 10.3 - 10–19. Solve part (a) of Prob. 10–4 using Mohr’s...Ch. 10.3 - *10–20. Solve part (a) of Prob. 10–5 using Mohr’s...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 - Prob. 10.24PCh. 10.5 - Prob. 10.25PCh. 10.5 - 10–26. The 60° strain rosette is attached to point...Ch. 10.5 - 10–27. The strain rosette is attached at the point...Ch. 10.5 - Prob. 10.28PCh. 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 - 10–39. The strain in the x direction at point A on...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 - Prob. 10.43PCh. 10.6 - *10–44. Strain gauge b is attached to the surface...Ch. 10.6 - Prob. 10.45PCh. 10.6 - 10?46. The principal strains in a plane, measured...Ch. 10.6 - 10–47. The principal stresses at a point are shown...Ch. 10.6 - *10–48. The 6061-T6 aluminum alloy plate fits...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 - Prob. 10.52PCh. 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. Express...Ch. 10.7 - The yield stress for a zirconium-magnesium alloy...Ch. 10.7 - Solve Prob. 1061 using the maximum distortion...Ch. 10.7 - Prob. 10.63PCh. 10.7 - Prob. 10.64PCh. 10.7 - Prob. 10.65PCh. 10.7 - Prob. 10.66PCh. 10.7 - Prob. 10.67PCh. 10.7 - If the material is machine steel having a yield...Ch. 10.7 - The short concrete cylinder having a diameter of...Ch. 10.7 - 10–70. Derive an expression for an equivalent...Ch. 10.7 - Prob. 10.71PCh. 10.7 - Prob. 10.72PCh. 10.7 - If the 2-in diameter shaft is made from brittle...Ch. 10.7 - If the 2-in diameter shaft is made from cast iron...Ch. 10.7 - 10–75. The components of plane stress at a...Ch. 10.7 - Prob. 10.76PCh. 10.7 - 10–77. If the A-36 steel pipe has outer and inner...Ch. 10.7 - Prob. 10.78PCh. 10.7 - Prob. 10.79PCh. 10.7 - Prob. 10.80PCh. 10.7 - Prob. 10.81PCh. 10.7 - Prob. 10.82PCh. 10.7 - Prob. 10.83PCh. 10.7 - Prob. 10.84PCh. 10.7 - 10–85. The state of stress acting at a critical...Ch. 10.7 - The shaft consists of a solid segment AB and a...Ch. 10.7 - Prob. 10.87PCh. 10.7 - Prob. 10.88PCh. 10.7 - 10–89. The gas tank has an inner diameter of 1.50...Ch. 10.7 - The gas tank is made from A-36 steel and has an...Ch. 10.7 - The internal loadings at a critical section along...Ch. 10.7 - *10–92. The shaft consists of a solid segment AB...Ch. 10.7 - Prob. 10.93PCh. 10 - In the case of plane stress, where the in-plane...Ch. 10 - The plate is made of material having a modulus of...Ch. 10 - If the material is machine steel having a yield...Ch. 10 - Determine if yielding has occurred on the basis of...Ch. 10 - The 60 strain rosette is mounted on a beam. The...Ch. 10 - Use the strain transformation equations to...Ch. 10 - If the strain gages a and b at points give...Ch. 10 - Use the strain-transformation equations and...Ch. 10 - Use the strain transformation equations to...Ch. 10 - Specify the orientation of the corresponding...
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- 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 components at a point in a body under a state of plane strain are shown in fig. Using Mohr's circle method, 140 u Determine: 66 M 1. Maximum shear strain 2. Principal strains 350 a 350 M 66 M 140 uarrow_forwardplease solve with all stepsarrow_forward
- Q.3) A structural member in plane strain has the following strains at a point: & 360 μ , E, = 230 µ, Ky = 150 µ (a) Determine the strains for an element oriented at an angle of 60° counter clockwise. (b) Determine the principal strains and the maximum shear strain using strain transformation equations. (c) Show the result of parts (a) and (b) via sketches of properly oriented elements. Ey Yxy 1 Exarrow_forward4. Show that Cp = as +45°. principal strain and shear strainarrow_forward(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_forward
- The average normal strain and half the maximum in-planeshear strain is determined from the circle as the coordinates. True or false?arrow_forwardThe 60° strain rosette shown below, is mounted on the surface of a thin shell. The following readings are obtained for each gage: Ea = -780 x 10-6 , Eb = 400 × 10-6, and ec= 500 × 10-6. Determine (a) the principal strains (b) the maximum in-plane shear strain and the associated average normal strain. C 60° 60° aarrow_forwardFor the state of a plane strain with Ex, Ey and yxy components: (a) construct Mohr's circle and (b) determine the equivalent in-plane strains for an element oriented at an angle of 30° clockwise. Ex = 250 x 10-6 Ey = 310 x 10-6 Yxy = -100 × 10-6arrow_forward
- 2. A sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are 0.40 x 10 - in the x direction and 0.30 x 10 in the y direction, determine the stresses in the x and y direction. Also, determine the strain in the z direction. The modulus of elastic and Poisson's ratio of copper is 110 GPa and 0.35 respectively. 3. If the copper in no. 2 is changed into steel with the same dimensions and with a modulus of elasticity of 200 GPa and a Poisson's ratio of 0.30, determine the strains in all direction if the same stresses in no. 2 where to be applied to the steel. €, E,arrow_forwardA sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are 0.40 x 10 -3 in thex direction and 0.30 x 10-3 in the y direction, determine the stresses in the x and y direction. Also,determine the strain in the z direction. The modulus of elastic and Poisson’s ratio of copper is 110GPa and 0.35 respectively.arrow_forwardThe state of strain in a plane element is ex =-200 x 10-6, Ey = 0, and yxy = 75 × 10-6 , as shown below. Determine the equivalent state of strain which represents (a) the principal strains (b) the maximum in-plane shear strain and the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain with respect to the original element. y Yxy 2 dy Yxy FExdx dxarrow_forward
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