MECHANICS OF MATERIALS
11th Edition
ISBN: 9780137605521
Author: HIBBELER
Publisher: RENT PEARS
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Textbook Question
Chapter 10.5, Problem 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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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.
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 ey
Chapter 10 Solutions
MECHANICS OF MATERIALS
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 leaf of...Ch. 10.3 - Use the strain transformation equations and...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. 10.5 - The strain at point A on the bracket has...
Ch. 10.5 - Determine (a) the principal strains at A, (b) the...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 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. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - Solve Prob. 1061 using the maximum distortion...Ch. 10.7 - Solve Prob.1063 using the maximum distortion...Ch. 10.7 - Prob. 70PCh. 10.7 - The plate is made of Tobin bronze, which yields at...Ch. 10.7 - If a machine part is made of titanium (TI-6A1-4V)...Ch. 10.7 - The components of plane stress at a critical point...Ch. 10.7 - If Y = 50 ksi, determine the factor of safety for...Ch. 10.7 - Prob. 82PCh. 10.7 - If the yield stress for steel is Y = 36 ksi,...Ch. 10.7 - Prob. 84PCh. 10.7 - The state of stress acting at a critical point on...Ch. 10.7 - The shaft consists of a solid segment AB and a...Ch. 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 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_forwardQ.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_forward
- 4. 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_forwardThe average normal strain and half the maximum in-planeshear strain is determined from the circle as the coordinates. True or false?arrow_forward
- The 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_forward2. 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_forward
- A 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_forwardQ.4) By using the strain rosette shown in figure below, we obtained the following normal strain data at a point on the surface of a machine part made of steel [E = 207 GPa, v= 0.29]: ε-770 μ, E = 520 µ, & = - 435 µ (a) Determine the strain components &, &, and %y at the point. (b) Determine the principal strains and the maximum in-plane shear strain at the point using Mohr's circle. (c) Draw a sketch showing the angle Op, the principal strain deformations, and the maximum in-plane shear strain distortions. (d) Determine the magnitude of the absolute maximum shear strain. b ' 60°| 60°arrow_forward
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