Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Chapter 10.3, Problem 13P
Determine the equivalent state of strain which represents (a) the principal strains, and (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.
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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 =-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
dx
The state of strain in a plane element is €x = -200 x 10-6 , Ey = 100 × 10-6 , and
Yxy = 75 x 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
Eydy
Yxy
2
dy
Yxy
FExdx
2
dx
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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- (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 state of strain at the point on the gear tooth has components €x = 850(106), €y = 480(106), Yxy = 650(106). Use the strain-transformation equations to determine (a) the in-plane principal strains and (b) the maximum in-plane shear strain and average normal strain. In each case specify the orientation of the element and show how the strains deform the element within the x-y plane.arrow_forwardThree readings are obtained from an equiangular strain gage rosette mounted on a free and unloaded surface of a part. Determine the magnitude of the principal strains and their orientation with respect to the 0° gage. Check the results with a Mohr circle.Assume The three known strains are all linear strainsarrow_forward
- The state of strain at the point on the spanner wrench has components of Px = 260(10-6), P y = 320(10-6), and gxy = 180(10-6). Use the strain transformation equations to determine (a) the in-plane principal strains and (b) the maximum in-plane shear strain and average normal strain. In each case specify the orientation of the element and show how the strains deform the element within the x–y plane.arrow_forwardThe 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.arrow_forwardThe piece of plastic is originally rectangular. Determine the average normal strain that occurs along the diagonals AC and DB. Determine the shear strain at corners A and B if the plastic distorts as shown by the dashed lines.arrow_forward
- The 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_forwardA differential element is subjected to plane strain that has the following components; Px = 950(10-6), Py = 420(10-6), gxy = -325(10-6). Use the strain transformation equations and determine (a) the principal strains and (b) the maximum in-plane shear strain and the associated average strain. In each case specify the orientation of the element and show how the strains deform the element.arrow_forwardThe average normal strain and half the maximum in-planeshear strain is determined from the circle as the coordinates. True or false?arrow_forward
- 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 × 10-6arrow_forwardThe 60° strain rosette is mounted on the surface of the bracket. The following readings are obtained for each gage: Pa = -780(10-6), Pb = 400(10-6), and Pc = 500(10-6). Determine (a) the principal strains and (b) the maximumin-plane shear strain and associated average normal strain. In each case show the deformed element due to these strains.arrow_forwardQUESTION 2: The state of plane strain on the element is e, = -300(10 ), €, = 0, and Yy = 150(10-"). Determine the equivalent state of strain which represents (a) the principal strains, and (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. dy T Yay --e,dx xp-arrow_forward
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