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Statics and Mechanics of Materials (5th Edition)
5th Edition
ISBN: 9780134382593
Author: Russell C. Hibbeler
Publisher: PEARSON
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Question
Chapter 14.8, Problem 93P
(a)
To determine
Find the in-plane principal strains on an element and specify the orientation of the element.
Sketch the deformed element due to the equivalent in-plane strains within x-y plane.
(b)
To determine
Find the maximum in-plane shear strain and average normal strain.
Sketch the deformed element due to the equivalent in-plane strains within x-y plane.
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Chapter 14 Solutions
Statics and Mechanics of Materials (5th Edition)
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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 × 10-6arrow_forwardThe 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 dxarrow_forwardThe strain components Ex, Ey, and Yxy are given for a point in a body subjected to plane strain. Using Mohr's circle, determine the principal strains, the maximum in-plane shear strain, and the absolute maximum shear strain at the point. Show the angle 0p, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Ex = 0 μE, Ey = 310 με, Yxy = 280 μrad. Enter the angle such that -45° ≤ 0,≤ +45° Answer: Ep1 = Ep2 = Ymax in-plane = Yabsolute max. = 0p = με με urad uradarrow_forward
- The state of strain at the point on the bracket has components Px = 350(10-6), Py = -860(10-6),gxy = 250(10-6). Use the strain transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of u = 45° clockwise from the original position. Sketch the deformed element within the x–y plane due to these strains.arrow_forwardThe strain components e x, e y, and γ xy are given for a point in a body subjected to plane strain. Using Mohr’s circle, determine the principal strains, the maximum in-plane shear strain, and the absolute maximum shear strain at the point. Show the angle θ p, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Ex Ey Yxy −1,570 με -430με -950 μradarrow_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
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