Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Chapter 10.3, Problem 5P
The state of strain at the point on the leaf of the caster assembly has components of εx = −400 (10−6), εy = 860 (10−6), and γxy = 375(10−6). Use the strain transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of θ = 30° counterclockwise from the original position. Sketch the deformed element due to these strains within the x–y plane.
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The state of strain at the point on the leaf of the caster assembly has components of P x = -400(10-6), Py = 860(10-6), and gxy = 375(10-6). Use the strain transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of u = 30 counterclockwise from the original position. Sketch the deformed element due to these strains within the x–y plane.
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.
Chapter 10 Solutions
Mechanics of Materials
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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 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_forwardThe state of strain at a point on the bracket has components of Px = 150(10-6), Py = 200(10-6), gxy = -700(10-6). Use the strain transformation equations and determine the equivalent in-plane strains on an element oriented at an angle of u = 60° counterclockwise from the original position. Sketch the deformed element within the x–y plane due to these strains.arrow_forward
- (b) A differential element on the bracket as shown in Figure Q1 is subjected to plane strain that has the following components: ex = 150µ, ey = 200μ , γχν = -700μ. By using the strain transformation equations, determine:- The equivalent in-plane strains on an element oriented at an angle 0 = 60° counterclockwise from the original position. (ii) Sketch the deformed element within the x' – y' plane due to these strains. (iii) The stresses on the oriented planes in (i) where the value of elasticity, E = 200 GPa and Poisson's ratio, v = 0.32. (iv) Give your comments on those stresses in (iii) in terms of elastic limit/failure if the material's yield strength in tension/compression is 250 MPa and in shear is 90 MPa.arrow_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_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_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 on an element has components εx=−270(10−6)εx=−270(10−6), εy=120(10−6)εy=120(10−6), γxy=130(10−6)γxy=130(10−6). Specify the orientation of the corresponding elements for these states of strain with respect to the original element.-Determine the orientation of principle strains for p1 and p2 -Determine the orientation of maximum in-plane shear strain for s1 and s2arrow_forwardA strain gauge that is attached to the surface of a stressed componentgives 3 readings (εa = 310, εb = B=150, εc = C=-300). If the strain gauge is of the 60 degreestype (indicating the angle between each of the gauges), construct a Mohr’s StrainCircle. Gauge A is aligned along the x-axis. Using Mohr’s Strain Circle calculate the:(i) principal strains (ε1, ε2) (ii) principal angles (φ1, φ2) (You should measure these anticlockwise from the y-axis)(iii) maximum shear strain in the plane (γmax)arrow_forward
- For the given plane strain state, use Mohr's circle to determine the strain state associated with the x' and y' axes rotated to θ indicated in the table: \epsilon_x \epsilon_y \gamma_{xy} θ -500\mu 250\mu 120\mu -15°arrow_forwardThe strain components for a point in a body subjected to plane strain are εx = -480 με, εy = -750με and γxy = -914 μrad. Using Mohr’s circle, determine the principal strains (εp1 > εp2), the maximum inplane shear strain γip, and the absolute maximum shear strain γmax at the point. Show the angle θp (counterclockwise is positive, clockwise is negative), the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch.arrow_forwardThe strain components εx, εy, and γxy 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 θp, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. εx = 350 με, εy = -540 με, γxy = -890 μrad. Enter the angle such that -45°≤θp≤ +45°.arrow_forward
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Lec21, Part 5, Strain transformation; Author: Mechanics of Materials (Libre);https://www.youtube.com/watch?v=sgJvz5j_ubM;License: Standard Youtube License