Solve Prob. 14–88 using Mohr’s circle.
*14–88. The state of strain at the point on the leaf of the caster assembly has components of
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Statics and Mechanics of Materials (5th Edition)
- 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.arrow_forward7- The state of strain at the point has components in the X-axis = -210x10-6, in the y-axis = 355x10-6, and in the x-y plane equations to determine the equivalent in-plane strains ( er,y.and Yx'y') on an element oriented at an angle -710x10-6. Use the strain-transformation of 55° counterclockwise from the original position.arrow_forward*10-8. The state of strain at the point on the bracket has components €, = -200(10-6 ), e, = -650(106 ), Ysy = -175(106 ). Use the strain-transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of 0 = 20° counterclockwise from the original position. Sketch the deformed element due to these strains within the x-y plane. Prob. 10-8arrow_forward
- The state of strain at a point on a wrench has components ϵx = 120(10-6), ϵy = -180(10-6), γxy= 150(10-6). Use Mohr's circle to solve the problem. Determine the orientations of the element at which the principal strains occur. θp1= θp2=arrow_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_forwardIf the normal strain is defined in reference to the final length Δs′, that is,P= = lim Δs′S 0 aΔs′ - Δs Δs′ b instead of in reference to the original length, Eq. 2–2, show that the difference in these strains is represented as a second-order term, namely, P - P= = P P′.arrow_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 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_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
- The strain components for a point in a body subjected to plane strain are εx = -270 με, εy = 730με and γxy = -799 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 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 at a point on the pin leaf has components €z =200 (10−6), €y = 180 (10-6), Yzy=−300 (10–6). Use the Mohr's circle to determine the equivalent in-plane strains on an element oriented at an angle of 0 = 30° clockwise from the original position. (Figure 1) Figure 1 of 1 > Part B Select the points that represent the strain on the inclined element. Select point P on Mohr's circle that represents and Ya'y' /2 for the given state of plane strain for the element and point Q that represen Ey!. 4 + 0 No elements selected -400 -300 -200 -100 -300 -200- -100- 100- 200- 300- + y/2, 10-6 R=150.33 100 8 C (190,0) I 1200 I I T I I P A (200,-150) i 300 E, 10-6 400arrow_forward
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