Solve Prob. 14–91 using Mohr’s circle.
14–91. The state of strain at the point on the spanner wrench has components of
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Statics and Mechanics of Materials (5th Edition)
- The state of strain on an element has components Px = -300(10-6), Py = 100(10-6), gxy = 150(10-6). Determine the equivalent state of strain, which represents (a) the principal strains, and (b) the maximum in-plane shear strainand the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain with respect to the original elementarrow_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 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 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_forwardFor 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_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
- A 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_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_forwardYour answer is partially correct. The strain components for a point in a body subjected to plane strain are ɛ, = -890 µɛ, ɛ, = -690µɛ and yy = -682 prad. Using Mohr's circle, determine the principal strains (ɛp1 > Ep2), the maximum inplane shear strain yip, and the absolute maximum shear strain ymax at the point. Show the angle 0, (counterclockwise is positive, clockwise is negative), the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Answers: Ep1 = 927.99 με. Ep2 = 1116.0 PE. Vip = 188.01 prad. Ymax = -188.01 prad. Op = 36.82arrow_forward
- The strain components ɛ Ey, and ywyare 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 0, the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Ex = 0 µE, Ɛy = 330 µɛ, Yxy = 270 prad. Enter the angle such that -45° <0,s+45°. Answer: Ep1 = Ep2 = Ymax in-plane prad Yabsolute max. pradarrow_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_forwardThe strain components ɛx = 466 µE, ɛy = -524 µe, and yxy = -646 µrad are given for a point in a body subjected to plane strain. Determine the angle Op corresponding to the orientation of the principal planes at the point. -12.12° None of the above -17.93° -13.75° -10.36° -16.56°arrow_forward
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