The state of strain at the point on the pin leaf has components of
14–87. Solve Prob. 14–86 for an element oriented θ = 30° clockwise.
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Statics and Mechanics of Materials (5th Edition)
- 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 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 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
- (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 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 the point on the pin leaf has components of ϵx=200(10−6)ϵx=200(10−6) , ϵy=180(10−6)ϵy=180(10−6) , and γxy=−300(10−6)γxy=−300(10−6) . (Figure 1) -Use the strain transformation equations and determine the normal strain in the xx direction on an element oriented at an angle of θ=−55∘θ=−55∘ clockwise from the original position. -Determine the shear strain along the xy plain Determine the normal strain in the y direction.arrow_forward
- 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 state of a plane strain at a point has the components E, = 500 (10-), ɛy = 250 (10-6) and yxy = -700 (10-5). Determine the principal strains and the maximum in plane shear strain. Select one: ɛz = -747 (10-6), ɛ2 = -3.35 (10-) and ymax in-piane = 743 (10). E1 = 747 (10-), E2 = 3.35 (10-) and ymax in-plare = 743 (10°). %3D E1 = -335 (10-), E2 = -747 (10 °) and ymax in-piane = 743 (10-°). %3D 21 = 747 (10-), E2 = 335 (10-) and ymax in-plane = 743 (10-*). E = 747 (10-), E2 = -3.35 (10-) and ymax in-plane = 743 (10-).arrow_forwardThe 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 dxarrow_forward
- The 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_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_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
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