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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EBK STATICS AND MECHANICS OF MATERIALS
- 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
- The 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(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 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 Ex = 400 (10 ), Ey = 200 (10 ) and yxy = 400 (10-6). Determine the principal strains and the maximum in plane shear strain. Select one: & =524 (10-6), ɛ2 = -76.4 (106) and ymax in-plane = 223 (10 ). E =524 (10-6), E2 = -76.4 (10-) and ymax in-plane = 447 (10-). E =524 (10 E2 = 76.4 (10-) and ymax in-plane = 223 (10-). %3D E1 = 524 (10-), E2 = 76.4 (10-) and ymax in-plane = 447 (10-). E=-76.4 (10), E2 = -524 (10-6) and ymax in-p ane = 447 (10-6).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 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_forwardA rectangular aluminum plate of uniform thickness has a strain gauge at the center. It is placed in a test rig which can apply a biaxial force system along the edges of the plate as shown below. If the measured strains are +0.0005 and +0.001 in the x and y directions respectively, a) Determine the corresponding stresses set up in the plate and the strain through the thickness, εz. Take E=72 GPa and ν=0.32. b) Construct the Mohr’s circle for the loaded plate. c) State the values of the principal stresses. d) Determine the maximum shearing stresses and the directions of the planes on which they occur.arrow_forward
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