The strain at point A on a beam has components
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Statics and Mechanics of Materials (5th Edition)
- The strain at point A on the bracket has components P x = 300(10-6 ), Py = 550(10-6 ), gxy = -650(10-6 ), P z = 0. Determine (a) the principal strains at A in the x9y plane, (b) the maximum shear strain in the x–y plane, and (c) the absolute maximum shear strain.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_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 state of strain at the point on the leaf of the caster assembly has components of Ex = -400(10-6), y = 860(10-6), and Yxy = 375(10-6). Use the strain transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of 0 = 30° counterclockwise from the original position. Sketch the deformed element due to these strains within the x-y plane.arrow_forwardThe 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_forwardThe strain components for a point in a body subjected to plane strain are ɛx = 630 µɛ, ɛy = 940µe and yxy = 1193 urad. 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 με. %3D Ep2 = HE. Vip = prad. Vmax prad. Op =arrow_forward
- If the two principal strains at a point are 1000 x 10-6 and-600 x 10 6, then the maximum shear strain is (a) 800 x 10-6 (c) 1600 x 10 6 (b) 500 x 106 (d) 200 x 106arrow_forwardThe 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_forwardQ4 A three strain gages have been attached directly to a piston used to raise a medical chair, the strain gages give strains as ɛa = 80 µ , Ep = 60 µ and Ec = 20 µ . Determine the principal strains and the principal strain directions for the given set of strains. And Compute the strain in a direction -30° (clockwise) with the x axis. a,x A c.y Pumparrow_forward
- The 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 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_forwardThe strain at point A on the pressure-vessel wall has components Px = 480(10-6), Py = 720(10-6), gxy =650(10-6). Determine (a) the principal strains at A, in the x9y plane, (b) the maximum shear strain in the x9y plane, and (c) the absolute maximum shear strain.arrow_forward
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