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_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
- Your 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_forwardThe 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_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_forward1. A circular aluminium tube of length L = 400 mm is loaded in compression by the force P. The outside and inside diameters are 60 mm and 50 mm, respectively. A strain gage is placed on the outside of the bar to measure normal strains in the longitudinal direction. 1.1 If the measured strain is ε = 550 x 10-6, what is the shortening δ of the bar? 1.2 If the compressive stress in the bar is intended to be 40 MPa, what should be the load P? 2. A cylindrical vessel has an internal diameter of 2 m. It is made of 15 mm thick plate. The efficiency of the longitudinal and circumferential joints are 80 % and 60 % respectively. If the ultimate tensile stress for the material is 500 MPa and the factor of safety is 6, determine the safe internal pressure to which the vessel may be subjected.arrow_forward
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