Question 3 If e and e2 have the same signs., then the absolute maximum shear strain will be equal to the maximum in-plane shear strain. True False
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- During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.A strain rosette (see figure) mounted on the surface of an automobile frame gives the following readings: gage A,310 × 10-6:gage B,180 × l0-6; and gage C. -160 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.From the stress states given, draw the 3D Mohr's circle (lable the principle normal stresses, maximum and absolute shear stresses), and sketch the principle and shear planes. σxx = 70 ksi, σzz = -50 ksi, ?xy = 50 ksi (counterclockwise)
- Draw Mohr's circle for the following plane strain state. Then compute (or extract from your drawing) the principal strains and max shear strain. (Positive sign convention for each is shown on the figure.) Ex = 200μ, Ey=-200μ, Yxy = 50μ (rad) You For the previous problem, compute the following six stress quantities: d. dy, dz. Txy, Tyz. Tzx. Assume this is an aluminum alloy (E = 10,000 ksi, G = 3800 ksi, v = 0.33). Do not forget units! Ex3 1 4 tIf the components of stress at pointp given by 1 2-5 Mpa, 4 -5 0 then the stress vector whose unit normal parallel to plane 2x +y-z=1 is (V(3/2), 3V(3/2), 3/(3/2)) .10 (V(3/2) 3V (3/2), V(3/2)) I1O ((3/2) , 2V(3/2), 2 v(3/2)).1 OFrom 3 forces, 2 bending moments and 1 toque acting on B, which ones are non zero, and the direction they are acting. Then indicate if they make shear or normal stress Draw 3-d stress state cust above plane a
- Given the stress element shown, determine the maximum in-plane shear stress, 0x = 54 MPa Oy = 30 MPa Txy = 40 MPa (Use the stress orientation shown in the figure to determine the sign on the stress values.) 58 MPal 65 MPa 74 MPa 88 MPa 96 MPa + 148 MPaQuestion: The stress components at point O of a part made of steel material (E = 210 GPa and v= 0.3) are given below. 25 40 - 20 40 30 35| MPа - 20 35 -10 a) Calculate the strain components (Exx, Eyy, Ezz, Yxy, Yxz and Yyz). b) Calculate the principal strain components (E,, E2, and E3) and the maximum shear stress (max). c) Draw the 3-D Mohr circle for the strain components.A thin triangular plate PQR forms a right angle at point Q. During deformation, point Q moves to the left by u = 2.3 mm and upward by v = 3.9 mm to new position Q'. Determine the shear strain y at corner Q' after deformation. Use c = 685 mm, a = 31°, and B = 59° If U Answer: y = i P B R urad
- At a point in an elastic material under strain, the stresses on the three mutually perpendicular planes are as follows:A normal tensile stress of 60 N/mm^2and shear stress of 40 N/mm2 on one plane and a normal tensile force of 40 N/mm^2and a complimentary shear stress of 40 N/mm^2 on another plane. Find the following using Mohr circle only (take 5 N/mm2 = 1 cm)a. The principal stresses and principal planes.b. The maximum shear stress and its plane.c. The normal and shear stress on a plane inclined at an angle of 30Oto major principal plane.A thin triangular plate PQR forms a right angle at point Q. During deformation, point Q moves to the left by u = 2.8 mm and upward by v = 5.4 mm to new position Q'. Determine the shear strain y at corner Q' after deformation. Use c = 635 mm, a = 26°, and 3 = 64° U Answer: y = P R uradA differential element on the bracket is subjected to plane strain that has the following components: , Ex = 300 x 10-6, Ey = 200 x 10-6, Exy = -500 x 10-6. Use the strain-transformation equations and determine the normal strain Ex' in the x' direction on an element oriented at an angle of 60°. Note, a positive angle is counter clockwise.