For the given stress [100 50 75 130| MPa 130 200] 50 80 75 a) Find the principal stresses and directions b) Find the stress invariants
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- The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.An element in plane stress on the fuselage of an airplane (figure part a) is subjected to compressive stresses with a magnitude of 42 MPa in the horizontal direction and tensile stresses with a magnitude of 9.5 MPa in the vertical direction (sec figure part b). Also, shear stresses with a magnitude of 15.5 MPa act in the directions shown. Determine the stresses acting on an element oriented at a clockwise angle of 40g from the horizontal. Show these stresses on a sketch of an element oriented at this angle.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.
- The stresses on an element are sx= 1000 Psi. sy= 500 psi, and txy= 350 psi. Find the stresses acting on an element oriented at an angle 0 = 250. Show these stresses on the rotated element.An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 × l0-6, and yxy= 420 × l0-6. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented elements.The stresses acting on a stress element on the arm of a power excavator (see figure) are ax= 52 MPa and txy= 33 MPa (sec figure). What is the allowable range of values for the stress if the maximum shear stress is limited to = 37 MPa?
- A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?For the plane-stress condition given below: σx = 400 MPa σy = 500 MPa τxy = - 30 MPa Construct a Mohr’s circle of stress, find: (a) the principal stresses and the orientation of the principal axes relative to the x,y axes (b) determine the stresses on an element, rotated in the x-y plane 60° counter?clockwise from its original position ; Show these stresses on a sketch of an element oriented at this angle (c) Also, using the matrix transformation law to compare the solutions with Mohr’s circleThe following stress condition is applied to a cubic material.Normal stress in the x direction is 15 Mpa, normal stress in the z direction is -7 Mpa and the shear stress in the x-z plane is 59 Mpa.(a) Write the stress tensor(b) Find the maximum normal stress(c) Find the angle with respect to the x- axis at which the maximum normal stress is applied(d) Find the maximum shear stress(e) Determine the angle with respect to the x-axis at which the maximum shear stress is experienced
- The state of stress at a point on an element of material is shown. Let sigmaX= 49.0 ksi, sigmaY= 17.0 ksi, and Txy= 11.0 ksi. Use this information to represent the principle state of stress and maximum in plane shear stress. Plot the mohr circle and state sigmaX' and sigmaY' and Tx'y' with unit. Also draw the state of stress on the rotated element.Choose the stress to which the size correction factor should be applied in Soderberg's formula. a. Mean stress b. Yield stress c. Variable stress d. Endurance limit stress Clear my choiceThe following stress condition is applied to a cubic material.Normal stress in the x direction is 15 Mpa, normal stress in the z direction is -7 Mpa and the shear stress in the x-z plane is 59 Mpa.(a) Write the stress tensor(b) Find the maximum shear stress(c) Determine the angle with respect to the x-axis at which the maximum shear stress is experienced