3. For the stress system shown, calculate the magnitude of the shear stresses On T, and the angle a. (72 MPa; 69.25°). 60 MPa 100 MPa 50 MPa α 70 MPa
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- -26 A rectangular plate of dimensions 125 mm × 75 mm is subjected to tensile stress sy= 67 kPa and compressive stress a. If it is known that the normal stress along the diagonal t—t is ??t= -6.57 kPa, find stress ??y on element A. a.4 The stresses on an clement arc known to be sx= 120 MPa, sy= 100 MPa, and txy= 75 MPa. Find the stresses on an inclined section through the element at an angle ? = 45°.At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with t = 1400 psi and trv = —900 psi, as shown in the figure part a. The figure part b shows an inclined plane aa cut through the same point in the material but oriented at an angle ft Determine the value of the angle 6 between zero and 90° such that no normal stress acts on plane aa. Sketch a stress clement having plane aa as one of its sides and show all stresses acting on the clement
- The stresses acting on an element are x= 750 psi, y= 600 psi, and xy = 400 psi. Determine the principal stresses and show them on a sketch of a properly oriented element.An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec figure). On this inclined clement, the normal and shear stresses have the magnitudes and directions shown in the figure. Determine the normal and shear stresses acting on an clement whose sides are parallel to the \y axes, that is, determine crv, tr(_, and t, Show the results on a sketch of an clement oriented at B .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.
- Solve the preceding problem for an element in plane stress on the bottom surface of a fuel tanker (figure part a); stresses are sx= 105 MPa, sy. = 75 MPa, and ??xy= 25 MPa. Determine the stresses acting on an element oriented at an angle ?? = 40° from the x axis, where the angle is positive when counterclockwise. Show these stresses on a sketch of an element oriented at the angle ??.For the stress element shown below, which 2 points (σ, τ) in the stress domain could be used to define the diameter of the Mohr's Circle? (50 MPa, 25 MPa) (- 80 MPa, - 25 MPa) (- 80 MPa, 25 MPa) (50 MPa, - 25 MPa)The state of stress at a point can be described by σx = 40 MPa , σy = 64 MPa , and τxy = 18 MPa . A second coordinate system is rotated by θ = 25 ∘ A) What is the normal stress in the direction of the x′-axis? B) What is the shear stress in the y′-direction for the faces with a normal in the x′-direction? C) What is the normal stress in the direction of the y′-axis?
- A body is subjected to a direct tensile stress of 300 MPa in one plane accompained by a simple shear stress of 200 MPa. Determine maximum normal stress on the plane.The state plane stress at a point is represented by the stress element below. Determine the stresses acting on an element oriented 30 degree counterclockwise respect to the original element. 1. Calculate the normal stress at the x-axis a. 69.8 MPa b. 75.25 MPa c. -39.8 MPa d. -24.60 MPa 2. Calculate the normal stress at the y-axis a. -39.8MPa b. 69.8 MPa c. -24.60 MPa d. 75.60 MPa 3. Calculate the shearing stress at the xy-face a. 55 MPa b. -55 MPa c. 65 MPa d. -65 MPaDetermine the principle stresses σ1, σ2, σ3 and their orientation φ, if σx, σy and σz are known as shown in Figure Q.4b. sigma x = 80 mpa sigma y = 10 mpa tau z = 40 mpa