At a point in a stressed material the stress components are: Ox= -30, dyy = 75, T₁ = 72, T - = 40. 0 = 110 T= 30, all are in MPa Calculate the normal, shear and resultant stresses on a plane whose normal makes an angle of 40° with the x axis and 60° with the y-axis.
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- The major and minor principal stresses acting at a point in a stressed material are 80 psi compression and 20 psi tension. (a) Draw the Mohr’s circle for this stress combination. (b) What is the maximum shear stress acting at the point, and what value of normal stress acts on the plane? (c) Determine the value of the shear and normal stresses acting on a plane that is 30° ccw from the major principal plane.At a point in a stressed material, the major principal stress is 66 kPa compression and the minor principal stress is 34 kPa tension. (a) Use the Mohr’s circle to determine the shear and normal stress on a plane 45° ccw from the major principal plane. (b) Determine the stress combination acting on the plane 75° ccw from the major principal plane.The stresses shown act at a point on the free surface of a machine component. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 23.6 ksi, Sy = 2.8 ksi, and Sxy = 7 ksi. Assume β=19∘. Determine the normal stresses σx and σy and the shear stress τxy at the point.
- At a creation point in a strained material, the principle stresses are 100N/mm2 and 40 N/mm2 both in tensile. Find normal, tangential and resultant stresses across a plane through the point at 480 to the major principal plane using Mohr's circle of stress.At a point in a stressed body, the cartesian components of stress are sigma xx = 60 MPa, sigma yy= -40 MPa, sigma zz = 20 MPa, tau xy = -40 MPa, tau yz = 20 MPa, and tau xz = 30 MPa. Determine: (a) The principle stresses and their direction cosines. (b) The normal and shear stresses on a plane whose outer normal has the following direction cosines: cos (n, x) = 0.429 ; cos (n, y) = 0.514; cos (n, z) = 0.743The stresses shown act at a point on the free surface of a machine component. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 12.4 ksi, Sy = 3.5 ksi, and Sxy = 3.6 ksi. Assume B = 29°. Determine the normal stresses ox, and oy, and the shear stress rxy, at the point.
- At a point in a stressed material, the major principal stress is 7.2 ksi compression and the minor principal stress is 3.6 ksi compression. Using Equations 1 and 2, determine the maximum shear stress that acts at the point and the normal stress that acts on the plane of the maximum shear stress.At a certain point in a stressed body, the principal stresses are σx = 98 mPa and σy = -40 mPa. Determine σx on the plane whose normal are +23∘ and 23+90∘A square post with a tubular cross section is loaded as shown in the figure below. a) Determine the state of the stress at point A having sides parallel to x and y axes. b) Determine the principal planes and principal stresses at point A at the base of the post.
- A 60˚ strain rosette measures the following strain at a point on the aluminum skin of an airplane. ϵo = 160 ×10-6 m/m, ϵ60 = -220 ×10-6 m/m and ϵ120 = 360 ×10-6 m/m. Using E= 10 ×106 psi and v = 0.3, Determine the principle stresses and the maximum in-plane shear stress.Solve alll subparts b, c, d and e B) determine the principal plane (for σmax) in radians. C) Determine the shearing stress in a plane, which is 330 with the vertical (clockwise). D) determine the normal stress (in MPa) in a plane, which is 330 with the vertical (clockwise). E) determine the minimum values of θ (in radians) for which the normal stress is the equal to or less than 35.2 MPa.A beam has a uniform dead load and live load has a fixed support at both ends. If the beam properties are given below, what is the stress at top of the beam section at the midspan. (MPa)