The Cartesian components of stress at a point are 0x = 15 Oy = 0₂ = 8, - Txy = 6, Tyz = 4, Txz = 4 MPa. the normal and shear stresses on a plane whose direc- 1 1 1 " 3' √3 given as below: Determine tion cosines are
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- .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°.Solve the preceding problem if the norm al and shear stresses acting on the element are sx = 2100 kPa, sy= 300 kPa, and txy= -560 kPa, and the seam is oriented at an angle of 22.5° to the clement.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 xy axes, that is, determine crv, tr(_, and t. Show the results on a sketch of an clement oriented at B = 10
- -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. aA state of stress is specified in the figure shown below. Determine the Normal stress σx (mPa) on the Principal Plane if Px = -60 mPa; Py = -84 mPa and v = 55 mPa3. Listed below is a combination of stresses acting at a point and referred to axes x and y in an elastic material. Using Mohr’s circle of stress determine the principal stresses at the point and their directions for each combination. 1}sigmax -60 n/mm2 , sigmay -36n/mm2 ,TAUxy=5n/mm2 2}}sigmax 30 n/mm2 , sigmay -50n/mm2, TAUxy= 30n/mm2
- 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 zx= 30 MPa. Determine: (a) 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 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 MPaA 60˚ strain rosette measures the following strain at a point on the aluminum skin ofan airplane. ϵ0 = 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.
- Forces of F1=15 kN in the z direction from the B point, F2=10 kN in the z direction from the C point and F3=10 kN in the y direction act on the arm in the figure. The lengths of the arm are also given as L1=0.15 m and L2=0.16 m. The radius r in the a-a section taken over the arm is r=0.2 m and it is desired to determine the stress state at point A. The shear modulus of the sleeve material is G=65 Gpa. According to this; WRITE YOUR RESULTS IN THE BOXES WITHOUT THE UNITS IN kPa. a) Find the shear stress due to the shear force at point A. Response b) Find the shear stress due to the torsional moment at point A. Response c) Find the total shear stress at point A. Response d) Find the normal stress due to the normal force at point A. Response e) Find the normal stress due to the bending moment at point A. Response f) Find the total normal stress at point A. ResponseA 60 ̊ strain rosette measures the following strain at a point on the aluminum skin of an airplane. ε0 = 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.The stresses at a point in a bar are 200 N/mm2 (tensile) and 80 N/mm2 (compressive). Determine the resultant stress in magnitude and direction on a plane inclined at 60° to the axis of the major stress. Also determine the maximum intensity of shear stress in the material at the point.