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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- 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 .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.3. 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
- 2- The state of stresses at a point are defined as follows. Find the normal and shear stress vector components (O₂. ) on a plane tangent to a cylinder of diameter D and coaxial with x-axis (Z-axis) at point (B.y.B). Also, determine the octahedral shear stress. Stu. Nom. D B Y 30 45 60 5.0 2.0 1.5 Ju = 45 20 50 MPa 60 50 103 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 O800 N D 120 N.m d = 8 cm 600 N Q / If the cross section of the femur can be approximated as a circular tube, determine the state of stresses on the 160 N.m points A and B at section due to the loads as shown in figure. r. = 22 mm n = 18 mm В L = 0.15 m
- Direct stresses of 120 N/mm2 (tension) and 90 N/mm2 (compression) are applied at a particular point in an elastic material on two mutually perpendicular planes. The principal stress in the material is limited to 200 N/mm2 (tension). Calculate the allowable value of shear stress at the point on the given planes. Determine also the value of the other principal stress and the maximum value of shear stress at the point using Mohr’s Circle.1.5 kN 120 mm Outer diameter: 72 mm Inner diameter: 62 mm 150 mm D 120 mm 4.5 kN A For element A find: (a) Torsional shearing stress (b) Transverse shear stress (c) Normal stress Q = [AS] × y 2rm TU y =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) = 0.743
- Problem 3: For the plane stress state listed below, draw a Mohr's circle diagram properly labeled. Keep in mind that the principal stress is that stress state where the shear stress is zero. That means it is the stress state along the normal stress line in Mohr's space. So, use your Mohr's circle to find the principal normal and shear stresses, and determine the angle from the x axis to o1. 0x = 16 kpsi, oy = 9 kpsi, Ty = 5 kpsi ccwThe state of stress at a point in a machine component is given by ox = 120 MPa, oy = 55 MPa, Oz = -85 MPa, Oxy = -55 MPa, Oxz = -75 MPa, and oyz = 33 MPa. Construct the Mohr's circles of stress for this stress state and find the maximum 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.