1. The state of plane stress at a point on a body is represented on the element shown in (a). Represent this stress state in terms of the maximum in-plane shear stress and associated average normal stress. 90 MPa 60 MPa 20 MPa (a)
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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 .-27 A square plate with side dimension of 2 in. is subjected to compressive stress a and tensile stress The stresses on element A oriented at angle ?? x1=45° aresy1= 75 psi. tx1y1= 275 psi. . Find the state of stress on the element lilt is rotated clockwise to align the x3 axis with the horizontal x axis.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
- Given the stress cube below, represent the Mohr Circle, demonstrating the stepsfollowing:a) Calculation of main stresses and directions;b) Calculation of stresses in a plane of rotation ?, clockwise;c) Circle of Mohr.q1 b In 2D XY-plane-stress analysis, how many stress components you need to calculate.Please write/show their names in XY plane on a plane element.Explain the method of representing the combination of normal and shear stresses acting on any plane through an incremental element on shear stress–normal stress coordinates.
- 1. At a point in a piece of elastic material, direct stresses of 92 MN/m2 tensile and -49 MN/m2 compressive are applied on mutually perpendicular planes. The planes are also subjected to a shear stress. If the greater principal stress is limited to 100 MN/m2 tensile, determine the value of shear stress. Give you answer to 2 significant figures in MN/m2At a point in a strained material the principal stresses are 200 N/mm2 (tensile) and 120 N/mm2 (compressive). Determine the normal stress, shear stress and resultant stress on a plane inclined at 30° to the axis of major principal stress. Also determine the maximum shear stress at the point.A stress element in a rock mass making up a slope experiences a 2D stress as follows: σx = 8 MPa, σy = 4 MPa , tauxy = 3 MPa a. Draw the Mohr circle. On Mohr's circle, mark the location of the x and y planes, mark the angle of rotation θ from the x plane to the σ₁,σ3,and taumax plane. Prove that the angle of rotation of the Mohr circle is 2 times the angle of rotation of the element. b. Write down the coordinates of the center of Mohr's circle and calculate its radius.
- The principal stresses at a point across two mutually perpendicular planes are 70 MN/m2 tension and 50 MN/m2 tension respectively. The shear stress across these planes is 30 MN/m? (Counter clockwise). Determine the magnitude of the normal, tangential, the resultant stress, and inclination of resultant stress on a plane inclined at 30° to the plane of greater principal stress. And also verify the answer by drawing the Mohr's circle.At a point of a material, the stresses forming a two-dimensional system are shown inFigure Q1. By using Mohr's circle of stress method: -(i) determine the magnitudes of the principal stresses.(ii) determine the directions of the principal stresses.(iii) Examine the value of the maximum shearing stress.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?