Derive the expressions for stresses around a hole in a plate (in polar coordinates) that is under biaxial loading, as shown the figure below. Assume plane stress condition. Hint: Apply the superposition principle (stress-based solutions can be additively decomposed!) 02 1
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- On the surface of a structural component in a space vehicle, the strains arc monitored by means of three strain gages arranged as shown in the figure. During a certain maneuver, the following strains were recorded: e, = 1100 X l0_6, 6h = 200 X lO_6, and e = 200 X 10-6. Determine the principal strains and principal stresses in the material. which is a magnesium alloy for which E = 6000 ksi and v = 0.35. Show the princ ipal strains and principal stresses on sketches of properly oriented elements.In a thin plate, the state of stress prevails according to the figure. Calculate the principal stresses and their directions (using both equations and Mohr's stress circle). Show the result in a figure. σx = 40 MPa; σy = 50 ; MPa and τxy = 30 MPa The question should contain clear solutions and be presented according to the following structure: Given, to find, Solution and Answer.For the plane-stress condition given below: σx = 400 MPa σy = 500 MPa τxy = - 30 MPa Construct a Mohr’s circle of stress, find: (a) the principal stresses and the orientation of the principal axes relative to the x,y axes (b) determine the stresses on an element, rotated in the x-y plane 60° counter?clockwise from its original position ; Show these stresses on a sketch of an element oriented at this angle (c) Also, using the matrix transformation law to compare the solutions with Mohr’s circle
- 3.For a body under three dimensional stress state, describe the procedure for obtaining the absolute maximum shearing stress at a given point. What is meant by strain transformation? Describe two procedures for obtaining stress form Mohr’s circle for strain.Find the axial stress (Subscript[\[Sigma], z]) and axial strain (Subscript[\[Epsilon], z]) for a thick-walled circular pipe subjected to an internal pressure Subscript[p, i] for the following three cases:a) the pipe is long and open (plane strain)b) the pipe is short and open (plane stress)c) the pipe is is closedExpress the above solutions in terms of the pressure Subscript[p, i], the the pipe inner and outer radii and the material constants.Please give detailed explanation. see photo for expected answer. For the following data, using the stress-transformation equations. (a) find the principal stresses and show their sense on properly oriented elements; (b) find the maximum (principal) shear stresses with the associated normal stresses and show the results on properly oriented elements; and (c) check theinvariance of the normal stresses for solutions in (a) and (b). Please give detailed explanation. See photo for expected answer.
- Consider the general case of plane stress as shown. Write a computer program that will show a plot of the three Mohr’s circles for the element, and will also determine the maximum in-plane shear stress and the absolute maximumshear 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?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.
- A rectangular block of material is subjected to a tensile stress of 90 N/mm2 along X axis and acompressive stress of 45 N/mm2 on a plane at right angle to it, together with shear stresses of80 N/mm2 on the same plane. Calculate the direction of principal planes, the magnitude ofprincipal stresses and the magnitude of greatest shear stresses.A differential stress element as shown in Figure Q1 is subjected to a planestrain.(given E = 73 Gpa , = 0.33.)(i) What the normal strains and by using Mohr Circle method:-(ii) Examine the in-plane principal stresses(iii) State the principle stresses direction(iv) Examine the maximum shear stresses and its angle(v) By using same stress element, identify the stress components when it is inclinedat 30⁰ clockwiseUse the principle of Strain energy due to direct stresses strength of materials 2