Verify the equality of the following shearing stresses: (2) σεν = σνε (b) σzz =σ22
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- Consider the given state of stress. Take X = 12 MPa and Y= 55 MPa. Y X 60 MPa Determine the maximum in-plane shearing stress using Mohr's circle. The maximum in-plane shearing stress is MPa.The distribution of stress in an isotropic aluminium machine component is given (in MPa) as: σ₂ = y +2z² - 6 σ₁ = x+z-6 oy σ₂ = 3x+y-13 6: T =3z² -11 xy (i) (ii) =x²-14 Tyz Txz = y² XZ x, y and z are coordinates of a point within the machine component. By taking Young's modulus, E = 70 GPa, Poisson ratio, v= 0.3 and yield stress, Y = 5 MPa, do the following for a point P located at (4, 1, 2): a) Provide the stress and strain tensors. b) Determine all the principal stresses and principal strains. c) Determine if the machine component will fail based on the failure criteria below: Tresca criterion Von Mises criterionFollowing plate is connected to the wall using 7 bolts. Cross sectional area of each bolt is A. Force F is applied to the plate. The magnitude of shear stress experienced by bolt B is, 100.00 25.00 25.00 25.00 O 1. Less than F/(7A) O 2. F/(7A) O3. More than F/(7A) 80.00 20.00 20.00 20.00 (40 00)
- 8 x = 17 MPa y = 41 MPa T = 56 MPa 5 T σχ X At a point on a structural member subjected to plane stress, normal and shear stresses exist on horizontal and vertical planes through a point as shown. Use the stress transformation equations to determine the normal stress to the nearest 0.01 MPa on the indicated plane. Be sure to use - as appropriate. 277The shear stress is maximum on the principal plane Select one: O True O FalseFor a steel rod with a circular cross section with a diameter of D = 20 mm, the following is required: 1. Draw a diagram of the longitudinal force 2. Draw a diagram of normal stresses 3. Determine the total elongation of the rod if Е = 2∙10^5 MPa When calculating, take: а = 2 m, b =1.2 m, F=10 кN - The point of application of force! The work must be done on one sheet of A4 paper, which must show: - Using the method of sections to determine the longitudinal forces in the rod. - Draw a diagram of longitudinal forces N - Determination of normal stresses based on the constructed plot of longitudinal forces. - Draw diagram a normal stresses - Determination of the full extension of the rod
- Determine the resulting maximum value of the normal stress. Specify the orientation of the plane on which these maximum values occur. **The answer is tensile stress is 0 ksi at 90 degrees. **The answer is compressive stress is 7 ksi at 0 degrees. Can you explain how that is? This was my thought process: I know that tensile would be zero because the force P is actually going inwards and not outwards. I know that means that there would be a compressive force. I am confused on the angles, how is a tensile force going 90 degress if there technically is no force in the tensile direction. And how is there a compressive force at 90 degrees if there is a stress? thank you!At a point on the surface of a pressurized cylinder, the material element is subjected to stresses; σx = 60 MPa, σy = - 40 MPa, and τxy = - 30 MPa. Construct Mohr’s circle, then use it to determine the following: Do not use the equations of transformations.1- The principal stresses and the maximum shear stress.2- Show these stresses on sketches of properly stress elements.3- A point on the circle where the element is only subjected to pure shear stress. Calculate the value of that pure shear stress.A carbon steel ball with 27-mm diameter is pressed together with an aluminum ball with a 35-mm diameter by a force of 11 N. Determine the maximum shear stress and the depth at which it will occur for the aluminum ball. Assume the figure given below, which is based on a typical Poisson's ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress occurs for these materials. Ratio of stress to Pma σ. T 1.0 0.8 0.6 0.4 0.2 0 J₂, J₂ 0.5a σ₂ Tmax a 2a Distance from contact surface 1.5a 2.5a 3a The maximum shear stress is determined to be 134.6 Z MPa. The depth in the aluminum ball at which the maximum shear stress will occur is determined to be 0.0519 mm.
- 2. determine the maximum normal stress and the maximum shear stress at point O in dia. B 15 in 7 in F = 15 lbfConsider the given state of stress. Take X = 35 MPa and Y = 50 MPa Determine the orientation of the planes of maximum in-plane shearing stress in the first and third quadrantsAt a point in the cross-section of an engineering component an element is subject to the following stresses: σx =100MPa σy =45MPa τxy = -50MPa Construct a Mohr’s Stress Circle and hence determine: (a) The Principal Stresses (σ1 & σ2) and the Directions of the Principal Planes (φ1 & φ2) (b) The Maximum Shear Stress (τmax) (c) Find the Normal Stress (σn) acting on a plane at 40 degs anticlockwise from the y-axis