Write the matrix equations in terms of stress tensors for the three equations
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Write the matrix equations in terms of stress tensors for the three equations.
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- Use the plane stress transformation equations to find the normal stress and the magnitude of the shear stress on plane A-A for the stress acting at a point in a machine component shown below. Find the principal stresses and the maximum in-plane shear stress for the stress condition acting at a point in a machine component shown. Show a Mohr's Circle plot depicting the principal stresses and the maximum in-plane shear stress for the stress condition acting at a point in an engineering structural member. Use the graphical method, and a tool to validates the process (as shown in class). 80MPa 35° 80MPa 80MPa 80MPa 110 MPa 110 MPa yx T=55 MPa xy yx yx 115 MPa T=55 MPa xy 115 MPa T=70 MPa xy 165 MPa [E า OCalcuate Bending From Point A to Point B and Point A to Point C.Calcuate Torsion From Point A to Point C (point C is where is connect it to the lug nut). Draw a FBD from point A to point B and another for point A to C indicating what stresses are been calculate. Use the stress tensor and stress cube to Indicate what forces are acting at point A. All the information need it is given Force apply at point B is 70lb Distacen from Point A to B is 12 in or 1 feet long Distacen from Point A to C is 3 in Handle diameter 0.625 in Modulus of elasticity for steel is 300000000 psiSolve the problem 4
- Q2 The state of stress at a point of an elastic solid is given in the x-yz coordinates by: (a) Using the matrix transformation law, determine the state of stress at the same point for an element rotated about the x-axis 60° clockwise from its original position;(b) Calculate the stress invariants and write the characteristic equation for the originalstate of stress;(c) Calculate the deviatoric invariants for the original state of stress;(d) Calculate the principal stresses and the absolute maximum shear stress at the point;(e) What are the stress invariants and the characteristic equation for the transformed state of stress.1) Given the figure below, answer the following questions: a) What are the x and y components offorce F? (use Fx and Fy)b) What are the x and y components offorce P? (use Px and Py)(Hint: The x-y plane is differentfrom the true horizontal and verticalaxes)c) What are the vertical and horizontalcomponents of force F? (use Fh & Fv)d) What are the vertical and horizontalcomponents of force P? (use Ph & Pv)e) What is the magnitude of the resultant?f) What angle does the resultant make withthe horizontal axisg) What angle does the resultant makewith the inclined x-axis.Write the solution for the following: Member BC= 600 N Member FG = -600 N
- The force P3 to make it to equilibrium in kN is The Stress in section 1 in N/mm2 is The Compressive Stress in section 2 in N/mm2 is The stress in section 3 in N/mm2 is The total change in length in x10-3 mm is3-4 Sketch a free-body diagram of each element in the figure. Compute the magnitude and direction of each force using an algebraic or vector method, as specified. F=400 N. 30° B 60° 2 1.9 m 0 9 m C D 60° E xTorsion From Point A to Point C (point C is where is connect it to the lug nut) Calcuate Bending From Point A to Point B and Point A to Point C. Draw a FBD from point A to point B and another for point A to C indicating what stresses are been calculate. Use the stress tensor and stress cube to Indicate what forces are acting at point A. All the information need it is given Force apply at point B is 70lb Distacen from Point A to B is 12 in or 1 feet long Distacen from Point A to C is 3 in Handle diameter 0.625 in Modulus of elasticity for steel is 300000000 psi
- For the stresses given with the cube below: 1. Compute the center, radius (R), principal normal stresses (0₁ and 03), max shear stress (Tmax) and draw the Mohr's Circle. 2. Compute the normal and shear stresses when the cube is rotated 20° clockwise from the horizontal plane and draw them on the cube. 3. The yield point stress (σyp) is 6 kPa. Determine if the material will fail under stresses shown using Tresca's Hexagon. вкра акра 6 экра 8 кра экра 4краDetermine the stress resultants N(x), V(x), M(x) and draw the diagrams of the stress resultants and calculate the extremal values. At first, consider all parameters (F, a, L, ...) as variables and fill in their actual values at the end of your calculation.Q1/ Find the two components of the force (150 N) if a= 40degrees, as shown in the figure below FY F= 150 N a= 40 FX (FX= 114.9 N) AND (FY= 96.4 N) O (FX= 96.4 N) AND (FY= 114.9 N) O (FX= 130 N) AND (FY= 90 N) O (FX= 90 N) AND (FY= 130N) O