For the prismatic bar in simple tension shown below, the stress state at any point "M" is characterized by Sig = p, and the other stress components are null. You are asked to determine the stress vector, as well as its normal and shear components, on a generic facet of normal parallel to the xy plane. M
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- A circular cylindrical steel tank (see figure) contains a volatile fuel under pressure, A strain gage at point A records the longitudinal strain in the tank and transmits this information to a control room. The ultimate shear stress in the wall of the tank is 98 MPa, and a factor of safety of 2,8 is required. (a) At what value of the strain should the operators take action to reduce the pressure in the tank? (Data for the steel are modulus of elasticity E = 210 GPa and Poisson's ratio v = 0.30.) (b) What is the associated strain in the radial directionA wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?The stresses shown act at a point in a stressed body. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are S, = 20 MPa, S, = 24 MPa, and Sy = 29 MPa. Assume ß = tan = 21.8°, a = 5, and b = 2. Using the equilibrium equation approach, determine the normal and shear stresses o (positive if tensile, negative if compressive) and z (magnitude only) at this point on the inclined plane shown. Answers: i MPa, T = i MPа.
- Calcuate Torsion From Point A to Point C and Bending from Point A to Point B and from 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. 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 inCalcuate Torsion and 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. 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(1) A steel cylinder (Øyp = 260 MPa) of inner radius a and outer radius 3a is subjected to an internal fluid pressure pi (Note: ratio of wall thickness (t) to inner radius indicates that this is a thick-walled cylinder). (a) Determine (i) the maximum radial stress (ơmax); (ii) the maximum tangential stress (o0max). (b) Determine the limiting values of p, using: (i) the maximum distortion energy theory of failure; and (ii) the maximum shear stress theory of failure. (Hint: Maximum radial and tangential stresses occur at the same radial distance, see slide 8 of Lecture 9 notes); use these maximum stresses as your principal stresses). (c) A steel gun barrel of inner radius 0.6 m is subjected to an internal explosive pressure of 80 MPa. The tensile and compressive elastic strengths of the material are 320 MPa. Assuming a factor of safety of 2, design the wall thickness of the gun barrel.
- In an elastic body system, a point has the following state of stress components, Ox= 16 kPa, Oyy = 12 kPa, Oz = 4 kPa, Txy = 4 kPa, Tz = 8 kPa, Tyz = 2 kPa. Without using Mohr's circle calculate: (A) The principal stresses (01, 02, 03) (B) Based on the principal stresses, calculate the maximum shear stress (Tmas) Construct Mohr's circle for XY plane, and determine the following: (C) The stress components with respect to ab axes which are inclined at 0 =45 to the XҮ ахes. (D) The magnitude of the maximum shearing stress and associated normal stresses. (E) For Mohr's Circle drawingCalcuate Bending From Point A to Point B and Point A to Point C, Calcuate torsion From 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. 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 inFind the stresses in each direction, also find the change in volume of the block of dimension 120 mm x 45 mm x 43 mm, subjected to 3 mutually perpendicular loads. The load along length, breadth and depth directions are 10 kN (tensile), 20 kN (compressive), 16 kN (compressive) respectively. Take E as 140 GPa, Poisson’s ratio as 0.3 The stress along length direction (Unit in MN/m2)= The compressive stress along width direction (Unit in MN/m2)= The compressive stress along depth direction (Unit in MN/m2)= The change in volume of the block is (unit in mm3) =
- Calcuate torsion From Point A to Point C, 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. 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 inConsider the 2-D state of stress shown below. Using the provided scales graph the Mohr's Circle for the 2-D state of stress with "full' details Draw the Planes of Principal and Maximum Shear Stresses Provide "full" details and Use 3 Sig. Fig. in this problem Oy = 15 Ksi Tcw → S Txy= -5 ksi Ox = 10 Ksi Tyx = 5 Ksi 10 5 -20 -10 5 10 15 20 5 10 Tccw → S'The thin rectangular plate (Fig. 1, not to scale) with sides 6 m and 4 m of thickness 112 mm is subjected to the stresses ox, Oy and txy. An Airy stress function is proposed to be: $(x, y) = Ax° + Bx'y+Cxy, with A=B=C =1 (a) Determine the values of stresses (ox, Oy and txy) at point (x_y) which satisfy the stress function (b) Draw a stress element showing the stresses on the four faces of the element (Use the face bounded by the X- and Y-axes with a line representing a face, that is, a 2-D stress element). (c) Neglecting body forces, determine the resultant normal and shearing forces on the right face of the plate that are consistent with o (Use the face bounded by the X- and Y-axes with a line representing a face, that is, a 2-D stress element). 112 mm 4 m 6 m Fig. 1 Biharmonic Equation ô*o(x, y) ôx o*o(x.y) ô*¢(X.y)=v*o(x,y) =0 +2 where o(x.y) is defined as: ô*o(x,y) o o(x, y) ôxcy