A plate was subjected to a tensile force P=100 KN as shown on the figure. If the allowable stress is 250 MPa, Calculate the following: (a) Minimum required thickness of the plate. (Hint: HOLE vs FILLET) (b) Maximum allowable stress based on minimum thickness of the plate, Let K= 1.20 (c) Percent decrease on stress concentration
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- A 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?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 direction(a) Solve part (a) of the preceding problem if the pressure is 8.5 psi, the diameter is 10 in., the wall thickness is 0,05 in., the modulus of elasticity is 200 psi, and Poisson's ratio is 0.48. (b) If the strain must be limited to 1.01, find the maximum acceptable inflation pressure
- At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with t = 1400 psi and trv = —900 psi, as shown in the figure part a. The figure part b shows an inclined plane aa cut through the same point in the material but oriented at an angle ft Determine the value of the angle 6 between zero and 90° such that no normal stress acts on plane aa. Sketch a stress clement having plane aa as one of its sides and show all stresses acting on the clementSolve the preceding problem for a plate of dimensions 100 mm × 250 mm subjected to a compressive stress of 2.5 MPa in the long direction and a tensile stress of 12.0 MPa in the short direction (see figure).Plastic bar of diameter d = 32 mm is compressed in a testing device by a Force P = 190 N that is applied as shown in the figure. (a) Determine the normal and shear stresses acting: on all faces of stress elements oriented at (1 ) an angle 8 = 00, (2) an angle ?? = 22.5s, and (3) an angle ?? = 45°. In each case, show the stresses on a sketch of a properly oriented element. What are smaxtmax (b) Find smax and tmax in the plastic bar if a re-cantering spring of stiffness k is inserted into the testing device, as shown in the figure. The spring stillness is 1/6 of the axial stiffness of the plastic bar.
- • - 3 A rectangular plate in biaxial stress (see figure) is subjected to normal stresses u = 67 MPa (tension) and s = -23 MPa (compression). The plate has dimensions 400 X 550 X 20 mm and is made of steel with E = 200 GPa and v = 0.30. (a) Determine the maximum in-plane shear strain ?max in the plate. (b) Determine the change ?t in the thickness of the plate. (c) Determine the change ?t in the volume of the plate.Solve the preceding problem for an element in plane stress on the bottom surface of a fuel tanker (figure part a); stresses are sx= 105 MPa, sy. = 75 MPa, and ??xy= 25 MPa. Determine the stresses acting on an element oriented at an angle ?? = 40° from the x axis, where the angle is positive when counterclockwise. Show these stresses on a sketch of an element oriented at the angle ??.A standard brick (dimensions 8 in. × 4 in. × 2.5 in ) is compressed lengthwise by a force P. as shown in the figure, If the ultimate shear stress for brick is 1200 psi and the ultimate compressive stress is 3600 psi. what force Pmax is required to break the brick?
- A copper bar with a rectangular cross section is held without stress between rigid supports (see figure). Subsequently, the temperature of the bar is raised 50°C (a) Determine the stresses on all faces of the elements A and B, and show these stresses on sketches of the elements. (Assume = 17.5 × 10-6/? and E = 120 GPa ) (b) If the shear stress at B is known to be 48 MPa at some inclination 8, find angleDuring a tension lest of a mild-steel specimen (see figure), the extensometer shows an elongation of 0.00120 in. with a gage length of 2 in. Assume that the steel is stressed below the proportional limit and that the modulus of elasticity E = 30 × 10 psi. (a) What is the maximum normal stress (j^, in the specimen? (b) What is the maximum shear stress tmax? (c) Draw a stress element oriented at an angle of 45° to the axis of the bar, and show all stresses acting on the faces of this element.A punch for making a slotted hole in ID cards is shown in the figure part a. Assume that the hole produced by the punch can be described as a rectangle (12 mm X 3 mm) with two half circles (r = 1.5 mm) on the left and the right sides. If P = 10 N and the thickness of the ID card is 1 mm, what is the average shear stress in the card?