An off-axis lamina (0=30°) for an S-glass/epoxy material (see Appendix A Table A.4) is subjected to stresses as follows: σx = 40 MPa, σy = -120 MPa, ts = 20 MPa Determine the safety factor Sf using (a) Tsai-Hill criterion and (b) Maximum Stress theory
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- A spherical steel pressure vessel (diameter 500 mm, thickness 10 mm) is coated with brittle lacquer that cracks when the strain reaches 150 X 10~ (see figure). (a) What internal pressure p will cause the lacquer to develop cracks? (Assume E = 205 GPa and v = 0.30.) (b) If the strain is measured at 125 x 10-6, what is the internal pressure at that point?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?The rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress ?? =6.5×10-6 /? is produced in the rails when they are heated by the sun to 120"F if the coefficient of thermal expansion a = the modulus of elasticity E = 30 × 106 psi?
- (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 pressureA joint between two glass plates A and B is filled with a flexible epoxy that bonds securely to the glass. The height of the joint is/p = 0.5 in, its length is L = 30 in, and its thickness is/ = 0.5 in. Shear force of I' = 25 kips is applied to the joint. Calculate the displacement of the joint if the shear modulus of elasticity G of the epoxy is 100 ksi. Calculate the average shear strain in the epoxy.A prismatic bar of length L = 1.8 m and cross-sectional area A = 480 mm" is loaded by forces P{= 30 kN and A = 60 kN (see figure) The bar is constructed of magnesium alloy having a stress-strain curve described by the Ram berg-Osgood equation: 45.000 618 UW id which u has units of mega pascals (MPa). (a) Calculate the displacement 8t- of the end of the bar when the load P:acts alone. (b) Calculate the displacement when the load P, acts alone. (c) Calculate the displacement when both loads act simultaneously.
- Rigid bar ACB is supported by an elastic circular strut DC having an outer diameter of 15 in. and inner diameter of 14.4 in. The strut is made of steel with a modulus elasticity of E = 29,000 ksi. Point load P = 5 kips is applied at B. Calculate the change in length of the circular strut DC. What is the vertical displacement of the rigid bar at point B?A high-strength steel bar used in a large crane has a diameter d = 2.00 in. (sec figure). The steel has a modulus of elasticity E = 29 × 10 psi and Poisson’s ratio is v = 0.29. Because of clearance requirements, the diameter of the bar is limited to 2.001 in. when it is compressed by axial forces. What is the largest compressive load Pmaxthat is permitted?Five bars, each having a diameter of 10 mm. support a load P as shown in the figure. Determine the plastic load Ppif the material is clastoplastic with yield stress
- A steel wire- and an aluminum allay wire have equal lengths, and support equal loads P (see figure). The moduli of elasticity for the steel and aluminum alloy are Ea= 30,000 ksi and Ea= 11,000 ksi, respectively. (a) IF the wires have the same diameters, what is the ratio of the elongation of the aluminum alloy wire to the elongation of the steel wire? (b) If the wires stretch the same amount, what is the ratio of the diameter of the aluminum alloy wire to the diameter of the steel wire? (c) If the wires have the same diameters and same load P, what is the ratio of the initial length of the aluminum alloy wire to that of the steel wire if the aluminum alloy wire stretches 1.5 limes that of the steel wire? (d) If the wires have the same diameters, same initial length, and same load P. what is the material of the upper wire if it elongates 1.7 times that of the steel wire?A two-story building has steel columns AB in the first floor and BC in the second floor, as shown in the figure. The roof load P:equals 400 KN, and the second-floor load P-, equals 720 kN. Each column has a length L = 3.75 m. The cross-sectional areas of the first- and second-floor columns are 11,000 mm" and 3900 mm", respectively. (a) Assuming that E = 206 GPa. determine the total shortenings aof the two columns due to the combined action of the loads Ptand P,. (b) How much additional load P0can be placed at t he top of t he column (point C) if t he total shortening: SACis not to exceed 4.0 mm?Solve correctly please.