Complete( any five) of the following: 1- In fatique, the load ratio equals to 2-The relationship beteeen residual stress and number of cycles required to fatique failure is 3- Gc for Cu is ..than Ge of glass
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- 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?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?An aluminum bar has length L = 6 ft and diameter d = 1.375 in. The stress-strain curse for the aluminum is shown in Fig. 1.34. The initial straight, line part of the curve has a slope (modulus of elasticity) of 10.6 × 106 psi. The bar is loaded by tensile forces P = 44.6 k and then unloaded. (a) That is the permanent set of the bar? (b) If the bar is reloaded. what is the proportional limit? hint: Use the concepts illustrated in Figs. l.39b and 1.40.
- 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?Repeat Problem 2.4-8, but assume that the bar is made of aluminum alloy and that BC is prismatic. Assume that P = 20 kim. L = 3 ft.t = 314 in., b1 2m.b 2.Sin.andElO.400ksi.Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.
- (a)Describe, with a labelled diagram, how you would measure accurately theextension of such a wire under an applied load. (b) The graph below shows how the extension of a wire varies with the loadapplied to it. The wire used has a length of 3m and a diameter of 5 x 10^-4m i. Calculate the tensile stress produced by a load of 50N.ii. Find the energy stored in the wire when the load is acting.iii. Calculate the reduction in gravitational PE of a 5kg mass used to providethe load.iv. Calculate Young's modulus for the metal of the wire.Please show a clear step-by-step solution. Thank you! What is the proportion of the alteration in length for Spring A to Spring B, supposing that both springs carry an equal amount of load? Springs A and B have the identical qualities, with the exception that Spring A has 12 times the number of turns as Spring B.MACHINE DESIGN TOPIC A short compression member with Do = 2Di is tosupport a dead load of 25 tons. The material isto be 4130 steel, WQT 1100 F. Calculate theoutside and inside diameters in terms of incheson the basis of (a) yield strength, (b) ultimatestrength.*For 4130 steel, WQT 1100 FSu = 127 ksiSy = 114 ksi*Use the following Safety FactorsNu = 4Ny = 2
- Find the equivalent stresses at Points 1 and 2 of the element with given geometry and loading conditions according to the Maximum shear stress hypothesis and the Maximum strain energy hypothesis. Shaft diameter: 20 mm, Shaft Length 120 mm, F1 = 750N, F2 = 3000N, Mb = 2400 N.mm. Steel if St37 and Safety coefficient is 2 If taken, will this stick work safely under these operating conditions? (Yield of given steel Strength 225 Mpa, Tensile strength 370 Mpa)A hydraulic cylinder with a bore radius of 100 mm and an outer radius of 200 mmhas been designed to withstand a maximum internal pressure of 200 MPa inservice. During operation, the pressure within the cylinder is retained by a freelysliding piston. The steel used in the manufacture has Young’s modulus of 210GNm-2. In an alternative design, the cylinder has been constructed as a compoundcylinder (duplex cylinder) with the same bore and outer radii by shrink-fitting twotubes of the same steel. The nominal radius at the common interface is 150 mmand the radial interference (shrinkage allowance, δ) is 100 μm (micro-meters).a) Determine using Lame’s equations, the radial and circumferentialstresses at the cylinder bore, common interface, and outer surface.b) Graphically present (sketch) the variation of each of these stresses acrossthe cylinder wall, clearly indicating the values at the inner and outer surfacesof each cylinder.c) Draw the Mohr's circles representing the stresses acting on…Fatigue data of steel is showed in the following stress-cycle curve.Write down the values of steel endurance limit and steel fatigue strength at 10^5 cycles in the spaces provided below.Steel Endurance Limit: _____ ksiteel Fatigue Strength at 10^5 cycles: _____ ksi