A two spring is connected in parallel attached to a single load. The maximum allowable stress is 200MPa, What will be the value of the load?
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- 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 rigid bar of weight W = 750 lb hangs from three equally spaced wires: two of steel and one of aluminum (see figure). The diameter of the wires is 1/8 in. Before they were loaded, all three wires had the same length. What temperature increase T in all three wires will result in the entire load being carried by the steel wires? (Assume Es= 30 × 106 psi, as= 6.5 × 10-6 /'F, and aa= 12 × 10-6F.)An idealized column is composed of rigid bars ABC and CD joined by an elastic connection with rotational stiffness ßRat C. There is an elastic support at B with translational spring stiffness ß and a pin support at D. Find the critical buckling loads for each of the two buckling modes of the column in terms of ßL. Assume that ßR= ßL2. Sketch the buckled mode shapes.
- A steel cable with a nominal diameter of 25 mm (see Table 2-1) is used in a construction yard to lift a bridge section weighing 38 kN. as shown in the figure. The cable has an effective modulus of elasticity E = 140 GPa. (a) If the cable is 14 m long, how much will it stretch when the load is picked up? (b) If the cable is rated for a maximum load of 70 kN, that is the factor of safety with respect to failure of the cable?An idealized column is composed of rigid bars ABC and CD joined by an elastic connection with rotational stiffness ßRIat C. There is a roller support at B and an elastic support at D with translationa1 spring stiffness ß and rotational stiffness ßR2. Find the critical buckling loads for each of the two buckling modes of the column. Assume that L = 3 m, ß = 9 kN/m, and ßR]= ßR1= ßL2. Sketch the buckled mode shapes.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.
- A lifeboat hangs from two ship's davits. as shown in the figure. A pin of diameter d = 0.80 in. passes through each davit and supports two pulleys. are on each side of the davit. Cables attached to the lifeboat pass over the pulleys and wind around winches that raise and lower the lifeboat. The lower parts of the cables are vertical and the upper parts make an angle a =15° with the horizontal. The allowable tensile force in each cable is 1800 lb, and the allowable shear stress in the pins is 4000 psi. If the lifeboat weighs 1500 lb, what is the maximum weight that can be carried in the lifeboat?The figure shows an idealized structure consisting of two rigid bars with pinned connections and linearly elastic rotational springs. Rotational stiffness is denoted ßR. Determine the critical load Pcrfor the structure.A pinned-end strut of aluminum (E = 10,400 ksi) with a length L = 6 ft is constructed of circular tubing with an outside diameter d = 1 in. (sec figure). The strut must resist an axial load F = 4 kips with a factor of safety n = 2.0 with respect to the critical load. Determine the required thickness t of the tube.
- 2.4-11 Three steel cables jointly support a load of 12 kips (see figure). The diameter of the middle cable is 3/4 in. and the diameter of each outer cable is 1/2 in. The tensions in the cables are adjusted so that each cable carries one-third of the load (ie., 4 kip). Later, the load is increased by 9 kips to a total load of 21 kips. (a) What percent of the total load is now carried by the middle cable? (b) What are the stresses crvand 0 in the middle and outer cables, respectively? Note: See Table 2-1 in Section 2.2 for properties of cables.A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?A hollow circular tube T of a length L = 15 in. is uniformly compressed by a force P acting through a rigid plate (see figure). The outside and inside diameters of the tube are 3.0 and 2.75 in., respectively. A concentric solid circular bar B of 1.5 in. diameter is mounted inside the lube. When no load is present, there is a clearance c = 0.0I0 in. between the bar B and the rigid plate. Both bar and tube are made of steel having an c[autoplastic stress-strain diagram with E = 29 X LO3 ksi and err= 36 ksi. (a) Determine the yield load Pt- and the corresponding shortening 3yof the lube. (b) Determine the plastic load Ppand the corresponding shortening Spof the tube. (c) Construct a load-displacement diagram showing the load Pas ordinate and the shortening 5 of the tube as abscissa. Hint: The load-displacement diagram is not a single straight line in the region 0 ^ P ^ Pr