Attempt all questions. A simple frame structure is simply supported by a roller at A and a pin at B as shown below. It 40 kN. The dimensions of the frame are: a = carried a udl, w = 12 kN/m and a point load, P 4 m, b=1m, c = 6 m, d = 3 m and e = 1.5 m.
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- Continuous cable A DB runs over a small friction less pulley al D to support beam OABC, which is part of an entrance canopy for a building (see figure}. The canopy segment has a weight W = 1700 lb that acts as a concentrated load in the middle of segment AB. (a) What is the maximum permissible value of load P at C if the allowable force in the cable is 4200 lb? (b) If P = 2300 lb, what is the required diameter of pins A, B, and D? Assume that the pins are in double shear and the allowable shear stress in the pins is 10 ksi.A long re Lai nine: wall is braced by wood shores set at an angle of 30° and supported by concrete thrust blocks, as shown in the first part of the figure. The shores are evenly spaced at 3 m apart. For analysis purposes, the wall and shores are idealized as shown in the second part of the figure. Note that the base of the wall and both ends of the shores are assumed to be pinned. The pressure of the soil against the wall is assumed to be triangularly distributed, and the resultant force acting on a 3-meter length of the walls is F = 190 kN. If each shore has a 150 mm X 150 mm square cross section, what is the compressive stressA sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the figure. The poles are being designed to resist a wind pressure of 75 lb/ft" against the full area of the sign. The dimensions of the poles and sign are hx= 20 ft, /r =5 ft, and h = 10 ft. To prevent buckling of the walls of the poles, the thickness e is specified as one-tenth the outside diameter d. (a) Determine the minimum required diameter of the poles based upon an allowable bending stress of 7500 psi in the aluminum. (b) Determine the minimum required diameter based upon an allowable shear stress of 300 psi.
- 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.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.An idealized column is made up of rigid bars ABC and CD that are joined by a rotational elastic connection at C with stiffness ßR. The column has a roller support at B and a pin support at D. Find an expression for the critical load Pcr of the column.
- 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?A long slender column ABC is pinned at ends A and C and compressed by an axial force F (sec figure). At the midpoint B, lateral support is provided to prevent deflection in the plane of the figure. The column is a steel wide-flange section (W 250 × 67) with E = 200 GPa. The distance between lateral supports is L = 5.5 m. Calculate the allowable load P using a factor of safety n = 2.4, taking into account the possibility of Eu 1er buckling about cither principal centroidal axis (i.e., axis 1-1 or axis 2-2).A plane truss has joint loads P, 2P, and 3P at joints D. C, and B. respectively (see figure) where load variable P — 5200 lb. All members have two end plates (see figure For Prob. 1.8-2) that are pin-connected to gusset plates. Each end plate has a thickness/ — 0.6.2.5 in., and all gusset plates have a thickness tg= 1.125 in. IT the allowable shear stress in each pin is 12,000 psi and the allowable bearing stress in each pin is 18.000 psi, what is the minimum required diameter dminof the pins used at either end of member BE1
- 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.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 hoisting arrangement for lifting a large pipe is shown in the figure. The spreader is a steel tubular section with outer diameter 70 mm and inner diameter 57 mm. Its length is 2.6 m, and its modulus of elasticity is 200 GPa. Based upon a factor of safety of 2.25 with respect to Euler buckling of the spreader, what is the maximum weight of pipe that can be lifted? (Assume pinned conditions at the ends of the spreader.)