(c) The cross section of a quarter circular concrete block XYZof width 1.8m is shown in Figure 3. The specific weight of the concrete mix is 24 kN/m3. The hinge is along XX. Calculate the vertical force R at Y to hold the gate in this position. K Fixed slab 1.2 m R Y W Fy 1.3 m D B Figure 3
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- A steel riser pipe hangs from a drill rig located offshore in deep water (see figure). (a) What is the greatest length (meters) it can have without breaking if the pipe is suspended in the air and the ultimate strength (or breaking strength) is 550 MPa? (b) If the same riser pipe hangs from a drill rig at sea, what is the greatest length? (Obtain the weight densities of steel and sea water from Table M, Appendix I. Neglect the effect of buoyant foam casings on the pipe.)A large precast concrete panel for a warehouse is raised using two sets of cables at two lift lines, as shown in the figure part a. Cable 1 has a length L1 = 22 Ft, cable 2 has a length L2= 10 ft, and the distance along the panel between lift points Band D is d = 14 ft (see figure part b). The total weight of the panel is W = 85 kips. Assuming the cable lift Forces F at each lift line are about equal, use the simplified model of one half of the panel in figure part b to perform your analysis for the lift position shown. Find the required cross-sectional area AC of the cable if its breaking stress is 91 ksi and a factor of safety of 4 with respect to failure is desired.: A hollow, pressurized sphere having a radius r = 4.8 in, and wall thickness t = 0.4 in. is lowered into a lake (see figure). The compressed air in the tank is at a pressure of 24 psi (gage pressure when the tank: is out of the water). At what depth D0will the wall of the tank be subjected to a compressive stress of 90 psi?
- 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 cylinder filled with oil is under pressure from a piston, as shown in the figure. The diameter d of the piston is 1,80 in. and the compressive force F is 3500 lb. The maximum allowable shear stress t^^, in the wall of the cylinder is 5500 psi. What is the minimum permissible thickness t„± of the cylinder wall? (Sec figureA retaining wall 6 ft high is constructed ofhorizontal wood planks 2.5 in. thick (actual dimension)that are supported by vertical wood piles of a12 in. diameter (actual dimension), as shown in thefigure. The lateral earth pressure is p1 125 lb/ft2at the top of the wall and p2 =425 lb/ft2 at the bottom.(a) Assuming that the allowable stress in the woodis 1175 psi, calculate the maximum permissiblespacing s of the piles.(b) Find the required diameter of the wood pilesso that piles and planks (t = 2.5 in.) reach theallowable stress at the same time.Hint: Observe that the spacing of the piles may begoverned by the load-carrying capacity of either theplanks or the piles. Consider the piles to act as cantileverbeams subjected to a trapezoidal distribution ofload, and consider the planks to act as simple beams between the piles. To be on the safe side, assume thatthe pressure on the bottom plank is uniform andequal to the maximum pressure.
- An aquarium tank holds salt water (RD 1.015) to a depth of 2.9 metres and has sides inclined at 75o to the horizontal. An access door A-B, measuring 1.1 metres by 1.1 metres, is pivoted at the base of the door (B) and held shut by a bolt at the top of the door (A). What is the tensile force in the bolt at point A.A wood-stave penstock of 1.8 m diameter is wrapped with steel hoops and subjected to a fluid pressure of 380 KPa. If the allowable tension in the hoop is 42.4 kN, what is the maximum hoop spacing?For the beam shown in the figure, the allowable bearing stress for the material under the supports at A and B is σb = 900 psi. Assume that w = 2,000 lb/ft, P = 4,500 lb, a = 20 ft, and b = 8 ft. Determine the size of square bearing plates required to support the loading shown. The size of the square bearing plate at support A is _____ inches The size of the square bearing plate at support B is _____ inches
- The cross section of a reinforced concrete beam is shown below. It has a modular ratio of 15. If the allowable compressive stress in the concrete is 6 MPa and the allowable tensile stress in the steel is 120 MPa, determine diameter of the three reinforcing steel rods to make the beam an economic section.A rod is composed of an aluminum section rigidly attached between steel and bronze sections, as shown in the figure. Axial loads are applied at the positions indicated. If P = 35000 lb and the stress in the steel, aluminum, and bronze sections are limited to 20 ksi, 28 ksi, and 18 ksi, respectively, determine the safest area considering the maximum stress in the aluminum.An aluminum pole for a street light weighs4600 N and supports an arm that weighs 660 N (seefigure). The center of gravity of the arm is 1.2 m from theaxis of the pole. A wind force of 300 N also acts in the (-y)direction at 9 m above the base. The outside diameter ofthe pole (at its base) is 225 mm, and its thickness is 18 mm. Determine the maximum tensile and compressivestresses σt and σc, respectively, in the pole (at its base)due to the weights and the wind force.