Problem 4: A barge shown in the figure carries 290kN/m and 580KN/m loads. 3m 6m Зт 580 kN/m a. Find the total length, L (m) so that the upward pressure is uniform, and the barge remains horizontal. b. If shear is zero at 5m from the left end, what is the upward pressure in kN/m? c. If the upward pressure is 145KN/m, what is the resulting moment (kN-m) at first point of zero shear? 290 kN /m
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- A pressurized cylindrical tank with flat ends is loaded by torques T and tensile forces P (sec figure), The tank has a radius of r = 125 mm and wall thickness t = 6.5 mm. The internal pressure p = 7.25 MPa and the torque T = 850 N m. (a) What is the maximum permissible value of the forces P if the allowable tensile stress in the wall of the cylinder is 160 MPa? (b) If forces P = 400 kN, what is the maximum acceptable internal pressure in the tank?: 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 cantilever beam(Z, = 6 ft) with a rectangular cross section (/> = 3.5 in., h = 12 in.) supports an upward load P = 35 kips at its free end. (a) Find the state of stress ((7T, o^., and r in ksi) on a plane-stress element at L/2 that is i/ = 8 in. up from the bottom of the beam. Find the principal normal stresses and maximum shear stress. Show these stresses on sketches of properly oriented elements. (b) Repeat part (a) if an axial compressive centroidal load N = 40 kips is added at B
- A standpipe in a water-supply system (see figure) is 12 ft in diameter and 6 in. thick. Two horizontal pipes carry water out of the standpipe; each is 2 ft in diameter and 1 in. thick. When the system is shut down and water fills the pipes but is not moving, the hoop stress at the bottom of the standpipe is 130 psi, (a) What is the height h of the water in the standpipe? (b) If the bottoms of the pipes are at the same elevation as the bottom of the stand pipe. what is the hoop stress in the pipes?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 hemispherical window (or viewport) in a decompression chamber (see figure) is subjected to an internal air pressure of 85 psi. The window is attached to the wall of the chamber by 14 bolts. (a) Find the tensile force Fin each bolt and the tensile stress (T in the viewport if the radius of the hemisphere is 14 in. and its thickness is 1.25 in. (b) If the yield stress for each of the 14 bolts is 50 ksi and the factor of safety is 3.0, Find the required bolt diameter. (c) If the stress in the viewport is limited to 500 psi, find the required radius of the hemisphere.
- 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 ^ PrA retaining wall 6 ft high is constructed of horizontal wood planks 2.5 in. thick (actual dimension) that are supported by vertical wood piles of a 12 in, diameter (actual dimension), as shown in the figure. The lateral earth pressure is pt=125 lb/ft2 at the top of the wall and p2= 425 lb/ft2 at the bottom. Assuming that the allowable stress in the wood is 1175 psi, calculate the maximum permissible spacing s of the piles. Find the required diameter of the wood piles so that piles and planks (f = 2.5 in.) reach the allowable stress at the same time. Hint: Observe that the spacing of the piles may be governed by the load-carrying capacity of either the planks or the piles. Consider the piles to act as cantilever beams subjected to a trapezoidal distribution of load, and consider the planks to act as simple beams between the piles. To be on the safe side, assume that the pressure on the bottom plank is uniform and equal to the maximum pressure.A beam with a width h = 6 in. and depth h = 8 in. is simply supported at A and B. The beam has a length L = 10 ft and is subjected to a linearly varying distributed load with peak intensity q0= 1500 lb/ft. Calculate the state of plane stress at point C located 3 in. below the top of the beam and 0.1 ft to the left of point B. Also find the principal stresses on element C. Neglect the weight of the beam.
- A steel post (E=30×106) having thickness t = 1/8 in. and height L = 72 in. support a stop sign (see figure), where s = 12.5 in. The height of the post L is measured from the base to the centroid of the sign. The stop sign is subjected to wind pressure p = 20 lb/ft2 normal to its surface. Assume that the post is fixed at its base. What is the resultant load on the sign? (Sec Appendix E, Case 25, for properties of an octagon, n =8.) What is the maximum bending stress in the post? Repeat part (b) if the circular cut-outs arc eliminated over the height of the post.A large spherical tank (see figure) contains gas at a pressure of 420 psi. The tank is 45 ft in diameter and is constructed of high-strength steel having a yield stress in tension of 80 ksi. (a) Determine the required thickness (to the nearest 1/4 inch) of the wall of the tank if a factor of safety of 3,5 with respect to yielding is required. (b) If the tank wall thickness is 2.25 in., what is the maximum permissible internal pressure?A foot bridge on a hiking trail is constructed using two timber logs each having a diameter d = 0.5 m (see figure a). The bridge is simply supported and has a length L = 4 m. The top of each log is trimmed to form the walking surface (see Fig, b)LA simplified model of the bridge is shown in Fig. g. Each log must carry its own weight w = 1.2 kN/m and the weight (P = 850 N) of a person at mid-span, (see Fig. b). Determine the maximum tensile and compressive stresses in the beam (Fig, b) due to bending. If load h is unchanged, find the maximum permissible value of load ... if the allowable normal stress in tension and compression is 2.5 M Pa.