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A temporary wood flume serving as a channel for irrigation water is shown in the figure. The vertical boards forming the sides of the flume are sunk in the ground, which provides a fixed support. The top of the flume is held by tic rods that are tightened so that there is no deflection of the boards at that point. Thus, the vertical boards may be modeled as a beam AB, supported and loaded as shown in the last part of the figure.
Assuming that the thickness t of the boards is 1,5 in., the depth d of the water is 40 in., and the height h to the tie rods is 50 in., what is the maximum bending stress
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Mechanics of Materials (MindTap Course List)
- A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1= 3 ft and d2= 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area. Determine the maximum height H if there is to be no tension in the brickwork.arrow_forwardA 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.arrow_forwardA 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.arrow_forward
- 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.)arrow_forwardCantilever beam AB carries an upward uniform load of intensity q1from x = 0 to L/2 (see Fig. a) and a downward uniform load of intensity q from x = L/2 to L. Find q1in terms of q if the resulting moment at A is zero. Draw V and M diagrams for the case of both q and qtas applied loadings. Repeat part (a) for the case of an upward triangularly distributed load with peak intensity q0(see Fig. b). For part (b), find q0, instead of q1arrow_forwardA fixed-end beam AB of a length L is subjected to a uniform load of intensity q acting over the middle region of the beam (sec figure). Obtain a formula for the fixed-end moments MAand MBin terms of the load q, the length L, and the length h of the loaded part of the beam. Plot a graph of the fixed-end moment MAversus the length b of the loaded part of the beam. For convenience, plot the graph in the following nondimensional form: MAqL2/l2versusbL with the ratio b/L varying between its extreme values of 0 and 1. (c) For the special case in which ù = h = L/3, draw the shear-force and bending-moment diagrams for the beam, labeling all critical ordinates.arrow_forward
- The main cables of a suspension bridge (see figure part a) follow a curve that is nearly parabolic because the primary load on the cables is the weight of the bridge deck, which is uniform in intensity along the horizontal. Therefore, represent the central region AOB of one of the main cables (see part b of the figure) as a parabolic cable supported at points A and B and carrying a uniform load of intensity q along the horizontal. The span of the cable is L, the sag is /i, the axial rigidity is EA\ and the origin of coordinates is at mid span. (a) Derive the following formula for the elongation of cable AOB shown in part b or the figure: (b) Calculate the elongation 5 of the central span of one of the main cables of the Golden Gate Bridge for which the dimensions and properties are L = 4200 ft,h = 470 ft, q = 12,700 lb/ft, and E = 23,300,000 psi The cable consists of 27,572 parallel wires of diameter 0.196 in. Hint: Determine the tensile force Tal any point in the cable from a free-body diagram of part of the cable; then determine the elongation of an element of the cable of length ds: finally, integrate along the curve of the cable to obtain an equation for the elongation £.arrow_forwardThe L-shaped arm ABCD shown in the figure lies in a vertical plane and pivots about a horizontal pin at A. The arm has a constant cross-sectional area and total weight W. A vertical spring of stiffness k supports the arm at point B. (a) Obtain a formula for the elongation of the spring due to the weight of the arm. (b) Repeat part (a) if the pin support at A is moved to D.arrow_forwardA 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 stressarrow_forward
- An L-shaped reinforced concrete slab 12 Ft X 12 ft, with a 6 Ft X 6 ft cut-out and thickness t = 9.0 in, is lifted by three cables attached at O, B, and D, as shown in the figure. The cables are are combined at point Q, which is 7.0 Ft above the top of the slab and directly above the center of mass at C. Each cable has an effective cross-sectional area of Ae= 0.12 in2. (a) Find the tensile force Tr(i = 1, 2, 3) in each cable due to the weight W of the concrete slab (ignore weight of cables). (b) Find the average stress ov in each cable. (See Table I-1 in Appendix I for the weight density of reinforced concrete.) (c) Add cable AQ so that OQA is one continuous cable, with each segment having Force T, which is connected to cables BQ and DQ at point Q. Repeat parts (a) and (b). Hini: There are now three Forced equilibrium equations and one constrain equation, T1= T4.arrow_forwardA beam ABCD with a vertical arm CE is supported as a simple beam al A and D (see figure part a). A cable passes over a small pulley that is attached to the arm at E. One end of the cable is attached to the beam at point B. (a) What is the force P in the cable if the bending moment in the beam just lo the left of point C is equal numerically to 640 lb-ft? Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations. (b) Repeat part (a) if a roller support is added at C and a shear release is inserted just left of C (see figure part b).arrow_forwarda beam is supported by a pin support at A and a roller support at B. For this question, leave your answer in terms of the variables w and L. (a) Using equilibrium of the full beam, find the support forces at A and B. (b) First section: Make an arbitrary cut between points A and B. Take the distance of the cut to be x along the beam from point A. Draw the free-body diagram for the left section and find functions for the internal shear force, V(x), and bending moment, M(x), in the section of the beam between A and B. (c) Second section: Repeat part (b) for the section of the beam between B and C. Take x to still be the distance from point A. (f) Find the value of x at which V(x) = 0. The internal bending moment reaches a maximum at the same point as V(x) = 0. Find the maximum bending mo- ment. pin Sketch the shear and bending moment diagrams. B L W C rollerarrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning