A flanged wooden shape is used to support the loads shown on the beam. The dimensions of the shape are shown in the second figure. Assume LAB=7 ft, Lgc = 2 ft, LcD=4ft, LDE = 3ft, Pc=1720 lb, Pe=2360 lb, WAB=850 lb/ft, b₂ = 8 in., b₂ = 2 in., b3=4 in., d₁=2 in., d₂= 12 in., d3=2 in. Consider the entire 16-ft length of the beam and determine: (a) the maximum tension bending stress or at any location along the beam, and (b) the maximum compression bending stress ocat any location along the beam. Answers: (a) GT (b) o = i WAB LAB N B Pc Lac b₁ · b3 C LCD ·b₂ psi. psi. D d₁ d3 LDE PE E

A flanged wooden shape is used to support the loads shown on the beam. The dimensions of the shape are shown in the second figure. Assume LAB=7 ft, Lgc = 2 ft, LcD=4ft, LDE = 3ft, Pc=1720 lb, Pe=2360 lb, WAB=850 lb/ft, b₂ = 8 in., b₂ = 2 in., b3=4 in., d₁=2 in., d₂= 12 in., d3=2 in. Consider the entire 16-ft length of the beam and determine: (a) the maximum tension bending stress or at any location along the beam, and (b) the maximum compression bending stress ocat any location along the beam. Answers: (a) GT (b) o = i WAB LAB N B Pc Lac b₁ · b3 C LCD ·b₂ psi. psi. D d₁ d3 LDE PE E

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter5: Stresses In Beams (basic Topics)

Section: Chapter Questions

Problem 5.5.28P: A foot bridge on a hiking trail is constructed using two timber logs each having a diameter d = 0.5...

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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.
A seesaw weighing 3 lb/ft of length is occupied by two children, each weighing 90 lb (see figure). The center of gravity of each child is 8 ft from the fulcrum. The board is 19 ft long, 8 in. wide, and 1.5 in. thick. What is the maximum bending stress in the board?
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.
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 suspender on a suspension bridge consist of a cable that passes over the main cable (see figure) and supports the bridge deck, which is Far below. The suspender is held in position by a metal tie that is prevented from sliding downward by clamps around the suspender cable. Let P represent the load in each part of the suspender cable, and let represent the angle of the suspender cable just above the tie. represent the allowable tensile stress in the metal tie. (a) Obtain a formula for the minimum required cross-sectional area of the lie. (b) Calculate the minimum area if P = 130 kN, = 75°, and allow=80 .
A T-frame structure is torn posed of a prismatic beam ABC and a nonprismatic column DBF. The beam and the column have a pin support at .A and D, respectively. Both members are connected with a pin at B. The lengths and properties of the members are shown in the figure. Find the vertical displacement of the column at points F and B. Plot axial force (AFD) and axial displacement (ADD) diagrams For column DBF.
A steel riser pipe hangs from a drill rig located offshore in deep water (see figure). Separate segments are joined using bolted flange plages (see figure part b and photo). Assume that there are six bolts at each pipe segment connection. Assume that the total length of the riser pipe is L = 5000 ft: outer and inner diameters are d2= l6in.and d1= 15 in.; flange plate thickness t1= 1.75 in.; and bolt and washer diameters are db= 1.125 in..and dW. = 1.875 in., respectively. (a) If the entire length of the riser pipe is suspended in air. find the average normal stress a in each bolt, the average bearing stress abbeneath each washer, and the average shear stress t through the flange plate at each bolt location for the topmost bolted connection. (b) If the same riser pipe hangs from a drill rig at sea. what are the normal, bearing, and shear stresses in the connection? Obtain the weight densities of steel and sea water from Table I-1. Appendix I. Neglect the effect of buoyant foam casings on the riser pipe
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 stress
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 £.
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.
Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (L1or L2) and outer diameters (d1or different for each column. Assume the inner diameter of each column is 3/4 of outer diameter. Uniformly distributed downward load q = 2PIL is applied over a distance of 3L/4 along BC, and concentrated load PIA is applied downward at D. (a) Derive a formula for the displacement
A column ABC is supported at ends A and C and compressed by an axial load P (figure a). Lateral support is provided at point B but only in the plane of the figure; lateral support perpendicular to the plane of the figure is provided only at A and C. The column is constructed of two channel sections (C 6 × 8.2) back to back (see figure b). The modulus of elasticity of the column is E = 29,500 ksi and the proportional limit is 50 ksi. The height of the column is L = 15 ft. Find the allowable value of load P using a factor of safety of 2.5.