"Simply supported beam, with distributed load 2KN\m as shown infigure below if have maximum stress 10 KN\m find d Circular crosssection diameter ?5 KN2KN\m- Im2 m

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Engineering

Mechanical Engineering

ve maximum str

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter9: Deflections Of Beams

Section: Chapter Questions

Problem 9.6.6P: A cantileverbeam^Cßsupportstwo concentrated loads Ptand A, as shown in the figure. Calculate the...

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A wide-flange member (W200 × 22.5) is compressed by axial loads that have a resultant P acting at the point shown in the figure. The member has modulus of elasticity E = 200 GPa and pinned conditions at the ends. Lateral supports prevent any bending about the weak axis of the cross section. If the length of the member is 6.2 m and the deflection is limited to 6.5 mm. what is the maximum allowable load Pallow.
An S6 × 12.5 steel cantilever beam AB is supported by a steel tic rod at B as shown. The tie rod is just taut when a roller support is added at Cat a distance s to the left of £, then the distributed load q is applied to beam segment AC, Assume E = 30 × 106 psi and neglect the self-weight of the beam and tie rod. Sec Table F-2(a) in Appendix F for the properties of the S-shape beam. (a) What value of uniform load q will, if exceeded, result in buckling of the tie rod if L1, =6 ft, s = 2 ft, H = 3 ft, and d = 0.25 in.? (b) What minimum beam moment of inertia ibis required to prevent buckling of the tie rod if q = 200 lb/ft, L1, = 6 ft, H = 3 ft, d = 0.25 in., and s = 2 ft? (c) For what distance s will the tic rod be just on the verge of buckling if q = 200 lb/ft, L1= 6 ft, M = 3 ft, and d = 0.25 in.?
.2 A ligmio.irc ii supported by two vorlical beams consistins: of thin-walled, tapered circular lubes (see ligure part at. for purposes of this analysis, each beam may be represented as a cantilever AB of length L = 8.0 m subjected to a lateral load P = 2.4 kN at the free end. The tubes have a constant thickness ; = 10.0 mm and average diameters dA = 90 mm and dB = 270 mm at ends A and B, re s pec lively. Because the thickness is small compared to the diameters, the moment of inerlia at any cross section may be obtained from the formula / = jrrf3;/8 (see Case 22, Appendix E); therefore, the section modulus mav be obtained from the formula S = trdhlA. (a) At what dislance A from the free end docs the maximum bending stress occur? What is the magnitude trllul of the maximum bending stress? What is the ratio of the maximum stress to the largest stress (b) Repeat part (a) if concentrated load P is applied upward at A and downward uniform load q {-x) = 2PIL is applied over the entire beam as shown in the figure part b What is the ratio of the maximum stress to the stress at the location of maximum moment?
A square wood platform is 8 ft × 8 ft in area and rests on masonry walls (see figure). The deck of the platform is constructed of 2-in. nominal thickness tongue-and-groove planks (actual thickness 1.5 in.; sec Appendix CL) supported on two S-ft long beams. The beams have 4 in. × (i in. nominal dimensions (actual dimensions 3.5 in. × 5.5 in.). The planks arc designed to support a uniformly distributed load n ( lb/ft" i acting over the entire top surface of the platform. I be allowable bending stress for the planks is 2400 psi and the allowable shear stress is 100 psi. W ben analyzing the planks, disregard their weights and assume that their reactions are uniformly distributed over the top surfaces of the supporting beams. (a) Determine the allowable platform load Mr. (lb/ft2) based upon the bending stress in the planks. (b) Determine the allowable platform load if-. (lb/ft-) based upon the shear stress in the planks. (c) Which of the preceding values becomes the allowable load alolow on the platform? Hints: Use care in constructing the loading diagram for the planks, noting especially that the reactions are distributed loads instead of concentrated loads. Also, note that the maximum shear forces occur at the inside faces of the supporting beams.
A tie-down on the deck of a sailboat consists of a bent bar boiled at both ends, as shown in the figure. The diameter dBof the bar is 1/4 in., the diameter D Wof the washers is 7/8 in., and the thickness is of the fiberglass deck is 3/8 in. If the allowable shear stress in the fiberglass is 300 psi, and the allowable bearing pressure between the washer and the fiberglass is 550 psi, what is the allowable load P allowon the tie-down?
A flying but tress transmit s a load P = 25 kN, acting at an angle of 60º to the horizontal, to the top of a vertical buttress AB (see figure). The vertical buttress has height h = 5.0 m and rectangular cross section of thickness t = 1.5 m and width b = 1.0 m (perpendicular to the plane of the figure). The stone used in the construction weighs y = 26 kN/m3. What is the required weight W of the pedestal and statue above the vertical buttress (that is, above section A) to avoid any tensile stresses in the vertical buttress?
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Determine the plastic modulus Z and shape factor/for a W 12 x 14 wide-flange beam. Obtain the cross-sectional dimensions and section modulus of the beam from Table F-l(a) in Appendix F.
A hollow box beam is constructed with webs of Douglas-fir plywood and flanges of pine, as shown in the figure in a cross-sectional view. The plywood is 1 in. thick and 12 in. wide; the flanges are 2 in. × 4 in. (nominal size). The modulus of elasticity for the plywood is 1,800,000 psi and for the pine is 1,400,000 psi. If the allowable stresses are 2000 psi for the plywood and 1750 psi for the pine, find the allowable bending moment Mmaxwhen the beam is bent about the z axis. Repeat part (a) if the beam is now bent about its y-axis.
A beam of wide-flange shape, W 8 x 28, has the cross section shown in the figure. The dimensions are b = 6.54 in., h = 8.06 in., fw = 0.285 in., and tf = 0.465 in.. The loads on the beam produce a shear force V = 7.5 kips at the cross section under consideration. Use center line dimensions to calculate the maximum shear stress raiaxin the web of the beam. Use the more exact analysis of Section 5,10 in Chapter 5 to calculate the maximum shear stress in the web of the beam and compare it with the stress obtained in part .
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