A laminated plastic beam of square cross section is built up by gluing together three strips, each 20 mm x 60 mm in cross section (see figure). The beam has a total weight of 4.6 N and is simply supported with span length L = 460 mm.M.t20 mmt20 mm 60 mm20 mm60 mmConsidering the weight of the beam (9) calculate the maximum permissible CCW moment M that may be placed at the right support.(a) If the allowable shear stress in the glued joints is 0.3 MPa. Round to the nearest tenth.Mmax =N.m(b) If the allowable bending stress in the plastic is 6 MPa. Round to the nearest hundredth.Mmax =N.m

A laminated plastic beam of square cross section is built up by gluing together three strips, each 20 mm x 60 mm in cross section (see figure). The beam has a total weight of 4.6 N and is simply supported with span length L = 460 mm. 20 mm 20 mm 60 mm 20 mm 60 mm Considering the weight of the beam (G) calculate the maximum permissible CCW moment M that may be placed at the right support. (a) If the allowable shear stress in the glued joints is 0.3 MPa. Round to the nearest tenth. Mmax = N. m (b) If the allowable bending stress in the plastic is 6 MPa. Round to the nearest hundredth. Mmax =| N.m

A laminated plastic beam of square cross section is built up by gluing together three strips, each 20 mm x 60 mm in cross section (see figure). The beam has a total weight of 4.6 N and is simply supported with span length L = 460 mm. 20 mm 20 mm 60 mm 20 mm 60 mm Considering the weight of the beam (G) calculate the maximum permissible CCW moment M that may be placed at the right support. (a) If the allowable shear stress in the glued joints is 0.3 MPa. Round to the nearest tenth. Mmax = N. m (b) If the allowable bending stress in the plastic is 6 MPa. Round to the nearest hundredth. Mmax =| N.m

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 5.8.5P: Two wood beams, each of rectangular cross section (3.0 in. x 4.0 in., actual dimensions), are glued...

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A beam with a guided support and 10-ft span supports a distributed load of intensity q = 660 lb/ft over its first half (see figure part a) and a moment Mq = 300 ft-lb at joint B. The beam consists of a wood member (nominal dimensions 6 in. x 12 in. and actual dimensions 5.5 in. x 11.5 in. in cross section, as shown in the figure part b) that is reinforced by 0.25-in.-thick steel plates on top and bottom. The moduli of elasticity for the steel and wood are £s = 30 X 106 psi and £"w = 1.5 X 106 psi, respectively. Calculate the maximum bending stresses trs in the steel plates and rw in the wood member due to the applied loads. If the allowable bending stress in the steel plates is = 14,000 psi and that in the wood is (T.dV!= 900 psi, find qmiiX. (Assume that the moment at .fi, A/0, remains at 300 ft-lb.) If q = 660 lb/ft and allowable stress values in part (b) apply, what is Müm^ at B?
-14 A simply supported composite beam with a 3.6 m span supports a triangularly distributed load of peak intensity q0at mid-span (see figure part a). The beam is constructed of two wood joists, each 50 mm x 280 mm, fastened to two steel plates, one of dimensions 6 mm × 80 mm and the lower plate of dimensions 6 mm x 120mm (see figure part b). The modulus of elasticity for the wood is 11 GPa and for the steel is 210 GPa. If the allowable stresses are 7 MPa for the wood and 120 MPa for the steel, find the allowable peak load intensity q0maxwhen the beam is bent about the z axis. Neglect the weight of the beam.
A simple beam that is 18 ft long supports a uniform load of intensity q. The beam is constructed of two C8 x 11.5 sections (channel sections or C-shapes) on either side of a 4 × 8 (actual dimensions) wood beam (see the cross section shown in the figure part a). The modulus of elasticity of the steel (E; = 30,000 ksi) is 20 times that of the wood (Ew). (a) If the allowable stresses in the steel and wood are 12,000 psi and 900 psi, respectively, what is the allowable load qmax Note: Disregard the weight of the beam, and see Table F-3(a) of Appendix F for the dimensions and properties of the C-shape beam. (b) If the beam is rotated 90° to bend about its v axis (see figure part b) and uniform load q = 250 lb/ft is applied, find the maximum stresses trs and crw in the steel and wood, respectively Include the weight of the beam. (Assume weight densities of 35 lb/ft3 and 490 lb/ft3 for the wood and steel, respectively.)
The hollow box beam shown in the figure is subjected to a bending moment M of such magnitude that the flanges yield but the webs remain linearly elastic. (a) Calculate the magnitude of the moment M if the dimensions of the cross section are A = 15 in., A] = 12.75 in., h = 9 in., and ey =7.5 in. Also, the yield stress is eY = 33 ksi. (b) What percent of the moment M is produced by the elastic core?
A W 12 x 50 steel wide-flange beam and a segment of a 4-inch thick concrete slab (see figure) jointly resist a positive bending moment of 95 kip-ft. The beam and slab are joined by shear connectors that are welded to the steel beam. (These connectors resist the horizontal shear at the contact surface.) The moduli of elasticity of the steel and the concrete are in the ratio 12 to 1. Determine the maximum stresses r1 and xtin the steel and concrete, respectively. Note: See Table F-l(a) of Appendix F for the dimensions and properties of the steel beam.
A propped cantilever beam of length L = 54 in. with a sliding support supports a uniform load of intensity q (see figure). The beam is made of steel {<7y = 36 ksi) and has a rectangular cross section of width/) = 4.5 in. and height h = 6.0 in. What load intensity q will produce a fully plastic condition in the beam?
A simple beam with a W 10 x 30 wide-flange cross section supports a uniform load of intensity q = 3.0 kips/ft on a span of length L = 12 ft (sec figure). The dimensions of the cross section are q = 10.5 in., b = 5.81 in., t1= 0.510 in., and fw = 0.300 in. Calculate the maximum shear stress tjuly on cross section A—A located at distance d = 2.5 ft from the end of the beam. Calculate the shear stress rat point Bon the cross section. Point B is located at a distance a = 1.5 in. from the edge of the lower flange.
The cantilever beam AB shown in the figure is an S6 × 12.5 steel I-beam with E = 30 × 106 psi. The simple beam DE is a wood beam 4 in. x 12 in. (nominal dimensions) in cross section with E = 1.5 x 106 psi. A steel rod AC of diameter 0.25 in., length 10 ft, and E = 30 x 106 psi serves as a hanger joining the two beams. The hanger fits snugly between the beams before the uniform load is applied to beam DE. Determine the tensile force Fin the hanger and the maximum bending moments MABand MDEin the two beams due to the uniform load, which has an intensity q = 400 lb/ft. Hint: To aid in obtaining the maximum bending moment in beam DE, draw the shear-force and bending-moment diagrams.
A steel beam of rectangular cross section is 40 mm wide and 80 mm high (see figure). The yield stress of the steel is 210 MPa, (a) What percent of the cross-sectional area is occupied by the clastic core if the beam is subjected to a bending moment of 12.0 kN · m acting about the z axis? (b) What is the magnitude of the bending moment that will cause 50% of the cross section to yield?
A cantilever beam AB of length L = 6.5 ft supports a trapezoidal distributed load of peak intensity 4, and minimum intensity q/2tthat includes the weight of the beam (see figure). The beam is a steel W 12 × 14 wide-flange shape (see Table F-l(a), Appendix F). Calculate the maximum permissible load q based upon (a) an allowable bending stress eallow = 18 ksi and (b) an allowable shear stress eallow = 7,5 ksi. Note: Obtain the moment of inertia and section modulus of the beam from Table F-l(a).
Two wood beams, each of rectangular cross section (3.0 in. x 4.0 in., actual dimensions), are glued together to form a solid beam with dimensions 6.0 in. x 4.0 in. (sec figure). The beam is simply supported with a span of S ft. What is the maximum moment Mmaxthat may be applied at the left support if the allowable shear stress in the glued joint is 200 psi? (Include the effects of the beams own weight, assuming that the wood weighs 35 lb/ft3.) Repeat part (a) if Mmaxis based on allowable bending stress of 2500 psi.
A beam with a channel section is subjected to a bending moment M having its vector at an angle 0 to the 2 axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress et and maximum compressive stress ecin the beam. Use the following data: C 8 × 11.5 section, M = 20 kip-in., tan0=l/3. See Table F-3(a) of Appendix F for the dimensions and properties of the channel section.