A built-Lip I-section steel beam with channels attached to the flanges (sec Figure part a) is simply supported at the ends. Two equal and oppositely directed bending moments I/2, act at the ends of the beam, so the beam is in pure bending. The moments act in plane mm. which is oriented at an angle a to
(a)
Determine the orientation of the neutral axis and calculate the maximum (ensile stress on till due to the moments Ma.
(b)
Repeat pan (a) if (he channels now have their flanges pointing away from the beam flange, as shown in the figure part b. Data for the beam are S 6 x 12.5 section with C 4 x 5.4 sections attached to the Hanges, .V/2— 45 kip-in., and a = 40°. See Tables F-2(a) and F-3(a) of Appendix F l or the dimensions and properlies of the S and shapes.
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Mechanics of Materials (MindTap Course List)
- A composite beam consisting of fiberglass faces and a core of particle board has the cross section shown in the figure. The width of the beam is 2,0 in., the thickness of the faces is 0,10 in., and the thickness of the core is 0.50 in. The beam is subjected to a bending moment of 250 lb-in, acting about the - axis. Find the maximum bending stresses tr(and ctc in the faces and the core, respectively, if their respective moduli of elasticity are 4 x 106 psi and 1.5 x 106 psi.arrow_forwardA 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?arrow_forwardA 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.arrow_forward
- A wood beam with cross-sectional dimensions 200 mm x 300 mm is reinforced on its sides by steel plates 12 mm thick (see figure). The moduli of elasticity for the steel and wood are E±= 190 GPa and Ew= 11 GPa, respectively. Also, the corresponding allowable stresses are eS= 110 MPa and ew = 7.5 MPa, (a) Calculate the maximum permissible bending moment Mmaxwhen the beam is bent about the- axis. Repeat part (a) if the beam is now bent about its y axis. Find the required thickness of the steel plates on the beam bent about the y axis so that Mmaxis the same for both beam orientations.arrow_forwardThe 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?arrow_forwardA 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.arrow_forward
- A r o lukI f/frm f «m t ub e of ou t sid e d ia met er ^ and a copper core of diameter dxare bonded to form a composite beam, as shown in the figure, (a) Derive formulas for the allowable bending moment M that can be carried by the beam based upon an allowable stress <7Ti in the titanium and an allowable stress (u in the copper (Assume that the moduli of elasticity for the titanium and copper are Er- and £Cu, respectively.) (b) If d1= 40 mm, d{= 36 mm, ETl= 120 GPa, ECu= 110 GPa, o-Ti = 840 MPa, and ctqj = 700 MPa, what is the maximum bending moment Ml (c) What new value of copper diameter dtwill result in a balanced design? (i.e., a balanced design is that in which titanium and copper reach allow- able stress values at the same time).arrow_forward-1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^ The shear force carried in the web and the ratio K b/K. Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-2 Dimensions of cross section: b = 180 mm, v = 12 mm, h = 420 mm, i = 380 mm, and V = 125 kN.arrow_forwardA 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.)arrow_forward
- -1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^ The shear force carried in the web and the ratio V^tV. Noie: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-3 Wide-flange shape, W 8 x 28 (see Table F-L Appendix F); V = 10 karrow_forward-1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^ The shear force carried in the web and the ratio V^tV. Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-4 Dimensions of cross section: b = 220 mm, f = 12 mm, h = 600 mm, hx= 570 mm, and V = 200 kN.arrow_forwardA cantilever beam AB with a circular cross section and length L = 750 mm supports a load P = 800 N acting at the free end (see figure). The beam is made of steel with an allowable bending stress of 120 MPa. Determine the required diameter dmm(figure part a) of the beam, considering the effect of the beam's own weight. Repeat part (a) if the beam is hollow with wall thickness t = df$ (figure part b); compare the cross-sectional areas of the two designs.arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning