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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Chapter 6 Solutions
Mechanics of Materials (MindTap Course List)
- 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.arrow_forwardThe Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7arrow_forwardA beam with a channel section is subjected to a bending moment M having its vector at an angle 8 to the 2 axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress tt and maximum compressive stress crc in the beam. Use a C 200 × 20.5 channel section with M = 0.75 kN - m and 0 = 20°.arrow_forward
- 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 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_forwardThe cross section of a rectangular beam having a width b and height h is shown in part a of the figure. For reasons unknown to the beam designer, it is planned to add structural projections of width b/9 and height d/9 the top and bottom of the beam (see part b of the figure). For what values of d is the bending-moment capacity of the beam increased? For what values is it decreased?arrow_forward
- A steel beam of I-section (see figure) is simply supported at the ends. Two equal and oppositely directed bending moments M0act at the ends of the beam, so the beam is in pure bending. The moments act in plane mmalwhich is oriented at an angle of to the x-y plane. Determine the orientation of the neutral axis and calculate the maximum tensile stress tarm, due to the moments MnData for the beam are S 200 x 21A section, M0= 4 kN m, and a = 24°. Noie: See Table F-2(b) of Appendix F for the dimensions and properties of the beam.arrow_forwardA C 200 x 17.1 channel section has an angle with equal legs attached as shown; the angle serves as a lintel beam. The combined steel section is subjected to a bending moment M having its vector directed along the z axis, as shown in the figure. The cent roi d C of the combined section is located at distances xtand ycfrom the centroid (C1) of the channel alone. Principal axes yl and yvare also shown in the figure and properties Ix1,Iy1and 0pare given. Find the orientation of the neutral axis and calculate the maximum tensile stress exand maximum compressive stress if the angle is an L 76 x 76 x 6.4 section and M = 3.5 kN - m. Use the following properties for principal axes for the combined section:/^, = 18.49 X 106 nrai4,/;| = 1.602 X 106 mm4, ep= 7.448*(CW),_r£ = 10.70 mm,andvf= 24.07 mm.arrow_forwardA beam with a semicircular cross section of radius r is subjected to a bending moment M having its vector at an angle 9 to the z axis (see figure). Derive formulas for the maximum tensile stress tcand the maximum compressive stress tc in the beam for 0 = 0,45º and 90º, Express the results in the form or A/r where a is a numerical value.arrow_forward
- A beam having a cross section in the form of a channel (sec figure) is subjected to a bending moment acting about the z axis. Calculate the thickness t of the channel in order that the bending stresses at the top and bottom of the beam will be in the ratio 7:3, respectively.arrow_forwardThe cross section of a steel beam is shown in the figure. This beam is subjected to a bending moment M having its vector at an angle 8 to the - axis. Determine the orientation of the neutral axis and calculate the maximum tensile stress tiand maximum compressive stress tcin the beam. Assume that e = 22.5° and M = 4.5 kN · m. Use cross-sectional properties Ix=93.14 × 106 mm4, Iy= 152.7 X 10e mm4, and 9 = 27.3º.arrow_forwardThe cross section of a steel beam is constructed of a W 18 × 71 wide-flange section with a 6 in. × 1/2 in, cover plate welded to the top flange and a C 10 × 30 channel section welded to the bottom flange. This beam is subjected to a bending moment M having its vector at an angle tc to the - axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress oxand maximum compressive stress tcin the beam. Assume that S = 30e and M = 75 kip-in. Note: The cross-sectional properties of this beam were computed in Examples D-2 and D-5.arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning