The cross-sectional dimensions of a beam are shown in the figure. Assume a = 45 mm, b = 75 mm, t = 4 mm and d = 55 mm. (a) If the bending stress at point Kis 54 MPa (C), determine the internal bending moment M₂ acting about the z centroidal axis of the beam. (b) Determine the bending stress at point H. The bending stress is positive if in tension and negative if in compression. K b y d
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- The 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.Two identical, simply supported beams AB and CD are placed so that they cross each other at their midpoints (sec figure). Before the uniform load is applied, the beams just touch each other at the crossing point. Determine the maximum bending moments (mab)max* and (MCD)max beams AB and CD, respectively, due to the uniform load if the intensity of the load is q = 6.4 kN/m and the length of each beam is L = 4 m.The 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?
- Determine the maximum bending stress emaxdue to pure bending by a moment (M) for a beam having a cross section in the form of a circular core (see figure). The circle has diameter d and the angle ß = 60°. Hint: Use the formulas given in Appendix E, Cases 9 and 15.A simple beam A B of a span length L = 24 ft is subjected to two wheel loads acting at a distance d = 5 ft apart (see figure). Each wheel transmits a load P = 3.0 kips, and the carriage may occupy any position on the beam. Determine the maximum bending stress Gmaxdue to the wheel loads if the beam is an I-beam having section modulus S = 16.2 in3. If d = 5 ft. Find the required span length L to reduce the maximum stress in part (a) to 18 ksi. If L = 24 ft, Find the required wheel spacing s to reduce the maximum stress in part (a) to 18 ksi.The beam ABC shown in the figure is simply supported at A and B and has an overhang from B to C. The loads consist of a horizontal force P1= 4,0 kN acting at the end of a vertical arm and a vertical force P2= 8.0 kN acting at the end of the overhang, Determine the shear force Fand bending moment M at a cross section located 3,0 m from the left-hand support. Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations, Find the value of load A that results in V = 0 at a cross section located 2.0 m from the left-hand support. If P2= 8.0 kN, find the value of load P1that results in M = 0 at a cross section located 2,0 m from the left-hand support.
- The cross section of a sandwich beam consisting of fiberglass faces and a lightweight plastic core is shown in the figure. The width b of the beam is 50 mm, the thickness I of the faces is 4 mm, and the height hcof the core is 92 mm (total height A = 100 mm). The moduli of elasticity are 75 GPa for the fiberglass and 1.2 GPa for the plastic. A bending moment M = 275 N · m acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams and (b) the approximate theory for sandwich beams.The cross section of a sand wie h beam consisting of aluminum alloy faces and a foam core is shown in the figure. The width b of the beam is 8.0 in, the thickness I of the faces is 0.25 in., and the height hcof the core is 5.5 in. (total height h = 6.0 in). The moduli of elasticity are 10.5 × 106 psi for the aluminum faces and 12.000 psi for the foam core. A bending moment M = 40 kip-in. acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams and (b) the approximate theory for sandwich beams.The beam ABC shown in the figure is simply supported at A and B and has an overhang from B to C Draw the shear-force and bending-moment diagrams for beam ABC. Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations.
- A 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°.-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 i^/t^ 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. 5.10-6 Dimensions of cross section: b = 120 mm, a = 7 mm, h = 350 mm, hx= 330 mm, and K=60kN.-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.