8-48 A beam is loaded and supported as shown in Fig. Using the coordinate axes shown, write equations tor the shear V and bending moment M for any section of the beam In the interval 2 m
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- The shear stresses t in a rectangular beam arc given by Eq. (5-43): in which Fis the shear force, / is the moment of inertia of the cross-sectional area, /lis the height of the beam, and i] is the distance from the neutral axis to the point where the shear stress is being determined (Fig. 5-32). By integrating over the cross-sectional area, show that the resultant of the shear stresses is equal to the shear force V.The T-beam shown in the figure has cross-sectional dimensions: b = 210 mm, t = 16 mm, h = 300 mm, and A, = 280 mm. The beam is subjected to a shear force V = 68 kN. Determine the maximum shear stress tntijlin the web of the beam.Derive the following formula for the distance e from the centerline of the wall to the shear center S for the hat section of constant thickness shown in the figure: Also, check the formula for the special case of a channel section (a = 0).
- Calculate the maximum shear stress tmax. in the web of the T-beam show ninth o figure if b = 10 in., I = 0.5 in, h = 1 in., h1= 6,2 in., and the shear force V = 5300 lb.A cross section in the shape of a circular arc of constant thickness is shown in the figure. Derive the following formula for the distance e from the center of the arc to the shear center S: in which ß is in radians. Also, plot a graph showing how the distance e varies as ß varies from 0 to tlFind required distance d (in terms of L) so that rotation Ss= 0 is due to M and q loadings applied at the same time. Also, what is the resulting net rotation
- Find expressions for shear force V and moment M at x = L/2 of beam BC. Express V and M in term s of peak load intensity q0and be a m length variable L.A hollow steel box beam has the rectangular cross section shown in the figure. Determine the maximum allowable shear force K that may act on the beam if the allowable shear stress is 36 MPa. c8-7 Determine the bending moment capacities around the horizontal axes for the cross-sectional areas with the dimensions shown in the figures. The allowable elastic stress is either 165 MPa or 24 ksi.
- 7-58 Plot shear and moment diagrams for the beams shown in the figure.10-26. A beam is made up of four 50 X 100-mm full-sized Douglas Fir pieces that are glued to a 25 x 500-mm Douglas Fir plywood web, as shown in the figure. Determine the maximum allowable shear and the maximum allowable bending moment that this section can carry if the allowable bending stress is 10 MPa; the allowable shear stress in plywood is 600 KN /m, and the allowable shearing stress in the glued joints is 300 kN/m^2. AIl dimensions in the figure are in mm.8-49 Using transformed sections, determine the maximum bending stresses in each of the two materials tor the composite beams shown in the figures when subjected to positive bending moments of 80 kN.m each.Esteel, = 210GPa and E aluminium = 70 GPa.