Q.3 The overhanging beam and its cross section is shown in figure below; a) Calculate maximum flexure stress and draw flexure stress distribution diagram for section subjected to maximum bending moment. 20 kN 200 mm 20 kN /m 10 mm: 150 mm 10 mm 10 mm 4 m 2 m Cross section of beam
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- 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?A rectangular beam with semicircular notches, as shown in part b of the figure, has dimensions h = 120 mm and h1= 100 mm. The maximum allowable bending stress in the plastic beam is emix = 6 M Pa, and the bending moment is M = 150 N · m. Determine the minimum permissible width bminof the beam.The cross section of an unbalanced wide-flange beam is shown in the figure. Derive the following formula for the distance /h from the centerline of one flange to the shear center S: h1t2b23ht1b13+t2b23 Also, check the formula for the special cases of a T-beam (b2= t2=0) and a balanced wide-flange beam (t2= ttand b2= ty).
- .10 A built-up bourn supporting a condominium balcony is made up of a structural T (one half of a W 200 x 31.3) for the top flange and web and two angles (2 L 2 / b / 6.4. long legal back-lo-backl lot the bottom flange and web. as shown. The beam is subjected to a bending moment .1/ having its vector at an angle ft lo the z axis (see figure). Determine the or ion ta I ion of the neutral axis and calculate the maximum tensile stress ir, and maximum compressive stress tr. in ".he beam. .Assume that 9 = 30°andM = 15 kN · m. Use the numerical properties: c =4.111mm, c2 =4.169 mm, of = 134 mm, I, = 76 mm, A = 4144 mm 3 =3.88 X 106 mm 4, and = 34.18 X 10 mm 4.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 simple beam ACE is constructed with square cross sections and a double taper (see figure). The depth of the beam at the supports is dAand at the midpoint is dc= 2d 4. Each half of the beam has length L. Thus, the depth and moment of inertia / at distance x from the left-hand end are, respectively, in which IAis the moment of inertia at end A of the beam. (These equations are valid for .x between 0 and L, that is, for the left-hand half of the beam.) Obtain equations for the slope and deflection of the left-hand half of the beam due to the uniform load. From the equations in part (a), obtain formulas for the angle of rotation 94at support A and the deflection Scat the midpoint.
- A rectangular beam with notches and a hole (see figure) has dimensions h = 5.5 in., h1= 5 in., and width b = 1.6 in. The beam is subjected to a bending moment M = 130 kip-in., and the maximum allowable bending stress in the material (steel) is emax = 42,000 psi. What is the smallest radius Rminthat should be used in the notches? What is the diameter dmixof the largest hole that should be drilled at the mid height of the beam?-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 t (obtained by dividing the shear force by the area of the web) and the ratio tmax/taver. The shear force Vweb/V carried in the web and the Vweb/V. 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. 5.10-1 Dimensions of cross section: b = 6 in,, ï = 0.5 in., h = 12 in,, A, = 10.5 in., and V = 30 k.A tapered cantilever beam A B supports a concentrated load P at the free end (see figure). The cross sections of the beam are rectangular with constant width A, depth d Aat support A, and depth ds= ^dJ2 at the support. Thus, the depth d and moment of inertia / at distance x from the free end are, respectively, in which / 4 is the moment of inertia at end A of the beam. Determine the equation of the deflection curve and the deflection S 4at the free end of the beam due to the load P.
- 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.-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 k-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.