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- Determine the plastic modulus Z and shape factor/for a W 12 x 14 wide-flange beam. Obtain the cross-sectional dimensions and section modulus of the beam from Table F-l(a) in Appendix F.A simple beam with a W 10 x 30 wide-flange cross section supports a uniform load of intensity q = 3.0 kips/ft on a span of length L = 12 ft (sec figure). The dimensions of the cross section are q = 10.5 in., b = 5.81 in., t1= 0.510 in., and fw = 0.300 in. Calculate the maximum shear stress tjuly on cross section A—A located at distance d = 2.5 ft from the end of the beam. Calculate the shear stress rat point Bon the cross section. Point B is located at a distance a = 1.5 in. from the edge of the lower flange.The 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.
- A circular pole is subjected to linearly varying distributed force with maximum intensity t0. Calculate the diameter daof the pole if the maximum allowable shear stress for the pole is 75 M Pa.A bridge girder A B on a simple span of length L = 14 m supports a distributed load of maximum intensity q at m id-span and minimum intensity q/2 at supports A and B that includes the weight of the girder (sec figure). The girder is constructed of three plates welded to form the cross section shown. Determine the maximum permissible load q based upon (a) an a I lowable bending stress tra]Um = 110 M Pa and (b) an allowable shear stress r ,. = 50 M Pa.Solve the preceding problem for a column with e = 0.20 in,, L = 12 ft, I = 2L7in4, and E = 30 × 106psi.
- A box beam is constructed of four wood boards as shown in the figure part a. The webs are S in, x 1 irt and the flanges arc 6 in. X 1 in. boards (actual dimensions), joined by screws for which the allowable load in shear is F = 250 lb per screw. Calculate the maximum permissible longitudinal spacing ,vfflax of the screws if the shear force ^is 12001b. Repeat part (a) if the flanges arc attached to the webs using a horizontal arrangement of screws as shown in the figure part b.The beams shown in the figure are subjected to bending moments M = 250 N · m. Each beam has a rectangular cross section with height f1= 44 mm and width d = 10 mm (perpendicular to the plane of the figure). For the beam with a hole at m id height, determine the maximum stresses for hole diameters d = 10, 16,22, and 28 mm. For the beam with two identical notches (inside height d= 40 mm), determine the maximum stresses for notch radii R = 2,4, 6, and 8 mm.An S6 × 12.5 steel cantilever beam AB is supported by a steel tic rod at B as shown. The tie rod is just taut when a roller support is added at Cat a distance s to the left of £, then the distributed load q is applied to beam segment AC, Assume E = 30 × 106 psi and neglect the self-weight of the beam and tie rod. Sec Table F-2(a) in Appendix F for the properties of the S-shape beam. (a) What value of uniform load q will, if exceeded, result in buckling of the tie rod if L1, =6 ft, s = 2 ft, H = 3 ft, and d = 0.25 in.? (b) What minimum beam moment of inertia ibis required to prevent buckling of the tie rod if q = 200 lb/ft, L1, = 6 ft, H = 3 ft, d = 0.25 in., and s = 2 ft? (c) For what distance s will the tic rod be just on the verge of buckling if q = 200 lb/ft, L1= 6 ft, M = 3 ft, and d = 0.25 in.?
- During construction of a highway bridge, the main girders are cantilevered outward from one pier toward the next (see figure). Each girder has a cantilever length of 48 m and an I-shaped cross section with dimensions shown in the figure. The load on each girder (during construction) is assumed to be 9,5 kN/m, which includes the weight of the girder. Determine the maximum bending stress in a girder due to this load.A frame ABCD is constructed of steel wide-flange members (W8 x 21; E = 30 x ID6 psi) and subjected to triangularly distributed loads of maximum intensity q0acting along the vertical members (see figure). The distance between supports is L = 20 ft and the height of the frame is h = 4 ft. The members are rigidly connected at B and C. Calculate the intensity of load q0 required to produce a maximum bending moment of 80 kip-in. in the horizontal member BC. If the load q0 is reduced to one-half of the value calculated in part (a), what is the maximum bending moment in member BC? What is the ratio of this moment to the moment of 80 kip-in. in part (a)?A beam ABC with an overhang from B to C is constructed of a C 10 × 30 channel section with flanges facing upward (sec figure). The beam supports its own weight (30 lb/ft) plus a triangular load of maximum intensity g0 acting on the overhang. The allowable stresses in tension and compression arc IS ksi and 12 ksi, respectively. Determine the allowable triangular load intensity allow if tne distance L equals 4 ft. What is the allowable triangular load intensity fallow ^tnc Dcam is rotated 180e about its longitudinal centroidal axis so that the flanges are downward?