Q.1: The simply supported wood beam in Fig below is fabricated by gluing together three 160 mm by 80 mm plans as shown. Calculate the maximum shear stress in (1) the glue; and (2) the wood. A 8 kN/m 6 m B 80 mm 80 mm 80 mm 160 mm Glue -NA
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- A square tube section has side dimension of 20 in. arid thickness of 0.5 in. If the section is used for a 10-ft-long beam subjected to 1250 kip-in, torque at both ends, calculate the maximum shear stress and the angle of twist between the ends. Use G = 11,600 ksi.Solve the preceding problem using the following data: beam cross section is 100 x 150 mm, length is 3 m, and point load is P = 5 kN at mid-span, Point C is located 25 mm below the top of the beam and 0.5 m to the right of support A.Two wood beams, each of rectangular cross section (3.0 in. x 4.0 in., actual dimensions), are glued together to form a solid beam with dimensions 6.0 in. x 4.0 in. (sec figure). The beam is simply supported with a span of S ft. What is the maximum moment Mmaxthat may be applied at the left support if the allowable shear stress in the glued joint is 200 psi? (Include the effects of the beams own weight, assuming that the wood weighs 35 lb/ft3.) Repeat part (a) if Mmaxis based on allowable bending stress of 2500 psi.
- A tie-down on the deck of a sailboat consists of a bent bar boiled at both ends, as shown in the figure. The diameter dBof the bar is 1/4 in., the diameter D Wof the washers is 7/8 in., and the thickness is of the fiberglass deck is 3/8 in. If the allowable shear stress in the fiberglass is 300 psi, and the allowable bearing pressure between the washer and the fiberglass is 550 psi, what is the allowable load P allowon the tie-down?A floor system in a small building consists of wood planks supported by 2-in. (nominal width) joists spaced at distance s and measured from center to center (see figure). The span length L of each joist is 12 ft, the spacing s of the joists is 16 in., and the allowable bending stress in the wood is 1250 psi. The uniform floor load is 120 lb/ft", which includes an allowance for the weight of the floor system itself. Calculate the required section modulus S for the joists, and then select a suitable joist size (surfaced lumber) from Appendix G, assuming that each joist may be represented as a simple beam carrying a uniform load. What is the maximum floor load that can be applied to your final beam selection in part (a)?Repeat Problem 6.2-1 but now assume that the steel plate is smaller (0.5 in. × 5 in.) and is aligned with the top of the beam as shown in the figure.
- A hollow box beam is constructed with webs of Douglas-fir plywood and flanges of pine, as shown in the figure in a cross-sectional view. The plywood is 1 in. thick and 12 in. wide; the flanges are 2 in. × 4 in. (nominal size). The modulus of elasticity for the plywood is 1,800,000 psi and for the pine is 1,400,000 psi. If the allowable stresses are 2000 psi for the plywood and 1750 psi for the pine, find the allowable bending moment Mmaxwhen the beam is bent about the z axis. Repeat part (a) if the beam is now bent about its y-axis.A wood beam reinforced using two channels is subjected to a positive bending moment M_ = 25 kip-ft. Calculate the largest tensile and compressive stresses in the wood and steel if Ew = 1500 ksi and £s = 30,000 ksi.A pontoon bridge (see figure) is constructed of two longitudinal wood beams, known as bulks, that span between adjacent pontoons and support the transverse floor beams, which arc called chesses. For purposes of design, assume that a uniform floor load of 7.5 kPa acts over the chesses. (This load includes an allowance for the weights of the chesses and balks.) Also, assume that the chesses are 2.5 m long and that the balks are simply supported with a span of 3.0 m. The allowable bending stress in the wood is 15 MPa. If the balks have a square cross section, what is their minimum required width b^l Repeat part (a) if the balk width is 1.5 b and the balk depth is b; compare the cross-sectional areas of the two designs.
- Calculate the distance e from the cent crime of the web of a C 15 x 40 channel section to the shear center 5 (see figure). Note: For purposes of analysis, consider the flanges to be rectangles with thickness teequal to the average flange thickness given in Table F-3(a) in Appendix F.The wood joists supporting a plank Floor (see figure) are 38 mm × 220 mm in cross section (actual dimensions) and have a span length of L = 4.0 m. The floor load is 5.0 kPa, which includes the weight of the joists and the floor. (a) Calculate the maximum permissible spacing s of the joists if the allowable bending stress is 14 M Pa. (Assume that each joist may be represented as a simple beam carrying a uniform load.) (b) If spacing s = 406 mm, what is the required depth ft of the joist? Assume all other variables remain unchanged.Calculate the distance e from the centerline of the web of a C 310 × 45 channel section to the shear center E (see figure). Note: For put poses of analysis, consider the flanges to be rectangles with thickness îrequal to the average flange thickness given in Table F-3(b) in Appendix F.