5. Determine the moment of inertia of the section in x10^6 mm^4
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5. Determine the moment of inertia of the section in x10^6
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- 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)?A W 12 x 50 steel wide-flange beam and a segment of a 4-inch thick concrete slab (see figure) jointly resist a positive bending moment of 95 kip-ft. The beam and slab are joined by shear connectors that are welded to the steel beam. (These connectors resist the horizontal shear at the contact surface.) The moduli of elasticity of the steel and the concrete are in the ratio 12 to 1. Determine the maximum stresses r1 and xtin the steel and concrete, respectively. Note: See Table F-l(a) of Appendix F for the dimensions and properties of the steel beam.A two-axle carriage that is part of an over head traveling crane in a testing laboratory moves slowly across a simple beam AB (sec figure). The load transmitted to the beam from the front axle is 2200 lb and from the rear axle is 3800 lb. The weight of the beam itself may be disregarded. Determine the minimum required section modulus S for the beam if the allowable bending stress is 17,0 ksi, the length of the beam is 18 ft, and the wheelbase of the carriage is 5 ft. Select the most economical I-beam (S shape) from Table F-2(a), 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.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 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.
- 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.Solve the preceding problem for a wide-flange beam with h = 404 mm, b = 140 mm, bf= 11.2 mm, and rf. = 6.99 mm.A steel beam of length L = 16 in. and cross-sectional dimensions h = 0.6 in. and h = 2 in. (see figure) supports a uniform load of intensity if = 240 lb/in., which includes the weight of the beam. Calculate the shear stresses in the beam (at the cross section of maximum shear force) at points located 1/4 in., 1/2 in., 3/4 in., and I in, from the top surface of the beam. From these calculations, plot a graph showing the distribution of shear stresses from top to bottom of the beam.
- 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 reinforced concrete slab (see figure) is reinforced with 13-mm bars spaced 160 mm apart at d = 105 mm from the top of the slab. The modulus of elasticity for the concrete is Ec= 25 GPa, while that of the steel is £s = 200 G Pa. Assume that allowable stresses for concrete and steel arecrac = 9.2 MPa and us = 135 MPa. l()5 mm Find the maximum permissible positive bending moment for a l-m wide strip of the slab. What is the required area of steel reinforcement, A^ if a balanced condition must be achieved? What is the allowable positive bending moment? (Recall that in a balanced design, both steel and concrete reach allowable stress values simultaneously under the design moment.)A simple beam with a rectangular cross section (width, 3,5 inL; height, 12 in,) carries a trapczoi-dally distributed load of 1400 lb/ft at A and 1000 lb/ft at B on a span of 14 ft (sec figure). Find the principal stresses 2 and the maximum shear stress r__ at a cross section 2 ft from the left-hand support at each of the locations: (a) the neutral axis, (b) 2 in. above the neutral axis, and (c) the top of the beam. (Disregard the direct compressive stresses produced by the uniform load bearing against the top of the beam.)