5.8-9 A laminated wood beam on simple sup- ports (figure part a) is built up by gluing together four 2 in. × 4 in. boards (actual dimensions) to form a solid beam 4 in. X 8 in. in cross section, as shown in the fig- ure part b. The allowable shear stress in the glued joints is 62 psi, the allowable shear stress in the wood is 175 psi, and the allowable bending stress in the wood is 1650 psi.
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- A steel plate (called a cover ploie) having cross-sectional dimensions 6,0 in. × 0.5 in. is welded along the full length of the bottom flange of a W 12 × 50 wide-flange beam (sec figure, which shows the beam cross section). What is the percent increase in the smaller section modulus (as compared to the wide-flange beam alone)?-15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide). The wood and the steel are securely fastened to act as a single beam. The beam is subjected to a positive bending moment M. = 75 kip-in. Calculate the required thickness of the steel plate based on the following limit states: Allowable compressive stress in the wood = 2 ksi Allowable tensile stress in the wood = 2 ksi Allowable tensile stress in the steel plate = 16 ksi Assume that Ew= 1,500 ksi and es= 30,000 ksi.A seesaw weighing 3 lb/ft of length is occupied by two children, each weighing 90 lb (see figure). The center of gravity of each child is 8 ft from the fulcrum. The board is 19 ft long, 8 in. wide, and 1.5 in. thick. What is the maximum bending stress in the board?
- 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.Two flat beams AB and CD, lying in horizontal planes, cross at right angles and jointly support a vertical load P at their midpoints (see figure). Before the load P is applied, the beams just touch each other. Both beams are made of the same material and have the same widths. Also, the ends of both beams are simply supported. The lengths of beams AB and CD are LABand LCD, respectively. What should be the ratio tABltCDof the thicknesses of the beams if all four reactions arc to be the same?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.
- 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.A square wood platform is 8 ft × 8 ft in area and rests on masonry walls (see figure). The deck of the platform is constructed of 2-in. nominal thickness tongue-and-groove planks (actual thickness 1.5 in.; sec Appendix CL) supported on two S-ft long beams. The beams have 4 in. × (i in. nominal dimensions (actual dimensions 3.5 in. × 5.5 in.). The planks arc designed to support a uniformly distributed load n ( lb/ft" i acting over the entire top surface of the platform. I be allowable bending stress for the planks is 2400 psi and the allowable shear stress is 100 psi. W ben analyzing the planks, disregard their weights and assume that their reactions are uniformly distributed over the top surfaces of the supporting beams. (a) Determine the allowable platform load Mr. (lb/ft2) based upon the bending stress in the planks. (b) Determine the allowable platform load if-. (lb/ft-) based upon the shear stress in the planks. (c) Which of the preceding values becomes the allowable load alolow on the platform? Hints: Use care in constructing the loading diagram for the planks, noting especially that the reactions are distributed loads instead of concentrated loads. Also, note that the maximum shear forces occur at the inside faces of the supporting beams.AB beam three rectangular planks obtained by gluing and as shown in the figure has been loaded. According to this; i) Maximum draft and compression in the beam their stress, ii) Adhesive at each of the links a and b since its width is 20 mm, in the n-n section, both average slip at the joint stresses and maximum shear stress in the cross section, calculate. section dimensions in mm
- A laminated wood beam on simple supports (figure part a) is built up by gluingtogether four 2 in. X 4 in. boards (actual dimensions) to form a solid beam 4 in. x 8 in.in cross section, as shown in the figure part b. The allowable shear stress in the gluedjoints is 62psi, the allowable shear stress in the wood is 175 psi, and the allowablebending stress in the wood is 1650 psi.(a) If the beam is 12 ft long, what is the allowable load P acting at the one-third pointalong the beam, as shown? (Include the effects of the beam s own weight, assumingthat the wood weighs 35 lb/ft3.)(b) Repeat part (a) if the beam is assembled by gluing together two 3 in. x 4 in. boardsand a 2 in. X 4 in. board (sec figure part c).4. A wood post 12 in. by 12 in. is braced by four steel angles. The wood post and the pieces of angles are exactly the same length of 20 feet. The reinforced post carries a total compressive load of 200 kips. For steel: E = 29 x 10^3 ksi, for wood: Area = 0.938 sq. in., E = 1.9 x 10^3 ksi a. Find the axial stress (in kips) in the steel. b. Find the axial stress in the wood. c. Find the deformation (in inches) if the length of the reinforced post is 12 ft. IVERSITask 1 (a) A steel cantilever beam with a 1-in-diameter round cross section and length of 10 in is loaded at the tip with a transverse force of 1000 lbf and an axial force of 5000 lbf, as shown in the figure. Study the significance of the transverse shear stress in combination with tension and bending by calculating magnitudes of the stresses. Explain and comment on the stresses and strains generated. 1000 Ibf 1 in dia. Cross section at the wall 5000 Ibf (b) Consider a square element in the x-y plane with side length of 3 cm. The thickness of the element is 7 mm. The element has modulus of elasticity of 200 GPa and Poison's ratio of 0.33. If the element is subjected to forces in the x and y directions of 3 KN and 1.5 KN, respectively, find the dimensions of the loaded element. (c) Consider a cubic element with side length of 4 cm. The element has modulus of elasticity of 80 GPa and Poison's ratio of 0.3. If the element is subjected to equal forces in the x, y and z direction of 3 KN.…