A cantilever beam of length L= 5 m supports a load P = 8 kN, shown in figure. The beam is made of wood with rectangular cross-sectional dimensions; b = 110 mm and %3D height h = 190 mm. Calculate the shear stress due to the load at points located 25 mm from the top surface of the beam. P. L.
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- A fixed-end b earn is subjected to a point load at mid-span. The beam has a rectangular cross section (assume that the h/b ratio is 2) and is made of wood (E = 11GPa). Find height h of the cross section if the maximum displacement of the beam is 2 mm. Calculate the displacement of the beam at the inflection points.Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses Jt(and k2^ and the beam has flexural rigidity EI. What is the downward displacement of point C, which is at the midpoint of the beam, when the moment MQis applied? Data for the structure are M0 = 7.5 kip-ft, L = 6 ft, EI = 520 kip-ft2, kx= 17 kip/ft, and As = 11 kip/ft. Repeat part (a), but remove Af0 and instead apply uniform load q over the entire beam.A cantilever beam of length L = 2 m supports a load P = 8,0 kN (sec figure). The beam is made of wood with cross-sectional dimensions 120 mm x 200 mm. Calculate the shear stresses due to the load/"at points located 25 mm, 50 mm, 75 mm, and 100 mm from the top surface of the beam. From these results, plot a graph showing the distribution of shear stresses from top to bottom of the beam.
- 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.A singly symmetric beam with a T-section (see figure) has cross-sectional dimensions b = 140 mm, a = 190, 8 mm, b. = 6,99 mm, and fc = 11,2 mm. Calculate the plastic modulus Z and the shape factor.-5-7 A cantilever beam AB carries three equalaly spaced concentrated loads, as shown in the figure. Obtain formulas for the angle of rotation B and deflaction B at the free end of the beam.
- The cross section of a composite beam is shown below. The Young's modulus of steel is 200 GPa and for aluminum it is 70 GPa. The distance between the neutral axis (Z-axis) and the bottom surface is approximately: stepl 1s mm aluminum 30 mm 25 mmThe simply supported W8X24 A-36 steel beam AB is loaded as shown in the figure. What is the slope of point B in radians if w = 5.7 kip/ft, L 16.5 ft, Mo = 6.2 kip-ft? Note: Your answer should include units and be to 4 decimal places. Mo Aरू 늘 -The cross section of a rectangular beam having wodht b and height h is shown in part a of a figure 1. For reasons unknown to the beam designer, it is planned to add structural projections of width b/9 and height d to the top and the bottom of the beam(see part b of figure 1)For what values of d is the section modulus S of the beam increased?For what values is it decreased?Hint: Express the section modulus S of the modified section as function of d.then divide S by the section modulus of the orignal section,and plot the result as a function of d/h. The plot will indicate for which values od d, in reference to h, the new section modulus is increased/decreased.