Determine the largest allowable value of P if the bending stress for simply supported beam (shown in the figure) is not to exceed 10 MPa.
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- -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 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.A beam having a cross section in the form of a channel (sec figure) is subjected to a bending moment acting about the z axis. Calculate the thickness t of the channel in order that the bending stresses at the top and bottom of the beam will be in the ratio 7:3, respectively.
- A beam supporting a uniform load of intensity q throughout its length rests on pistons at points A, C and B (sec figure). The cylinders are filled with oil and are connected by a tube so that the oil pressure on each piston is the same. The pistons at A and B have diameter d1and the piston at C has diameter D2. (a) Determine the ratio of d2to d1so that the largest bending moment in the beam is as small as possible. Under these optimum conditions, what is the largest bending moment Mmaxin the beam? What is the difference in elevation between point C and the end supports?A U-shaped cross section of constant thickness is shown in the figure. Derive the following formula for the distance e from the center of the semicircle to the shear center. Also, plot a graph showing how the distance e (expressed as the non dimensional ratio e/r varies as a function of the ratio b/r. (Let b/r range from 0 to 2.)Two identical, simply supported beams AB and CD are placed so that they cross each other at their midpoints (sec figure). Before the uniform load is applied, the beams just touch each other at the crossing point. Determine the maximum bending moments (mab)max* and (MCD)max beams AB and CD, respectively, due to the uniform load if the intensity of the load is q = 6.4 kN/m and the length of each beam is L = 4 m.
- The cross section of a rectangular beam having a width b and height h is shown in part a of the figure. For reasons unknown to the beam designer, it is planned to add structural projections of width b/9 and height d/9 the top and bottom of the beam (see part b of the figure). For what values of d is the bending-moment capacity of the beam increased? For what values is it decreased?A solid rectangular homogeneous section (total length = 7.2m) is simply supported, where b = 50 mm and d= 175 mm. A concentrated load F = 140 N acts at point C where L1 = 4.00 m L2 = 3.20 m. Calculate the maximum bending stress and give your answer in N/mm2 to 2 decimal places. *Assume the weight of the beam is negligible and zero. F A B L1 L2 d A B Answer:Determine the minimum allowable height (h) in mm of the beam shown in the figure if the bending stress is not to exceed 20 MPа. 5 kN 2.5 kN/m 80 mm A E D 1.0 m 1.0 m 2 m
- 1: Calculate the shear force V and bending moment M at a cross section just to the right of middle point. 1 90 = P= 80 lb | 40 in.- 10 lb/in. -1/2- 40 in. -A solid rectangular homogeneous section (total length = 7.2m) is simply supported, where b = 50 mm and d = 175 mm. A concentrated load F = 140 N acts at point C where L1 = 4.00 m L2 = 3.20 m. Calculate the maximum bending stress and give your answer in N/mm2 to 2 decimal places. *Assume the weight of the beam is negligible and zero.A wood beam carries the loading shown in the figure. calculate the magnitude of the bending stress (in Pa) at a point 16 mm from the top of the of the beam on a section 2.9 m from A if P = 5486 N. W = 2434 N/m, a = 1.5 m, b = 2.13 m, c = 1.33 m, L = 74 mm and h = 239 mm. Round off the final answer to two decimal places. W P +²+ A B bi .c→ C h