In the Figure below, a cantilever beam is subjected to an inclined force (P); calculate the: 1- Normal stress. 2- Shear stress. P = 100 N 30° Area 30 mm 20 mm
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- 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.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?-3 The deflection curve for a simple beam AB (see figure) is given by v=q0x360LEI(7L410L2x2+3x4) Describe the load acting on the beam.
- -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.A simple beam thai is IS ft long supports a uni¬form load of intensity a. The beam is constructed of two angle sections, each L (1 × 4 × 1/2, on either side of a 2 in. x 8 in. (actual dimensions! wood beam (see the cross section shown in the figure part a]. The modulus of elasticity of the s I eel is 10 limes that of the wood, (a) If the allowable stresses in the steel and wood are 12,000 psi and 900 psi. respectively, what is the allow atile load a t. A olc. Disregard the weight of the beam, and see Table F-5(a) of Appendix I ' for I lie dimensions and properties of the angles. (b) Repeal partial if a I in. 10 in. wood Hange tactual dimensions) is added i see figure pallhi b).A simple beam that is 18 ft long supports a uniform load of intensity q. The beam is constructed of two C8 x 11.5 sections (channel sections or C-shapes) on either side of a 4 × 8 (actual dimensions) wood beam (see the cross section shown in the figure part a). The modulus of elasticity of the steel (E; = 30,000 ksi) is 20 times that of the wood (Ew). (a) If the allowable stresses in the steel and wood are 12,000 psi and 900 psi, respectively, what is the allowable load qmax Note: Disregard the weight of the beam, and see Table F-3(a) of Appendix F for the dimensions and properties of the C-shape beam. (b) If the beam is rotated 90° to bend about its v axis (see figure part b) and uniform load q = 250 lb/ft is applied, find the maximum stresses trs and crw in the steel and wood, respectively Include the weight of the beam. (Assume weight densities of 35 lb/ft3 and 490 lb/ft3 for the wood and steel, respectively.)
- 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.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)?A propped cantilever beam A BC (see figure) has a shear release just right of the mid-span. (a) Select the most economical wood beam from the table in Appendix G; assume4 = 55 lb/ft, L = 16 ft, o~aw= 1750 psi, and raw= 375 psi. Include the self-weight of the beam in your design. (b) If a C 10 x 25 steel beam is now used for beam ABC, what is the maximum permissible value of load variable q? Assume üi = 16 ksi and L = 10 ft. Include the self-weight of the beam in your analysis.
- Obtain a formula for the ratio c/maxof the deflection at the midpoint to the maximum deflection for a simple beam supporting a concentrated load P (see figure). From the formula, plot a graph of c/max versus the ratio a/L that defines the position of the load (0.5 < a/L < ) What conclusion do you draw from the graph? (Use the formulas of Example 9-3.)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.What is the span length L of a uniformly loaded, simple beam of wide-flange cross section (see figure) if the maximum bending stress is 12,000 psi, the maximum deflection is 0.1 in., the height of the beam is 12 in., and the modulus of elasticity is 30 × 106psi? (Use the formulas of Example 9-1.)