Find the cross sectional dimensions of the smallest square beam that can be loaded as shown in the figure if the allowable shearing stress is 1.0 MPa and the allowable bending stress is 8 MPa. 12 kN 4 kN m B 4 m- 2 m- 3 m
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- 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.Calculate the distance e from the centerline of the web of a C 310 × 45 channel section to the shear center E (see figure). Note: For put poses of analysis, consider the flanges to be rectangles with thickness îrequal to the average flange thickness given in Table F-3(b) in Appendix F.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.
- A wood beam AB on simple supports with span length equal to 10 ft is subjected to a uniform load of intensity 125 lb/ft acting along the entire length of the beam, a concentrated load of magnitude 7500 lb acting at a point 3 ft from the right-hand support, and a moment at A of 18,500 ft-lb (sec figure). The allowable stresses in bending and shear, respectively, are 2250 psi and 160 psi. From the table in Appendix G, select the lightest beam that will support the loads (disregard the weight of the beam). Taking into account the weight of the beam (weight density = 35 lb/ft3), verify that the selected beam is satisfactory, or if it is not, select a new beam.-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.Solve the preceding problem if the length L = 56 in., the inner radius r1— 1.25 in., the angle of twist is 0.5°, and the allowable shear strain is 0.0004 rad.
- A full quarter-circular fillet is used at the shoulder of a stepped shaft having diameter D2= 1.0 in. (see figure), A torque T = 500 lb-in. acts on the shaft. Determine the shear stress at the stress concentration for values as follows: D1= 0.7,0.8, and 0.9 in. Plot a graph showing versus D?A steel beam is built up from a W 410 × 85 wide flange beam and two 180 mm X 9 mm cover plates (see figure). The allowable load in shear on each bolt is 9.8 kN. What is the required bolt spacing s in the longitudinal direction if the shear force V = 110 kN Noie: Obtain the dimensions and moment of inertia of the W shape from Table F-l(b).The Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7
- A freight-car axle AS is loaded approximately as shown in the figure, with the forces P representing the car loads (transmitted to the axle through the axle boxes) and the forces R representing the rail loads (transmitted to the axle through the wheels). The diameter of the axle is d = 82 mm, the distance between centers of the rails is Z., and the distance between the forces P and R is A = 220 mm. Calculate the maximum bending stress vmaxin the axle if P = 50 kN.When drilling a hole in a table leg, a furniture maker uses a hand-operated drill (see figure) with a bit of diameter d = 4.0 mm. If the resisting torque supplied by the table leg is equal to 0.3 N · m, what is the maximum shear stress in the drill bit? If the allowable shear stress in the drill bit is 32 MPa, what is the maximum resisting torque before the drill binds up? If the shear modulus of elasticity of the steel is G = 75 GPa, what is the rate of twist of the drill bit (degrees per meter)?Derive the following formula for the distance e from the centerline of the wall to the shear center S for the hat section of constant thickness shown in the figure: Also, check the formula for the special case of a channel section (a = 0).