Use singularity functions to determine the deflection at mid-span for the solid steel shaft shown in the figure, where a = 5 in, b = 15 in, da = 1.375 in, db = 2 in, and w = 180 lbf/in. da db k a W b The deflection at midspan for the solid steel shaft is in. d.
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- An object of weight Wis dropped onto the midpoint of a simple beam AB from a height h (see figure). The beam has a rectangular cross section of area A. Assuming that h is very large compared to the deflection of the beam when the weight PFis applied statically, obtain a formula for the maximum bending stress crniilx in the beam due to the falling weight.A simple beam with an overhang is subjected to d point load P = 6kN. If the maximum allowable deflect ion at point C is 0.5 mm, select the lightest W360 section from Table F-l{b) that can be used for the beam. Assume that L = 3 m and ignore the distributed weight of the beam.The cantilever beam ACE shown in the figure has FlexuraI rigidity EI = 2,1 x 106kip-in". Calculate the downward deflections Scand 8Sat points C and B, respectively, due to the simultaneous action of the moment of 35 kip-in. applied at point C and the concentrated load of 2,5 kips applied at the free end B.
- A cantilever beam A3, loaded by a uniform load and a concentrated load (sec figure), is constructed of a channel section. (a) Find the maximum tensile stresser, and maxi-mum compressive stress trcif the cross section has the dimensions indicated and the moment of inertia about the - axis (the neutral axis) is t = 3.36 in4. Note: The uniform load represents the weight of the beam. Find the maximum value of the concentrated load if the maximum tensile stress cannot exceed 4 ksi and the maximum compressive stress is limited to 14.5 ksi. How far from A can load P = 250 lb be positioned if the maximum tensile stress cannot exceed 4 ksi and the maximum compressive stress is limited to 14.5 ksi?A cantilever beam(Z, = 6 ft) with a rectangular cross section (/> = 3.5 in., h = 12 in.) supports an upward load P = 35 kips at its free end. (a) Find the state of stress ((7T, o^., and r in ksi) on a plane-stress element at L/2 that is i/ = 8 in. up from the bottom of the beam. Find the principal normal stresses and maximum shear stress. Show these stresses on sketches of properly oriented elements. (b) Repeat part (a) if an axial compressive centroidal load N = 40 kips is added at BA 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.
- Solve the preceding problem for a box beam with dimensions h = 0.5 m, h = 0.18 m, and t = 22 mm. The yield stress of the steel is 210 MPa.Each girder of the lift bridge (sec figure) is 180 ft long and simply supported at the ends. The design load for each girder is a uniform load of intensity 1,6 kips/ft. The girders are fabricated by welding three steel plates to form an I-shaped cross section (see figure) having section modulus S = 3600 in3. What is the maximum bending stress rmaxin a girder due to the uniform load?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 cantileverbeam^Cßsupportstwo concentrated loads Ptand A, as shown in the figure. Calculate the deflections SBand 8Cat points B and C, respectively. Assume Px= 10 kN, P\ = 5 kN, L = 2.6 m, E = 200 GPa, and / = 20.1 x I0ft mm4.Compound beam ABC is loaded by point load P = 1.5 kips at distance 2aB from point A and a triangularly distributed load on segment BC with peak intensity qü= 0.5 kips/ft. If length a = 5 ft and length/) = 10 ft, find the deflection at B and rotation at A. Assume that £ = 29,000 ksi and / = 53.8 in4.-1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities: The maximum shear stress tinixin the web. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^ The shear force carried in the web and the ratio V^tV. Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. 5.10-5 Wide-flange shape, W 18 x 71 (sec Table F-l, Appendix F); V = 21 k.