Find the shear force and bending moment at point C. 500 lb/ft 900 lb-ft A -3 ft Answer: Vc = 0 Mc = 8.10 kip-ft 6 ft- C 6 ft- B 900 lb-ft -3 ft-
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- A frame ABCD is constructed of steel wide-flange members (W8 x 21; E = 30 x ID6 psi) and subjected to triangularly distributed loads of maximum intensity q0acting along the vertical members (see figure). The distance between supports is L = 20 ft and the height of the frame is h = 4 ft. The members are rigidly connected at B and C. Calculate the intensity of load q0 required to produce a maximum bending moment of 80 kip-in. in the horizontal member BC. If the load q0 is reduced to one-half of the value calculated in part (a), what is the maximum bending moment in member BC? What is the ratio of this moment to the moment of 80 kip-in. in part (a)?A hollow steel box beam has the rectangular cross section shown in the figure. Determine the maximum allowable shear force K that may act on the beam if the allowable shear stress is 36 MPa. cA rectangular beam with semicircular notches, as shown in part b of the figure, has dimensions h = 0,88 in. and h1 = 0.80 in. The maximum allowable bending stress in the metal beam is emax = 60 ksi, and the bending moment is M = 600 lb-in. Determine the minimum permissible width bminof the beam.
- A wood box beam is constructed of two 260 mm × 50 mm boards and two 260 mm × 25 mm boards (sec figure). The boards are nailed at a longitudinal spacing. b = 100 mm. If each nail has an allowable shear force F = 1200 N. what is the maximum allowable shear force Vmax?The T-beam shown in the figure has cross-sectional dimensions: b = 210 mm, t = 16 mm, h = 300 mm, and A, = 280 mm. The beam is subjected to a shear force V = 68 kN. Determine the maximum shear stress tntijlin the web of the beam.The shear stresses t in a rectangular beam arc given by Eq. (5-43): in which Fis the shear force, / is the moment of inertia of the cross-sectional area, /lis the height of the beam, and i] is the distance from the neutral axis to the point where the shear stress is being determined (Fig. 5-32). By integrating over the cross-sectional area, show that the resultant of the shear stresses is equal to the shear force V.
- Two W 310 × 74 Steel wide-flange beams are bolted together to form a built-up beam as shown in the figure. What is the maximum permissible bolt spacing s if the shear force V = 80 kN and the allowable load in shear on each bolt is F = 13.5 kN. Note: Obtain the dimensions and properties of the W shapes from Table F-l(b).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 cant i levé r b ea m i s supported by a tie rod at B as shown. Both the tie rod and the beam are steel with E = 30 x 106 psi. The tie rod is just taut before the distributed load q = 200 lb/ft is applied. Find the tension force in the tie rod. Draw shear-force and bending-moment diagrams for the beam, labeling all critical ordinates.
- A thin-walled rectangular tube has uniform thickness t and dimensions a x b to the median line of the cross section (see figure). How does the shear stress in the tube vary with the ratio = a/b if the total length Lmof the median line of the cross section and the torque T remain constant? From your results, show that the shear stress is smallest when the tube is square (ß = 1).The three beams shown have approximately the same cross-sectional area. Beam 1 is a W 14 X 82 with flange plates; beam 2 consists of a web plate with four angles; and beam 3 is constructed of 2 C shapes with flange plates. Which design has the largest moment capacity? Which has the largest shear capacity? Which is the most economical in bending? Which is the most economical in shear? Assume allowable stress values are: = 18 ksi and ra=11 ksi. The most economical beam is that having the largest capacity-to-weight ratio. Neglect fabrication costs in answering parts (c) and (d) above. Note: Obtain the dimensions and properties of all rolled shapes from tables in Appendix F.A circular pole is subjected to linearly varying distributed force with maximum intensity t0. Calculate the diameter daof the pole if the maximum allowable shear stress for the pole is 75 M Pa.