The steel beam has the cross section shown. The beam length is L = 17 ft, and the cross-sectional dimensions are d = 15.5 in., be = 10.7 in, tę = 0.635 in., and tw = 0.340 in. Calculate the maximum bending stress in the beam if wo = 4.7 kips/ft. Answer: Omax i ksi
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- A two-axle carriage that is part of an over head traveling crane in a testing laboratory moves slowly across a simple beam AB (sec figure). The load transmitted to the beam from the front axle is 2200 lb and from the rear axle is 3800 lb. The weight of the beam itself may be disregarded. Determine the minimum required section modulus S for the beam if the allowable bending stress is 17,0 ksi, the length of the beam is 18 ft, and the wheelbase of the carriage is 5 ft. Select the most economical I-beam (S shape) from Table F-2(a), Appendix F.A rectangular beam with notches and a hole (see figure) has dimensions h = 5.5 in., h1= 5 in., and width b = 1.6 in. The beam is subjected to a bending moment M = 130 kip-in., and the maximum allowable bending stress in the material (steel) is emax = 42,000 psi. What is the smallest radius Rminthat should be used in the notches? What is the diameter dmixof the largest hole that should be drilled at the mid height of the beam?A weight W = 20 kN falls through a height h = 1,0 mm onto the midpoint or a simple beam of length L = 3 m (see figure). The beam is made of wood with square cross section (dimension don each side) and E = 12 GPa. If the allowable bending stress in the wood is °aLLow =10MPa, what is the minimum required dimension
- 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 weight W = 4000 lb falls through a height h = 0.5 in, onto the midpoint of a simple beam of length L = 10 ft (see figure). Assuming that the allowable bending stress in the beam is = 18,000 psi and E = 30 x 10* psi, select the lightest wide-flange beam listed in Table F-l(a) in Appendix F that will be satisfactory.A 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 simple beam ACE is constructed with square cross sections and a double taper (see figure). The depth of the beam at the supports is dAand at the midpoint is dc= 2d 4. Each half of the beam has length L. Thus, the depth and moment of inertia / at distance x from the left-hand end are, respectively, in which IAis the moment of inertia at end A of the beam. (These equations are valid for .x between 0 and L, that is, for the left-hand half of the beam.) Obtain equations for the slope and deflection of the left-hand half of the beam due to the uniform load. From the equations in part (a), obtain formulas for the angle of rotation 94at support A and the deflection Scat the midpoint.The hollow box beam shown in the figure is subjected to a bending moment M of such magnitude that the flanges yield but the webs remain linearly elastic. (a) Calculate the magnitude of the moment M if the dimensions of the cross section are A = 15 in., A] = 12.75 in., h = 9 in., and ey =7.5 in. Also, the yield stress is eY = 33 ksi. (b) What percent of the moment M is produced by the elastic core?A hollow box beam with height h = 9.5 in., inside height/i, = 8.0 in., width? = 5,25 in., and inside width =4.5 in. is shown in the figure. Assuming that the beam is constructed of steel with yield stress ty= 42 ksi calculate the yield moment My, plastic moment MPand shape factor f.
- 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.)An overhanging beam ABC with a rectangular cross section has the dimensions shown in the figure. A weight W = 750 N drops onto end C of the beam. If the allowable normal stress in bending is 45 MPa, what is the maximum height h from which the weight may be dropped? (Assume E = 12 G Pa,)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.