4. Determine the maximum shear stress and maximum bending stress in the beam shown. Ans: Timmy= 5,36 impa 6.2 kN 3 kN/m W310 x 60 18 m e 18 m 0.9 m 0.9 m
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- 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 = 120 mm and h1= 100 mm. The maximum allowable bending stress in the plastic beam is emix = 6 M Pa, and the bending moment is M = 150 N · m. Determine the minimum permissible width bminof the beam.A simple beam with a W 10 x 30 wide-flange cross section supports a uniform load of intensity q = 3.0 kips/ft on a span of length L = 12 ft (sec figure). The dimensions of the cross section are q = 10.5 in., b = 5.81 in., t1= 0.510 in., and fw = 0.300 in. Calculate the maximum shear stress tjuly on cross section A—A located at distance d = 2.5 ft from the end of the beam. Calculate the shear stress rat point Bon the cross section. Point B is located at a distance a = 1.5 in. from the edge of the lower flange.
- A fixed-end b earn is subjected to a point load at mid-span. The beam has a rectangular cross section (assume that the h/b ratio is 2) and is made of wood (E = 11GPa). Find height h of the cross section if the maximum displacement of the beam is 2 mm. Calculate the displacement of the beam at the inflection points.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 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.
- 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 = 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 dimensionThe 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?
- 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,)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?Determine the plastic modulus Z and shape factor/for a W 12 x 14 wide-flange beam. Obtain the cross-sectional dimensions and section modulus of the beam from Table F-l(a) in Appendix F.