360X79 wide-flange section and is such that ced load P = 10 kN and to the couple moment at is the bending moment just to the right of
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- 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 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 deflection curve for a simple beam AB (sec figure) is given by v=q0L44EIsinxL Describe the load acting on the beam. Deter mine the reactions RAand RBat the supports, Determine the maximum bending moment Mmax.
- .20 Determine the plastic moment Mpfor beam having the cross section shown in the figure ey=210 MPa.The cross section of an unbalanced wide-flange beam is shown in the figure. Derive the following formula for the distance e from the centerline of the web to the shear center S: Also, check the formula for the special cases of a channel section (by= 0 and b2= b) and a doubly symmetric beam (6 = b2= bf2).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?
- 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.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.An overhanging beam ABC is subjected to a couple MAat the free end (see figure). The lengths of the overhang and the main span are a and L, respectively. Determine the angle of rotation 04and deflection S4at end A. (Obtain the solution by using the modified form of Castigliano's theorem.)
- 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.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 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?