A W310 x 129 I-beam, made of A36 steel, is shown in the figure. This I-beam is 4 m long and has a distributed load and a concentrated load as shown 15 kN/m 20 AN in the figure. Determine the slope at point B and deflection at point C. OB = C Ac = 2 m 2m
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- A wide-flange member (W200 × 22.5) is compressed by axial loads that have a resultant P acting at the point shown in the figure. The member has modulus of elasticity E = 200 GPa and pinned conditions at the ends. Lateral supports prevent any bending about the weak axis of the cross section. If the length of the member is 6.2 m and the deflection is limited to 6.5 mm. what is the maximum allowable load Pallow.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.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 simple beam AB of length L and height h (see figure) is heated in such a manner that the temperature difference 7= T{between the bottom and top of the beam is proportional to the distance from support A: that is, assume the temperature difference varies linearly along the beam: T2- Tt= Tax in which 7"0 is a constant having units of temperature (degrees) per unit distance. Determine the maximum deflection SW9Xof the beam, Repeat for a quadratic temperature variation along the beam, so T2+T1= TaxThe tapered cantilever beam AB shown in the figure has a thin-walled, hollow circular cross sections of constant thickness t. The diameters at the ends A and B are dAand dB= 2dA, respectively. Thus, the diameter d and moment of inertia / at distance x from the free end are, respectively, in which IAis the moment of inertia at end A of the beam. Determine the equation of the deflection curve and the deflection 8 Aat the free end of the beam due to the load P.The cross section of a sand wie h beam consisting of aluminum alloy faces and a foam core is shown in the figure. The width b of the beam is 8.0 in, the thickness I of the faces is 0.25 in., and the height hcof the core is 5.5 in. (total height h = 6.0 in). The moduli of elasticity are 10.5 × 106 psi for the aluminum faces and 12.000 psi for the foam core. A bending moment M = 40 kip-in. acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams and (b) the approximate theory for sandwich beams.
- A cantilever beam AB having rectangular cross sections with varying width bxand varying height hxis subjected to a uniform load of intensity q (sec figure). If the width varies linearly with x according to the equation hx= bBxiL^ how should the height hxvary as a function of v in order to have a fully stressed beam? (Express hxin terms of the height hBat the fixed end of the beam.)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 simple beam ACB supports a uniform load of intensity q on the left-hand half of the span (see figure). Determine the angle of rotation ÔBat support B>(Obtain the solution by using the modified form of Castigliano's theorem.)
- The cantilever beam shown in the figure supports a triangularly distributed load of maximum intensity qü. Determine the deflection SBat the free end B. (Obtain the solution by determining the strain energy of the beam and then using Castigliano's theorem.)A simple beam AB of length L is loaded at the left-hand end by a couple of moment MQ(see figure). Determine the angle of rotation 0 , at support A. (Obtain the solution by determining the strain energy of the beam and then using Castigliano's theorem.)A hollow box beam with height h = 16 in,, width h = 8 in,, and constant wall thickness r = 0.75 LiL is shown in the figure. The beam is constructed of steel with yield stress ty = 32 ksi. Determine the yield moment My, plastic moment A/p, and shape factor.