05: Derive expressions for the maximum slop and deflection of the cantilever beam shown in Figure (3) below. Then, for W=12 kN/m, and L =3.5 m, determine the slop and deflection at 2 m from point A. E=200 GN/m2 and the moment of inertia, I 190 x 10 m.
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- A simple beam AB of length L and height /; undergoes a temperature change such that the bottom of the beam is at temperature 7™, and the top of the beam is at temperature Tx(see figure). Determine the equation of the deflection curve of the beam, the angle of rotation 9Aat the left-hand support, and the deflection 8mjLXat the midpoint.Copper beam AB has circular cross section with a radius of 0.25 in. and length L = 3 ft. The beam is subjected to a uniformly distributed load w = 3.5 lb/ft. Calculate the required load P at joint B so that the total deflection at joint B is zero. Assume that£ = 16,000 ksi.The deflection curve for a cantilever beam AB (sec figure) is given by v=q0x2120LEI(10L210L2x+5Lx2x3) Describe the load acting on the beam.
- The cantilever beam ACB shown in the figure has moments of inertia /, and I{in parts AC and CB, respectively. Using the method of superposition, determine the deflection 8Bat the free end due to the load P. Determine the ratio r of the deflection 8Bto the deflection S:at the free end of a prismatic cantilever with moment of inertia /] carrying the same load. Plot a graph of the deflection ratio r versus the ratio 12 //L of the moments of inertia. (Let /, II- vary from I to 5.)A simply supported beam (E = 1600 ksi) is loaded by a triangular distributed load from A to C(see figure). The load has a peak intensity q0= 10 lb/ ft, and the deflection is known to be 0.01 in, at point C. The length of the beam is 12 ft, and the ratio of the height to the width of the cross section is (h:b) 2:1, Find the height h; and width h of the cross section of the beam.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= Tax
- A cantilever beam JA of length Land height/; (see figure) is subjected to a temperature change such that the temperature at the top is 7[ and at the bottom is 7. Determine the equation of the deflection curve of the beam, the angle of rotation BBat end and the deflection 8Bat end B,Compound beam ABC is loaded by point load P = 1.5 kips at distance 2aB from point A and a triangularly distributed load on segment BC with peak intensity qü= 0.5 kips/ft. If length a = 5 ft and length/) = 10 ft, find the deflection at B and rotation at A. Assume that £ = 29,000 ksi and / = 53.8 in4.Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses Jt(and k2^ and the beam has flexural rigidity EI. What is the downward displacement of point C, which is at the midpoint of the beam, when the moment MQis applied? Data for the structure are M0 = 7.5 kip-ft, L = 6 ft, EI = 520 kip-ft2, kx= 17 kip/ft, and As = 11 kip/ft. Repeat part (a), but remove Af0 and instead apply uniform load q over the entire beam.
- The cantilever beam ACB shown in the figure supports a uniform load of intensity q throughout its length. The beam has moments of inertia I2and IYin parts AC and CB, respectively. Using the method of superposition, determine the deflection SBat the free end due to the uniform load. Determine the ratio r of the deflection 6Bto the deflection 3Xat the free end of a prismatic cantilever with moment of inertia /] carrying the same load. Plot a graph of the deflection ratio r versus the ratio 12 //t of the moments of inertia. (Let 7, tlxvary from I to 5.)-5 Calen1ate the deflections S 3a ndA simple beam AB of length L is subjected to loads that produce a symmetric deflection curve with maximum deflection S at the midpoint of the span (see figure). How much strain energy U is stored in the beam if the deflection curve is (a) a parabola and (b) a half wave of a sine curve?