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- Problem 1: (Please solve parts A and B of problem) A) A uniformly distributed load is subjected on the clamped-clamped beam and it is supported by a spring in the middle of the beam. Using Castigliano’s theorem, find the deflection in the spring. (Please use only Castigliano’s theorem to solve this part) B) Remove the spring in part A and use the Rayleigh-Ritz method to solve for the deflection at the middle of the beam. Assume that v(x) = C (1- Cos((2Pi*x)/L)) (Please use only Rayleigh-Ritz method for this part)Three extension springs are hooked in series and supports a weight of 70 kg. One spring has a rate of 0.209 kg ∕mm and the other two have equal spring rate of 0.643 kg ∕mm. Find the deflection.A cantilever of length 2 m carries a uniformly distributed load of 1.5 kN/m run over the whole length and a point load of 2 kN at a distance of 0.5 m from the free end. Draw the S.F. and B.M. diagrams for the cantilever beam.
- A cantilever of length 2.0 m carries a uniformly distributed load of 2 kN/m length over the whole length and a point load of 3 KN at the free end. Draw the S.F. and B.M. diagrams for the cantilever beam.A beam with a uniform load has a sliding support at one end and spring support at the other. The spring has a stiffness k = 48EI / L3. Derive the equation of the deflection curve by starting with the third-order differential equation (the shear-force equation). Also, determine the angle of rotation θB at support B.A simply supported beam of 6 m length with external diameter 150 mm and thickness15 mm has maximum deflection 4.25 mm at the centre. Calculate the uniformlydistributed load carried over by the beam. Take E=210 kN/mm2
- Determine the maximum upward and downward deflection and the rotation of the support on the left side of the beam shown in Figure 2. (F = 4kN; L = 8m) a) Use a second order differential equation. b) Use the moment area theorems to verify your answers.The deflection angles of two intermediate points R and S on the curve measured from the tangent passing through the P.C. are 6o15’ and 12o15’ respectively. The chord distance between R and S is 20 m. while the long chord is 100 m. meters long. Compute the radius of the curve Compute the angle of intersection of the simple curve. Compute the tangent distanceFind the deflection of the beam in the middle of AB using the Castigliano method.
- Find the equation of deflection of the beam of length 1, with point charges, w0 located at 1/4 of the length, and load w1 located at 1/2 of the length.A spring sustains 200 ft-lb of energy with a deflection of 3’’. Assume that the mean coil diameter is 7 times the wire diameter and that the allowable stress is 100ksi. Determine the wire diameter.A simply supported beam of length “L” is subjected to linearly varying load distribution. The magnitude of the left end of the linearly varying load distribution is Zero and the magnitude of the right end of the linearly varyingload distribution is Q. Draw the shear force diagram (SFD) and bending moment diagram (BMD) over the span length and also find the magnitude of maximum bending moment and its position.