P1: A cantilevered beam of constant El and length L is loaded with distributed load w. Determine eflection at the free end of the beam.

A beam 19 ft in length has concentrated live loads of 6 kips and 9 kips at 5 ft and 13 ft, respectively, from the left-hand support. In addition, there is a uniformly distributed dead load of 1.2 kips/ft beginning 5 ft from the left support and continuing to the right support. Design the beam for flexure.

Only have to answer part E

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)