problem 1) Water weights 9790 N/m^{3} and Concrete weights 23.5 kN/m^{3}. Coefficient of friction between dam and foundation is 0.55. Find out the factors of safety against sliding and against overturning, and also soil pressure at heel and toe. Suppose hydrostatic uplift differs uniformly from full hydrostatic head at heel of dam to zero at toe. Let 1m length of dam.
problem 2) Let the cantilever mass-less beam subjected to the concentrated mass at a tip of beam. Suppose, flexural stiffness EI, length L, and mass m.
i) Suppose mass is applied statically on beam. Deduce beam deflection by using Euler’s beam theory.
ii) Suppose mass is released at once from zero height. Compute the beam deflection by using energy equation.
iii) For part b, deduce the equation of motion as the function of time that is time history of beam deflection by using free vibrational response of the spring-mass system.
iv) Design time histories of acceleration, velocity, and displacement for part c.
v) Proof part b by using section c.
vi) Compute maximum static and dynamic deflections of the 6-ft steel beam with 4-in by 6-in hollow section and 1/8-in thick walls, subject to 200 lbs weight.