Consider a cantilever mass-less beam subjected to a concentrated mass at the tip of the beam. Assume, length L, flexural stiffness EI, and mass m.
a) Assume the mass is applied statically on the beam. Use Euler's beam theory to derive the beam deflection.
b) Assume the mass is released at once from zero height. Use energy equation to calculate the beam deflection.
c) For part b, use free vibrational response of a spring-mass system to derive the equation of motion as a function of time, i.e. time history of beam deflection.
d) Plot time histories of acceleration, velocity, and displacement for part c.
e) Use section c to proof part b.
f) Calculate maximum static and dynamic deflections of a 6-ft steel beam with 4-in by 6-in hollow section and 1/8-in thick walls, subject to 200 lbs weight.