A cantilever beam is made by connecting two rods together. The left half, , of the beam has properties, , and , and the right half, , has properties, , and . The beam is subjected to a distributed load, and a horizontal load at the free end, P. The length of the beam is denoted as . Assume that the material is linear elastic and the beam follows the linear strain-displacement relation. The beam is fixed at Thus, it is with given boundary conditions, u(0)=w(0)=w^' (0)=0. The displacement field of the beam is assumed as:

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Coiled springs ought to be very strong and stiff. si3n4 is a strong, stiff material. would you select this material for a spring? explain.

Draw the engineering stress-strain curve for (a) bcc; (b) fcc metals and mark important points.