A stepped shaft has the appearance shown in figure. The region AB is aluminum, having G 28 GPa, and the region BC is steel, having G 84 GPa. The aluminum portion is of solid circular cross section 45 mm in diameter, and the steel region is circular with 60-mm outside diameter and 30-mm inside diameter. Determine the maximum shearing stress in each material as well as the angle of twist at B where a torsional load of 4000 N. m is applied at B. Ends A and C are rigidly clamped.

The sum of the normal stresses does not change as the stress state rotates through an angle. a)-trune b)- false

Starting wih an energy balance on a rectangular volume element, derive the one- dimensional transient heat conduction equation for a plane wall with constant thermal conductivity and no heat generation.

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?