Problem 6.3 (dimensioning of a shaft under torsion and bending): consider a cylindrical, solid transmission shaft working in torsion coupled with bending. the most loaded cross-section is subjected to a couple m having components mt , 0, mb along principal axes with mt denoting the torque component and mb the bending component; the magnitude of the couple is m = 10 kn · m. the allowable stress is σa = 50 mpa and an equivalent (von mises) stress is defined as σeq = √ σ2 + 4τ 2 where σ and τ respectively refer to the normal stress and shear stress acting on the cross-section. dimension the radius r of the shaft.

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)?