Astepped shaft abc consisting of two solid circular segments is subjected to torques t1 = 20,000 lb-in and t2 = 8,000 lb-in acting in opposite directions. the larger diameter of the shaft is d1 = 2.25 in, and the smaller diameter is d2 = 1.75 in. if the radius of curvature at the transition between the larger and smaller diameters is a quarter circle, calculate the maximum shear stress τmax in the shaft.

Acarpenter builds an exterior house wall with a layer of wood 2.9 cm thick on the outside and a layer of styrofoam insulation 2.3 cm thick on the inside wall surface. the wood has k=0.080w/(m⋅k), and the styrofoam has k= 0.010 w/(m⋅k). the interior surface temperature is 19.0 ∘c , and the exterior surface temperature is -15.0 ∘c . a.)what is the temperature at the plane where the wood meets the styrofoam? celsius b.)what is the rate of heat flow per square meter through this wall? /m^2