Consider a rectangular entry 12 ft high and 22 ft wide that is driven at a depth of 950 ft. The immediate roof layer which is 2.25 ft thick separates from the layers above. Layer properties are E = 3.7 × 106 psi, ν = 0.28, γ = 134pcf, To = 690 psi. Find the maximum tensile stress σt , maximum sag w max and safety factor with respect to tensile failure Ft if

(a) The roof ends are simply supported and

(b) The ends are built-in.