Consider a rectangular entry 3.66 m high and 6.71 m wide that is driven at a depth of 290 m. The immediate roof layer which is 0.69 m thick separates from the layers above. Layer properties are E = 25.52GPa, ν = 0.28, γ = 21.2kN/m3, To = 4.7 MPa. 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.