Given the geologic column, strata depths and rock properties in Table 5.8, find:

(a) The maximum possible roof span when mining the lower coal seam full height,

(b) The safe roof span, if a safety factor of 4 with respect to tension is required,

(c) The factor of safety of the massive sandstone (M.S.) roof layer above the sandy shale when the layer below is at maximumspan.

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E-106 psi (Gpa) Rock type Co-psi (Mpa) h-ft (m) To-psi (Mpa) Y-pef (kNim?) 50 (0.34) 850 (5.86) I Over-burden 1694 (516) 1714 (522) 144.0 (22.8) 148.2 (23.4) 1.70 (I1.7) 0.25 3.00 (20.7) 0.20 1,000 (6.9) 19,000 (131.0) 2 Massive Sandstone 75.0 (11.9) 3 Coal 1719 (524) 1741 (531) 0.30 3,500 (24.1) 149.5 (23.6) 1.50 (10.3) 0.10 17,500 (120.7) 700 (4.83) 0.35 (2.4) 130 (0.90) 4 Layered sandstone 5 Massive sandstone 1744 (532) 148.2 (23.4) 3.00 (20.7) 0.20 19,000 (131.0) 850 (5.86) 6 Sandy shale 7 Coal 8 Massive sandstone 170.0 (26.9) 75.0 (I1.9) 148.2 (23.4) 4.50 (31.0) 0.10 0.30 0.35 (2.4) 3.50 (24.1) 0.20 15,000 (103.4) 3,500 (24.1) 19,500 (134.5) 1,000 (6.90) 1,300 (8.97) 1,000 (6.90) 1747 (533) 1754 (535) 1778 (542) 9 Layered sandstone 2250 (658) 149.5 (23.6) 1.50 (10.3) 0.10 17,500 (120.7) 700 (4.83)