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ERHIBIT VI <br />PARACHUTE PIPELINE <br />STRESS MODEL <br />FOR <br />DORCHESTER COAL MINE <br />ASSUME: 1) The subsidence model shown below. In this model all <br />stresses and strains are caused by a displacement of one <br />of the ends. No unit .eight is assumed due to the fact <br />that the line was carrying any soil or fluid loadings <br />prior to the displacement, and the loading will not <br />change due to the displacement. <br />2) Pipe is 8.625", 0.250" W.T. X-52 Grade. <br />A <br />o : io.2 ~~ <br />-~ <br />B <br />,Q. 2 97. S -~ <br />From statically indeterminate beam analysis <br />ME = 2EI ~2 9B + 6A - 3~1 + M Fixed End <br />Due to the model shown above allows for no rotation at the ends, 8 = 0 <br />and the no unit loading allows MFE = 0 <br />(x8.62514 - x8.125141 <br />So for a cylinder I = ~ 12 J ` 12 J J = 2.784 R 10-3 FT4 <br />64 <br />Moment = 6EI~ = 6 (30 x 106) 144 (2.784 x 10-3) 10.2 = 8,315 Ft - #'s <br />12 (297.5)2 <br />08.6251 <br />Max. Bend Stress = 8.315 24 J = 1,073,349 ~/Ft2 = 7 455 ~/In2 <br />2.784 x 10_3 <br />(8.625 + 8.125 2 <br />A = ~ l 2 (12) ~_ .383 q = 8315 = 10,868 <br />4 2(.383) <br />