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,~ <br />Layer No. 3 is the thickest of the three roof units considered <br />in this analysis and is a sandstone. Once again, the friction rein- <br />forcement affects a decrease in bending stresses of 168 to 250. HOW- <br />ever, since the sandstone unit is the thickest and stiffest of the <br />three considered, the effect of suspension is to actually increase <br />the bending stresses in this stiff sandstone layer. The effect of <br />suspension is to increase the bending stresses by something on the <br />order of 350. The net effect of combined friction and suspension in <br />this layer is a slight increase in bending stress of from 28 to 158. <br />This same data has been represented in another form in Table <br />No. 3. This table indicates a factor of safety against failure for <br />each layer and each roof span condition, as well as indicating changes <br />in factor of safety for different types of roof reinforcement and <br />support. For purposes of this table, the factor of safety is defined <br />as the modulus of rupture for that material divided by the theoretical <br />bending stresses in that layer. In this table it may be seen that <br />for consideration of friction effects only, the lowest and thinnest <br />of the rock strata are associated with the lowest factors of safety. <br />The thin shale layer immediately above the coal, in fact, does indicate <br />a factor of safety less than 1, which would imply a failure condition. <br />In the case of suspension effects only, stress conditions are, in <br />effect, reversed. The highest factors of safety are associated with <br />the thinner lower strata which are now transferring stress into the <br />upper, thicker layer causing a substantial reduction in the factors <br />of safety there. This would imply that under the effects of suspension <br />only, failure would initiate in the sandstone layer well up into the <br />roof material. In realtiy, if a tension failure were to initiate in <br />this upper sandstone layer, we would not anticipate that any significant <br />7 <br />