If the four shale layers in the sketch are clamped such that they deform as a single beam what is the maximum shear stress, and where does it occur in the clamped roof? In this regard, if the coefficient of friction between shale strata is 0.35, what bolting pressure is required to mobilize sufficient interlayer shear for monolithic roof beamaction?

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Surface Overburden E-10° psi (GPa) 7-pcf(kN/m³) h -in. (cm) R5 Shale 5 59(150) 8.0(55.2) 160(25.3) 1.0(6.90) 7(17.8) R4 Shale 4 135(2.14) 1.0(6.90) 135(2.14) 8(20.3) R3 Shale 3 1.0(6.90) 135(2.14) 10(25.4) R2 Shale 2 1.0(6.90) RI Shale I 135(2.14) 12(30.5) Seam FI Sandstone