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Bulkhead Design for AMD Page 9 <br />Moment of inertia (in') = bz~ <br />b = beam width (in) <br />L = beam depth (bulkhead length) (in) <br />Centroidal distance (in) = z <br />Therefore, allowable flexural stress (ft) in psi is <br />_ M~ _ Mu _ M~ _ 6M~ <br />f ~1 S 1 oL~ bL~ <br />Cz) <br />LZ = 6M~ <br />blfil <br />(11) <br />(12~ <br />(13) <br />Required length (L).of plain concrete bulkhead, obtained by solving <br />equation (13) for the beam depth (L), the bulkhead length, is <br />presented for the Ransom Tunnel Bulkhead in Appendix A. The length <br />of the bulkhead can be decreased by the use of tensile <br />reinforcement, provided the plain concrete bulkhead is longer than <br />needed to limit the hydraulic pressure gradient to an acceptable <br />level. Normally a trial bulkhead length is selected and the <br />reinforcement required to support the tensile bending stress <br />calculated. <br />Reinforced Concrete Deen Beam BendincT Stress Design <br />The length of an alternative reinforced plain concrete <br />bulkhead depends on providing sufficient reinforcing steel to <br />support the entire tensile bending stress developed in the deep <br />beam bulkhead. The ACI capacity reduction factor for bending of a <br />reinforced concrete deep beam (ACI 318-95, Section 9.3.2.1) is <br />0.90. The method employs the rectangular compressive stress <br />distribution approximation. The ACI method is described in Section <br />10.2, for a reinforced simple concrete beam and Section 10.7 for <br />deep beams. These ACI Sections define a simple, simply supported, <br />deep beam as one whose depth exceeds 4/5 the span. ACI defines a <br />reinforced continuous concrete beam as a deep beam if the depth <br />exceeds 2/5 the span. A bulkhead that can rotate at its supports, <br />a simply supported beam, would be unlikely to be able to retain a <br />fluid. The recommended low-pressure grouting is designed to fix <br />the roof, walls and floor of the bulkhead, preventing rotation. In <br />the case of the 10-foot width of the Ransom Tunnel Bulkhead design <br />in Appendix A, the 8-foot thick bulkhead is a deep beam for design <br />in either case. <br />October 27-29, 1998 <br />- 9 - <br />