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Bulkhead Design for AMD Page 11 October 27-29, 1998 <br />M„ = Asfy~ (L-m~) - z ~ = 60000A5~ (L-m~) (12 ) - 1.96078 zs ~ in•lb <br />M„ = 60000A5[(L-m~)12-0.98039A5] in•lb (18) <br />The design flexure resisting bending moment is: <br />M„ _ ~ = 60000AS[(L-m~)12-0.98039AsJ in•lb (19) <br />The solution for reinforcing steel area per foot of the one-way <br />beam from rib to rib requires equating Equation 19 to the bending <br />moment resulting from factored load. The nominal maximum bending <br />moment is M„ = wee ft~lb, as calculated by Equation 7. However, the <br />strength factor (~) for the steel tensile reinforcement is 0.90 <br />and the factored bending moment from loading becomes: <br />w~ <br />w„ ~iQ~ ft•1b (20) <br />Therefore, the minimum required steel area per foot (AS) is <br />calculated from equating Equation 19 and Equation 20. <br />The design bulkhead thickness typically required to prevent <br />leakage due to the hydraulic pressure gradient and to resist the <br />perimeter shear forces makes the use of a simple beam design for <br />bending of a possibly fixed-end beam extremely conservative. The <br />bending deformations causing appreciable reinforcing steel strain, <br />and therefore tensile stress, will not be linear due to the <br />bulkhead thickness and the lateral restraint provided by the tunnel <br />ribs. Bulkhead failure would most likely occur by concrete <br />yielding of a pressure arch that would develop in the. upstream <br />side, rather than as the result of yielding of the reinforcing <br />steel. Reinforcing steel is required at both the downstream and <br />upstream bulkhead faces to control temperature and shrinkage <br />induced stresses in the large bulkhead pour. <br />Critical Section Shear <br />ACI requires evaluation of critical section shear if the ratio <br />of the bulkhead span (Q) divided by the distance (d) from the <br />upstream bulkhead face to the centroid of the reinforcing steel <br />Ce~ is less than 5 (ACI 318-95, Section 11.8.1). This appears to <br />always be the case for bulkheads that meet the pressure gradient <br />requirement. This evaluation is very complex and has not been <br />critical to bulkhead design. An example of the critical section <br />shear evaluation method is presented in Appendix A. <br />- 11 - <br />