Analysis of Flexural Failure

For the ultimate limit state conditions, the stress block given in Fig. 5.28 is adopted. The general flexural theory may be modified to include tendon strain pb at ultimate conditions which is made up of the two parts, namely ps, the effective tendon prestress after losses as dictated earlier, and the additional strains pa = ece + u, as shown later on. The value of ce= (l/Fc)x the concrete prestress at the tendon level and the value of is the average concrete strain at the level of the tendon at ultimate conditions. This of course is true for a bonded tendon. For an unbonded tendon pa is always less than the algebraic sum of Sce and u. In general pa is written as 

For bonded tendon in the vessel mi=m2= 1. In the examples chosen where unbonded tendons are used, the values of mi and m2 are assumed to be 0.5 and 0.25, respectively, as are normally assumed for heavy beams and slabs. 

For the limit state flexural analysis of the barrel wall. Fig. 5.28 shows one-half of the barrel wall. The equations of equilibrium of forces on the wall have been computed and are given below. The axial force F v on segment 29 is then related as 

Since F is a function of Pq for iterative solutions on the computer, it will be convenient to separate constant terms from the F l and Pq dependent terms. 

Equation (5.42a) can be used directly for the HTGCR and Hartlepool vessels. For the Dungeness B and Oldbury vessels, equation (5.42a) is reduced to 

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