REINFORCED DESIGN

At 117.00 feet (First Pier):

M_{L L} = (1.208) (0.773) (- 1757.8 k - f t) = - 1641.4 k - f t

M_{S D L} = (0.176) (- 2129.3 k - f t) = - - 355.6 k - f t

M_{u} = 1.3 (- 355.6 + 1.67 (- 1641.4)) = - 4025.5 k - f t

$d = 80.50 i n - 0.5 i n - \frac{8.00 i n}{2} = 76.00 i n$

1.2*Mcr (Art. 8.17.1.1)

- 7.5 \sqrt{3500} = - 443.7 p s i

M_{c r} = \frac{(55882.7 {i n}^{3}) (- 443.7 l b / {i n}^{2})}{\frac{12000 l b - i n}{k - f t}} = 2066.29 k - f t

1.2 M_{c r} = (1.2) (- 2066.29 k - f t) = - 2479.55 k - f t

R_{u} = \frac{M_{u}}{ϕ b d^{2}} = \frac{(402.5 k - f t) (12000 \frac{l b - i n}{k - f t})}{(0.90) (26.00 i n) {(76.50 i n)}^{2}} = 325.75 p s i

ρ = \frac{1}{m} (1 - \sqrt{(1 - \frac{2 m R_{n}}{f_{f}})})

where:

m = \frac{f_{y}}{0.85 {f `}_{c}} = \frac{60 k s i}{0.85 \times 6.00 k s i} = 11.76

ρ = \frac{1}{11.76} (1 - \sqrt{(1 - \frac{2 \times 11.76 \times 325.75}{60000})}) = 0.006099

Ast = (0.006099)(26.00 in)(76.50) = 12.13 in²