Question 10.6: A road bridge of seven equal span lengths crosses a 106 m wi......
A road bridge of seven equal span lengths crosses a 106 m wide river. The piers are 2.5 m thick, each with semicircular noses and tails, and their length:breadth ratio is 4. The streamflow data are given as follows: discharge = 500 m ^3 s ^{-1} ; depth of flow downstream of the bridge = 2.50 m. Determine the afflux upstream of the bridge.
The velocity at the downstream section, V_3=500 / 106 \times 2.5=1.887 \, m s ^{-1} \text {. } Therefore the Froude number, Fr _3= 0.381. Flow conditions within the piers are as follows: the limiting value of \sigma \simeq 0.55 (equation (10.14)),
\sigma=(2+1 / \sigma)^3 F_3^4 /\left(1+2 F r_3^2\right)^3 (10.14)
while the value of σ provided =b/B = 13/15.5 = 0.839. Since the value of σ provided is more than the limiting σ value, subcritical flow conditions exist between the piers. Using equation (10.12)
\Delta y / y_3=K F r_3^2\left(K+5 F r_3^2-0.6\right)\left(\alpha+15 \alpha^4\right) (10.12)
with K = 0.9 (Table 10.3) and α = 1 – σ = 0.161, the afflux, Δy = 5.41 × 10^{-2} m.
| Table 10.3 Values of K as a function of pier shape | ||
| Pier shape | K | Remarks |
| Semicircular nose and tail |
\left.\begin{array}{l} 0.9 \\ \\0.9 \\ \\ \\ \\ 0.95 \end{array}\right\} |
All values applicable for piers with length to breadth ratio equal to 4; conservative estimates of Δy have been found for larger ratios; |
| Lens-shaped nose and tail | ||
| Twin-cylinder piers with connecting | ||
| diaphragm | ||
| Twin-cylinder piers without diaphragm | \left.\begin{array}{l} 1.05 \\ \\1.05 \\ \\ \\ \\ 1.25 \end{array} \right\} | Lens-shaped nose is formed from two circular curves, each of radius to twice the pier width and each tangential to a pier face |
| 90° triangular nose and tail | ||
| Square nose and tail | ||