Use this simple rock movements calculation tool helps to compute the deflection due to moment for your hydraulics and waterworks problems. If the ends of the arch elements are vertical, and the bases of the cantilever elements, horizontal, rock rotations and deflections of elements with parallel sides 1 ft apart may be calculated by the formula: γ" = (M * K5) / (Er * t).
| Values of K | |||||
| Values of b/a | K1 | K2 | K3 | K4 | K5 |
| 1.0 | 4.32 | 0.62 | 1.02 | 4.65 | 0.345 |
| 1.5 | 4.65 | 0.78 | 1.23 | 4.80 | 0.413 |
| 2.0 | 4.84 | 0.91 | 1.39 | 5.18 | 0.458 |
| 3.0 | 5.04 | 1.10 | 1.60 | 5.64 | 0.515 |
| 4.0 | 5.15 | 1.25 | 1.77 | 5.90 | 0.550 |
| 5.0 | 5.22 | 1.36 | 1.89 | 6.08 | 0.574 |
| 6.0 | 5.27 | 1.47 | 2.00 | 6.20 | 0.592 |
| 8.0 | 5.32 | 1.63 | 2.17 | 6.37 | 0.614 |
| 10.0 | 5.36 | 1.75 | 2.31 | 6.46 | 0.630 |
| 15.0 | 5.41 | 1.98 | 2.55 | 6.59 | 0.653 |
| 20.0 | 5.43 | 2.16 | 2.72 | 6.66 | 0.668 |
Formula:
γ" = (M × K5) / (Er × t)
where,- M - Arch and cantilever moments
- K5 - Poisson’s ratio constants
- Er - Elastic modulus of the rock
- t - Radial thickness of the element
- γ" - Deflection Due to Moment