Research Article
Dynamic Responses of Continuous Girder Bridges with Uniform Cross-Section under Moving Vehicular Loads
Table 11
Various analysis of numerical simulation without interaction.
(a) Dynamic load allowance in the side span () |
| Factor | | dof | Initial | Modification | | | | | | |
| B | 0.8830 | 2 | 0.4415 | 11.01 | 0.10 | 0.4415 | 9.95 | 0.01 | C | 0.4764 | 2 | 0.2382 | 5.94 | 0.25 | 0.2382 | 5.37 | 0.05 | D | 0.3311 | 2 | 0.1656 | 4.13 | 0.25 | 0.1656 | 3.73 | 0.10 | E | 0.2776 | 2 | 0.1388 | 3.46 | 0.25 | 0.1388 | 3.13 | 0.10 | F | 0.1697 | 2 | 0.0848 | 2.12 | >0.25 | — | — | | G | 0.0237 | 2 | 0.0119 | 0.30 | >0.25 | — | — | | H | 0.5193 | 2 | 0.2596 | 6.48 | 0.25 | 0.2596 | 5.85 | 0.05 | I | 0.1290 | 2 | 0.0645 | 1.61 | >0.25 | — | — | | J | 0.3551 | 2 | 0.1775 | 4.43 | 0.25 | 0.1775 | 4.00 | 0.05 | K | 0.2684 | 2 | 0.1342 | 3.35 | 0.25 | 0.1342 | 3.02 | 0.10 | L | 0.0327 | 2 | 0.0163 | 0.41 | >0.25 | — | — | | M | 0.0121 | 2 | 0.0060 | 0.15 | >0.25 | — | — | | Error | 0.0802 | 2 | 0.0401 | | | 0.0444 | | | Sum | 3.5581 | 26 | | | | | | |
|
|
(b) Dynamic load allowance in the middle span () |
| Factor | | dof | Initial | Modification | | | | | | |
| B | 0.2762 | 2 | 0.1381 | 4.07 | 0.25 | 0.1381 | 2.36 | 0.25 | C | 0.8983 | 2 | 0.4492 | 13.23 | 0.10 | 0.4492 | 7.67 | 0.01 | D | 1.2312 | 2 | 0.6156 | 18.13 | 0.10 | 0.6156 | 10.52 | 0.01 | E | 0.6344 | 2 | 0.3172 | 9.34 | 0.10 | 0.3172 | 5.42 | 0.05 | F | 0.1002 | 2 | 0.0501 | 1.48 | >0.25 | — | — | | G | 0.3232 | 2 | 0.1616 | 4.76 | 0.25 | 0.1616 | 2.76 | 0.25 | H | 0.5709 | 2 | 0.2855 | 8.41 | 0.25 | 0.2855 | 4.88 | 0.05 | I | 0.3674 | 2 | 0.1837 | 5.41 | 0.25 | 0.1837 | 3.14 | 0.10 | J | 0.0934 | 2 | 0.0467 | 1.38 | >0.25 | — | — | | K | 0.1627 | 2 | 0.0814 | 2.40 | >0.25 | — | — | | L | 0.1598 | 2 | 0.0799 | 2.35 | >0.25 | — | — | | M | 0.1183 | 2 | 0.0592 | 1.74 | >0.25 | — | — | | Error | 0.0679 | 2 | 0.0340 | | | 0.0585 | | | Sum | 5.0039 | 26 | | | | | | |
|
|
(c) Vibration acceleration in the side span () |
| Factor | | dof | Initial | Modification | | | | | | |
| B | 0.0477 | 2 | 0.0239 | 16.99 | 0.10 | 0.0239 | 12.57 | 0.01 | C | 0.0135 | 2 | 0.0068 | 4.82 | 0.25 | 0.0068 | 3.57 | 0.10 | D | 0.1598 | 2 | 0.0799 | 56.92 | 0.05 | 0.0799 | 42.10 | 0.01 | E | 0.0531 | 2 | 0.0266 | 18.92 | 0.10 | 0.0266 | 13.99 | 0.01 | F | 0.0121 | 2 | 0.0061 | 4.31 | 0.25 | 0.0061 | 3.19 | 0.10 | G | 0.0069 | 2 | 0.0034 | 2.44 | >0.25 | — | — | | H | 0.0010 | 2 | 0.0005 | 0.37 | >0.25 | — | — | | I | 0.0181 | 2 | 0.0091 | 6.45 | 0.25 | 0.0091 | 4.77 | 0.05 | J | 0.0465 | 2 | 0.0232 | 16.56 | 0.10 | 0.0232 | 12.25 | 0.01 | K | 0.0114 | 2 | 0.0057 | 4.05 | 0.25 | 0.0057 | 2.99 | 0.25 | L | 0.0045 | 2 | 0.0022 | 1.60 | >0.25 | — | — | | M | 0.0249 | 2 | 0.0125 | 8.88 | 0.25 | 0.0125 | 6.57 | 0.05 | Error | 0.0028 | 2 | 0.0014 | | | 0.0019 | | | Sum | 0.4024 | 26 | | | | | | |
|
|
(d) Vibration acceleration in the middle span () |
| Factor | | dof | Initial | Modification | | | | | | |
| B | 0.3544 | 2 | 0.1772 | 30.63 | 0.05 | 0.1772 | 47.46 | 0.01 | C | 0.3096 | 2 | 0.1548 | 26.76 | 0.05 | 0.1548 | 41.46 | 0.01 | D | 0.5061 | 2 | 0.2531 | 43.74 | 0.05 | 0.2531 | 67.78 | 0.01 | E | 0.3331 | 2 | 0.1666 | 28.79 | 0.05 | 0.1666 | 44.61 | 0.01 | F | 0.0093 | 2 | 0.0046 | 0.80 | >0.25 | — | — | | G | 0.0115 | 2 | 0.0057 | 0.99 | >0.25 | — | — | | H | 0.0102 | 2 | 0.0051 | 0.88 | >0.25 | — | — | | I | 0.0315 | 2 | 0.0158 | 2.72 | >0.25 | 0.0158 | 4.22 | 0.05 | J | 0.0403 | 2 | 0.0202 | 3.48 | 0.25 | 0.0202 | 5.40 | 0.05 | K | 0.0012 | 2 | 0.0006 | 0.10 | >0.25 | — | — | | L | 0.0011 | 2 | 0.0006 | 0.10 | >0.25 | — | — | | M | 0.0402 | 2 | 0.0201 | 3.48 | 0.25 | 0.0201 | 5.39 | 0.05 | Error | 0.0116 | 2 | 0.0058 | | | 0.0037 | | | Sum | 1.6601 | 26 | | | | | | |
|
|
(e) Vibration acceleration of the vehicle body () |
| Factor | | dof | Initial | Modification | | | | | | |
| B | 1.3451 | 2 | 0.6726 | 12.43 | 0.10 | 0.6726 | 17.11 | 0.01 | C | 1.0364 | 2 | 0.5182 | 9.58 | 0.10 | 0.5182 | 13.18 | 0.01 | D | 0.8230 | 2 | 0.4115 | 7.60 | 0.25 | 0.4115 | 10.47 | 0.05 | E | 0.4458 | 2 | 0.2229 | 4.12 | 0.25 | 0.2229 | 5.67 | 0.05 | F | 0.6294 | 2 | 0.3147 | 5.81 | 0.25 | 0.3147 | 8.01 | 0.05 | G | 0.0936 | 2 | 0.0468 | 0.86 | >0.25 | — | — | | H | 5.4978 | 2 | 2.7489 | 50.79 | 0.05 | 2.7489 | 69.93 | 0.01 | I | 1.8752 | 2 | 0.9376 | 17.32 | 0.10 | 0.9376 | 23.85 | 0.01 | J | 0.9799 | 2 | 0.4899 | 9.05 | 0.10 | 0.4899 | 12.46 | 0.01 | K | 1.5926 | 2 | 0.7963 | 14.71 | 0.10 | 0.7963 | 20.26 | 0.01 | L | 0.8165 | 2 | 0.4082 | 7.54 | 0.25 | 0.4082 | 10.38 | 0.05 | M | 0.0340 | 2 | 0.0170 | 0.31 | >0.25 | — | — | | Error | 0.1082 | 2 | 0.0541 | | | 0.0393 | | | Sum | 15.2776 | 26 | | | | | | |
|
|