## 480

a Limit not intended to safeguard against ponding. Ponding should be checked by suitably calculating deflection, including added deflections due to ponded water, and considering long-term effects of all sustained loads, camber, construction tolerances, and reliability of provisions for drainage.

b Long-term deflection has to be determined, but may be reduced by the amount of deflection calculated to occur before attachment of nonstructural elements. This reduction is made on the basis of accepted engineering data relating to time-deflection characteristics of members similar to those being considered.

c Ratio limit may be lower if adequate measures are taken to prevent damage to supported or attached elements, but should not be lower than tolerance of nonstructural elements.

AASHTO permissible deflection requirements, shown in Table 8.13, are more rigorous because of the dynamic impact of moving loads on bridge spans.

### 8.8.3.1 Approximate Time-Steps Method

The approximate time-steps method is based on a simplified form of summation of constituent deflections due to the various time-dependent factors. If Cu is the long-term creep coefficient, the

Type of member |
Deflection considered |
Maximum permissible deflection Vehicular traffic only Vehicular and pedestrian traffic |

Simple or continuous spans Cantilever arms |
Instantaneous due to service live load plus impact |
1/800 1/1000 1 /300 1 /375 |

curvature at effective prestress Pe can be defined as

Ve EcIc Vi ^ EcIc V 2 J EcIcCu The following expression can predict the time-dependent increase in deflection Ad:

Ct = creep coefficient at time t

Ka = factor corresponding to age of concrete at superimposed load application = 1.25t-0118 for moist-cured concrete = 1.131-0 095 for steam-cured concrete t = age, in days, at loading kr = 1/(1 + As/Aps) when As/Aps < 1.0 ffi 1 for all practical purposes

For the final deflection increment, Cu is used in place of Ct in Equation 8.96. For noncomposite beams, the total deflection dT,t becomes [4]

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