# Fundamentals of Bridge Rating

Bridge rating is a continuous activity of the agency to ensure the safety of public. It provides information to repair, rehabilitate, post, close or replace the existing bridge.

### NEED:

If designed with AASTHO then the bridge has no problem as it has sufficient capacity. But if changes in a few details during construction phase, failure to attain the recommended concrete strength, unexpected settlements of the foundation after construction and unforeseen damage to a member could influence the capacity of the bridge.

Also live load capacity can be altered over time. Like old bridge are designed as per lighter vehicle and cannot withstand fully to the current live load carrying capacity to transport heavy machinery.

### Rating Principle

$Resistance (R) \geq Demand (Q)$ $R \geq Q_D + Q_L +\sum_{i}{Q_i}$ $Q_L \leq R – ( Q_D +\sum_{i}{Q_i})$

So to understand this inequality, rating factor (RF) is introduced with is the ratio between available capacity of the liveload to the rating vehicle load demand. From the above equation the rating factor equation is:

$RF=\frac{ R – ( Q_D +\sum_{i}{Q_i}) }{Q_L}$

If $RF \geq 1$, the bridge is capable of carrying the rating vehicle.

If $RF < 1$, then bridge may be over-stressed carrying the rating vehicle load.

### RF in LRFD

Since resistance and load effect cannot be established with certainty, engineers use safety factors to give adequate assurance against failure.

In ASD, safety factors are kept in the form of allowable stresses of material.

In LFD, safety factors are kept in the form of load factors to account for the uncertainity of the loadings and resistnace factors to account for the uncertainity of structural response.

In LRFD, safety factors are kept in the form of load and resistance factors that are based on the probability of loadings and resistances.

In LRFD, the rating equation is,

$RF=\frac{\phi R – \sum{\gamma_D \cdot D} -\sum_{n}{\gamma_{Li} \cdot L_i(1+I)} }{ \gamma_L \cdot L(1+I) }$

Here, $L_i$ is live load effect for load i, and I is the impact factor.

Effect of individual live loads vehicles on structural member could only be obtained by analyzing the bridge using a 3D analysis. Thus, obtaining the rating factor using the above expression is very difficult and time consuming. In order to simplify the calculation:

Assumption: Similar rating vehicles will occupy all the possible lanes to produce the maximum effect on structure.

This assumption allows us to use AASTHO liveload distribution factor approach to estimate the liveload demand and eliminate the need of 3D analysis.

### Simplified LRFD Rating Equation:

$RF=\frac{\phi R – \sum{\gamma_D \cdot D} }{ \gamma_L \cdot L(1+I) }$

Assumptions:

1. Resistance of member is independent to the loads.
2. In Beam-Column member, axial capacity or moment capacity depends upon the applied moment or applied axial load on member. Thus as liveload forces in the member increases, the capacity of the member would decrease. In other words, the numerator of the above equations (available live-load capacity) will drop as the live-load increases. Rating factor will no longer be a constant value but will be a function of liveload.

### Levels of Rating

 Inventory Operating Load that can be safely carried by the bridge for indefinite period Absolute maximum permissible load that can be safely carried by the bridge Life of bridge depends on fatigue life or serviceability limits of a bridge materials. Higher frequent loading and unloading may affect the fatigue life. To maintain a bridge for an indefinite period, liveload carrying capacity for frequent passing vehicles need to be estimated at service. This process is referred to as inventory rating. Less frequent vehicles may not affect the fatigue life, thus live load carrying capacity for less frequent vehicles need not to be estimated using serviceability criteria. In addition, since less frequent vehicles do not damage the bridge structure, bridge structure could be allowed to carry higher loads. This process is referred to as operating vehicles.

### Failure Mode

For ASD, no check is needed because material never exceed the yield stress. For LRFD, failure can occurs at two limit states:

a) Strength: When member load reaches ultimate capacity, it is considered to be failed at its ultimate strength limit state.

b) Serviceability: When structure reaches its maximum allowable serviceability limits, the structure is considered to be failed at its serviceability limit state.

LRFD approach: Satisfying one of the limit states will not automatically guarantee the satisfaction of other limit state. Thus BOTH serviceability and strength criteria needs to be checked.

For operating level: Serviceability limits needs not to be checked.

References:

 AASTHO Manual for Condition Evaluation of Bridges, 1994

 Wai-fah Chen, Lion Duan, Bridge Engineering Handbook