AASHTO Limit States and Load Modifiers

1. The Four Limit States: Defining the Boundaries of Performance

In LRFD, a limit state is formally defined as "a condition beyond which a bridge or component ceases to satisfy the provisions for which it was designed." Simply put, it's a failure mode, but "failure" can mean anything from catastrophic collapse to excessive vibration that alarms the public. The LRFD specifications group these conditions into four distinct categories to ensure the design is checked for safety, durability, and serviceability.

To get a comprehensive overview of these four limit states and the engineering concerns associated with each, please watch the following segment from an AISC presentation.

As you saw, each limit state addresses a different aspect of the bridge's performance over its life. Now, let's look at each one more formally, as they are presented within the context of AASHTO load combinations.

2. A Deeper Look at Each Limit State

The following sections will refer to the AISC Steel Bridge Design Handbook chapter on "Loads and Load Combinations," a resource we briefly touched upon in our last lesson. It provides excellent, concise descriptions of the purpose behind the various load combinations associated with each limit state.

Strength Limit State

The Strength Limit State is arguably the most critical. It ensures the bridge has adequate strength and stability to resist the statistically largest load combinations it is expected to encounter over its 75-year design life. At this limit state, extensive structural damage may occur, but the primary goal is to prevent collapse and maintain overall structural integrity.

As you've read, the different Strength combinations cover various scenarios:

• Strength I: This is the primary and most frequently used combination. It represents normal vehicular use without significant wind.
• Strength II: Used for owner-specified permit vehicles. It has a lower live-load factor because the loading event is more controlled than random traffic.
• Strength III: Checks the structure for design wind loads, assuming no significant live load is present.
• Strength IV: A special check for very long-span bridges where the dead load is exceptionally high compared to the live load. It provides an extra safeguard by increasing the dead load factor.
• Strength V: Represents a combination of normal vehicular live load with a moderate wind speed.

For a typical highway overpass, Strength I will almost always govern the design of the main members.

Service Limit State

The Service Limit State addresses the day-to-day performance of the bridge under normal operational loads. It is not about strength but about durability and public perception. The checks are intended to prevent issues like:

• Excessive deflections or vibrations that might alarm users.
• Permanent deformations from heavy vehicle loads that could impair ride quality.
• Excessive cracking in the concrete deck that could compromise durability.

Unlike the Strength limit states, which are calibrated to a target reliability index, the Service limit states are often calibrated to match satisfactory performance observed in past designs.

For steel trapezoidal tub girders, two service combinations are particularly important:

• Service I: Primarily used for optional live load deflection checks and to control cracking in the concrete deck.
• Service II: This is a crucial check for steel structures. It controls permanent deformations in the steel flanges from localized yielding and is also used to prevent slip in slip-critical bolted connections under vehicular live load. We will apply this check extensively later in the course.

Fatigue and Fracture Limit State

The Fatigue and Fracture Limit State is intended to prevent crack growth under the repetitive stress cycles from daily traffic. This is fundamentally different from the Strength limit state, which considers a single application of a maximum load. Fatigue is caused by many millions of passages of much lighter, everyday trucks. The "Fracture" part of the limit state refers to material toughness requirements to ensure the steel is not susceptible to brittle fracture.

The key concepts here are:

• Fatigue I: Used to check for "infinite" fatigue life. If a detail satisfies this limit, it is considered to have enough fatigue resistance to last indefinitely without cracking.
• Fatigue II: Used to check for "finite" fatigue life. This is applied when the traffic volume is low enough that infinite life is not required. The detail is checked to ensure it can withstand the predicted number of cycles over the bridge's 75-year design life.

Extreme Event Limit State

The Extreme Event Limit State is intended to ensure the bridge can survive rare but catastrophic events like earthquakes, vessel or vehicle collisions, and scour from major floods. Because these events have a very low probability of occurring, the design philosophy accepts a higher level of risk and potential for damage than for the Strength limit state. The primary goal is to prevent total collapse and preserve life safety.

These checks are often most critical for the bridge substructure (piers, abutments) but can also influence the design of bearings and superstructure connections.

3. The Load Modifier, η (eta)

Now, let's address the final component of the LRFD equation's load side: ${\eta }_i$. The load modifier adjusts the factored loads based on three system-level properties of the bridge: Ductility, Redundancy, and Operational Importance.

It is calculated as:

Where:

• ${\eta }_D$ is the modifier for ductility.
• ${\eta }_R$ is the modifier for redundancy.
• ${\eta }_I$ is the modifier for operational importance.

The logic is to penalize less desirable systems and reward more robust ones.

As the reading explains, the factors are applied as follows:

• Ductility (${\eta }_D$):

  • For conventional designs that meet all AASHTO requirements for ductile detailing, ${\eta }_D=1.0$.
  • For structures with non-ductile components, a penalty is applied (${\eta }_D\ge 1.05$). This increases the load side of the equation, requiring a stronger member.
  • A reward can be applied for exceptional ductility (${\eta }_D=0.95$).

• Redundancy (${\eta }_R$):

  • This is particularly relevant to our course. Redundancy refers to the ability of a bridge to carry load after one of its primary members has failed.
  • For non-redundant members, where failure could lead to collapse, a penalty is applied (${\eta }_R\ge 1.05$). A two-girder system, like many tub girder bridges, is typically considered non-redundant.
  • For conventional levels of redundancy (e.g., a multi-girder I-beam bridge), ${\eta }_R=1.0$.
  • For exceptional levels of redundancy, a reward is given (${\eta }_R=0.95$).

• Operational Importance (${\eta }_I$):

  • This is determined by the owner. If a bridge is on a critical route for defense or emergency services, the owner may classify it as operationally important.
  • For important bridges, a penalty is applied (${\eta }_I\ge 1.05$).
  • For typical bridges, ${\eta }_I=1.0$.

In practice, as the reading notes, for most standard bridges designed according to the AASHTO specifications, each factor is taken as 1.0, resulting in ${\eta }_i=1.0$. However, for a two-girder tub bridge, it is common for an owner to specify that the redundancy modifier ${\eta }_R$ be taken as 1.05, resulting in ${\eta }_i=1.05$. This effectively increases all load factors in the Strength limit state by 5%.

Conclusion

In this lesson, we have fully assembled the conceptual components of the LRFD design equation. You now understand that this equation must be checked against a series of limit states, each with a unique objective for ensuring a safe and reliable structure.

Key Takeaways:

• LRFD design involves checking the structure against four primary limit states: Strength, Service, Fatigue and Fracture, and Extreme Event.
• The Strength limit state ensures safety against collapse under maximum factored loads.
• The Service limit state controls everyday performance aspects like deflection, vibration, and cracking under service loads.
• The Fatigue limit state prevents crack growth due to millions of repetitive stress cycles from traffic.
• The Extreme Event limit state aims to prevent collapse during rare, high-impact events like earthquakes or collisions.
• The load modifier (${\eta }_i$) adjusts the factored loads to account for system-level characteristics of ductility (${\eta }_D$), redundancy (${\eta }_R$), and operational importance (${\eta }_I$). For typical designs, ${\eta }_i=1.0$, but non-redundant systems like tub girders may be penalized with ${\eta }_i\ge 1.05$.

With this framework in place, our next step is to begin populating the "load" side of the equation. In the next lesson, we will start with the most predictable loads: permanent loads, specifically the self-weight of structural components (DC) and wearing surfaces (DW).