Hello!
In our last lesson, we quantified the permanent loads (DC and DW) that form the baseline weight of our bridge structure. We now turn our attention from the static to the dynamic, from the predictable to the probabilistic. This lesson focuses on transient loads, specifically the vehicular live load, which is one of the most significant and complex loads a highway bridge must be designed to resist.
Our goal is to understand and apply the AASHTO HL-93 vehicular live load model. We will dissect this model into its core components, and then learn how to modify it to account for the dynamic effects of moving vehicles (Dynamic Load Allowance, IM) and the probability of multiple lanes being loaded simultaneously (Multiple Presence Factors, m). This will give us the final piece of the puzzle needed to assemble our first complete AASHTO load combination.
1. The HL-93 Vehicular Live Load Model
Unlike permanent loads which are calculated from the designed geometry and material densities, live loads are statistical in nature. It is impractical to design a bridge for every possible real-world truck. Instead, AASHTO LRFD specifies a notional live load model, the HL-93, which is calibrated to produce force effects that envelop the effects of the vast majority of legal and routine permit vehicles.
To get a high-level overview of this concept, let's start with a short video from the Short Span Steel Bridge Alliance.
Live Load Distribution - Part One
This video provides an excellent introduction to the concept of transient loads and the rationale behind the HL-93 live load model.
Please watch the segment from transient loads to impact factor. Pay attention to the distinction between permanent and transient loads, and how the HL-93 model is composed of three distinct parts to simulate the "worst case exclusionary vehicular loading."
As the video explains, the HL-93 model is not a single vehicle but a combination of three distinct loads that the designer must place on the structure to maximize the force effect (e.g., moment, shear, deflection) at the point of interest. These three components are:
- The Design Truck
- The Design Tandem
- The Design Lane Load
For any given force effect, the AASHTO specifications state that the design vehicular live load, , shall be taken as the greater of the following two combinations:
- The Design Truck + The Design Lane Load
- The Design Tandem + The Design Lane Load
Let's examine each of these components in detail.
The Design Truck
This is a three-axle vehicle intended to model the effect of a heavy semi-trailer. It has a total weight of 72 kips (320 kN).
The variable axle spacing is a critical feature. To find the maximum moment in a span, you will adjust this spacing to position the axles optimally, a process you are likely familiar with from using influence lines in your previous design work.
The Design Tandem
This load consists of two 25-kip (110 kN) axles spaced 4 feet (1.2 m) apart. It is intended to model the effects of vehicles with closely spaced heavy axles, such as a dump truck or certain specialty vehicles. It often governs the design for shear on shorter spans or for moments on secondary members like deck slabs.
The Design Lane Load
This is a uniformly distributed load of 0.64 kips per linear foot (klf) or 9.3 kN/m. It is intended to represent the effect of a queue of standard traffic in a design lane. This load is always applied in conjunction with either the Design Truck or the Design Tandem and is distributed over a 10-foot wide lane. It has no dynamic allowance applied to it.
2. Dynamic Load Allowance (IM)
Moving vehicles cause impact and vibration, leading to force effects greater than what would be produced by the same vehicle if it were applied statically. AASHTO accounts for this by applying a Dynamic Load Allowance, , also known as impact.
Crucially, the dynamic load allowance is applied only to the Design Truck or Design Tandem component of the HL-93 load. It is NOT applied to the Design Lane Load.
For most design calculations (all limit states except fatigue), AASHTO specifies:
Therefore, the force effects from the truck or tandem are increased by a factor of 1.33.
The following reading from Caltrans' Bridge Design Practice manual provides a concise explanation.
BDP Chapter 3 -LOADS AND LOAD COMBINATIONS
This document clearly defines the dynamic load allowance and shows its application.
In the document, find the section titled "Vehicular Dynamic Load Allowance, IM". Read this short section to understand the purpose of IM and review the example calculation provided. Notice how the 33% factor is applied only to the truck moment, not the lane load moment.
3. Multiple Presence Factors (m)
When designing a multi-lane bridge, it is statistically improbable that every single lane will be simultaneously occupied by a maximum-weight design vehicle producing the worst possible effect. To account for this, AASHTO specifies Multiple Presence Factors, m, which reduce the total live load effect as more lanes are considered to be loaded.
The factors are applied to the total live load effect of a single lane. It is important to remember that the number of "design lanes" is determined by dividing the clear roadway width by 12 ft, not necessarily the number of striped lanes.
BDP Chapter 3 -LOADS AND LOAD COMBINATIONS
This section provides the standard AASHTO table for multiple presence factors.
Locate the section "Multiple Presence Factors (m)" and review the accompanying table.
The table specifies the following factors:
| Number of Loaded Lanes | Multiple Presence Factor, m |
|---|---|
| 1 | 1.20 |
| 2 | 1.00 |
| 3 | 0.85 |
| >3 | 0.65 |
The factor of 1.20 for a single loaded lane may seem counter-intuitive, as it increases the load. This factor is typically used in conjunction with simplified live load distribution factors (a topic for a future lesson) and accounts for the higher probability that a single loaded lane might contain an illegally overweight vehicle. When performing a refined analysis, this factor is often handled differently. For our current purposes, it's key to know these are the standard factors to apply based on the number of lanes you are simultaneously loading to produce a given effect.
4. Putting It All Together: A Conceptual Example
Let's summarize the total live load effect. For a given structural component, the factored live load is found by:
- Determining the force effect from .
- Determining how many design lanes (
N) need to be loaded to maximize this effect. - Multiplying the result by the appropriate multiple presence factor
mforNlanes.
The design manual from Caltrans provides an excellent worked example for substructure design that demonstrates this process clearly. While we are focused on superstructure, the principles of applying m are identical and universally applicable.
BDP Chapter 3 -LOADS AND LOAD COMBINATIONS
This example clearly demonstrates the practical application of positioning live loads and applying multiple presence factors to find maximum force effects on a column.
Navigate to the example that begins with the text "Example Consider the following bridge..." near the end of the document. Focus on the logic of these two cases: Maximum Transverse Moment (MT)max Case: Observe how two lanes are placed on one side of the bent to create the largest moment. Because two lanes are loaded, the calculation uses m = 1.0. Maximum Axial Force Pmax Case: To get the maximum axial load, the engineer must load all four lanes. Consequently, the calculation correctly uses m = 0.65. This demonstrates the core principle: you, the engineer, decide how many lanes to load to create the worst-case scenario for the effect you are checking, and then you apply the corresponding m factor.
This process gives you the unfactored live load effect per lane, which is then combined with other loads in the LRFD load combinations.
Conclusion
In this lesson, we have deconstructed the AASHTO HL-93 live load model, which is fundamental to modern bridge design in the U.S. We have established that it is a notional model designed to envelop real-world traffic effects.
Key Takeaways:
- The AASHTO HL-93 live load consists of three components: the Design Truck, the Design Tandem, and the Design Lane Load.
- The design live load effect is the greater of (Truck + Lane) or (Tandem + Lane).
- A Dynamic Load Allowance (IM) of 33% is applied only to the truck or tandem component to account for impact.
- Multiple Presence Factors (m) are applied to account for the reduced probability of simultaneous maximum loading in multiple lanes. The factor depends on the number of lanes loaded to create the worst-case effect.
We have now defined and calculated both permanent (DC, DW) and transient (LL+IM) loads. In our next lesson, we will combine these into the standard AASHTO load combinations, such as Strength I and Service II, which form the basis of all subsequent design checks.