Plastic hinges and earthquakes in columns
When they need to be considered. But mainly when they don't.
Plastic hinge refresh
A plastic hinge occurs in a section of beam where the stresses are so large they begin to cause massive strain (rotation) with little to no increase in load. The strain is only resisted by a constant moment which develops at the plastic hinge.
In reality, regions of high stress will gradually develop a plastic hinge, however in analysis we often assume that it’s at this plastic moment the material transitions abruptly from elastic to plastic.
When inserted into a statically determinate system, plastic hinges can create a collapse mechanism. Multiple plastic hinges can also form in a given system.
Plastic hinges are also used in earthquake engineering as a damping device to allow rotation and absorb energy around an otherwise rigid column connection.
Generally we don’t design columns for plastic hinges to form. When considering an earthquake event, however, we must consider the potential for a plastic hinge to form in a column and ensure the column is ductile and can absorb energy.
Predicting plastic hinges
I don’t want to get into the weeds of designing plastic hinge zones today. I want to highlight that for most large infrastructure projects, you don’t even need to consider it.
Here’s Clause 10.2.4.3 of AS 5100.5-2017 which gives guidance around when a plastic hinge will occur in our column.
There are two important aspects of this clause which we must satisfy to predict a plastic hinge.
“Where the force-based method is used…”
“… if M* is greater than the design flexural capacity using µ ≤ 2”
Force-based method
The general design procedure for earthquake is to undertake a force-based analysis. This involves calculating the seismic acceleration as a fraction of gravitational acceleration and then essentially subjecting the entire structure to this acceleration for the different earthquake vectors.
The vast majority of bridges are assessed using the force-based method for earthquake, so we tick this first part of the clause.
Ductility factor
For limit state design, we almost always design for M* ≤ ΦM. This aligns with basic intuition. The design action should be less than the design capacity.
The ductility factor, µ, is an important parameter in determining the seismic acceleration. It is a codified value based on the structure arrangement and required performance level of the structure.
From AS 5100.2-2017:
We can see that depending on our structure type, the ductility factor ranges from 1.0 to 4.0. This ductility factor is used to scale the seismic acceleration inversely. That is, a factor of 1 results in no scaling, while a factor of 2 cuts the seismic acceleration in half.
Service (immediate use)
The interesting result is the “service (immediate use)” performance level. Note that none of the values are above 2.
A reminder of the provisions of Clause 10.2.4.3 above:
Where the force-based method is used in design, a plastic hinge shall be predicted to occur if M* is greater than the flexural design capacity using µ ≤ 2.
For the service (immediate) use performance level, the ductility factor is always less than 2. And since we need to design for this µ ≤ 2 case, the design action will always be less than the design capacity.
The result? Plastic hinges will never occur.
When a hinge forms
Designing to the “damage control” performance level can form plastic hinges, however.
Let’s say you have some piers and a ductility factor of 3. You’re in soft ground which has significant displacement. You’d size up and design your piers and piles considering µ = 3.
Once you’ve done this, however, you’d need to do another assessment, this time using µ ≤ 2. If, during this assessment, you find the design moment, M*, is greater than the capacity of your design, plastic hinges will form in this location.
You’ll then need to comply with Clause 10.7.6 of AS 5100.5-2017 for detailing around plastic hinge zones.
Performance level definitions
Back to the “service (immediate use)” performance level. What does this actually mean?
A structure designed to the “service (immediate use)” performance level is designed to be… well, exactly that. Immediately used.
After an earthquake event, there should be no need to reduce the traffic load over the bridge, or carry out immediate repairs. It’s a structure that’s essential for post-disaster works.
When you think about it, it makes sense why plastic hinges shouldn’t occur in these types of structures. A plastic hinge will not necessarily cause collapse of the structure, but it will show large displacements and require repair.
This is essentially what the Australian bridge code says on the matter:
… a bridge designed for the damage control performance level shall retain its structural integrity. Parts of the bridge susceptible to damage by their contribution to energy dissipation during the design earthquake shall be designed in such a manner that the structure can sustain the actions resulting from use by emergency traffic, and that inspection/repairs can be performed.
In Australia, most large infrastructure projects now have requirements that bridges shall be designed to the “service (immediate use)” level.
Plastic hinges shouldn’t occur in these designs. The bridge is built to withstand earthquake effects without dissipating energy through damage.