The stringer method, also called the stringer panel method, is widely used in Denmark. Outside Denmark, most engineers have never heard of it. That is about to change: it is being added to the next generation of Eurocodes.
Why use the stringer method?
The stringer method works well for any structure where in-plane shear forces govern the design, for example:
- Diaphragms
- Shear walls
The stringer method is especially powerful for transferring shear forces around openings. It is most common in precast concrete buildings but applies to any structure with shear-dominated behavior.
What is the stringer method?
The stringer method is a lower-bound plastic design method, in the same category as the strut-and-tie method. A stringer model uses just two types of elements:
Stringer
A stringer can only take normal force.
Shear field
A shear field can only take in-plane shear forces.
Take a simply supported beam with a point load at mid-span. The minimum stringer layout looks like this:
- Top stringer aligned with the compression zone of the concrete
- Bottom stringer aligned with the longitudinal reinforcement
- Two stringers over the supports
- One stringer below the applied load
The space between stringers is a shear field. Here, there are two.
Each shear field is surrounded by stringers. Forces transfer constantly between them. The external forces are known. The internal forces are what we solve for.
For this beam, equilibrium gives τ1 = 5kN/m and τ2 = −5kN/m. From there, the stringer forces follow directly. The top stringer is in compression, the bottom in tension, exactly what you would expect.
Statically indeterminate structures
Now divide each shear field into 9 smaller ones. The stringer model now has 18 unknowns and is statically indeterminate. There are infinitely many solutions that satisfy equilibrium.
Solution 1
All the shear forces can be set to 5, and we would end up at the same solution as before.
Solution 2
Alternatively, the shear force varies in each row. This activates the horizontal stringers and gives a result close to what an elastic model would produce.
Solution 3
You can also model a hole in the middle by setting the shear and stringer forces to zero in that region.
Which solution is correct for the stringer method?
All solutions that satisfy equilibrium are valid, that is what lower-bound theory says. The one constraint: the Danish national annex requires the chosen solution to be within a factor of 3 of the elastic or optimal plastic solution, to ensure sufficient ductility.
The optimal plastic solution minimizes the required reinforcement. It is also accurate enough for SLS checks.
PolyStringer
Setting up a stringer model is quick. Solving it by hand is not, especially as the number of shear fields grows.
PolyStringer does it instantly. It finds the optimal plastic solution automatically. And it still gives you full control: you can adjust the solution to use the available plasticity where it makes sense.
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