Static Systems
Post #1 of the Engineering Mechanics Series
Hi friends, 👋👋
Today we’re kicking off the new series about Engineering Mechanics with the first topic: Static Systems. And it couldn’t be a more important part of structural engineering.
In structural engineering, we use static systems in almost every calculation. Static systems have a big influence on the internal forces and therefore the outcome and behaviour of the design as it. Because of that, it’s crucial to have a good understanding of it.
In university, we get introduced to simply supported beams and cantilever beams in our first semester. However, I personally could never understand how these static systems represent real structures until I had my first design class, because lecturers never mentioned that the simply supported beam we calculate is actually a pedestrian bridge or that the static system of a cantilever beam is used to design balconies.
So today, we’ll look at the most used static systems and show real-world examples.
#1 Simply supported beam
This is without doubt the most used static system. It’s a beam that is supported by a roller and a pin support (we’ll talk about supports in one of our next posts).
So, here are examples of structures which can be calculated as simply supported beams:
Secondary timber beams of a timber flat roof (most beams in timber are designed as simply supported beams)
Wooden panels/beams of a bench
Precast concrete slabs and beams
Steel beams (could also have a different static system)
Pedestrian bridge (could also have a different static system)
Precast concrete and timber beams (for columns, bending moments occur mostly due to eccentricities of the vertical loading)
And many more. Comment below of what simply supported structures you are thinking about.
#2 Cantilever beam
The static system of the cantilever beam has a fixed support, meaning that it takes up vertical and horizontal reaction forces and a bending moment.
Examples are:
An in-situ concrete core of a high-rise building. This is an approximation that can be done in the early design phase to verify the deflections and reaction forces.
Every roof overhang is a cantilever beam
Balconies
Outdoor light
These are a few examples of where the cantilever beam is used in structures.
#3 2-span continuous beam
The 2-span continuous beam has 3 supports: 2 roller and 1 pin support. This static system is statically indeterminate compared to the statically determinate systems of the simply supported and cantilever beam. This means that we can’t calculate the reaction forces and internal forces with the 3 equilibrium equations. We’ll cover static indeterminacy and determinacy in one of our next posts.
Examples are:
A rafter roof supported by 3 purlins
The primary beams of a timber flat roof. The same applies to concrete or steel beams.
#4 X-span continuous beam
A continuous beam can have many more supports. Here’s the static system of a continuous beam with x+1 supports.
Here are 2 examples:
2D static system of a cable stayed bridge. An x-span continuous beam can be used in a very early design phase to quickly estimate the cable forces. A more accurate way is to define the cables as spring supports instead of rollers.
Another example are foundation beams that are supported by pile foundations. The project I am working on right now uses in-situ concrete beams to distribute the loads from walls to the piles. As the spacing of the piles is between 2-5 meters, some of the beams have 8-10 supports (piles)
#5 Fixed beam
The fixed beam is characterized by having 2 fixed supports.
Examples are:
A steel, concrete or steel beam that is part of a rigid frame.
Most in-situ concrete beams have fixed supports
#6 Beam with roller & fixed support
There is of course also static systems which combine the characteristics of other static systems. This static system has a roller and a fixed support:
An example could be a steel beam which needs to have one fixed support to limit deflections.
#7 Frames
Frames are used for warehouses, sports halls, auditoriums - anywhere where there is a requirement of long spans.
Frames are characterized by having at least 3 elements, 2 columns and a beam. Most frames have moment stiff connections, fixed supports or both. The more moment stiff, the more rigid a frame become and the less the deflections. A downside is that moment stiff connections usually cost more.
Recently, I designed a timber Glulam frame. The frame is used to attach a folding door to it. This would actually be an interesting topic for a blog post, because of multiple reasons I couldn’t connect the frame to the existing structure. This meant that the frame had to function as a cantilever out of plane to resist horizontal loads.
#8 Arches
Arches were used a lot in old structures such as the Colosseum and before the invention of reinforcement. That’s because arches are a very efficient static system acting mostly in compression.
As for frames, arches can have different static systems. But the easiest to calculate is the 3-hinge arch.
Examples:
Facade or window openings in masonry
Old structures like the Colosseum or the Familia Sagrada.
#9 Trusses
Another great and efficient static system are trusses, as most of the elements act in compression and tension.
Again, the static system can vary. If the top and bottom chords are delivered as one piece then you should model them as “continuous” allowing for shear force and bending moment.
Examples of trusses:
Roof trusses
Bridges
Trusses are often used for long spans to reduce the material such as sports halls, train stations, airports or stadiums.
Conclusion
Static systems are really one of the most important fundamentals of structural engineering. Picking the right static system can be challenging and it needs experience.
In this post, we’ve covered the most common static systems, but keep in mind that there are more.
I hope this first part of the new series was helpful to you and that you could gain some practical knowledge from it.
This was it for this week. Hope to see you next Wednesday for the #2nd post about Engineering Mechanics.
Have a great rest of the week. ✌️✌️
Cheers,
Laurin.