Balance of forces
◦ To keep loads on the joint balanced — is it actually important? Why?
◦ Common mistakes engineers make when loading joints and how to prevent them.
◦ Load combinations and the related pitfalls.
Example 1
Here we go!
Today we will examine a 2-dimensional statically indeterminate frame.
Beam B1 has simple pinned connections, all other elements connected rigidly.
I created a model, loaded it with some various loads in FEM Design and exported the results to IDEA StatiCa Checkbot — topology of beams and joints and, naturally, load effects.
FEM Design calculated the combinations based on Eurocode rules. What is a load combination? Each combination may be considered as and extreme scenario of various loads and actions acting on the structure. It means that each set of load effects on the joint should also be considered as a possible scenario. Please keep this in mind — it is not just a table with numbers.
Structural model in FEM Design
In this example I want to draw your attention to the pinned connections of beam B1, both to column C1 and C2 (joints J.1 and J.2 respectively).
Which options to model the joints are possible?
Two options of modelling the joint J.1 — with or without load effects on the column
Four options of modelling the joint J.2 — with or without beam B2 and with or without load effects on B2 and C2.
Try to guess which options I consider optimal for this joints (select an answer and click the button in the bottom right corner to proceed to the next question):
Why isn’t the approach the same even though connections are similar?
First thought here, I believe, that both connections of beam B1 are the same and hence should be calculated using the same approach, and, to be honest, this thought is not far from the truth. However, in certain cases, there may be nuances.
Before we continue with the results of the calculation, I want to describe the “Loads in equilibrium” feature in IDEA StatiCa.
How “Loads in equilibrium” actually affects the calculation?
Members in IDEA StatiCa can have one of two geometrical types — Ended or Continuous.
When the bearing member is of the continuous type, it has two cut ends which means that the whole system gets two separate supports and becomes statically indeterminate.
This means that reactions are not clearly defined — technically, there is an infinite number of possible proportions of reaction forces.
Loads in equilibrium mode description
When the “Loads in equilibrium” mode is turned off the reactions on both supports are calculated according to the rules of structural mechanics for a statically indeterminate system.
On the contrary, when the “Loads in equilibrium” mode turned on, it is supposed that you are the one who is responsible for reactions distribution. In this case, the table “Unbalanced forces” appears under the load effects table to help you.
All the unbalanced forces in this case will be applied to only one support, so to be sure it is better to balance the values in this table to zero.
Difference between the Loads in equilibrium mode on and off
So, after a short explanation, let’s return to our example.
The results are the same whether the loads are balanced or not.
Joint J.1 consist of only two elements — beam B1 and column C1, and the column C1 has geometrical type “Ended”. It has only one cut end and the whole system may be considered as a statically determinate one.
For such a joint, it makes no difference whether the 'Loads in equilibrium' mode is on or off.
Moreover, if you activate this mode for this joint, it wouldn't matter what numbers you input into the load effects table for the column.
This happens because the reactions in column are determined only by the beam loading. Even if you set the 'wrong reactions,' they will still be the same for all three options here.
Okay, it’s time to examine joint J.2.
… and let’s make some mistakes!
What? I'm serious, it's very important to make a mistake once to avoid it later!
Mistake 1 — lack of loads
I calculated joint J.2 in all four scenarios with activated “Loads in equilibrium” mode to show why it is a mistake. Take a look — the results for numbers 1, 3, and 4 are too similar; I would even say they are the same.
As we discussed earlier, since the “Load in equilibrium” mode is activated, all the unbalanced forces compensated with the reactions at the only one support.
J.2.1 and J.2.3
Since we omitted the loadings on the column (and the right beam), the unbalanced forces consists of the loading on the left beam.
The right beam and upper part of the column act here like useless cantilevers.
Same loads, same reaction forces — same result.
J.2.4
It's quite similar to J.2.3, but the reactions at the top and bottom ends of the column are applied, and they are taken directly from results of FEM-Design calculation.
Why does it look exactly like the 1st and 3rd models?
Because we haven't just excluded the right beam here; we also excluded the loads on it!
It makes no sense at all to use the accurate force distribution between upper and lower ends of the column if we don’t consider all the members in the joint.
This is the main mistake for case J.2.4.
To summarize:
“Loads in equilibrium” won't function properly if you:
miss the actual force distribution on all the elements of the joint
overlook elements, that plays role in stress distribution in the joint
So there is only one proper way to use “Loads in equilibrium”
As for the classical method of joints that you surely use for hand calculations, you need to make sure that:
all elements attached to the joint are considered
the loads applied on all these elements
the applied forces are balanced
Why is the balance of forces important?
As I mentioned before, in the FEM Design model I had a few different loads applied to the frame and combinations of these loads.
When I exported the joint from FEM Design to IDEA StatiCa using CheckBot, I got some load effects that correspond to the load combinations causing the maximum forces in the joint elements, including ultimate, quasi-permanent, and characteristic combinations.
Each combination is balanced — all unbalanced forces are equal to zero. By the way, this is a good indicator that the export was successful.
So, I can calculate the joint for each of these load combinations to obtain a range of stress-strain states and ensure that the joint is ready to handle any possible loading, right?
Absolutely! This is the only correct way.
But why the results of calculation of the Joint J2 may differ to J1?
Difference of joint fragment considered in hand and CBFEM calculations
The connection of the beam B1 in this example is simple — it is described in detail in many books, including SCI’s Green Book P358 (Simple Joints to Eurocode 3). And none of these hand calculation methods consider anything but the beam, the fin plate, and, partially, the base element.
I can't imagine how you could consider the overall deformation of the joint in a hand calculation.
Difference of stress-strain state as a result of hand and CBFEM calculations
This exact example, though slightly exaggerated, shows that the deformation of the structure can affect the stress-strain state of the parts of even a pinned connection.
Here, beam B1 resists rotation, which causes additional stresses in the fin plate and, at the same time, additional shear forces in the bolts.
While an experienced engineer would avoid such decisions, an engineer with a powerful tool has the opportunity to accurately check even a less-than-ideal design solution.
Mistake 2 — using the envelope values
Sometimes an engineer may act lazily. They might think: “Why apply many different combinations when it's enough to apply just the critical, the worst one?”
But “the worst one” is not always a thing. Usually your structure bears alternating, variable, movable and/or partial loads. There are many stress-strain situations for the structure itself, and particularly for the examined joint.One load combination might be “the worst one” for shear in bolts, another for stresses in the column, and a third for welds, punching shear, etc.
So, what does the “lazy engineer” do if they want to use only one combination? Exactly, they use the maximum value of each force factor on each element — the values from the envelope diagrams.
As shown in this picture:
The way when “a lazy engineer” uses the maximal values in one combination
Results of calculation based on envelope values
Such a "lazy engineer” will obtain the envelope “combination” of extreme values and the “extreme” result.
Does this result have anything in common with the real calculation based on actual combinations?
Of course, nothing!
Based on this result, this “lazy engineer” will overdesign the connection.
Even though this calculation is not accurate enough, it is still conservative!
It may be a common misbelief that envelope values deliver conservative results, but this is not always true.
I would like to illustrate this to you with the next example!
Example 2
Example 2. Model in FEM Design.
Here is the frame, even simpler than the previous one. All the connections are rigid, and the beam is continuous over the middle column.
I created 5 loads — self-weight, one wind load and 3 alternative snow loads. Let’s assume that, for some reason, snow can be cleared from either left or right half of the roof.
This time we will be investigating the connection of the beam and middle column.
First, I modeled a connection and applied forces from the envelope moment diagrams.
Envelope values applied to the connection
And result is pretty passable — “all green”, bolts feeling okay, no exceed of stresses.
Envelope values applied to the connection. Results
So… envelope forces gave us the conservative scenario? Are you sure?
Let’s check with combinations exported from FEM Design properly:
Values from combinations applied to the connection. Results
Now you can see that envelope values is not always “the worst”.
The combinations LC3ULS consists of self weight, wind load and only half of the snow load
In our case, the answer is the combination that included only half of the snow load, which caused an additional moment in the column and rotation of the beam around its head.
Yes, partial load can not only cause problems in structures but also in their connections, so be careful!
Of course, if you are an experienced engineer, this case would have seemed predictable from the beginning, but keep in mind that the more sophisticated your structure becomes, the less obvious such potential pitfalls can be.
Conclusion
Sometimes it is important to consider all the elements converging in the joint
It is important to consider them correctly — using the combination of forces from actual combinations from FEM-model
The envelope values can not be applied as a design combination of loads to the joint
For simple joints with ended bearing member equilibrium of forces may be not necessary, but it is crucial for more complex connections
STILL HAVE QUESTIONS?
Torsion is not the most well-known topic about structural design. But there are a lot of interesting topics and a lot of possibilities to apply IDEA StatiCa.
If want to deepen your knowledge or want to get acquainted with the program, consider joining one of our comprehensive IDEA StatiCa courses.
Explore our courses to find the one that suits your needs best or request a custom course.
Get in touch with us today to learn more or to sign up!
