center of mass and rigidity and torsions

rodsika

I've been researching about this for hours at internet reading dozens of pdfs.. but can't seem to understand the concept. What does it mean if the center of mass and center of rigidity are not coincident, torsions would be produced.. can you give an example of it in more intuitive or using fundamental objects? Thanks.

Simon Bridge

Why not start by telling us what you understand about the center of mass and center of rigidity - what are they, how are they defined, what is their usefulness? It is likely you just have a slight misunderstanding of the concepts.

haruspex

Centre of rigidity is somewhat analogous to centre of mass. Mass produces a resistance to acceleration; if the force is through the centre of mass then the resistance from the masses either side of the line of action balance and no rotation occurs. Rigidity (of the building) produces a resistance to movement (of a floor, laterally); if a lateral force is applied through the centre of rigidity then the resistances either side of it balance and the floor does not rotate.
When a seismic movement shifts a building sideways, the floor's inertia acts as a force resisting that movement. This acts through the centre of mass of the floor. If that is not the centre of rigidity then the floor will rotate.
This is all from reading http://www.eng-tips.com/viewthread.cfm?qid=68312. I'd not heard of the concept until reading your post a few minutes ago, so I may have misunderstood.

Studiot

There is also this gem buried in the middle of the link you posted haruspex

I concur with that sentiment entirely.

rodsika

yes.. that's the concept. But I can't quite connect it with the case where there are different elements of different sizes in the building.. during seismic movement.. heavier elements move more.. this would produce more damage than when all elements are symmetrical and movement the same. Let's give an example. Refer to the following picture.



In the 10.16 meter girder between the columns at the middle. The girder is heavier with more width and depth. During seismic movement, it along with the larger columns supporting it would move more. This would pull on the other smaller beams. This may make it more unstable during earthquake. Right guys? Now how do you connect it with the concept of torsions where the center of mass and center of rigidity must be concident to avoid torsions. Where is the approximate center of mass and center of rigidity from the layout plan itself? how do you determine it? note this is not a homework.. but just curious how it works, thanks.

Simon Bridge

Center of Rigidity thing is only a guide - a rule of thumb. Kinda assumes the structure is classically rigid. You can comply with getting it in the same place as the com and still have a building that falls down.

You cannot avoid torsions. The floor will try to twist about it's com but can only manage to twist about it's cor. This swings the com around and makes the whole structure more unstable. If you've every tried to carry or rotate something at a point other than the com you'll know the effect.

In the above diagram, the different arts of the building are going to try to move differently - which sets up stresses in the bracing which is trying to hold the building rigid. The closest relationship you'll get will be from treating the heavy supports as off-center com's. Noting where they are tells you where to put extra bracing to get you closer to the rigid-model dynamics.

rodsika

But according to the concept of Diaphragms. If you pour the entire RC slabs at the same time, it will form one solid floor. So during seismic movement, only the perimeter walls will be affected, the center will become part of the entire frame so there would be no individual movements in the columns at middle in an RC frame with solid poured slabs, contrary to what you described above. Do you agree with me and if not, why.

Simon Bridge

I said they will "try to move differently". In your example that will stress the floor as it tries to maintain it's rigidity. This is the diaphragm action - basically another kind of bracing. In a biggish shock the floor cracks (breaks, collapses etc) because the different bits want to move differently in response.

Details are tricky - in the CCTV building in CHCH the outer walls gave way first and the floors collapsed onto each other... breaking away from the heavy structures.

See: R.B. Fleischman and K.T. Farrow; On the Seismic Behavior and Design of Long Span Precast Concrete Diaphragms; Pacific Conference on Earthquake Engineering (2003).
... for some detail on the behavior of diaphragm floors in Earthquakes.

rodsika

I'm not talking about precast concrete but one where fresh concrete are poured into the rebars with formwork all over.

Anyway. Are you saying that in concrete floor slabs that were poured at the same time and set at the same time. The unequal sized columns underneath it would try to move differently.. causing the diaphragms portions above it to move differently? In other words, the columns and slabs both contribute to the torsion movements... or seismic forces can transfer forces to both columns and slabs with different proportions? The past week I sat dinner with 3 structural engineers and ask many questions. What I told you was what he told me. That the slabs would become one and it is the whole RC frame or building that would twist.. not individuality. It's like this. Imagine you have a dinner plate put on top of matchboxes. The dinner plate becomes one unit and move at the same time. It doesn't depends on each of the matchboxes positions. Why aren't concrete slabs like this too as they put on top of beams and columns?

Simon Bridge

Your engineer at dinner tells you, as part f informal dinner conversation, that the diaphragm makes the structure move as a whole. Naturally he has not gone into great detail about how each of the parts contribute to this and what happens under different circumstances.

I have told you here that the different parts of the structure will try not to - under lots of stress they will break apart because of this.

I have agreed with the engineer.

In your dinner-plate analogy, the plate is not attached to the matchboxes like a floor is attached to columns. Also the plate is very rigid compared with the stresses you placed on the system.

If you looked under the plate at the matchboxes you'd see that they shifted around. If you had different mass matchboxes they would have moved differently. If the matchboxes were attached to the plate, then the different ways they try to move (but are restrained by the rigidity of the plate) place stresses on the plate.

I don't know why this is so hard to understand: if I twirl a ball on the end of string, the ball will try to move off in a line but the string stops it - so there is tension in the string.

rodsika

So in such cases, the stress would be on the floor with strong seismic movement breaking them apart.. but I wonder what happens to the rc beams themselves. Imagine a column both connected to a 5 meter beam and another 10 meter beam on the opposite side of it (see the previous picture). If a strong seismic wave would hit from say the north portion, is it possible the middle column moving south more due to its more mass with respect to the rear column just stresses or breaks the column-beam joint connection (although partially restrained by the floor)? What do you think?

Simon Bridge

As with everything: depends.
But I believe your question has been answered.

rodsika

Ok. I just remembered seismic wave moves thru the ground. For some few unlucid moments, I was thinking of them as shock waves in the air from say supersonic jets moving or nuclear bomb detonation sending shock waves in air. In this case, the diaphagms would be initially affected then the columns.

But then I don't think I have to worry about nuclear. Just seismic from ground. I'll have meeting with the 4th structural engineer tomorrow. I plan to make every columns symmetric... but then the lot is irregular.. so maybe would build it in portions... if this scheme won't make it worse.

Simon Bridge

Oh you are trying to design a building to withstand an earthquake without being an engineer?

I've been responding just for understanding - the structural engineer will have math and knowledge of the regulations. I can only do the general from here.

Studiot

When discussing diaphragm you need to have a proper understanding of what the structural engineer means. There are two different and distinct uses for the term.

On the one hand a diaphragm refers to a thin plate or membrane that is constrained at the edges and develops internal resisting stresses to transverse loads in the plane of of the plate or membrane. These are sometimes known as diaphragm stresses and may be found in standard volumes such as Roark.
Mechanical engineers often use this version of the term.

On the other hand diaphragms are also thick slabs or beams at right angles to floor or deck slab or wall ie a thick plate. They resist the transverse loads imposed on the plate and some transfer these loads to the plate supports. They are not the plate itself, which may have many diaphragms.

rodsika

I'm not trying to design a building but just want to be seismic aware.. my architect didn't even understand what was Torsion or center or mass or rigidity.. when queried about best structural positionings... he just replied he was an architect and didn't know any about structural.. hence he didn't prioritize on symmetrical lots.. all his designs were assymetrical... this was the reason why I parted ways with him and looked for a new architect last week.

Well. I just sat a few hours with the 4th structural engineer to come up with the best symmetrical design. We kept on discussing about seismic wave that would come from the vertical and horizonal. We forgot to talk about seismic wave that comes from the slant or other angles besides them. According to Studiot here... it would make the different portions move differently causing torsions too even on symmetrical lots especially in columns with individual footing. This means the most important is not so much to make the lot perfectly symmetrical but to make the connections much stronger? Maybe time to consult a 5th structural engineer on this. What I learnt was not all structural engineers have same knowledges. They have their own biases and opinions.

Studiot

Well you have absorbed some of what I said but look back at it again.

There are two waves in a seismic event. One is vertical.
One is horizontal.
They arrive at different times.

There is no 'slant wave' betwen these two.

However as each wave passes along the ground it does does in a line we call the wavefront.
The wave arrives at every point along this line at the same time.
However, this line can be slanted at any angle to the building so it can arrive so that it meets the two front columns at the same time or different times. If the arrival times are different that will introduce a twist or torsion into the effect on the building.
Since there are many, many ways it can arrive slanted and only one way it can arrive paralle to the building line torsion is most likely.

The effect on pad foundations and importance of connections are correctly noted.