Virtual vs Real Neutral Axis 3

[hocho]

The neutral axis in the interaction diagram doesn't really correspond to the physical location of the column. Or do they?

For example. Below the balanced point. At zero moment. The neutral axis is very small (or infinitely small). At zero moment (edit: I meant at zero axial load). It acts like a beam. Yet in a beam. The real neutral axis is the middle of the beam. So the interaction diagram neutral axis doesn't correspond to the physical location of the neutral axis. What is the formula that relates the virtual and real neutral axis (what official terms distinguish these two)? Is there a software that can show or distinguish them and plot them both?

 

[BAretired]

The principle is called "changing the structure". If you omit the upper column and second floor beam from your analysis, then naturally the moment in the bottom tier will increase because there is no upper column to share the moment applied by the first floor beam. If you want to find the effect of removing topping from the second floor, analyze it with the structure left the same and simply remove or reduce the second floor load.

Removal of topping on the second floor is not warranted given the current state of knowledge about the design and would likely do more harm than good. Leave the structure alone until you know what you are doing.

BA

 

[hocho]

The principle is called "changing the structure". If you omit the upper column and second floor beam from your analysis, then naturally the moment in the bottom tier will increase because there is no upper column to share the moment applied by the first floor beam. If you want to find the effect of removing topping from the second floor, analyze it with the structure left the same and simply remove or reduce the second floor load.

That's just a more extreme example (omitting entire column and beam in the analysis). Initially I have reduced the load in the second floor top and there is an increase in the column moment at ground floor. For example.. this is the dead load loading of my structure (dead load of slabs connected to the beams, the left lower column is the one with epoxy void):

If there is additional 10kN uniform load on top of the 2nd floor.. the moment in the ground floor column is lower at 7.48kN-m. Whereas if there is no additional 10kN uniform load.. the ground floor column moment is higher at 9.39kN-m.

With more load in the 2nd floor top. The base moment of the 2nd floor is higher at 16.87kN-m instead of 13.05kN-m. However this makes the ground floor top column moment smaller. This is what I'm pointing out. What is the technical explanation for this. It's as if the 2nd floor column base moment takes some moment away (shares more) from ground floor top column.

 

[BAretired]

The moments should be correct if you have entered the data correctly. I have no way of checking your input. You are indicating all columns hinged at the base. This is not consistent with the design concept explained in previous posts by mes7a. All columns were intended to be fixed at foundation level. A hinge at that location would be completely inadequate for seismic loading unless you have shear walls or cross bracing to handle lateral forces.

I think the building should be left as it is until there is good reason to take remedial measures. At the present time, I am unaware of any such reason. Design and review during construction has been carried out by a local structural engineer who appears to be unwilling or unable to expend any effort in resolving the issues which are of concern to the owner (mes7a). If there are serious concerns about the safety of the building, another engineer must be retained to review the design and to inspect the facility. It cannot be done in a forum such as this.

BA

 

[hocho]

The moments should be correct if you have entered the data correctly. I have no way of checking your input. You are indicating all columns hinged at the base. This is not consistent with the design concept explained in previous posts by mes7a. All columns were intended to be fixed at foundation level. A hinge at that location would be completely inadequate for seismic loading unless you have shear walls or cross bracing to handle lateral forces.

I think the building should be left as it is until there is good reason to take remedial measures. At the present time, I am unaware of any such reason. Design and review during construction has been carried out by a local structural engineer who appears to be unwilling or unable to expend any effort in resolving the issues which are of concern to the owner (mes7a). If there are serious concerns about the safety of the building, another engineer must be retained to review the design and to inspect the facility. It cannot be done in a forum such as this.

That output is not meant to accurately depict the exact structural framing and loading because it is the designer who is good in that especially seismic. I'm asking just how opposite moments seem to interact. And I showed it to you pinned bases because I thought most are more familiar with pinned bases because to make really fixed bases in reinforced concrete, there must be massive top reinforcement which is not usually done in footings. We spent over $10,000 extra for the top reinforcement...

Anyway. My concern is the physics principle. Because if moments all lined up together, no building can stand up because all the edge columns would bend and bend from increased moments until they just collapse. But in reality, the moments are S shaped.. the lower part of the S can seem to cancel the higher part of the moment of the lower floor. This is unexpected physics principle I learnt. I just want to know if you have another way of explaining it.. why the moments seem to cancel. In the following case. Even with fixed bases, the column moments in the ground floor is lower with additional load in the eccentric beam of the second floor top. Normally you'd expect the moments in the ground floor to increase when eccentric loading are done in the upper floor. But it seems to have equilibrium effect.

With no additional load applied on second floor top:

WITH additional load applied on second floor top (moment in ground floor got lower.. becomes 7.93kN-m from 10kN-m. see below.. Before I thought moment should increase.. but some physics principle seems at work.. what is your other way to state this physics principle.. something to do with opposite moments cancel? ):

 

[BAretired]

Why does C1 have a large moment at Story 3 (-22.17 or -20.88kN-m), C2 has less than half as much (about 8) and C6 has zero moment?



BA

 

[hocho]

Oh its just showing the middle elevation longitudinally. Right now in actual bldg C6 is only up to 3rd floor without any roof yet. So column has zero moment at top. In C1 or the middle. I didnt delete the beams on its transverse side and longitudinal rear. Note the building was designed for 4 storeys but.only 2 stories built. I was jus testing to see.how unbalance moments on top floor columns can affect the lower. Im not trying to determine actual values bec im not expert in etabs. I jus use it to compare to manual computations of members like moments in beam. Rear.column moment is lower.bec its rear so moment is less. For now. I jus want to understand the moments can indeed subtract or cancel? If your moment on higher floor.is opposite.to.that of lower floor top part. They can.somehow cancel? Is this true.or wrong.concept.

 

[BAretired]

I have no idea what your moment diagrams mean. I don't know what kind of load could produce the results that you are showing. It doesn't look right.

I jus want to understand the moments can indeed subtract or cancel? If your moment on higher floor.is opposite.to.that of lower floor top part. They can.somehow cancel? Is this true.or wrong.concept.

I don't know what you mean by your question. Your language is not precise. Moments do not subtract or cancel, whatever that means.

It is normal for an edge column under gravity load to have stress reversal from top to bottom in each story. It bends in the shape of an "S"; the top is stretched on the outside while the bottom is stretched on the inside. Somewhere near mid-height, the moment is zero. The moment diagram is a straight line which peaks at top and bottom and passes through zero at the point of inflection. The moment at the top does not cancel the moment at the bottom or vice versa. They each must be reinforced as required by a frame analysis.

BA

 

[hocho]

Im referring to column above the storey. It can affect the moment in the lower storey right below it right? For example you have 10kN-m at top of a storey. If you can pull or push by hydraulic the column above the joint in the next higher storey. You can change the moment in the joint and hence moments of column below it. Hope you got my point. Tnx

(Edit here are clearer illutration

S
S

Imagine the 2 S above are moments of columns in each storey. You will notice that the moment at bottom of second storey is opposite to the moment of column in top of ground floor. Or in your earlier statement. The above column can share the moments used by first storey beam. In the case of normal edge column with the 2 S. Load above a storey can lessen the moments below it bec it seems to restrain the beam in opposite direction. Gets?)

 

[BAretired]

Yes, that is true. Putting a high moment on an upper tier would affect the column below. It would also affect the beam and in fact, would affect every member in the frame to some extent. A sparrow landing on the roof of a twenty story building stresses every column, every beam and every foundation throughout the entire structure.

BA

 

[hocho]

You got my point but my other point is there is moment cancel (edit: not complete moment cancel but moment lessening effect on lower column) or restrain effect in every normal building at edge columnw right? To post my edit above with additional comments. Here is what i said

Here are clearer illustration

S
S

Imagine the 2 S above are moments of columns in each storey. You will notice that the moment at bottom of second storey is opposite to the moment of column in top of ground floor. Or in your earlier statement. The above column can share the moments used by first storey beam. In the case of normal edge column with the 2 S. Load above a storey can lessen the moments below it bec it seems to restrain the beam in opposite direction. Gets?)

Post Edited

 

 

[hocho]

BA. On Monday next week (4 days from now).. we'll start to add the roof designed by the same designer company to cover the third floor. Again he doesn't want to think about epoxy being soft modulus and say the building was originally designed for 4 storey with concrete roof so all forces are lower than designed anyway (because now it's only 3 storey with light roofing). But I'm worried about the epoxy void.

The red is the third floor column position with the epoxy void at ground floor. Originally the sides of the front rafter (see blue arrows) has the sides rested on the perimeter w8x21 wide flange (rafter is also w8x21). But I told designer it may deflect and the column may take majority of the load. I told him what if I rested the rafter on the columns at side. He said it's up to me.. because he didn't want to consider the epoxy soft modulus (he didn't want to review the meaning of modulus.. he is a civil engineer.. in our country.. our structural engineers are mostly civil engineers not familiar with the physics of it). So I and the contractor kept discussing these past 2 days about this slant implementation right on the column tops. Do you think there is problem if rafters were put on the slant at front resting on all columns?


Now the most important part I'm concerned these past 3 days is.. is it possible to balance (or diminish) the ground floor unbalanced column moments by the position of the rafter on the front column. This is the reason I'm asking what is the effect of column moments at third floor on ground floor and whether it is possible to diminish the moments. In your 60 years of practice.. how often do you need to diminish the edge ground column moments with loading in the third floor. Please share your experience on this.

This is related to the heart of this thread when Doug mentioned earlier "The combined axial load and moment are equivalent to an eccentric vertical load, with the eccentricity on the compressive side. If you apply an additional load at the column centroid it reduces the eccentricity of the resultant load, and the width of the compression region increases, so the total compression force increases, but the maximum stress reduces. It's a similar situation to a footing with a vertical load outside the middle third. If you apply an additional load on the uplift side, the pressure on the compression side will reduce, even though the total reaction force is increased."

I'm wondering if you can diminish the ground floor column moments by loading in the third floor? Thanks.

 

[BAretired]

Here are clearer illustration

S
S

Imagine the 2 S above are moments of columns in each storey. You will notice that the moment at bottom of second storey is opposite to the moment of column in top of ground floor. Or in your earlier statement. The above column can share the moments used by first storey beam. In the case of normal edge column with the 2 S. Load above a storey can lessen the moments below it bec it seems to restrain the beam in opposite direction. Gets?)

Where the two "S"s meet, the moment acting on both upper and lower columns are clockwise. They are not opposite. They are the same. The only thing opposite about them is that they put tension on different sides of the column, but that is a consequence of geometry.

Load above a story does not lessen moments below. If anything, it increases them as a result of the P-delta effect.

Moments applied to a joint above a story can lessen or increase moments elsewhere depending on the direction of the applied moment. If you want to see how an applied moment affects your structure, remove all load and apply a single moment to any joint of your choosing and see how that affects moments elsewhere.


BA

 

[BAretired]

hocho,
In response to your last post, the roof will be a light structure which will have no significant effect on the moment on the first story column at X2/Y4 irrespective of how you frame it.

I would be much more concerned about moments resulting from earthquake or typhoon. Without any shear walls, your structure relies totally on bending of nine columns to provide stability. Are the exterior walls capable of acting as shear walls?

BA

 

[hocho]

hocho,
In response to your last post, the roof will be a light structure which will have no significant effect on the moment on the first story column at X2/Y4 irrespective of how you frame it.

Tomorrow we will spend about 5 hours to bring it up because they are so heavy. W8x21 is 21 lbs per foot.. so per piece (21 x 20 feet)is about 420 lbs.. can't be carried by even 3 people. They need to pulley chain it up. 420 lbs is about 1.868253072 Kilonewton. So 1 complete rafters composing of 2 pcs are 3.736kN. Now there are many C-purlin sized 2x6" 1.8mm crisscrossing it spaced at 0.6 mtr apart.. so weight can reach 4.5 kN.. added the roof can reach 5 kN (do you have formulas to get weight of rafters and purlins over a rafter or column?). I'm worried this can further strain the column with epoxy void. We even plan to just put rafters at the sides and just welded it at middle without any support (meaning not connected to middle front column) but they don't seem competent for such connections and we are nervous about if such will even be stable. What you think? Is this connection stable?

The contractor wants to connect the sides at the perimeter w8x21 but I'm not allowing him. If he does that and the perimeter beam is flexible. How much load would the column sees? (remember rigidity can take more load than flexibility)

I would be much more concerned about moments resulting from earthquake or typhoon. Without any shear walls, your structure relies totally on bending of nine columns to provide stability. Are the exterior walls capable of acting as shear walls?

No the exterior walls are just composed of hollow blocks with mortar thrown into them. These mortars don't even mostly fill up the gap between column and hollow block for example. So it's effect on seismic may be insignificant.. or is it? We can't put braced frames either. What is your opinion. Also I plan not to use hollow blocks walls at the third floor to avoid more seismic base shear (our headache now is now to put up light wall walls). We still don't know what kind of wall to put up. (remember we were discussing how to put hollow blocks parapet above.. but decided not to do it anymore because of twisting problem). It must surely be lightweight for less base shear. Last if we remove the waterproof topping which becomes unnecessary because the presence of the roof. It's about 2 inches thickness so we will be removing unnessary SD load. But if I remove them all. I notice the moments in the ground column (one with epoxy) can increase. I'm still trying to understand your explanation of the 2 S put in top of each other signifying floors. You said a beam is shared by lower and top column. What scenario when the top column will have decrease in moment by certain pattern of column above the joint in next floor. This is what I've been trying to show you and understand.. You still haven' see the slight moments decrease between them?

 

[BAretired]

Tomorrow we will spend about 5 hours to bring it up because they are so heavy. W8x21 is 21 lbs per foot.. so per piece (21 x 20 feet)is about 420 lbs.. can't be carried by even 3 people. They need to pulley chain it up. 420 lbs is about 1.868253072 Kilonewton. So 1 complete rafters composing of 2 pcs are 3.736kN. Now there are many C-purlin sized 2x6" 1.8mm crisscrossing it spaced at 0.6 mtr apart.. so weight can reach 4.5 kN.. added the roof can reach 5 kN (do you have formulas to get weight of rafters and purlins over a rafter or column?). I'm worried this can further strain the column with epoxy void. We even plan to just put rafters at the sides and just welded it at middle without any support (meaning not connected to middle front column) but they don't seem competent for such connections and we are nervous about if such will even be stable. What you think? Is this connection stable?

You are modifying the design on the fly? You can't do that! If you want to change the roof framing, get the approval of the design engineer.

The contractor wants to connect the sides at the perimeter w8x21 but I'm not allowing him. If he does that and the perimeter beam is flexible. How much load would the column sees? (remember rigidity can take more load than flexibility)

I don't understand what you mean and I don't wish to comment. Check with the design engineer.

BA

 

[BAretired]

No the exterior walls are just composed of hollow blocks with mortar thrown into them. These mortars don't even mostly fill up the gap between column and hollow block for example. So it's effect on seismic may be insignificant.. or is it? We can't put braced frames either. What is your opinion.

My opinion is that the masonry walls will likely crack during an earthquake and cannot be relied upon structurally.

Also I plan not to use hollow blocks walls at the third floor to avoid more seismic base shear (our headache now is now to put up light wall walls). We still don't know what kind of wall to put up. (remember we were discussing how to put hollow blocks parapet above.. but decided not to do it anymore because of twisting problem). It must surely be lightweight for less base shear.

Why don't you get all these ideas on the drawing before proceeding with the work? What is the point of having architects and engineers if you are going to change everything as you go? Perhaps you could suggest a steel stud wall system to the architect; much lighter than masonry.

Last if we remove the waterproof topping which becomes unnecessary because the presence of the roof. It's about 2 inches thickness so we will be removing unnessary SD load. But if I remove them all. I notice the moments in the ground column (one with epoxy) can increase.

That does not sound right to me. I suspect your input is wrong.

I'm still trying to understand your explanation of the 2 S put in top of each other signifying floors. You said a beam is shared by lower and top column. What scenario when the top column will have decrease in moment by certain pattern of column above the joint in next floor. This is what I've been trying to show you and understand.. You still haven' see the slight moments decrease between them?

Consider any joint in your frame. Assume that a clockwise moment is applied to it. All members meeting at the joint rotate in a clockwise direction. The upper column feels tension on the right face. The lower column feels tension on the left face. The left beam feels tension on top while the right beam feels tension on bottom. That is all I was saying, nothing very mysterious. Since the opposite ends of those members are not free to rotate, a moment is introduced at the far end of each member which distributes among the members meeting at that joint according to their relative stiffness. That moment is counterclockwise.

I have seen your moment output but I haven't seen your input so I cannot draw any firm conclusions.

BA

 

[hocho]

I don't understand what you mean and I don't wish to comment. Check with the design engineer.

The contractor wants to follow the original plan where the sides of the rafter rested on the perimeter beam. I asked the designer if I can rest the rafter sides at columns instead. Designer said I can do either because it's just light roofting anyway and depends on the skill of the contractor. designer is just 22 years old.. and just operator of Etabs.. not really a pure blooded structural engineer. He has only 3% of your knowledge. Anyway. I'm talking of the following concept shared by Kootk in other threads where he stated:

"1) if an end deflects downwards, it will decrease the reaction at that end, increase the reaction in the middle, and decrease the reaction at the opposite end.

2) if an end deflects upwards, it will increase the reaction at that end, decrease the reaction in the middle, and increase the reaction at the opposite end.

3) if both ends and the middle support deflect the same amount, you're back to 5P/16 & 11P/8. "

So if the rafters ends at the perimeter beams deflect downwards, it will decrease the reaction at that ends, increase the reaction in the middle column.

Anyway. We'll just put the ends on columns to equally distribute the load.

I'd like to go back to this double S curvature... because with roofing put, the waterproof 2" topping below is useless and it's unnecessary SD load. The 22 year old designer said I could remove it or not.. depends if I want increased expenses of removal. We won't use jackhammer but just manually lifting the topping piece by piece..

This decision depends on my understanding of the moments redistribution of columns between floors. Back to the column curvature in the 2nd and second floor.

S
S

Note if the value of the 2nd floor S moment curvature is much larger.. there would be decrease in the moments at the top of the 1st floor column. You said earlier "Where the two "S"s meet, the moment acting on both upper and lower columns are clockwise. They are not opposite. They are the same. The only thing opposite about them is that they put tension on different sides of the column, but that is a consequence of geometry."

But there is clearly a decrease in the moments right below the joint. I was asking yesterday the explanation for the decrease. Again note you said a beam moment is shared by the column below and above it. So if the moment above is big it's because the bigger moment curvature above the joint makes it share more load from the beam and why the moments at the column below that joint decrease?? Of course we won't mean removing the reinforcement (because they are already casted in concrete.. just want this understanding as the last concept in this thread).

But this may not affect the moment much in the column base with epoxy void at ground.. isn't it. So I'm thinking it's better to remove the topping to lessen seismic load. Btw.. the columns are all rested on very big combined foundation designed for 4 storey (see below). So the other moment resisting system may hopefully compensate for the pinned like condition at the epoxy void (esp when almost 1.5 storey were not actually built and designer said the forces in the columns are much lower).

 

[hocho]

Consider any joint in your frame. Assume that a clockwise moment is applied to it. All members meeting at the joint rotate in a clockwise direction. The upper column feels tension on the right face. The lower column feels tension on the left face. The left beam feels tension on top while the right beam feels tension on bottom. That is all I was saying, nothing very mysterious. Since the opposite ends of those members are not free to rotate, a moment is introduced at the far end of each member which distributes among the members meeting at that joint according to their relative stiffness. That moment is counterclockwise.

I have seen your moment output but I haven't seen your input so I cannot draw any firm conclusions.

Let's just create a very simple beam span supported by 2 columns. The 3D of it is the following:

The following shows the beam and column moments.

In the following. Uniform load of 5 kN were added to the top beam. You can see that the moments of the lower columns decrease.. I simply want to understand why. Are you saying the counterclockwise thing you mentioned makes it looks like it decreases?

 

[BAretired]

In the following. Uniform load of 5 kN were added to the top beam. You can see that the moments of the lower columns decrease.. I simply want to understand why. Are you saying the counterclockwise thing you mentioned makes it looks like it decreases?

The upper sketch on the attached file shows column deformation when the Second Floor beam is loaded. The lower sketch shows column deformation when the First Floor beam is loaded. The blue shading indicates load.

The curved dashed lines show the column deformation under each load. It is apparent that a uniform load on the Second floor beam produces the opposite effect to a load on the First floor beam, that is the curvatures are reversed. That would explain why your base moment decreased with the addition of 5kN to the upper beam.

BA

 

[hocho]

The upper sketch on the attached file shows column deformation when the Second Floor beam is loaded. The lower sketch shows column deformation when the First Floor beam is loaded. The blue shading indicates load.

The curved dashed lines show the column deformation under each load. It is apparent that a uniform load on the Second floor beam produces the opposite effect to a load on the First floor beam, that is the curvatures are reversed. That would explain why your base moment decreased with the addition of 5kN to the upper beam.

Gee. Thanks. I couldn't have figured this out myself for many months. It's like the concept of superposition, isn't it. In superposition, there is really cancellation effect. Can't you say the decrease is due to some cancellation. So more load in the 2nd floor top can lessen the moments in the ground floor column. Now i'm in dilemma. If I remove the useless waterproof topping below the soon to be built roofing system above second floor slabs (not adhesively connected to topping), the moments in the ground would increase (making the epoxy void even more compressed). But if I retain it. It would be less bent even fulfilling what Doug described in the following because by lessening moments in the epoxy void.. more concrete can be mobilized and axial capacity increased much more. Note in gravity mode, if your column are more straight.. even in seismic base mode.. it won't be as bent.

Doug stated:
"The combined axial load and moment are equivalent to an eccentric vertical load, with the eccentricity on the compressive side. If you apply an additional load at the column centroid it reduces the eccentricity of the resultant load, and the width of the compression region increases, so the total compression force increases, but the maximum stress reduces. It's a similar situation to a footing with a vertical load outside the middle third. If you apply an additional load on the uplift side, the pressure on the compression side will reduce, even though the total reaction force is increased."

My problem is. If I didn't remove the waterproof topping. It would attract greater seismic load. Given similar situation. Would you remove the topping or not?