## Sign Convention !

## Sign Convention !

(OP)

Hi all

As a matter of interest to learn how to design a reinforced concrete buildings, I have started reading a book named "Reinforced Concrete Design (7th edition) to EuroCode 2, by Mosley ... "

My questions may seem to be obvious and easy, but it really confused me. While I am reading Analysis Section, the book considers the following sign convention;

the question is how the equation shown in the photo below has been found ? I mean the signs of all actions (loads) and Moments.

Should not the book show the direction of M(AB) and M(BA) in the free body diagram to expect the sign of them ?

Hope find anyone who could explain to me.

Thank you

As a matter of interest to learn how to design a reinforced concrete buildings, I have started reading a book named "Reinforced Concrete Design (7th edition) to EuroCode 2, by Mosley ... "

My questions may seem to be obvious and easy, but it really confused me. While I am reading Analysis Section, the book considers the following sign convention;

the question is how the equation shown in the photo below has been found ? I mean the signs of all actions (loads) and Moments.

Should not the book show the direction of M(AB) and M(BA) in the free body diagram to expect the sign of them ?

Hope find anyone who could explain to me.

Thank you

## RE: Sign Convention !

Your moment diagram will follow the basic deflected shape of the beam, the non-Euro book would be opposite. The bottom line for the design stays the same, so don't let it hinder your learning.

## RE: Sign Convention !

the equation looks to be sum moments about end B (as stated), CW moments +ve. The possible ambiguity is whether the moment terms are signed or absolute values.

The reaction moments are … Ma is CCW and Mb is CW, to react the applied loads/deflections. So … I guess I'd change the moment terms sign … but …

another day in paradise, or is paradise one day closer ?

## RE: Sign Convention !

Yes exactly. that what I notice the moment orientation is different from European to Americans. For Example in american book CW FEM

consider as positive and CCW FEM as negative which is opposite to European.

This is one of the reason that confused me as the structural analysis book that we used in university "Structural Analysis 7th edition, by Hibbeler" is an american book, where the book I am using for concrete design is European book as we here follow British Standard in Design.

## RE: Sign Convention !

if we follow the sign convention in point 1 as shown in the photo below

the signs of M(AB) and M(BA) shown in the equation is correct if we consider M(AB) as CW and M(BA) as CCW.

However what about the remaining loads; uniform load and V(AB)?

I am wondering why the direction of moments M(AB) and M(BA) are not shown in the free body diagram? it would be easier for the reader to follow-up the author idea.

## RE: Sign Convention !

Va*L-1/2*w*L^2 -Ma+Mb = 0 … with the moments drawn the way I assume them to be, but these directions cause hogging so by the sign convention …

Va*L-1/2*w*L^2 +Ma-Mb = 0 … given that moments are +ve in a "sagging" sense (ie CW at A, CCW at B)

another day in paradise, or is paradise one day closer ?

## RE: Sign Convention !

## RE: Sign Convention !

another day in paradise, or is paradise one day closer ?

## RE: Sign Convention !

But the sign of loads Vab and w are opposite to what shown in the book itself.

## RE: Sign Convention !

another day in paradise, or is paradise one day closer ?

## RE: Sign Convention !

## RE: Sign Convention !

I assumed the same directions and came up with a different moment equation and then figured out the difference so I could get the same equation with some logical reasoning.

The point to my last sentence (in my previous post) was much like your post … the moment is acting in a particular direction … +ve in one sign convention, -ve in the other.

another day in paradise, or is paradise one day closer ?

## RE: Sign Convention !

So we can say the direction of Ma and Mb shown in my last sketch are correct. BUT still the signs of Va and w in my equation is different to the one shown in the book I use.

In general, I used to consider different sign convention by other book for analysis, which is different to the one considered in this design book. But I raised this question to know exactly how this equation found.

## RE: Sign Convention !

I think the sign convention used is:

V is positive upwards.

M is positive sagging.

W is positive downwards, sometimes adopted as most loads are due to gravity.

## RE: Sign Convention !

"In general, I used to consider different sign convention by other book for analysis, which is different to the one considered in this design book. But I raised this question to know exactly how this equation found."

If you Know your positive sign convention then you can work with it. If you can understand a different sign convention (like in this book) then you should be able to show that the answer does not depend on the +ve sign convention (only the sign of the moment will change as you change which way is +ve).

another day in paradise, or is paradise one day closer ?

## RE: Sign Convention !

I got the feeling it's part of a continuous Beam, that's why no moment reactions are shown, moment is an internal force at the ends of this segment.

## RE: Sign Convention !

yes, I agree. They've shown w positive down, and the shear reactions +ve up … both pretty standard conventions.

They're being "pedantic" about the "+ve moments cause sagging" convention 'cause in the general case (of moment distribution along a multi-span beam) it is difficult to see which way the moments would be so apply one convention consistently. Had they used "+ve moments cause hogging" this would have been more consistent with their force convention but … meh!

another day in paradise, or is paradise one day closer ?

## RE: Sign Convention !

Yes it is a part of continuous beam. But even though shouldnt moment direction to be shown ?

See the image below

## RE: Sign Convention !

They could easily have draw their +ve convention (sagging moments) on the BM diagram, where the -ve value shows the end moments to be hogging (as we'd expect).

another day in paradise, or is paradise one day closer ?

## RE: Sign Convention !

Agent666, the shear force is also an internal force, but is nonetheless shown on the diagram? The external reaction will be the sum of the shear forces from the two adjacent spans.

(So glad this thread hasn't wandered into shear force sign convention. Does my head in.)

## RE: Sign Convention !

If shear is above the member segment on a free body diagram its going up working left to right, moment acts in a direction on any free body diagram consistent with tension on that face of the member. Take your hands and twist at each end of an imaginary member in the air to put tension due to bending on the same side as the diagram, the twist direction your hands are making is the direction/sign convention of the moment (EDIT - at any point on the beam).

## RE: Sign Convention !

End moments coming out of analysis methods like moment distribution are like support reactions. They're usually considered positive when counterclockwise in the global coordinate system.

That's different from a "bending moment" which is with respect to the member local coordinate system. Typically, a positive bending moment puts the bottom in tension.

## RE: Sign Convention !

## RE: Sign Convention !

Hope u did not forget the subject .

I have contacted one of the authors through the publisher.

Please see attachment No 1 addressing the sign convention point.

Attachment No. 1

https://files.engineering.com/getfile.aspx?folder=...

Attachment No. 2, he solved one exampled for more clarification. However, to understand the example u need to have the table below.

Attachment No. 2

https://files.engineering.com/getfile.aspx?folder=...

Regards.