## Relative Rigidity of Shear Walls

## Relative Rigidity of Shear Walls

(OP)

I am studying for my SE exam and am trying to understand some discrepancies in the equations for Relative Rigidity of Shear Walls. I have found several different sources that cannot seem to agree on an equation.

For example, the Masonry Chronicles from Spring of 2009 states that a fixed-fixed wall has a deflection of ((h/l)^3)+3(h/l)) and therefore a rigidity of 1/(((h/l)^3)+3(h/l))). I am finding other sources that say the rigidity equation for a fixed-fixed wall should be 1/((0.1(h/l)^3)+0.3(h/l))). I recognize that these are merely a difference in order of magnitude of 10, but where is this discrepancy being resolved?

Ultimately, the forces in each wall will end up being the same with either equation due to the distribution of forces being a ratio of the relative rigidities, but why the difference in deflection?

For example, the Masonry Chronicles from Spring of 2009 states that a fixed-fixed wall has a deflection of ((h/l)^3)+3(h/l)) and therefore a rigidity of 1/(((h/l)^3)+3(h/l))). I am finding other sources that say the rigidity equation for a fixed-fixed wall should be 1/((0.1(h/l)^3)+0.3(h/l))). I recognize that these are merely a difference in order of magnitude of 10, but where is this discrepancy being resolved?

Ultimately, the forces in each wall will end up being the same with either equation due to the distribution of forces being a ratio of the relative rigidities, but why the difference in deflection?

## RE: Relative Rigidity of Shear Walls

relativerigidities of the walls to be used in distributing forces. If you want to find the actual displacements, you will need to use the the first equation.## RE: Relative Rigidity of Shear Walls

I just used a first principles approach to try to find a corresponding shear deformation value for a concrete wall.

Long story short, I used a value of 0.15 for poisson's ratio (v) and got 2.3Ph/EA. Why would the masonry code give a smaller shear deformation all things remaining equal?

Some background, I used (delta) = Ph/GA, where G = E/2(1+v)

Furthermore, in order to achieve the masonry equation above (1.2Ph/EA), you would need a negative value for 'v.'...

What am I missing?

## RE: Relative Rigidity of Shear Walls

Dik

## RE: Relative Rigidity of Shear Walls

## RE: Relative Rigidity of Shear Walls

## RE: Relative Rigidity of Shear Walls

## RE: Relative Rigidity of Shear Walls

Thanks for the clear up. I was hoping I wasn't going crazy there.

## RE: Relative Rigidity of Shear Walls

## RE: Relative Rigidity of Shear Walls

Also, the masonry code, ACI 530-11 section 1.8.2.2.2 defines E

_{v}= 0.4 E_{m}. Similarly for concrete, ACI 318-11 commentary section R8.8.2 states ". . . the shear modulus may be taken as 0.4 E_{c}."## RE: Relative Rigidity of Shear Walls

I'm working in Canada with CSA A23.3 and as far as I can tell there's no clause stating that the shear modulus should be taken as 0.4Ec. I could be mistaken about this so if anyone's aware of this clause please let me know.

Anyhow, for that reason I revert to first principles: G = Ev = Ec/2(1+poisson), for poisson = 0.15, G = Ev = 0.43Ec. So far so good.

So then I compared the shear deformation formulas for masonry and concrete separately. The reason being is that I would expect more deformation to come out of the masonry formula, all things equal. (I realize that all things aren't equal, but bear with me).

For masonry, as per previous posts, = 1.2Ph/0.4EA = 3Ph/EA

For concrete, as per my derivation = Ph/0.43EA = 2.32Ph/EA

Hence the 30% more shear deformation in a masonry wall compared to a concrete wall with identical P,H,E,A (should such a thing exist).

## RE: Relative Rigidity of Shear Walls

## RE: Relative Rigidity of Shear Walls

Thanks for your time.

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## RE: Relative Rigidity of Shear Walls

## RE: Relative Rigidity of Shear Walls

I used to use P=1000KN based on my senior notes but I have never seen any books discussing why P is assumed to be 1000KN or other values if any.

Thank you.

## RE: Relative Rigidity of Shear Walls

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