Modulus of elasticity of masonry wall

[abouferass88]

Dear Colleagues

i made a experimental tests on Masonry wall (0.5mx0.5m) that consists of two type of materials (limestone and plain concrete)

The limestone is located on the facade. this limestone is backed with plain concrete.

i got stress-strain curve for the limestone face and stress-strain curve for the plain concrete face.

My question is:
how can i get the modulus of elasticity of this wall from the two stress-strain curves.

any suggestion and any referance?


best regards

 

[JAE]

E = stress / strain in the elastic portion of your stress strain curve.

 

[abouferass88]

i got two stress-strain curve, one for the limestone face and the other for the plain concrete face

so i got two modulus of elasticity with different values


any suggestion how to get equivelent modulus of elasticity

 

[ishvaaag]

How to proceed depends on the kind of analysis you want to make. The best would be to retain the two layers as they are, to properly identify stresses within them.

It may get complicated, the stone part may not show any strength (even if notionally) in tension, so if reduced to a single layer of smeared properties you would be having different properties in tension than in compression. Furthermore the layers seem not be concentrical, so you would need to resource to the theory of composite shells to just retain some interesting values to some specific in-plane purpose; then the problem becoming more complicated with bending of the shell. So you need first define well your target intent.

For some simple purposes, just a simple application of the same principles used in composite beams (i.e., the use of some equivalent width) could be enough to identify interesting axial, shear and bending values. This is most useful of course when seeing the masonry column-wise. The depth in tensile stress -as identified maybe iteratively- may be dismissed for the equivalent section in the stone layer.

 

[SteelPE]

Here is a guess (I'm not at the office so I don't have my texts in front of me).

I seem to remember that load is attracted to stiffness (Force = stiffness * displacement). If the concrete wall is twice as stiff as the limestone wall then 1/3 of the load will go into the limestone wall and 2/3 of the load will go into the concrete wall.

Stiffness will incorporate E and a geometric property of the wall. For instance, if you were transferring axial load through the wall you would use the stiffness of a column = A*E/L (area of the column * modulus of elasticity / column length).

Next question, why would you want to transfer load through a facade?

 

[DST148]

To elaborate on what is already stated by SteelPE.......
Let us use subscripts 's' for limestone, 'c' for concrete, and no subscripts for the composite. Using the principles of simple strain, let us assume the deformation is the same for a specimen of limestone, concrete, and the composite of length L and under an axial load of P.
As + Ac = A ; Ps + Pc = P
(Ps . L / As . Es) = (Pc . L / Ac. Ec) = (P . L / A . E)
You can substitute the values and obtain equivalent modulus of elasticity of the composite from pure axial strain point of view.
Per building codes, typically E is related to the compressive strength of the masonry.
By the way, what exactly is the objective of conducting this experiment?

 

[DST148]

abouferass88 - My previous response was based purely from strength of materials point of view using simple strain behavior.
You may refer to ASTM E 111 - Test method for Young's Modulus, Tangent Modulus, and Chord Modulus for better guidance.