Shear stress-strain curve

[hooman_m]

Dear colleagues
I`m working on liquefaction resistance of sand utilizing shaking table tests.
i want to draw shear stress-strain curves for each test and i need help from you,my Physicist colleagues. my model container is 200*70*50cm and i`ve put acceleration transducers at depth 7,21 and 35cm from top.I have a general idea of how i can draw shear stress-strain curves using time history of acceleration but i`m not sure about it.i would be more than happy if you can help me.
I guess for determining shear stress at any point i can use t=sigma miai from top to the point of interest.which t is shear stress ,mi is mass at any point and ai is acceleration at any point.and i simplify the process by assuming acceleration is linear through depth.am i right about the process? and i`m so confused how i can determine shear strain at any depth.
i would appreciate your help

 

[Studiot]

First you need to get your concepts correct.

Force (not stress) = mass x acceleration, .

Stress = force/area

Second it is a good idea to define all the terms in your proposed formula. What is sigma?

You also need to realize that in a granular material such as sand the mechanism for carrying stress depends upon the water content.

What do the accelerometers measure the acceleration of? The sand or the container wall?

 

[hooman_m]

τ=∑〖m_i a_i 〗/area of the face of container wall and sand is saturated.i put the mentioned accelerometers into the sand so it measures the acceleration of saturated sand.i also measure the acceleration of container wall with another accelerometer if it helps.