I have done an experiment on a continuous composite slab and have acquired displacement and strain data at different section. Now I want to calculate maximum bending moment capacity of it. The simple way to do it by using the eqn M/I=sigma/y
sigma=modulus of elasticity(E) * strain(e)
So, M=eEI/yHere, I used
e=max strain at which the specimen failed
I=moment of inertia of equivalent section below/above NA
I don't know if this gives the correct value of bending moment. Can anyone help me for the solution?
Hi Rajan Khadka,
The equation M/I=sigma(y)/y =sigmamax/ymax is correct for the beam bending theory. Here I is moment of inertia of whole section, ymax is maximum distance from NA. For example, in the case of rectangular section bxh: I=b*h3/12, ymax=h/2.
But your assumption that Hooke's low is valid until failure must be justified.
Thank you so much Om Prakash Chhangani sir and Victor J. Аdlucky sir for your reply. I am still not clear. So are the strain data from my experiment used just to find out the NA depth? Rest of the calculation is done based on a suitable theoretical concept or eqn?
Dear Rajan Khadka ....
Good question… Please check these references below.. hope it will be helpful for you…
http://academic.uprm.edu/pcaceres/Courses/INME4011/MD-3A.pdf
http://www.ae.utexas.edu/courses/ase369k/labs/sample_second_order.pdf
Regards…
Hi Rajan Khadka,
If the slab cross-section is symmetrical regarding horizontal axis, you needn't any experiment to find ymax, because ymax=1/2 slab depth. I meant that strain data are obtained on the slab top surface, that's why ymax is used. Of course, the strain data can be used to find M from eqn M=e*E*I/ymax. But this eqn implies that the slab behaviour remains elastic (i. e. sigma=E*e) until failure. This assumption must be somehow justified.
Hussam Ali Mohammed sir, I will check those. Thank you so much.
Victor J. Аdlucky now it pretty much clears what you suggested. The eqn holds true until the system remains elastic. So for ultimate failure, I must consider plastic criteria as well. Thanks for your response.
If strain data at surface is available beyond elastic range and upto failure, then one can take help of yield line theory .
Rajan Khadka .......
Please check references below.. hope it will be helpful for you…
Regards…
http://www.ae.utexas.edu/courses/ase369k/labs/sample_second_order.pdf
If the failure is in the elastic range(brittle type), then your calculations are correct.
Otherwise not.
Thank you Poonghat Adityan Krishanan sir. For my case, the failure is not in elastic range, then how can I calculate the bending moment at failure? Are there any simplified eqns? I want a quick method just like above mentioned one.
Hi Rajan Khadka,
You can use bilinear elasto-plastic model:
sigma =E*e, e=sigmayield/E,
where E – Young’s modulus; sigmayield – yield stress; Et – tangential modulus (0
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