Calculation of Punching Shear Control Perimeter Eccentricity

[willowman]

Hi all,

Continuing in my pursuit to understand the punching shear checks of EC2 I am performing some hand checks of software results.

It seems that I am stumbling on the calculation of the eccentricity Δe. I found a worked example but I don't understand the method used to calculate Δex. I have always calculated the centroid of an object with x(bar) = ∑Ai.xi/∑A...using my method I don't arrive at the same answer as the worked example. On first inspection I presumed it would be as simple as taking one centroid away from the other?

Would anyone be able to explain from first principles how this calculation is being formulated?

P.S. I understand and can follow the simplification step.

Thanks,

 

[HTURKAK]

Calculate the centroid of critical perimeter ( in this case calculate the centroid distance from the boundary of flat slab free side ), und then subtract the center dist .of the column ( bc/2)

I am sure you can manage..





According to the grace of God which is given
unto me, as a wise masterbuilder, I have laid the foundation, and another buildeth thereon. . . .
I Corinthians 3:10

 

[willowman]

Hi,

Thanks for your response. I understand that this is the required method, my issue is that I haven't been able to arrive at the same expression for the control perimeter centroid as indicated in the picture.

Appreciate that this might be easy for you, but is less easy for me....

 

[andrews2]

It is done using the exact method you describe in your original post.

[Area of the right section (b+d) x it's distance from the left edge (b+d/2) + Area of the top and bottom section (2*(b+d/2)) x their distance from the left edge ((b+d/2)/2)] / [Total area (b+d) + 2*(b+d/2)] - column centroid/load location (b/2)

Make sure to ignore the left edge. It is free and does not contribute to the critical section.

 

[HTURKAK]

Believe me it is easy for you also. Consider the critical perimeter composed of line elements . Do not look for areas. The problem is to calculate the CG of U shape wire .

According to the grace of God which is given
unto me, as a wise masterbuilder, I have laid the foundation, and another buildeth thereon. . . .
I Corinthians 3:10