Bearing Plate Calculation Over a Large Hole

[Geocontractor]

I have a hole cored through a 4,000 psi concrete wall at 30 degrees from horizontal. A grouted anchor has been installed through the wall and will be stressed to 100 kips maximum. The cored hole is 5" in diameter leaving a 6"(+/-) hole along the vertical face of the wall. The beveled washers that will go one prior to the anchor nut are approximately 5" square. I have calculated the size of the bearing plate to be 9" square with a 2.5" opening in the center. What I can't determine is the required thickness of the bearing plate. Any suggestions? Thanks.

 

[PEinc]

Try Roark's Formulas for Stress & Strain by Warren C. Young. I'm not sure if the book deals with oval shaped holes. However, you could conservatively assume a circular hole with the larger diameter.

Also, don't forget to account for the vertical component of the anchor force which will tend to push the bearing plate down the face of the wall. You will need to bolt the plate to the face of the wall. Since the anchor threadbar tendon is not normal to the bearing plate, the hole through the bearing plate will also need to be drilled at a 30 degree angle or be oversized.

Is this a permanent application or a temporary application? If permanent, don't forget to provide an extra hole in the plate (or, if using strand tendons, in the tendon anchor head) to be used in filling the "trumpet" with grease or grout.

 

[PEinc]

P.S. frequently the tendon supplier(s) will size the bearing plates for their customers. Just tell them exactly what you need.

 

[dik]

You may want to consider...

Round simply supported edge with a small circular loaded area at the centre...

M = 0.013[6 + 8 * ln(R/r) - (r/R)^2]W for simply supported circular edge.
W - total force
R - radius of hole
r - radius of strand
t - plate thickness
and deflection is approx

Delta = (0.21 * W * R^2)/(E * t^3)

from p29, Strength of Aluminum Handbook by ALCAN

and plastic moment resistance = 7 * t^2 * Fy / 4

from p39, Strength of Aluminum Handbook by ALCAN

 

[boo1]

dik, aluminium's stress strain relationship is different than steel. Is the eq. appliable to steel?

 

[dik]

boo1... and wood is different, too... <G>

I don't know for sure... but for small strains, I would suspect that aluminum stress-strain is relatively linear... and since the formula has an E value, not an embedded value, I would suspect and have used other formulae in the publication for steel... I don't know their source of the formulae...

 

[prex]

Geocontractor
see my reply in thread507-65619.

prex

http://www.xcalcs.com

Online tools for structural design

 

[PEinc]

Geocontractor,

The thread has gotten a little off topic from your particular tieback anchor application. I have designed lots of steel bearing plates for a major tieback anchor contractor and for a major tiedown anchor tendon and bearing plate supplier for loads up to almost 2000 kips over holes in concrete. I would use the Roark book as I suggested above.

 

[boo1]

Peterson, Stress Concentration Factors, 2nd Ed, page 191, Eq 4.26, lists an eq for symmetrically reinforced hole in finite - width element in uniaxial tension.