Correct Bending Moment in an Embedded Washer Plate (Anchor)
Correct Bending Moment in an Embedded Washer Plate (Anchor)
(OP)
I need to reduce the overall cost of a connection by as much as possible, and the only area where I see I could achieve that would be in the washer plate thickness. Right now I am not sure if my washer plate is too thick, so I am questioning whether I have the right bending moment.
The problem:
I need to fully develop a 1" threaded rod that has a 10" embedment depth in CIP concrete. In order to achieve the pullout and shear strength required, I need to attach a 4"x4" washer plate centered with a 1-1/8" diameter hole. The washer plate would be held in place by a nut threaded from the bottom. My question is what would be the most accurate way to determine the true moment in the washer plate?
I've seen some calculations (from an overly conservative engineer) where they considered M=PL/4, but that is ridiculous.
I believe considering a cantilever beam with a UDL (M=(wL^2)/2) is still too conservative. (half the moment as above)
Now I read about elastic theory of plates, and got that the max moment would be M=0.048wL^2
This number I like, but since the deflection is much greater than the thickness of the plate, it is not really applicable. However, since the plate is confined in the concrete, as in it is not going to deflect anywhere, would the moment I get from the elastic theory of plates be okay to use to design the washer plate thickness?
Any help or input on this would be greatly appreciated.
The problem:
I need to fully develop a 1" threaded rod that has a 10" embedment depth in CIP concrete. In order to achieve the pullout and shear strength required, I need to attach a 4"x4" washer plate centered with a 1-1/8" diameter hole. The washer plate would be held in place by a nut threaded from the bottom. My question is what would be the most accurate way to determine the true moment in the washer plate?
I've seen some calculations (from an overly conservative engineer) where they considered M=PL/4, but that is ridiculous.
I believe considering a cantilever beam with a UDL (M=(wL^2)/2) is still too conservative. (half the moment as above)
Now I read about elastic theory of plates, and got that the max moment would be M=0.048wL^2
This number I like, but since the deflection is much greater than the thickness of the plate, it is not really applicable. However, since the plate is confined in the concrete, as in it is not going to deflect anywhere, would the moment I get from the elastic theory of plates be okay to use to design the washer plate thickness?
Any help or input on this would be greatly appreciated.






RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
Perhaps a circular plate would be more efficient. What is your source for M=0.048wL^2? Your comment about the plate being confined in the concrete and not going to deflect anywhere is totally without merit.
BA
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
That is what I had used (except (wL^2)/2 , but it comes out to the same moment). I am just thinking that it is a square plate and it would behave in bending similar to a two-way slab (with a point load in the center), thus reducing your max moment because of two way action.
I got the M=0.048wL^2 from some online course notes or an article on plate theory. I'll provide the link tomorrow.
Just wanted to see if I am out to lunch on this, as I am getting an ear full in the office for being too conservative in my designs. So I am questioning whether my analysis is indeed to conservative.
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
However there is no account for the hole here: a more realistic approach would be by taking an annular plate with the same area as the square.
Also, depending on the thickness, shear in the plate at a diameter determined by nut size could be governing.
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RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
Draw the washer, including the hole, shade the area under the nut, that is the effective area. Divide the force by effective area above and below and check a series of free body pieces, probably starting at a corner and moving towards the center, then repeat starting at an edge. That should find your worst case.
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
@haynewp Interesting take. The only thing I would do differently would be to take out the hole area (~1 in^2), to get a plate area of 15 in^2. This would give M=0.133*P. However this topic is new to me, so I would have to read up on orthogonal yield lines and diagonal yield lines to get a better understanding of its application. Thanks for your suggestion.
@paddingtongreen Well according to my boss, a few years ago when our company was super busy I don't think anybody cared nearly as much about money as they do today. It is all about budget, being more competitive and saving every penny where possible. Right now I have the plate sized at 1" thick, but with the above suggestions I think a 1/2" thick plate could work. Factor in over 700 of these connections and the savings add up. I do agree with you on the labor being much more expensive, and in the grand scheme of things the savings would be tiny compared to the overall project cost, but it just goes back to the points of being more competitive on bids and every penny counts. No work...no job.
Regarding your suggestion, I do not understand the second part. Anywhere I could find an example of this or some reading on this topic?
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
I recall reading elsewhere that plate washers are rather ineffective. I think it may have been in AISC Design Guide 1.
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
With a 10" embedment, a standard nut and washer will satisfy the bearing requirements and the factored pull-out requirements of a threaded rod provided its yield strength does not exceed 400 MPa (58 ksi) and f'c = 25 MPa (3600 psi) or better.
Getting rid of the square plate entirely is the ultimate in economy.
BA
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
"The addition of plate washers or other similar devices
does not increase the pullout strength of the anchor rod,
and can create construction problems by interfering with reinforcing
steel placement or concrete consolidation under the
plate. Thus, it is recommended that the anchorage device be
limited to either a heavy hex nut or a head on the rod. As an
exception, the addition of plate washers may be of use when
high strength anchor rods are used, or when concrete blowout
could occur."
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
For a 1" dia. rod, the nut size is 1.5" across the flats, so the cantilever is (4 - 1.5)/2 = 1.25". The uniform pressure is P/16, so the one way bending moment per inch of plate is (P/16)*L2/2 = (P/16)*1.252/2 = 0.0488P or a total of 0.195P across the full 4" plate. I do not see a more critical yield line than this.
BA
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
See page 141.
http://books.google.com/books?id=yTFOLdUaG9EC&...
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)
BA
RE: Correct Bending Moment in an Embedded Washer Plate (Anchor)