Tension on bolts in anchor plate on concrete wall

[DMT69]

Hi. I need help calculated the tension on bolts in an anchor plate.

The plate is bolted to a concrete wall with four bolts (see the included image). A bending moment acts on the plate, offset a bit up/down. The bending moment acts from up to down so that the upper two bolts are in tension and concrete under the lower part is in compression.

I would like to know how to calculate the tension induced on the upper two bolts by this bending moment.

Image is here:

https://drive.google.com/file/d/0B7abncbCKejtT3RZUFU4QTM2WlU/view?usp=sharing

In case the image link isn't working:

Bending moment: M
Plate width: w
Plate height: h
Horizontal distance between bolts: a
Vertical distance between bolts: b
Distance from lower bolts to the horizontal axis that the bending moment bends around: d

Thanks.

 

[tech99]

Hi. I need help calculated the tension on bolts in an anchor plate.

The plate is bolted to a concrete wall with four bolts (see the included image). A bending moment acts on the plate, offset a bit up/down. The bending moment acts from up to down so that the upper two bolts are in tension and concrete under the lower part is in compression.

I would like to know how to calculate the tension induced on the upper two bolts by this bending moment.
Not sure if the moment is intended to be in the plane of the plate, or is it at right angles to the plate?
Image is here:

https://drive.google.com/file/d/0B7abncbCKejtT3RZUFU4QTM2WlU/view?usp=sharing

In case the image link isn't working:

Bending moment: M
Plate width: w
Plate height: h
Horizontal distance between bolts: a
Vertical distance between bolts: b
Distance from lower bolts to the horizontal axis that the bending moment bends around: d

Thanks.

 

[tech99]

Not sure if the moment is intended to be in the plane of the plate, or is it at right angles to the plate? [Apologies, I previously messed up the quotation].

 

[DMT69]

If you imagine a horizontal line across the plate then the moment is around that. Directly out of the wall on top and directly into the wall on the bottom.

Alternately imagine a beam attached to the plate sticking straight out of the wall with a weight on the end. The direction of the bending moment that would create.

 

[tech99]

If you imagine a horizontal line across the plate then the moment is around that. Directly out of the wall on top and directly into the wall on the bottom.

Alternately imagine a beam attached to the plate sticking straight out of the wall with a weight on the end. The direction of the bending moment that would create.

I think the assumption is going to be that the plate pivots on the lower bolts (imagine that the bolts are all slightly loose). The moment is resisted by the tension in each upper bolt times "b". There is also a compressive force beneath the plate at the lower bolt holes equal to the tension in the upper bolts, but not producing a moment as it acts through the fulcrum. All bolts will be additionally subject to shear caused by the weight. In practice, the bolts might be pre-tensioned so that no change in tension or movement occurs with load.

 

[OldEngr63]

Looks to me like a better model would be to say that the lower edge of the plate remains in the plane of the wall, and everything above that moves away from the wall (assuming an entirely rigid plate).

 

[DMT69]

I have a program I am using that gives the final results (I am trying to emulate the calculation). Changing the distance to the lower bolts and the lower edge both affect the result, so both must be used in the calculation. However the distance to the edge of the plate above the upper bolts doesn't make a difference (which makes instinctive sense).

There seems to be a "pivot point" that is not always level with the lower bolts or the lower edge, but moves depending on the geometry, but is usually somewhere "relatively near" the lower bolts. My guess is the the tension will be the bending moment divided by the distance from this point to the upper bolts, but the question is how to find this point?

As an example, with a completely symmetrical case: plate 300 mm on a side, 200 between the bolts in all directions (so 50 mm to the edges) with a 1 kNm bending moment, the program says the lower bolts are actually in tension, not compression (very, very little tension): 2.099 kN on each upper bolt, 0.095 kN on each lower bolt, 4.389 kN of compression on the concrete at the lower end of the plate. The "pivot point" appears to be near the lower edge. Reverse engineering it a bit gives a distance of roughly 228 mm from the upper bolts to the "pivot point", which puts it 28 mm below the lower bolts.