Calculate load from deflection.

[bpeirson]

I have a column made from W150 x 30 (W6 x 20) which is 3650mm (12 feet) tall. It is deflecting 102mm (4 inches) at the top. My calculations for the moment force (torque) at the base come to approximately 107 kNm (78920 Ft-lbs).

Can anyone confirm my calculations.

 

[aggman]

We need more information. What is the elastic modulus you used? How is the load applied? Is there any axial load? Why don't you post your calculations for us to look at?

 

[JAE]

Do you know if the base has rotated at all? This would have a large effect on the moment at the base.

Is it strong axis or weak axis bending?

 

[UcfSE]

We actually need a little more information. The stiffness of the column will depend on the load type and location, whether thats a point load at the top of the column, a uniformly distributed load, or some other load type. Because the stiffness varies with load type and position, the back-calculated load can also be different for a given deflection and hence the base moments would also be different.

 

[JAE]

jeesh UcfSE - there we go again!

 

[UcfSE]

 

[bpeirson]

The column is Ell shaped with a W6 x 20 base and is loaded by cantliver arms spaced evenly along one side with the top arm at 100" above the base. The 4" deflection was measured at 144" above the base. It is an assumption that the deflection measurement is accurate.

The arms and base are 48" long.

From the base up to the top the UDL's are 6,000 lbs (on W6 x 20 base), 1,000 lbs, 1,000 lbs, 2,500 lbs, 2,000 lbs, 2,000 lbs, 2,000 lbs & 1,500 lbs.

If I can find a web link to a suitable picture I will add it to the thread.

 

[haynewp]

UCFSE,

What do you mean when you say the column stiffness varies with load type and location?

 

[Dinosaur]

I just want to point out that your column is deflecting at a ratio of 1 : 36. Is this of any concern to you?

 

[bpeirson]

Dinosaur, the deflection is a concern but the column is not at my location so I can not confirm the deflection.

I have very little faith in the ability of people to measure this kind of thing unless they are required to sign off on a legal document regarding the accuracy of the measurement.

It is my opinion that the measurement was taken by an individual standing on the floor and guessing the measurement based on the spacing between the wall and the column.

I have personally stood beside people while they did the same type of measurement in similar situations. None of the people I have been with took into consideration the slope on the floor which can be a source of considerable lean.

My estimate for the true deflection for this column would be between 0.5" and 1". I have not calculated this kind of deflection for more than a year and a half. I do not trust that I am doing it 100% correctly, that is why I have opened it up in this forum.

 

[JAE]

bpeirson,

Yes, definitely post a picture. You didn't provide the height of each arm and exactly where the loads are located on the arms.

 

[UcfSE]

Perhaps I used the wrong terminology. I meant "stiffness" to be the force that causes a unit deformation. A point load at the top of the column will have a different stiffness than will a column with a point load in the middle of the column (different location) and will again be different for a uniformly distributed load.

For a point load at the top of the column (base fixed, top free to tanslate and rotate), the force per unit deformation is 3EI/H^3 where "H" is the full height of the column. A point load in the middle of the column will have a "stiffness" of 3EI/(H/2)^3, obviously different. Using a given deformation and the stiffness of the column for that load configuration, you can calulate the force that would cause the given deformation. With that force now known you can calculate the base moment that is induced by the deformation.

 

[bpeirson]

Jae, the top arm is at 100" the others are not evenly spaced but since there are 7 total I felt that evenly spacing them for calculations would be sufficient.

The loads are uniformly distributed along the arms. As an example the top arm has 1,500 lbs spread evenly along 4 feet.

The most important thing for me is to determine if the 4" deflection is possible given the loading. If an approximation of the loading gives a result of 1" deflection then I will ask the man in the field to determine if the measurement is correct.

I don't want to get hung up on exact numbers for arm placement etc. due to the unwavering ability of people to exceed or circumvent design limitation. As an example what if all the loads are within the 1 1/2 feet of the column. Some assumptions have to be made, loading conditions may be changing on an hourly basis.

If someone on the forum came back to me and said that a 4" deflection would only be possible if 6 times the loading were put on the 7 each 4 foot arms then that would be definitive enough for this case.

If I gave you the exact measurements of the arm elevations it may only complicate your calculations. Additionally the accuracy could be voided if the weights I have recieved from the field are guesses rather than actuals.

I am sending a trusted rep to the site to confirm measurements and I can post them Monday.

I'll check for web images today.