Calculate Beam Deflection Using Spreadsheets

[Bozzo]

I have created a simply supported beam spreadsheet to design wood beams. I have figured out that with the use of Superposition I can combine the affects of each load to determine the total affect on the beam. I have used this principle to determine the shear and moment at every 100th of a foot on the beam. Now that I know the moment at every point on the beam is there an easy way to calculate the deflection using the Moment-Area Method or Conjugate Beam Method?
I need something that will give the deflection at any point along the beam for any load case.

Can I Double Integrate the moment at each point on the beam to determine the slope and deflection?

 

[boo1]

yes

 

[desertfox]

Hi Bozzo

You can use any of the methods you mention however the method you choose should be one that suits your requirements best ie:- "the moment area method" is useful when you require a slope or deflection at a single point with reference to another point having zero slope.

The direct intergration method is useful when the bending moment equation is valid across the whole length of the beam.

I don't think you will find a single method suited for all loading conditions and you may have to choose a method as stated earlier.
Several other methods to mention which I have used in the past are "step functons","Macaulay's method","Castigliano" and "Srain Energy"

regards

desertfox

 

[Neilmo]

Hi Bozzo,

You already have the bending moments at every 100th of a foot, so why not continue along the same lines with the method of `virtual work`.
If you are not familiar with this method -

Apply a unit load (1.0 with no units) to the the beam at the position where the deflection is required and calculate the `unit bending moments` at every 100th of a foot.
Then at each 100th of a foot, multiply the two bending moment values to give a third value (lb.in^2) at each position. Calculate the area under the new set of values (lb.in^3) and divide by EI (lb.in^2) to give the deflection (in) at the point of `unit load`. Repeat the procedure at each point along the beam to find the deflection at each 100th of a foot.

The formula is simply - deflection = M.m.dx/EI

The calculations are repetitive, but should be easily programmable into a spreadsheet!

Regards,
Neilmo

 

[Bozzo]

Thanks everyone, especially Neilmo. The sheet is working great.

 

[Neilmo]

Glad to be of help.

Neilmo