Calculate the deflection of a column/beam

[ksk_10594232]

Hi

I want to calculate the deflection along a column (or a stand-up beam) subjected to a lateral point load. The column is fixed at both ends, A and B, and the load P is acting at a distance a from the top. I know that I can easily calculate the deflection at the point of action (P), however I don't know how to determine the deflection at an arbitrary position away from P, lets say L/2. If somebody can bring some knowledge to this, I'll be very thankful 🙂

[terryhendicott]

Hi,

Without an axial load it is the same as a beam.

https://www.engineersedge.com/beam_bending/beam_bending19.htm

[ksk_10594232]

Thank you.

I have made an attempt to plot the deflection along the column, but I didn't get it completely right for z-values (or x-values) exceeding a.

[LucMeekes]

Attach your Prime worksheet please.

[ksk_10594232]

The file is now attached 🙂

[LucMeekes]

Your expression for the part where z > a does not depend on z, so it's a constant.

Success!

Luc

[ksk_10594232]

True! So how do I define an expression for the deflection along the whole beam?

[LucMeekes]

As far as creating an expression for the entire range of z, you did the right thing, with (z<a)*(first part) and (a<z<L)*(second part).

Make sure you use z also for the second part. I've 0 knowledge of structural engineering, but the engineer in me suspects that v should not be the big player in that part.

Success!
Luc

[LucMeekes]

Found some expressions here https://home.engineering.iastate.edu/~shermanp/STAT447/STAT%20Articles/Beam_Deflection_Formulae.pdf

See if this looks right:

Success!
Luc

[LucMeekes · Accepted solution]

Ah,  I see now that your beam should be fixed (instead of just supported ) at both ends.

That apparently changes the situation. In the expression of the second part, simply replace v with (L-z), because that's what v is.

Then you get:

I've added a bar at height a from the top, to indicate the load point.

Success!
Luc

[ksk_10594232]

Amazing, thanks Luc! 🙂