Cantilever spreadsheet for dummies

  • Thread starter Dingomack
  • Start date
  • #1
3
0

Main Question or Discussion Point

Any (ideal) beam of length L, bent with a deflection of δ will have the same parabolic curve.

If that underlying assumption is wrong I am in trouble...

(Lots of views on the other thread, but no posts...so I'll try and boil it down to its essence)

Imagine:
Cantilever beam of length L with a concentrated load at the free end producing a curve. Draw a chord on the curve and you have an aerofoil with a width that varies along it's length - narrow at the ends and fatter near the middle. Lets call the widest point the maximum camber (Cmax).

I need to produce an excel spreadsheet where I can input a desired Cmax and a beam length L and output the required deflection of the beam, all in millimeters.

To help me get there I think I need equations for the following:

Q1. Calculate Cmax as a percentage of the chord length,
Q2. At what distance from the fixed end of the beam does the Cmax occur? If my first assumtion is correct - this should be a constant.
Q3. For a given Cmax and beam length L what is the deflection required.

I am not ignoring specific E (modulus of elasticity). The beam that is used will be made of all sorts of different materials, but if my assumption holds, then it is irrelevant.

A background of why I want to do this can be found on the:
Making an aerofoil with a cantilever thread.

Thanks in advance
 
Last edited:

Answers and Replies

  • #3
nvn
Science Advisor
Homework Helper
2,128
32
Any (ideal) [prismatic cantilever] beam of length L, bent with a deflection of delta, will have the same [strike]parabolic[/strike] [cubic] curve.
Dingomack: True, only if the type of applied loading is the same; i.e., in your case, only if there is a concentrated load (P) at the cantilever free end.

Q2. At what distance from the fixed end of the beam does the Cmax occur? If my first assumption is correct, this should be a constant.
My following answer applies if the cantilever deflection at the free end (y1max) does not exceed 10 % of the cantilever length (L). Cmax occurs at 42.265 % of L, measured from the fixed end; i.e., Cmax occurs at x = 0.42265*L.

If y1max exceeds 10 % of L, Cmax might still occur at 42.265 % of L, but I currently do not know if it does or not, because I have not checked that case.

Q3. For a given Cmax and beam length L, what is the deflection required?
What do you mean by "required"? Did you instead mean, "What is the deflection"? Which deflection? Deflection where, at what point?

I need to produce an excel spreadsheet where I can input a desired Cmax and a beam length L, and output the required deflection of the beam, all in millimeters.
What do you mean by "required deflection"?
 

Related Threads for: Cantilever spreadsheet for dummies

  • Last Post
Replies
3
Views
1K
Replies
6
Views
3K
Replies
20
Views
13K
  • Last Post
Replies
3
Views
10K
  • Last Post
Replies
2
Views
29K
  • Last Post
Replies
6
Views
5K
Replies
2
Views
3K
  • Last Post
Replies
6
Views
34K
Top