On Sun, 09 Apr 2017 10:11:22 -0400, Jim Wilkins wrote:
"James Waldby" ... wrote in message news
Could you double-check my use of on-line calculators to determine the
column buckling load of a pinned-end chain link fence post 1.90" OD,
1.77" ID (16 gauge) and 96" long as 4900 lbs?
I entered E=29,000,000. One end is pinned and loaded more or less
equally on both sides, the other is effectively a ball and socket on
the centerline.
I've been using 2-3/8" posts for a lifting tripod with a 3/4 ton chain
hoist, after proof-testing the tripod to (much more) by pulling a
stump with a larger hoist. The calculator I (mis?)used gave their
buckling load at around 8000 lbs.
The 2-3/8" post tripod requires one trip through the woods for it and
another with the rest of the gear. Someone gave me three leftover
1.90" posts which I can carry with one arm, but I'm not yet
comfortable with their safety factor, assuming one leg supports most
of the load as when moving boulders sideways.
....
As I'm not a trained engineer, except for a few brief classes
long ago that outlined some mechanical and civil engineering
stuff, I don't know the ins and outs of column design.
Anyhow, when I enter your numbers into Euler's formula for
pinned-end critical load, I get values about twice as high as
yours. Maybe a safety factor of 2 was used where you did the
calculation? Or possibly a different K (column effective length
factor) ? I calculated via the formula shown at
https://en.wikipedia.org/wiki/Euler%27s_critical_load with K=1
for the case "rotation free and translation fixed" at both ends
of the column. I think that's correct for the bottom ends of
your columns, but wasn't sure that the top is translation fixed.
Here is the Python code for several cases:
from math import pi, sqrt
od=1.9; id=1.77; r1=id/2; r2=od/2; I=(r2**4 - r1**4)*pi/2; K=1; L=96; Pcr=pi*pi*E*I/(K*L)**2; print 'Pcr={:.1f} at od={:.3f}, id={:.3f}, I={:.5f}'.format(Pcr, od, id, I)
od=1.9; id=od-2*0.055; r1=id/2; r2=od/2; I=(r2**4 - r1**4)*pi/2; K=1; L=96; Pcr=pi*pi*E*I/(K*L)**2; print 'Pcr={:.1f} at od={:.3f}, id={:.3f}, I={:.5f}'.format(Pcr, od, id, I)
od=2.375; id=od-2*0.055; r1=id/2; r2=od/2; I=(r2**4 - r1**4)*pi/2; K=1; L=96; Pcr=pi*pi*E*I/(K*L)**2; print 'Pcr={:.1f} at od={:.3f}, id={:.3f}, I={:.5f}'.format(Pcr, od, id, I)
Here are the results:
Pcr=9808.7 at od=1.900, id=1.770, I=0.31583
Pcr=8433.0 at od=1.900, id=1.790, I=0.27154
Pcr=16761.6 at od=2.375, id=2.265, I=0.53971
Some calculators below require I as an input, which is the reason for
printing it via the Python code. The 1.9" OD case is calculated two ways
because the following link shows wall thickness of 0.055" for "Standard
Residential" chain-link-fence posts (vs. 0.065 for Heavy Residential):
https://fence-material.com/fence-posts-galvanized-16ga/
Anyhow, those numbers above agree with results from calculator
http://www.engineersedge.com/calculators/ideal-pinned-column-buckling-calculator-1.htm
which is a fairly compact page with a few small images on it.
http://www.engineersedge.com/column_buckling/column_ideal.htm
also is mostly text, with images for some formulas. It explains
the inputs, distinguishes slender vs short columns, and has an
Effective Length Constant table for various fixed/guided/pinned
cases.
http://www.efunda.com/formulae/solid_mechanics/columns/calc_column_critical_load.cfm
also gets the same results.
http://www.tech.plym.ac.uk/sme/desnotes/buckling.htm is all text
except for two formula images and its associated calculator at
http://www.tech.plym.ac.uk/sme/desnotes/buccalc.htm looks like
all text too. It wants metric data, eg 200 GPa for Young's modulus.
https://mechanicalc.com/reference/column-buckling discusses pinned
columns and the Euler Formula vs Johnson Formula. It has a link to
https://mechanicalc.com/calculators/column-buckling/ which computes
Pcr and Scr and draws two plots, a "Critical force curve" and a
"Critical Stress Plot" to make the safety-factor size easy to
see at different loads and lengths. For this calculator, ASTM A572
appears to be the most suitable material to specify. However, I don't
see 1.9" OD and 2.375" OD tube on the cross section list presented to
non-subscribers; it appears that subscribers can create custom tube
sizes and can select some standard sizes from a cross-section database.
--
jiw