<theducksmail"AT"yahoo.com> wrote:> Looking for an online calculator that gives generic comparisons on the
Would the strength you be interested in be: tensile, torsion, buckling. In
tension, the load bearing strength would be proportional to the cross
sectional area, given the tensile strength. Calculating the cross
sectional area of tubing is, of course, elementary and no calculator is
needed. In torsion, the shear bearing strength is likewise elementary. In
buckling, vertical beam considerations involving a special modulus
involving the square of some critical dimension come into play and simple
methods vanish. Have you consulted any college level strength of materials
textbook. You would find a modulus formula that you could reproduce in any
credible spread sheet application.
I need to know for a racing chassis, I need to know if I can just go up on
wall instead of going to a bigger OD bar to get the strength and flex I
need. It's a lot easier to change wall thickness then reworking the jig and
reprogramming the tube bender. I'm mainly needing a moment of inertia and
modulus of steel calculator. I have found some formulas and some papers on
the subject online but I'm not much of a math whiz so I was hoping to find
something that was javascript or something.
"Darkwing Duck" <theducksmail"AT"yahoo.com> wrote in message
Calculations of Moment of Inertia, Section Modulus and cross sectional area
(weight of tube) can be
accomplished with a pocket calculator that can do squares and square roots.
Although the formulas
have variables to the fourth power or fourth root, you can square a variable
twice to get the fourth
power. Taking the square root twice will get the fourth root. Example: 3² = 9
and 9² = 81 which is 3
to the fourth power. Obtain the fourth root similarly using the square root
feature twice in
succession. (In the examples below I used my pocket calculator and show 3 or 4
decimal places even
though it stores ten significant figures. So you may have a slight difference in
the square and
square root figures. Note: .625^4 = .625 x .625 x .625 x .625 and .0338^.25 is
the fourth root of
.0338)
For the Moment of Inertia the formula is I = Pi(Ro^4 - Ri^4) / 4 where Ro is the
external radius, Ri
is the internal radius and Pi is ?. (? = 3.14159+)
For the 1.25 OD tube with 0.083 wall, R0 = 0.625 and Ri = 0.542.
I = ?(.625^4 - .542^4) / 4 = ?(.1526 - .0863) / 4 = 0.0521 in^4
For Section Modulus the formula is Z = I / Ro = 0.0521 / .625 = 0.0833 in^3
The cross sectional area of the tube is A = ?(Ro^2 - Ri^2). This is required to
determine the weight
difference in the various tube sizes.
A = ?(.625^2 - .542^2) = 0.3043 sq. in.
Now that you know what tube you are using and want to replace, we must
substitute the replacement
information in the above formulas. We have a 1.125 OD tube that must have a
Moment of Inertia equal
to or greater than 0.521 in^4 and a Section Modulus equal to or greater than
0.0833 in^3.
Re-arranging the formula for Moment of Inertia, we have: Ri = (Ro^4 -
(4I/?))^.25. (That is 4
times Mom. Inertia divide by Pi)
Ri = (.5625^4 - (4x.0521/?))^.25 = (.1001 - .0663)^.25 = (.0338)^.25 = 0.4288 in.
Wall thickness = (.5625 - .4288) = 0.134 inch (minimum wall thickness)
Assuming that a tube with 1.125 inch outside diameter and 0.134 inch wall
exists, we check them in
the formulae using .5625 - .134 = 0.4285 for Ri.
I = ?(.5625^4 - .4285^4) / 4 = 0.0522 in^4
Z = .0522 / .5625 = 0.0927 in^3
A = ?(.5625^2 - .4285^2) = 0.4172 sq. in.
The Moment of Inertia is good. The Section Modulus has improved. The weight has
increased by a
factor of .4172 / .3043 = 1.371 or more than one third. This could be a problem
with deflection of
the tube requiring a higher Moment of Inertia. From my experience, using a
smaller outside diameter
hollow tube tends to create more problems than it solves.
I hope that helps,
Jim Y
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