[Shop-talk] weight capacity of aluminum channel

[Donald H Locker]

BIG NOTE: please check my calculations and assumptions; I haven't
actually done any of this for nearly 40 years.

TLDR: They might not work.

The significant supporting bits are the two flanges (3in x 0.5in); the
plate across the top adds very little strength.

All calculations below in pounds and inches.

The maximum stress on the webs (if the weight is perfectly divided
between them; more on that later) will be (equation 1-1 in reference 1)
with the weight at the center of the ramp. Fb (bending stress in the
flange of the channel) must be less than the yield stress of the channel
material.

  Fb = M*c/I

[Ref 2] M for each web: PL/8 = P*120in/8 = P*15in [P is point load, lb]
[email] c for each web: 1.5in
[Ref 4] I for each web: (b*(h^3))/12 = ((0.5in)*(3in)^3)/12 = 1.125in^4

  Fb = (P*15in*1.5in)/1.125in^4 = P*20 lb/in^2

For the given situation, p=3840lb, so Fb (max) is 3840*20 = 76800lb/in^2
distributed between the two channels, each with two flanges. Since Fb
must be less than the material yield stress, 10000 psi for some kind of
structural Al, but not high-strength material [Ref 3], this doesn't look
very good. Each flange would be loaded to about 19200lb/in^2 if all
loads were perfectly distributed. (Note that high-strength Al (e.g.
6061) can have a yield stress of 45000lb/in^2 so looks much more likely
to succeed, but I don't know how much I'd trust that.)

My biggest concerns would be the division of stresses between flanges
(if one channel tilts a little or is not sitting perfectly flat on the
trailer or ground, stress sharing will be uneven and one flange make
take all stress) and the potential for flange instability (see notes in
1.3.1.5 in Ref 1.) This may not be a problem because the flanges are not
particularly deep, but I watched a boat hung from I-beams drop when a
structural I-beam twisted slightly from imperfect loading and the entire
structure quickly twisted into a totally unsupportive mess.

References:
1 Beam stress/strain:
<https://engineeringlibrary.org/reference/simple-beam-bending-air-force-stress-manual>

2 Beam force/reaction:
<https://engineeringlibrary.org/reference/beam-forces-moments-air-force-stress-manual>

3 Material properties:
<https://www.engineeringtoolbox.com/properties-aluminum-pipe-d_1340.html>

4 Area moments:
<https://www.engineeringtoolbox.com/area-moment-inertia-d_1328.html>

ATB,
Donald.
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On 2021-07-01 10:56 p.m., john niolon wrote:
> I'm thinking about using aluminum channel for a set of ramps for my car
> hauler.  I have some 'available' that is  10" wide with .50 web
> thickness and almost 3" flange... about 15# per ft.
>  
> ramps will be 7-8' long …..  and will go from ground to 17" high trailer
> deck...  truck weight is 5300 +/- … with front end weighting 3840.   I
> can't find a table telling me weight capacity of
> channel with the load traveling up the wide web...   like this   any
> ideas on capacity ??
>  
> Image87ABA31D
>  
> thanks
> john
>  
>  
> 
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