[Shop-talk] weight capacity of aluminum channel

[Donald H Locker]

First oops - I used 10ft length, not 8ft. At 8ft, the numbers look
better by about 20%

Donald.
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On 2021-07-02 6:16 a.m., Donald H Locker wrote:
> 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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> *Plain Text* email -- it's an accessibility issue
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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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