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- Summary:
- Calculating Maximum Load of Theoretical Model

Basically looking to find out what the maximum amount of load you could put on the center of a structure like this would be, in theory.

Top Beam:

The top "Beam" of the assembly in the drawing is 3"x 3"x 3/8" square tubing, 112.5" long

Supporting Beams:

The beams supporting each end of the Top Beam are the same 3"x 3"x 3/8" Tubing 46.59375" long, mitered at a 45 degree angle and theoretically welded or bolted

45 Degree Braces:

There are also two 45 degree braces to add some support to the center of the Top Beam. These are 34.171" long tip to tip, they are 45 degree mitered on each end and theoretically welded or bolted

Basically I've crunched numbers with some equations I found online for applying load to the center of a hollow square tube, but without just plugging in different amounts of force I'm unsure of how to figure out what the maximum load you could apply would be. Not really sure how to calculate in for the angled supports or even figure out what the Top Beam can actually take for load before plastic deformation occurs. My math comes out as follows:

Calculating the Moment Of Inertia

(Height^3 x Width)/12-(Inside Height^3 x Inside Width)/12

So

(3^3 x 3)/12-(2.25^3 x 2.25)/12

(81)/12-(25.62890625)/12

MoI = 4.614257812in^4

ASTM 1085 Spec Says HSS MoI = 3.89in^4

Then for Calculating Deflection, Assuming the Modulus of Elasticity is 29,000,000 for Steel

(Length^3 x Force Applied/(3 x MoE x MoI))

So

(112.5^3 x 10,000lb/(3 x 29,000,000 x 4.614257812))

(112.5^3 x 10,000lb/(401440429.644))

( 14238281250)(401440429.644)

Deflection = 35.4679802956" (With Calculated MoI)

Deflection = 42.07156945" (With ASTM 1085 MoI)

Obviously this is a lot of deflection in the Top Beam with the numbers I have plugged in for load but I know that I'm also not figuring in for the 45 degree braces. I did do some calculations for deflection using 88.328125" as the Top Beam length (which came out to a deflection of 17.16626947", about half of what I got with the full length), basically I figured that if I treated the math as if the Top Beam's endpoints were in the center of the space where the 45 degree braces intersect the Top Beam it would get me close to the actual deflection but I know that that's certainly not an accurate way to do that. The other thing is if I do the math treating where the 45 degree braces intersect the Top Beam as the end points of the Top Beam, and plug in a 1500lb load I get a deflection of 0.7480622661", and I have a really hard time believing that a 58.5" long section of 3"x 3"x 3/8" tubing would deflect more than 1/16th of an inch with only 1500lb load on it. If someone could walk me through figuring out how much load this design can actually take that would be amazing!

Top Beam:

The top "Beam" of the assembly in the drawing is 3"x 3"x 3/8" square tubing, 112.5" long

Supporting Beams:

The beams supporting each end of the Top Beam are the same 3"x 3"x 3/8" Tubing 46.59375" long, mitered at a 45 degree angle and theoretically welded or bolted

45 Degree Braces:

There are also two 45 degree braces to add some support to the center of the Top Beam. These are 34.171" long tip to tip, they are 45 degree mitered on each end and theoretically welded or bolted

Basically I've crunched numbers with some equations I found online for applying load to the center of a hollow square tube, but without just plugging in different amounts of force I'm unsure of how to figure out what the maximum load you could apply would be. Not really sure how to calculate in for the angled supports or even figure out what the Top Beam can actually take for load before plastic deformation occurs. My math comes out as follows:

Calculating the Moment Of Inertia

(Height^3 x Width)/12-(Inside Height^3 x Inside Width)/12

So

(3^3 x 3)/12-(2.25^3 x 2.25)/12

(81)/12-(25.62890625)/12

MoI = 4.614257812in^4

ASTM 1085 Spec Says HSS MoI = 3.89in^4

Then for Calculating Deflection, Assuming the Modulus of Elasticity is 29,000,000 for Steel

(Length^3 x Force Applied/(3 x MoE x MoI))

So

(112.5^3 x 10,000lb/(3 x 29,000,000 x 4.614257812))

(112.5^3 x 10,000lb/(401440429.644))

( 14238281250)(401440429.644)

Deflection = 35.4679802956" (With Calculated MoI)

Deflection = 42.07156945" (With ASTM 1085 MoI)

Obviously this is a lot of deflection in the Top Beam with the numbers I have plugged in for load but I know that I'm also not figuring in for the 45 degree braces. I did do some calculations for deflection using 88.328125" as the Top Beam length (which came out to a deflection of 17.16626947", about half of what I got with the full length), basically I figured that if I treated the math as if the Top Beam's endpoints were in the center of the space where the 45 degree braces intersect the Top Beam it would get me close to the actual deflection but I know that that's certainly not an accurate way to do that. The other thing is if I do the math treating where the 45 degree braces intersect the Top Beam as the end points of the Top Beam, and plug in a 1500lb load I get a deflection of 0.7480622661", and I have a really hard time believing that a 58.5" long section of 3"x 3"x 3/8" tubing would deflect more than 1/16th of an inch with only 1500lb load on it. If someone could walk me through figuring out how much load this design can actually take that would be amazing!

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