HSS Members Rotated 45° 1

[KB4444]

I am looking for help with finding the section properties of square HSS members that are rotated 45° (i.e. diamond).

I am using S16-14 to solve the moment capacity of an HSS beam, but I need to solve the Section Modulus (Z) first [Moment Resistance = (0.9)(Z)(Fy) , as per CL 13.5.a)]. The values given for the HSS members in Chapter 6 would not be correct with the 45° rotation.

I have run the rotated section through a design software called SkyCiv, but I have not managed to be successful in matching any hand calculations to those results.

 

[canwesteng]

Split the loads into components about the principal geometric axis instead. Likely that is what the software is doing.

 

[jayrod12]

Yeah I'd be surprised if SkyCIV was running it at the 45 degree properties. I'm with canwesteng, run it by hand. And if there's no breaking the loads down into components that match the beam, it would be my opinion to just use S, not Z.

For those non-canadian engineers (I believe the US is the same) S is the elastic section modulus, and Z is the plastic section modulus.

 

[KootK]

canwesteng's suggestion sounds good to me as a practical design solution. Even simpler if you just keep everything elastic.

I feel as though this procedure would replicate Zx effectively.

 

[KB4444]

An example on this would be an HSS 4x4x1/4 (CSA G40.20).

Z = 77.45 x 10^3 mm^3 (@ 45°), but I am not sure as to the hand calculations to verify this

 

[KB4444]

Thanks for the responses! Splitting the load makes sense, that would be relatively easy too with the angle being 45°. I wasn't sure if there were simple formulas to solve for

 

[bugbus]

Plastic section modulus for a square rotated 45 degrees is equal to (sqrt(2)/6)*a^3, a being the side length of the square.

For a hollow section, it would just be (sqrt(2)/6)*(a^3-b^3), b being the inside dimension.

So it is about 94% of that for a square in the normal orientation (which is 0.25(a^3-b^3)).

 

[JLNJ]

AISC manual 17-27 has the formulas which will get you pretty close. Corner radii won't be included.

 

[dik]

It's not a very efficient use of an HSS. Can you use a circular section? For Limeridge Mall in Hamilton, the architect wanted to use a space frame for the roof system. I talked him into using HSS trusses/joists at a 45deg angle, with the bridging acting as the other members... The final design used angles with the webs at 45deg. Looked like a space frame...

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[KootK]

JLNL's recommendation for anyone else who's curious to see it. I assume that one would use an area subtraction similar to gusmurr's approach.