Starred angle properties

[zestructural]

Hi all,

I am looking for the formulars to calculate the J (torsional constant) and Cw (warping constant)for the starred angle compression member (See attachment). Can anyone point me to the right directions or resources? Does a starred angle shape be considered as a single or double symmetrical shape? I assume it is a double symmetrical shape. Is my assumption right or wrong? Thank you in advanced.

 

[paddingtongreen]

I didn't know anybody still used these, the last time I saw one, on a new design, was back in the fifties, when material was more expensive than manhours.

Usually, there was a gap equal to the thickness of the plate, in the perpendicular direction for alternating direction gusset plates. With equal legged angles, that gave two axes of symmetry, diagonal in your picture.

With your layout I see only polar symmetry.

I don't know about torsional values, but angles have negligible torsional stiffness.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[DHKpeWI]

Try using Shape Builder. You can download a trial version for free.

http://www.iesweb.com/downloads/index.htm

If you need it in a hurry, post the angle sizes and I can run it for you.

 

[zestructural]

Thank you Michael and DHKpeWI. I will try the shape builder.

 

[prex]

If you go to Beams -> Cross sections -> Angles -> 2 starred in the first site below, you'll find the torsional properties. That's however for the common layout as described by paddingtongreen, but, for the properties you mentioned, there is no significant change with respect to your layout.
You can see the formulae on which they are based by clicking on Options -> Show formulae

prex

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[ishvaaag]

Sectional properties are established just out of the geometry of the section. For built-up members, along the member, you have different sectional properties. In the case of tie plates sometimes an approach of "smearing" the tie plate material along the length of the member has been taken to get sectional properties that give equivalent behaviour in torsion for the whole member; this smearing is not, by what I see in some example I have in books for double tees with tie plates, of the thickness of the material in the tie plate distributed in the tributary length; it is less in the example, what must be some way of acknowledging the additional flexibility introduced by the gaps between tie plates.

Respect how to get the sectional properties for a notional + section, you can look at

Design of Steel Structures
Gaylord, Gaylord, Stallmeyer
3d edition
McGraw Hill 1992
Example at p. 268

where
J=(4/3)*(b*t^3)
Cw=(b^3*t^3)/9
b is the width of just an angle, t its common thickness

Except finding the averaged equivalent sectional properties somewhere, that must exist since in the end this was a practical structural member sometimes used, we enjoy today the luxury of 3D FEM models able to properly portrait member, forces and constraints, and this could help where some application like this can become particularly critical for the determination of stresses and displacements.

 

[zestructural]

Prex,

Thanks a lot for the links.

 

[ishvaaag]

You can also work in a structural analysis setup for a more manageable result by using single angle members for the segments between ties, and the ties themselves other members joining the angle segments. This way you will have likely direct checks for all the components.

 

[DHKpeWI]

ishvaaaq:

In your post you have J = (4/3)*(b*t^3). I think you included the 4 is because you have 4 angles, correct?

According to AISC Design Guide 9 on torsion, for sections composed of rectangular shapes with b/t > 10

J = SUM (1/3)*b*t^3)

where t is the thickness and b is the width of the individual rectangle shapes.

DG#9 as specifies that if b/t < 10 then

J = (1/3 -0.2t/b)*b*t^3.

By the way Desgin Guides can be downloaded for free from AISC's web site, if you are a member.

DHKpeWI

David

 

[DHKpeWI]

ishvaaaq:
In your post you have J = (4/3)*(b*t^3). Is this formula specific to this cross section? Is the 4 included because there are 4 angles?

To all:

According to AISC Design Guide 9 on torsion, for sections composed of rectangular shapes with b/t > 10:
J = SUM (1/3)*b*t^3)

where t is the thickness and b is the width of the individual rectangle shapes.

DG#9 specifies that if b/t < 10 then:
J = SUM (1/3 -0.2t/b)*b*t^3.

By the way the Design Guides can be downloaded for free from AISC's web site, if you are a member.

DHKpeWI

 

[ishvaaag]

I really have only copied the formulae from the book this time. As you see coincides with the simplified expression; it is because there are 4 rectangular arms, and dimensions are defined the same way, length and thickness of the individual rectangles in the cross shape.

 

[BAretired]

Between gusset plates, you have two single angles each of which is singly symmetric. J is the sum of (b-t/2)t³/3 for each leg of each angle. Cw is 0.

As a composite section, it is close to a cruciform shape, which is doubly symmetric (not sure of the significance of that fact). J and Cw remain the same as above.

BA