1989 ASD Shear Eq. F4-2 Questions

[jdonville]

I am having trouble using this spec to check for shear issues for a pile load test reaction frame.

In my version of the spec, the definition of Cv is self-referential, to wit:

Cv = (45,000 * kv)/(Fy * (h/tw)^2) when Cv is less than 0.8

= (190/(h/tw))*(kv/Fy)^0.5 when Cv is more than 0.8

Additionally, kv is undefined when there are no stiffeners, to wit:

kv = 4.00 + 5.34/((a/h)^2) when a/h is less than 1.0

= 5.34 + 4.00/((a/h)^2) when a/h is more than 1.0

a = clear distance between transverse stiffeners, in.
h = clear distance between flanges at the section under investigation, in.

My questions are,

1) What are the corrected limiting conditions for the equations for Cv?
2) What is the procedure to follow when 'a' is undefined (i.e., no stiffeners)?

Thanks in advance for your responses.

Jeff

 

[JAE]

When you have no stiffners, a goes to infinity and the second term in the kv formula goes away. kv then = 5.34.

 

[jdonville]

JAE,

Thanks. This is a big help. Now, what about the self-reference in the Cv definition?

Jeff

 

[JAE]

I think you calculate both Cv's and then see where the first one occurs - if it is over 0.8, you use the second one?

(authoritatively spoken but with lots of ???? after it..heh)

 

[jdonville]

JAE,

I could see using one or the other based on h/tw (this is in fact what happens in the 2005 version), but I can only imagine that the self-reference is a typo. I was hoping that someone had an errata sheet that would cover this instance.

Jeff

 

[271828]

Calculate the first Cv and see if it's < 0.8. If so, use it. Otherwise, calc the other.

I think that's one of the most doofus ways that Cv could've possibly been expressed. The top one is for elastic buckling and the bottom one for inelastic. Putting them in that order makes it double-doofus.

Can you just use the 05 Spec.? Chapter G is very logical and easy to read and apply. kv is easier too and the difference is comical. The underlying theory is the same. See Salmon & Johnson for a great derivation of all that stuff.

 

[271828]

Darn, forgot to type something. Where's that edit function when I need it to save me?

This should help remembering how to figure out which Cv to use.

Cv is the ratio of shear buckling stress to shear yield stress, presumably about 0.6Fy, IIRC, or maybe Fy/sqrt(3)--can't remember which was used.

0.8 is the presumed proportional limit which in this case is used to separate inelastic and elastic buckling.

Sooooo, by calculating the first one (elastic buckling), you're assuming that the buckling stress is < 0.8 * the shear yield stress. If it comes out > 0.8, then your assumption was wrong and you have inelastic buckling-->now use the other one.

I still say that's an uber-doofus way to formulate it, but it is what it is (about to be extinct Thank God).

 

[JAE]

271828 - you said very well what I was trying to say...well done.

I especially like the highly technical term, "doofus".

 

[271828]

My pleasure. It's an interesting topic.

 

[UcfSE]

If it helps, in the second equation you can solve for the required h/t_w. If your h/t_w is less than that value, you use the second equation (190/...). If it is greater, you use the first equation. What that limit is exactly will depend on k_v and F_y. It would take a little playing around with the equations and some different variable values to get an idea of just what you want to do with it.

 

[jdonville]

All,

Thanks for the insightful commentary. "Doofus" is very polite.

I have pretty much decided to adopt the 2005 spec for reasons of improved clarity over the 9th and compatibility with AASHTO (we are a highway bridge contractor, among other things).

Cheers,

Jeff