question on equation K2-2 of AISC 13th edition manual

[Jakrayer]

I want to know if anyone has information on some of the variables in this equation. I am unsure what they are exactly. The equation is

U=Pr/(Ag*Fc)+Mr/(S*Fc)

where

Pr= required axial strength in chord
Mr= required flexural strength in chord
Fc= Available stress
S= chord elastic section modulus
Ag=gross area

What I want to know is what are Pr, Mr, and Fc? And where do I get these values?

 

[JAE]

Aren't they defined right below the same section you are reading? I see definitions for them for both LRFD and ASD.

Just read down a bit.

 

[frv]

These should all be defined within AISC 360-05 (13th Ed. of the manual). Look at p.16.1-xxix

 

[Jakrayer]

So how do you calculated Pr and Mr? So is required axial strength what I want the structure to hold or what a section of selected pipe can hold? Same with required flexural strength?

I went through the text to where each part was referenced and Pr= Pnt+B2*Plt but how would you get B2 and Plt and Pnt?

 

[slickdeals]

You probably need to go through a steel textbook like Salmon and Johnson.

We are Virginia Tech
Go HOKIES

 

[ToadJones]

Pr and Mr are simply the force and moment you are designing the connection for.

 

[ToadJones]

"Pr" and "Mr" are the axial force and moment that your connection is "required" to withstand.
They use this general term, "required", because they cover both ASD and LFRD design with the same equation.
ASD: Pr = Pa = load resulting from controlling service level load commbination
LRFD: Pr = Pu = load resulting from controlling factored load combination
same for Mr...= Ma, or Mu

 

[Jakrayer]

but if I am using LRFD for example doesn't that put the anaylsis by LRFD load combinations on both sides of the equation since I want Ru<=Rn*(resistance factor) and

Rn=5.5*Fy*t^2*(1+0.25*N/D)*Qf

Qf=1-.3*U*(1+U)

U=Pr/(Ag*Fc)+Mr/(S*Fc)

Or am I overlooking something?
So if I have to assume a load being lifted then do a force analysis to get loads and moments on the structure then determine the nominal strength based on specification provisions to see if they exceed those that the assumed load imparted on the structure....How do I do this if those same assumed loads are in the calculation that is needed to determine safety?

I apologize if this is a trivial issue and I am over looking something, but to me the equations to analyze I-beams and welds and bolts are a lot different then HSS members, which this is my first time working with.

 

[ToadJones]

I'm getting lost here:
For LRFD:
Mu <= phi*Mn
Mu is the moment resulting from factored loads from analysis.
Mn is the nominal or theoretical moment capacity of the beam.
Phi= a reduction factored for various reasons
Meaning, the factored moment on the beam from analysis must be less than the theoretical moment capacity of the section multiplied by a reduction factor.
The same principles to moments, forces, axial...whatever.
They call it Mu, Ru, Pu etc.

 

[Jakrayer]

So if I am thinking about this correctly though, then Ru=Pu=Pr which would yield and equation as follows for dead and live loads...

Ru=Pu=1.2*D+1.6*L <= Rn=5.5*Fy*t^2*(1+.25*N/D)*[1-.3*(Pr/(Ag*Fc)+Mr/(S*Fc)]

?

 

[ToadJones]

Is there someone at your workplace that you can go over this with?

 

[Jakrayer]

I talked with my initial boss and he said he would have to talk to his boss who is busy today. I showed my boss the same things that I have here just in the AISC text and he sees what I am seeing, and it seems like something doesn't add up right or we are missing something key to using the equation.

Thank you for your responses though.

 

[nutte]

You have an HSS member that you're applying some load to, perpendicular to the axis of the HSS member. That force is the Pu you compare to Equation K1-8 (Rn=5.5 Fy t^2 ...).

The chord stress interaction factor Qf is based on the utilization ratio U, equal to |Pr/(Ag Fc)+Mr/(S Fc)|. The Pr and Mr here are the force and moment in the HSS member itself. These are different than the Pu you're applying perpendicularly to the HSS member.

 

[ToadJones]

Nutte has explained it quite clearly, other than usually when comparing "Rn" we would use "Ru", not Pu.

 

[Jakrayer]

Gotcha, yep that helped. Thank you.