Design of Beams in Special Concentric Braced Frames

[CivilSigma]

Hello,

I'm studying steel seismic design from the textbook: Seismic and Wind Forces: Structural Design Examples, 5th Edition.

I am on Example 3-3 which illustrates the seismic design forces on a beam in a chevron braced frame.

Per AISC 341 Section F2.3, we need to check the beam for a) Expected tensile brace force + Expected compressive brace force and b) Expected tensile brace force + 0.3*Expected compressive brace force. Section F2.3 tells you how to calculate these forces.

However, in the example on page 288, the author is using the true nominal brace capacity in compression to design the beam. Please see the below screenshot. I disagree with this. Do you agree with me or am I missing something?

Thank you,

 

[Ron247]

I do not have the publication you cite, and the picture is a little fuzzy but I noticed the formula for Pr looks like it has Pn, not Pu in it. Pn above is 149. But I also noticed the formula for Pn looks (again fuzzy) like Pn = phic*PN/phic. If so, that looks odd. The numerator and denominator have the same symbol.

 

[CivilSigma]

Hi Ron, please see the attached PDF snippet.

What the author was doing is using the design tables in AISC 360 to determine the compression capacity of the HSS brace, and then dividing by the saftey factor to get the unfactored capacity. I don't think that's how we determine the seismic capacity limited force on the beam though.

 

[BulbTheBuilder]

It is a mistake in the book. AISC 341 references nominal capacity so it should be 190k as you pointed out

 

[Ron247]

I guess I am confused, I do not own the publication but I thought nominal was generally subscripted with an "n" and ultimate was a "u".

 

[BulbTheBuilder]

I am mixing up terminologies here. My apologies.

The available strength = øPn
Nominal strength = Pn
The required strength = Pu

I will recheck what AISC 341 calls for once I have the code by me

 

[CivilSigma]

Thank you everyone, I've read it over again, and actually agree with the textbook author.

The wording in AISC Section F2.3 is a bit awkward and requires some engineering judgment to interpret properly.

The code states:

“The expected post-buckling brace strength shall be taken as a maximum of 0.3 times the expected brace strength in compression.”

The key word is maximum. The code sets an upper limit but does not require using that exact value.

The User Note below clarifies that for braces with a slenderness ratio (KL/r) less than 200, it’s reasonable to approximate the post-buckling strength as 0.3Fn. This is equivalent to taking 0.3 × Pn, which aligns with the approach shown in the textbook.

Also, it’s important to note that 0.3Fn is less than 0.3 × expected compression strength. This results in a larger net force on the connected element, which is what we want in design, and what the author does in the example.

 

[BulbTheBuilder]

To begin with, I am not a seismic person but I going to share my opinion anyways. The use of nominal compressive strength is wrong, and the author is wrong for using that. However, his method results in a conservative earthquake load.

For the analysis and determination of EQ (earthquake load), clause F2.3 states that EQ is the maximum of three options.
1. "An analysis in which all braces are assumed to resist forces corresponding to their expected strength in compression or in tension".
Which is Expected tension (RyFyAg) [+ve] + Expected Compression (lesser of RyFyAg and (1/0.877)FcreAg) [-ve]
=311kips + (-ve of lesser of 313 or 190)
=311kips - 190kips
=121k

2. "An analysis in which all braces in tension are assumed to resist forces corresponding to their expected strength and all braces in compression are assumed
to resist their expected post-buckling strength". Which is Expected tension (RyFyAg) [+ve] + post-buckling compression (0.3 * expected brace strength in compression.) [-ve]

But the expected brace strength in compression = the lesser of RyFyAg and (1/0.877)FcreAg,

=311kips + (-ve 0.3 * 190) : The expected braced strength was determined from previous calc`
=311kips - 57kips
=254kip

3. "For multi-tiered braced frames, analyses representing progressive yielding and buckling of the braces from weakest tier to strongest. Analyses shall consider both directions of frame loading."
-I haven't seen this used before.

The maximum of option 1 and 2 is option 2 which ought to be (311-57)0.707 = 179.578kips < 188kips

 

[CivilSigma]

I agree with you 100%.

Funny enough, in Ordinary Concentric Braced frame design, F1.4a, it limits the compressive capacity of the brace when designing beams to 0.3 * The nominal capacity (Pu).

Not sure why this is different in SCBF design