# STEEL MANUAL - TABLE 3-10



## EBAT75 (Oct 7, 2020)

Selecting beams using Table 3-10 requires accounting for the weight of the beam. Cb is 1.0. Simply supported beams, easy enough to take off the moment due to self weight of the beam. But if we are doing a continuous beam, and the maximum moment   includes beam’s self weight how does one deal with the reduction? Usually, the maximum positive moment comes not from all bays loaded with floor dead plus live loads.


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## thedaywa1ker (Oct 8, 2020)

If you add the beams self weight to your applied dead load instead of subtracting it from the capacity that should take care of it, right?  Unless I'm confused, which does happen frequently.  Subtracting the self weight moment from the capacity seems to be a complicated way of doing it. 

You'd have to check unbalanced live load cases like you mention, but the self weight will always be there


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## EBAT75 (Oct 8, 2020)

Verbatim from Manual: The plots include the beam weight, which should be deducted when calculating the maximum uniform load the beam will support. Cb is taken as unity.

TDW, I see what you are saying but what threw me off was I was thinking of Moment. Now I see “maximum uniform load the beam will support“. 

The table is Available Moment vs Unbraced Length. If someone wants to find the maximum uniform load a beam can carry, why would they not use Table 3-6 Maximum Uniform Load instead. There also one has to deduct the beam self weight but it is a deduction from loads.

3-10 is good for moments, to calculate maximum uniform load through the moment route is circuitous.


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## thedaywa1ker (Oct 10, 2020)

Where is that in the manual? I must be going crazy, I'm looking at the paragraph about the charts on page 3-11 and dont see it

The difference between 3-10 and 3-6 is that the 3-10 charts include lateral torsional buckling, and table 3-6 considers the beam fully braced


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## organix (Oct 10, 2020)

I also took a look in the manual and didn't see it... curious as well.


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## EBAT75 (Oct 11, 2020)

Let me explain my understanding.
3-6 has plastic (yielding) up to Lp, then inelastic LT up to Lr. Up to only Lr, fully braced, you can use 3-6 (or 3-2 if selecting by Zx). LT is not confined to 3-10. 3-6 also has the linear reduction.
Up to Lr, unbraced, you can use 3-10 for moments/span. Beyond Lr, one cannot use other than 3-10. Limit is span/depth of 30.

My take was based on floors (concrete, steel decking...) bracing the beam. 3-10 is useful when say, concentrated loads are applied (equipment, cranes, .....) in longer unbraced spans.

Looked at 13th and 14th editions. The paras explaining these tables - 14th, 3-10 has an omission Re the linear reduction between Lp and Lr. 13th has the full explanation.


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## thedaywa1ker (Oct 11, 2020)

I'm looking at the 14th - Table 3-6 is based on braced (Lb always &lt; Lp, therefore not considering LTB) beams - I don't see anything about a reduction up to Lr.  I have never used any edition besides the 14th so I don't know if that is different between the two.

Are the moment capacities in the 3-10 charts consistent between the 13th and 14th?  If the 13th has the note about reducing the values in the chart, and the 14th doesn't have that note, that makes me think that they changed the chart so you don't have to do that adjustment.  That makes more sense than them omitting the note but still wanting you to adjust the chart values.


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## EBAT75 (Oct 12, 2020)

_14th - Table 3-6 is based on braced (Lb always &lt; Lp, therefore not considering LTB) beams -...._

If so, why are spans many times Lp listed in that table? For the same material properties, Lp is a function of section property only. Lb can be more or less than Lp. Up to Lp, Mp is constant (compact).  Beyond that M reduces linearly by BF factor up to Mr at Lr (non-compact).

There is no reason for 13th and 14th Values to be different in Section F - Flexure based tables/charts because there is no difference in Specifications between 2005 and 2010 on which 13th and 14th are based. I have compared and confirmed 3-10 and 3-6 values in both editions.

14th, 3-2 para on explanation on non-compact range is the same as in 13th. That language was there in 13th 3-10 also, but not there in 14th 3-10. I think it is an omission. May check with AISC after the exam.

There seems to be a misunderstanding in what I referred to as reduction. What was meant was the linear reduction in capacity (moment/load) from Lp to Lr. It is the term BF in reducing linearly from Mp to Mr.


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## thedaywa1ker (Oct 12, 2020)

EnergizerBunnyAt75 said:


> If so, why are spans many times Lp listed in that table? For the same material properties, Lp is a function of section property only. Lb can be more or less than Lp. Up to Lp, Mp is constant (compact).  Beyond that M reduces linearly by BF factor up to Mr at Lr (non-compact).


Because the spans in 3-6 aren't related to Lp - a 40' unsupported span in table 3-6 can still have an Lb of zero if it is constantly braced laterally. The paragraph regarding table 3-6 on page 3-10 says 'Maximum total uniform loads based on braced (Lb&lt;Lp) simple span beams...are given'

If Lb&lt;Lp, then LTB isn't a thing, in that case the linear interpolation you mention would put the strength of the beam higher than Mp, so the reduction isn't applied to table 3-6


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## EBAT75 (Oct 12, 2020)

Lb is not zero just because the compression flange is restrained from lateral displacement along the full span. It is the distance between points where both top and bottom flanges are restrained from twisting - the span, say 40 ft in a section with Lp of 10 ft.

...._based on..._meaning the Mp is the upper limit. BF Reduction factor is applied with Mp as the take off point.

If you use 3-6 and 3-10 for a given section, load, span and do moment/load/span conversions, you will arrive at the same result.

From 14th:

Notes on Table 3-2:

For compact W-shapes, when Lb ≤ Lp, the strong-axis available flexural strength, φbMpx or Mpx /Ωb, can be determined using the tabulated strength values. When Lp &lt; Lb ≤ Lr, linearly interpolate between the available strength at Lp and the available strength at Lr
as follows:
 
Notes on Table 3-6:
The uniform load constant, φbWc or Wc /Ωb (kip-ft), divided by the span length, L (ft), provides the maximum total uniform load (kips) for a braced simple-span beam bent about the strong axis. This is based on the available flexural strength as discussed for Table 3-2.
Here is a good source also:
https://www.aisc.org/globalassets/continuing-education/quiz-handouts/steel-design-after-college-handout.pdf


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## E720 (Oct 12, 2020)

EnergizerBunnyAt75 said:


> Lb is not zero just because the compression flange is restrained from lateral displacement along the full span. It is the distance between points where both top and bottom flanges are restrained from twisting - the span, say 40 ft in a section with Lp of 10 ft.


I am going to disagree with that definition of Lb. From the Spec F2.2 "Lb = length between points that are *either *braced against lateral displacement of the compression flange *or *braced against twist of the cross section."


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## thedaywa1ker (Oct 12, 2020)

Lb absolutely is zero if the top flange is continuously braced

The definition of Lb in section F2-3, page 16.1-47 of the 14th edition: 'Lb = *length between points that are either braced against lateral displacement of the compression flange* OR braced against twist of the cross section'

E720 is quicker to the draw!


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## thedaywa1ker (Oct 12, 2020)

Over at eng-tips.com they had a monster thread a few months ago about LTB where they argued about lateral bracing of top flanges and a bunch of other stuff, complete with fem simulations and bluebeam sketches...its some great reading.

https://www.eng-tips.com/viewthread.cfm?qid=459248


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## thedaywa1ker (Oct 12, 2020)

In the 3-10 charts, the horizontal portion of each beams line matches the moment given by taking (loads from 3-6)/(L)*L^2/8 - and the 3-10 charts start sloping at Lp because that is when LTB starts to apply...once the line in the 3-10 charts are sloping, the chart and table no longer match.


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## EBAT75 (Oct 12, 2020)

OK dear forum members, thank you for the spirited discussion.

 I will be happy to return to the forum on 23 October, yes 2020 and pick up where I left. 
 

It is not about who is right but about what is the correct thinking behind the Tables. If I fail the exam because of this topic, so be it.


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## thedaywa1ker (Oct 12, 2020)

Absolutely - I sincerely appreciate any discussion like this right now that makes me get into the nitty gritty of the code, and has a chance to improve my understanding of the topics before the test


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## organix (Oct 17, 2020)

thedaywa1ker said:


> Over at eng-tips.com they had a monster thread a few months ago about LTB where they argued about lateral bracing of top flanges and a bunch of other stuff, complete with fem simulations and bluebeam sketches...its some great reading.
> 
> https://www.eng-tips.com/viewthread.cfm?qid=459248


Definitely good read.  I will have to revisit post-SE... bigger fish to fry.  However, I did go about 15% through and it definitely made me feel a little less adequate.


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## EBAT75 (Oct 19, 2020)

thedaywa1ker said:


> Absolutely - I sincerely appreciate any discussion like this right now that makes me get into the nitty gritty of the code, and has a chance to improve my understanding of the topics before the test


Good luck TDW. It is down to the wire now.


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## thedaywa1ker (Oct 20, 2020)

organix said:


> Definitely good read.  I will have to revisit post-SE... bigger fish to fry.  However, I did go about 15% through and it definitely made me feel a little less adequate.


Lol. Yeah those guys are rock stars, somewhere in the thread one of the main contributors reveals that he did his masters thesis on LTB.  My favorite part is how they seamlessly transition from referencing one countries code provisions to another countries, and discuss their differences.  I'm still trying to get fully comfortable with my own countries provisions.

Good luck to everybody this week...


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## EBAT75 (Oct 24, 2020)

I am back as I said I would. I took a brief look at the eng-tips thread. My initial impression is that it dwells on too many codes of other countries and not enough on the US codes which is our prime interest. An engineer cannot stand up in a US court and invoke those codes in defense. Also, code making and revising them often has become an industry in itself in the US and code writers are not unfamiliar with at least some of the foreign codes. e.g. after the Kobe earthquake US engineers learnt a lot from the Japanese seismic codes and revised our seismic codes. Australia, New Zealand have very different climatic conditions. Or for that matter India or China. I have seen adoption of some Euro codes. And Canadian codes in wood, masonry, cold formed steel.

Wish to continue where we left off after I have taken some time to dwelt on it.


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## EBAT75 (Oct 26, 2020)

thedaywa1ker said:


> Lb absolutely is zero if the top flange is continuously braced
> 
> The definition of Lb in section F2-3, page 16.1-47 of the 14th edition: 'Lb = *length between points that are either braced against lateral displacement of the compression flange* OR braced against twist of the cross section'
> 
> E720 is quicker to the draw!


(c) *When Lb &gt; Lr*
Mn = FcrSx ≤ Mp (F2-3)
where
Lb = length between points that are either braced against lateral displacement of
the compression flange or braced against twist of the cross section, in.

This definition of Lb in *ONLY WHEN* Lb&gt;Lr. Please remember what I said earlier -Up to only Lr, fully braced, you can use 3-6.

The danger is when we do not match the definitions to the context in hand. When the context or boundary conditions change, the definition, in this case the definition of Lb changes. It is not static.


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## thedaywa1ker (Oct 26, 2020)

EnergizerBunnyAt75 said:


> This definition of Lb in *ONLY WHEN* Lb&gt;Lr. Please remember what I said earlier -Up to only Lr, fully braced, you can use 3-6.
> 
> The danger is when we do not match the definitions to the context in hand. When the context or boundary conditions change, the definition, in this case the definition of Lb changes. It is not static.


I remember what you said earlier, I just don't think that is true.  Can you give me a code reference for this alternate definition of Lb?

'Up to Lr, fully braced'

I am confused. If a beam is unbraced up to Lr, then it is not fully braced.


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## EBAT75 (Oct 26, 2020)

thedaywa1ker said:


> 'Up to Lr, fully braced'


I had the code reference in the post itself - Eq. F2-3.

As for 'Up to Lr, fully braced', beyond Lr, braced or not does not matter. Why? Because, Fcr in Eq F2-4 has Lb squared in the denominator. The effect on Mn is not linear now. The (1/Lb squared) factor makes it curvilinear and as Lb approaches say infinity becomes asymptotic to zero i.e. even a gentle breathing can cause buckling. AISC cuts the 3-10 table values at 30 times beam depth as a practical limit. 

Reading the full sections in F2.2 1 through 3 will answer the questions on this topic. On the definitions of bracing, lateral restrained, segments, points of inflection, twist, bracing of which flange etc, I will get to them later.

I am glad we started with the beam weight and got to the meat of LTB.


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## thedaywa1ker (Oct 26, 2020)

EnergizerBunnyAt75 said:


> I had the code reference in the post itself - Eq. F2-3.
> 
> As for 'Up to Lr, fully braced', beyond Lr, braced or not does not matter. Why? Because, Fcr in Eq F2-4 has Lb squared in the denominator. The effect on Mn is not linear now. The (1/Lb squared) factor makes it curvilinear and as Lb approaches say infinity becomes asymptotic to zero i.e. even a gentle breathing can cause buckling. AISC cuts the 3-10 table values at 30 times beam depth as a practical limit.
> 
> ...


F2-3 has the definition of Lb that I am familiar with.  I am asking why you think that the definition of Lb changes, and where that is in the code. 

Your changing definition of Lb is why your interpretations of 3-10 and 3-6 are off.  3-6 assumes Lb of zero (for all intents and purposes), aka fully laterally braced. Lb/Lr/Lp aren't relevant to that table at all.



> This definition of Lb in *ONLY WHEN* Lb&gt;Lr. Please remember what I said earlier -Up to only Lr, fully braced, you can use 3-6.





> the definition of Lb changes. It is not static.


I don't think these statements are correct.


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## thedaywa1ker (Oct 26, 2020)

Looking at the capacities in 3-6

Say you have a beam spanning 40 feet.

You are saying that you can use this table for unbraced lengths up to Lr.

How do you tell the table what your unbraced length is?

A particular beam that spans 40 feet only has one capacity per table 3-6.  As the beams laterally unbraced length increases, the capacity will decrease.  How is this reflected in that table?  It isnt.


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## EBAT75 (Oct 26, 2020)

thedaywa1ker said:


> I am asking why you think that the definition of Lb changes, and where that is in the code.


Fig.C-J-10.2 might help.

There are many other instances where this is borne out. Why I mentioned On the definitions of bracing, lateral restrained, segments, points of inflection, twist, bracing of which flange etc, I will get to them later.


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## thedaywa1ker (Oct 26, 2020)

EnergizerBunnyAt75 said:


> Fig.C-J-10.2 might help.
> 
> There are many other instances where this is borne out. Why I mentioned On the definitions of bracing, lateral restrained, segments, points of inflection, twist, bracing of which flange etc, I will get to them later.


I'm on the edge of my seat


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## thedaywa1ker (Oct 26, 2020)

Are you saying that you back-calculate phi*Mpx from 3-6, to then use with equation 3-4a?


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## EBAT75 (Oct 26, 2020)

thedaywa1ker said:


> Are you saying that you back-calculate phi*Mpx from 3-6, to then use with equation 3-4a?


I am a bit lost in the woods. 

F3. Doubly Symmetric I-Shaped Members with Compact Webs and Noncompact
or Slender Flanges Bent About Their Major Axis

The tables have footnotes to cover compact, non-compact, slender..........all F sub-sections. Looking for 3-4a, I cannot find a 3-4a.

TDW, I will pick up after work. Appreciate your spirit.


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## thedaywa1ker (Oct 26, 2020)

EnergizerBunnyAt75 said:


> I am a bit lost in the woods.
> 
> F3. Doubly Symmetric I-Shaped Members with Compact Webs and Noncompact
> or Slender Flanges Bent About Their Major Axis
> ...


It is on page 3-9

I am most curious for your answer to this post:



> Looking at the capacities in 3-6
> 
> Say you have a beam spanning 40 feet.
> 
> ...


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## dauwerda (Oct 26, 2020)

I agree with thedaywa1ker on this one. Lb is not only defined in F2-3, it is also defined in the index of the Manual (under "General Nomenclature") the definition given here is the exact same as mentioned above.

The intent of F2.2(c) is not to change the definition of Lb, it is saying the definition of Mn given by that equation is only applicable when Lb is greater than Lr.


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## EBAT75 (Oct 26, 2020)

dauwerda said:


> I agree with thedaywa1ker on this one. Lb is not only defined in F2-3, it is also defined in the index of the Manual (under "General Nomenclature") the definition given here is the exact same as mentioned above.
> 
> The intent of F2.2(c) is not to change the definition of Lb, it is saying the definition of Mn given by that equation is only applicable when Lb is greater than Lr.


Have either of you  (you and daywa1ker) looked at Fig.C-J10.2 and also Fig. C-F1.4. ?

Here is the text that goes with the latter, Fig. C-F1.4:  "In this case, the Cb = 5.67 would be used with the lateral-torsional buckling strength
for the beam using an unbraced length of 20 ft which is defined by locations where twist or lateral movement of both flanges is restrained."

I have also seen the General Nomenclature thing, but it is "General" or generic. I also have seen the following definitions for Lb in the same General Nomenclature. They are :

Lb Length between points that are either braced against lateral
displacement of compression flange or braced against twist
of the cross section, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F2.2 (ALREADY HACKED TO DEATH)

Lb Distance between braces, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . App. 6.2
Lb Largest laterally unbraced length along either flange at the point
of load, in. (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J10.4
 

The eng-tips thread had one gem from a contributor after a lot of posts from him. I have no time to look at it again, but it ran something like  he doesn't care about all of this, what really matters is going back to the fundamentals.


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## EBAT75 (Oct 26, 2020)

thedaywa1ker said:


> It is on page 3-9


Page 3-9 of what?


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## thedaywa1ker (Oct 26, 2020)

Page 3-9 of the steel manual...immediately prior to tables 3-6 and 3-10...

I don't see anything in what you've posted that would lead me to believe that the writers of that code mean anything by Lb other than what they have explicitly defined.

The question of specifically what kind of restraint is sufficient in real life to prevent LTB is a can of worms.  But, AISC simplifies it for us dumb designers with their definition of Lb, so that we can do a quick check and move on


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## EBAT75 (Oct 26, 2020)

thedaywa1ker said:


> Looking at the capacities in 3-6
> 
> Say you have a beam spanning 40 feet.
> 
> ...


Thx for the info where 3-9 is. My edition of 14th is page 3-10. Anyway, let us look at the 40 ft span. Say Lp is 10 ft. 

from manual  for table 3-6: Maximum total uniform loads on braced (Lb ≤ Lp) simple-span beams bent about the strong
axis are given for W-shapes with Fy = 50 ksi (ASTM A992).

So, say you have that beam with a span of only 10 ft, Lb=10ft, the max load corresponds to that which generates Mp (yield limit state ie no LTB). 

Increase the span to 20 ft. Isn't there going to be LTB? In an earlier post, you said "Table 3-6 is based on braced (Lb always &lt; Lp, therefore not considering LTB) beams". 

Why are spans longer than Lp listed? Because they are braced at intervals of Lp or less, but beyond the first Lp, LTB kicks in, the Mn is not Mp anymore but the table 3-6 is based on beam being braced at least every Lp. "..............braced (Lb ≤ Lp) simple-span beams". Keep going to say Lr for that beam section, because of inelastic LTB the Mn (consequently load carrying capacity goes down linearly. Beyond Lr, the limit state is non-linear. 

From your earlier thread -*Lb absolutely is zero if the top flange is continuously braced*

Does this mean Mn *= *Mp regardless of the span? 

Anyway, it was an interesting discussion and thank you for it. Software programs are there for those smart engineers. Good luck.


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## thedaywa1ker (Oct 27, 2020)

EnergizerBunnyAt75 said:


> So, say you have that beam with a span of only 10 ft, Lb=10ft, the max load corresponds to that which generates Mp (yield limit state ie no LTB).
> 
> Increase the span to 20 ft. Isn't there going to be LTB? In an earlier post, you said "Table 3-6 is based on braced (Lb always &lt; Lp, therefore not considering LTB) beams".


Yes there will be LTB if Lb&gt;Lp, but then you can't use table 3-6 anymore, because the table values assume Lb&lt;Lp.



EnergizerBunnyAt75 said:


> Why are spans longer than Lp listed? Because they are braced at intervals of Lp or less, but beyond the first Lp, LTB kicks in, the Mn is not Mp anymore but the table 3-6 is based on beam being braced at least every Lp. "..............braced (Lb ≤ Lp) simple-span beams". Keep going to say Lr for that beam section, because of inelastic LTB the Mn (consequently load carrying capacity goes down linearly. Beyond Lr, the limit state is non-linear.
> 
> From your earlier thread -*Lb absolutely is zero if the top flange is continuously braced*
> 
> Does this mean Mn *= *Mp regardless of the span?


If you are looking at table 3-6, then yes, the moments from those loads equal Mp (unless it is above the bold line where shear controls)


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## dauwerda (Oct 28, 2020)

EnergizerBunnyAt75 said:


> Have either of you  (you and daywa1ker) looked at Fig.C-J10.2 and also Fig. C-F1.4. ?
> 
> Here is the text that goes with the latter, Fig. C-F1.4:  "In this case, the Cb = 5.67 would be used with the lateral-torsional buckling strength
> for the beam using an unbraced length of 20 ft which is defined by locations where twist or lateral movement of both flanges is restrained."


Fig C-F1.4 and the associated text is speaking to the situation where reverse curvature is possible (the example for this used in the text is wind uplift on a roof beam). So, yes, in this case the the bottom flange sees compression so the unbraced length is 20 ft.  

Chapter J.10 is dealing with concentrated forces, not flexure. It specifically states that Lb is the unbraced length along *either* flange at the point of the concentrated load for equations J10-6 and J10-7 exclusively. The figure C-F1.4 is referring to this specific case, not the Lb used when determining the moment capacity of a beam in flexure. 



EnergizerBunnyAt75 said:


> Why are spans longer than Lp listed? Because they are braced at intervals of Lp or less, but beyond the first Lp, LTB kicks in, the Mn is not Mp anymore but the table 3-6 is based on beam being braced at least every Lp. "..............braced (Lb ≤ Lp) simple-span beams". Keep going to say Lr for that beam section, because of inelastic LTB the Mn (consequently load carrying capacity goes down linearly. Beyond Lr, the limit state is non-linear.


I'm not completely following this - which questions are yours, what you are agreeing or disagreeing with, etc.



EnergizerBunnyAt75 said:


> From your earlier thread -*Lb absolutely is zero if the top flange is continuously braced*
> 
> Does this mean Mn *= *Mp regardless of the span?


Yes, for a simply supported beam that does not undergo uplift (meaning only the top flange ever sees compression) and the top flange is continuously braced Lb = 0 and Mn = Mp regardless of the overall span.


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## EBAT75 (Oct 28, 2020)

thedaywa1ker said:


> EnergizerBunnyAt75 said:
> 
> 
> > From your earlier thread -*Lb absolutely is zero if the top flange is continuously braced*
> ...





Feeding Lb=0   Mn becomes &gt; Mp because the second term will become positive. How is* **Lb absolutely is zero if the top flange is continuously braced** *satisfying Mn= Mp? or, Eq F2-2?

Ex: W16X100;  Zx = 198 in^3 ; span = 20 ft ;  W = 297 K; 

Lp = 8.87 ft  ;  phi Mp'= 743 k-ft ; Note the ', this is not Mp as you infer in the posts.

Lr = 32.8 ft ; phi Mr' = 459 k-ft ; Note '

w = 297/20 = 14.85 k/ft  ;  Span L = 20 ft; Mu = 14.85x20^2/8 = 742.5, rounded to 743 k-ft. 

Quote:  " If you are looking at table 3-6, then yes, the moments from those loads equal Mp". 

From Manual:  Mp′ Maximum available flexural strength for noncompact shapes, when Lb ≤ Lp′, kip-in. or kip-ft, as indicated


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## thedaywa1ker (Oct 29, 2020)

EnergizerBunnyAt75 said:


> View attachment 19143
> 
> 
> Feeding Lb=0   Mn becomes &gt; Mp because the second term will become positive. How is* **Lb absolutely is zero if the top flange is continuously braced** *satisfying Mn= Mp? or, Eq F2-2?
> ...


I don't understand why you are feeding Lb=0 into F2-2 when (a) says that LTB doesn't apply when Lb&lt;Lp.  F2-2 only applies when Lp&lt;Lb&lt;Lr

Regardless, the end of F2-2 says &lt;=Mp, so if the equation does equal more than Mp, then you still use Mp.  This is meant for the case of Cb &gt; 1, because you shouldn't even be going down this rabbit hole if Lb=zero, per (a).

I'm not sure what you're saying with the W16x100.  The moment from the loads in table 3-6 equal Mp, like I've been saying.  Am I missing something?


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## organix (Oct 29, 2020)

I'm getting fairly lost in this topic or maybe I'm missing something.  You only seem to be proving their point now, EBA75.



EnergizerBunnyAt75 said:


> View attachment 19143
> 
> 
> Feeding Lb=0   Mn becomes &gt; Mp because the second term will become positive. How is* **Lb absolutely is zero if the top flange is continuously braced** *satisfying Mn= Mp? or, Eq F2-2?


Again, not sure if I'm missing the point, but are you trying to show Mn would exceed Mp?  For one, F2-2 simply doesn't apply if you're continuously braced.  But even if it did, it says less than or equal to Mp.  So Lb is zero, the second term is positive and you get Mp plus some value less than or equal to Mp = Mp.  So yes, Mn would exceed Mp if you use the left side of the equation, but you can't ever exceed Mp anyway.



EnergizerBunnyAt75 said:


> Ex: W16X100;  Zx = 198 in^3 ; span = 20 ft ;  W = 297 K;
> 
> Lp = 8.87 ft  ;  phi Mp'= 743 k-ft ; Note the ', this is not Mp as you infer in the posts.
> 
> ...


I don't get this example either.  You've proven their point that the distributed load is equal to Mp.  If you're point is based on the *-`-* next to the terms, that's simply for cross sections with noncompact flanges.  You have to adjust Lp and Mp accordingly.


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## EBAT75 (Oct 30, 2020)

These are items for consideration in totality:

1. The prime (') and non-compact. Yes, the example section is compact. Why then is the table showing primes at the bottom which tie in with the values in the table for different spans? If anyone is confused, I am too.

2. Lb=0. Yes, &lt; or= Mp. For that to happen, shouldn't Cb then become &lt; 1? The Table is based on Cb=1, the minimum for any condition.

3. Continuously braced, prevented from lateral displacement, twist, etc are terms that need clarification. The Specs simply give formulae for bracing strength requirements per brace point. These are based on the flange compressive force Pf which becomes infinity (as to be expected) when Lb=0. Something to think about.

4. Does not deflection become the controlling factor, not strength as the span increases? How does deflection affect flange force and consequently the required brace strength?


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## EBAT75 (Oct 30, 2020)

Just to clarify 2. above, this is under the F2-2 scenario, whether bracing strength is checked to be adequate for all spans. If as have said before, the bracing interval is &lt; Lp and the stiffness provided is adequate based on that Lb=Lp, then the stiffness requirement would be met regardless of the span.


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## thedaywa1ker (Nov 11, 2020)

EnergizerBunnyAt75 said:


> These are items for consideration in totality:
> 
> 1. The prime (') and non-compact. Yes, the example section is compact. Why then is the table showing primes at the bottom which tie in with the values in the table for different spans? If anyone is confused, I am too.
> 
> ...






EnergizerBunnyAt75 said:


> Just to clarify 2. above, this is under the F2-2 scenario, whether bracing strength is checked to be adequate for all spans. If as have said before, the bracing interval is &lt; Lp and the stiffness provided is adequate based on that Lb=Lp, then the stiffness requirement would be met regardless of the span.


Sorry to beat a dead horse, I was going to just leave it and stop going in circles, but I couldn't help myself.  Brother, I don't claim to be an expert on LTB but your posts are going to confuse the hell out of anyone browsing that is trying to get familiar with steel design.

1.  I'm not sure what you're talking about.  Are you talking about the bottom of 3-6 showing prime values?  The Mp values in the bottom of 3-6 should equal the Mp' values where applicable.  I'm not sure where the confusion is, W16x100 is compact anyways

2. That is not what inequalities mean in the steel manual.  It is giving an upper bound to the values you can use out of the first equation, it is not saying that the equation will always be under the second value no matter what.  This is a common notation in the manual (bolt hole bearing strength is an example off the top of my head), and if that is how you interpret the inequality then you are probably doing other things incorrectly as well.

3. Those definitions are indeed vague.  They leave it up to engineering judgement.  What equation is Pf from in the specification?  It is not in the symbols list of the spec on 16.1-xxvii, don't see it in Appendix 6 either

You have posted a number of things that you say are direct from the manual but are not in fact in the manual.  Can you please be more specific when you are citing the manual

'flange compressive force Pf goes to infinity when Lb=0'  That doesn't sound right, again I don't know what equation you're referencing but it sounds like Pf would at least be limited by yielding.  Can you give a code reference please.

4. Yes deflection controls at longer spans. I dont think that deflection in and of itself would effect LTB at all. I don't know of any way that deflection would come into play with LTB unless it is enough that it starts screwing with the layouts of your bracing


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## EBAT75 (Nov 11, 2020)

'flange compressive force Pf goes to infinity when Lb=0'  That doesn't sound right, again I don't know what equation you're referencing but it sounds like Pf would at least be limited by yielding.  Can you give a code reference please.
 

Pardon my reference to flange compressive force Pf......MY SLIP. Meant to say required brace strength. Ref: App 6.3

Let me take up the topic with AISC Steel Solutions. They have questions answered. 
For now, I feel some of these are counter intuitive.


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## EBAT75 (Nov 11, 2020)

https://lsc-pagepro.mydigitalpublication.com/publication/?m=7946&amp;i=676603&amp;view=articleBrowser&amp;article_id=3785160

https://lsc-pagepro.mydigitalpublication.com/publication/?m=7946&amp;i=656537&amp;view=articleBrowser&amp;article_id=3646852

Just after I sent an email to AISC, I saw these. I will post their answers when I get them.

I am sorry if I caused confusion. I am thinking of asking the EB moderator to delete this post if it will help.


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## EBAT75 (Nov 17, 2020)

*AS PROMISED, HERE ARE THE ANSWERS I JUST RECEIVED. AS I HAVE SAID EARLIER, WHEN THE ANSWERS HAVE BEEN SEEN BY OTHER MEMBERS, I AM FINE WITH IT BEING ARCHIVED OR DELETED IF IT HELPS AVOIDING CONFUSION.*

[SIZE=12pt]I have addressed your [/SIZE]questions[SIZE=12pt] below in red:[/SIZE]


From Steel Solutions: A direct brace may be provided for a primary member by a properly attached floor system itself ..... What constitutes a properly attached floor system itself .....? I assume you are referring to the Engineering FAQ 4.3.1. The technical answer is “a floor system that is attached such that the strength and stiffness requirements provided in Appendix 6 of the Specification are satisfied can be considered a “properly attached floor system” relative to the statement in the FAQ. It is not common in my experience for explicit checks to be performed relative to the floor system and its attachments. It is common in my experience for engineers to judge such conditions by inspection based on engineering judgment and experience. A concrete floor on a steel decking - is it sufficient? In my experience most engineers would deem “a concrete floor on a steel decking” to be sufficient. It might be possible to attach “a concrete floor on a steel decking” to a beam in a manner that is not sufficient, though it would seem that someone would have to go out of their way to do so, at least relative to conditions commonly found in buildings. It is my understanding that in bridges the deck is sometimes attached in ways that can reduce the ability of the deck to provide bracing to the beams. Does it provide required bracing strength per App 6.3? It can be evaluated using Section 6.3. Is it continuous bracing? In my experience beams are sometimes designed in practice based on the assumption that they are “continuously braced”. I suspect different engineers apply/intend somewhat different subtleties when using the term, but generally it can be taken to mean that Lb&lt;&lt;Lp. I suspect that there are few engineers that would assert that Lb is actually zero, if they stopped to seriously consider what they intend. Generally it probably does not make sense (or at least is not necessary) to treat “a concrete floor on a steel decking” as continuous torsional bracing as addressed in Section 6.3.2b in building construction, though as discussed in the Commentary this can be done.




Is it correct to say continuous bracing means Lb=0; Mn=Mp regardless of beam’s span? (as another engineer says it is) If a beam is truly continuously braced, then the unbraced length would seem to be zero by definition and since stability would not be a concern Mn=Mp – unless local buckling of the elements governs. However, if the compression element is continuously braced, it is difficult to see how the local buckling strength would not be beneficially impacted as well, though the Specification does not directly address this issue.




In Table 3-6 Maximum Total Uniform Load, if a beam is continuously braced, and the Mn is equal to Mp regardless of the span (as an engineer on a forum says it is), what is the meaning of values marked with ‘ (prime) at the bottom of the pages? I do not understand the question. Some sections are marked with an ‘f’. This indicates, “Shape does not meet compact limit for flexure with Fy = 50 ksi; tabulated values have been adjusted accordingly” as stated in the footnotes to the table. Note that I have also mentioned this possibility above.




For compact W sections, are Tables 3-6 and 3-10 equivalent? Tables 3-6 and 3-10 address different conditions and therefore are not (and cannot be) “equivalent”. They should converge where the conditions overlap. In other words they should be consistent or should not conflict.  If we consider a W24x229 (just to pick a section at random) Table 3-6 lists φbMp as 2530 k-ft. Table 3-10 on page 3-97 seems to top off at about this value. This is because stability is not an issue at low (though not necessarily continuous) unbraced lengths. However if we look at a unbraced length of 18 feet in Table 3-10 φbMp is about 2340 k-ft. If we go to Table 3-6 and look at the same W24x229 with a 18 foot span the maximum total uniform load is 1130 kips. This can be converted to w, the uniform load, by dividing by the span to get 1130/18 = 62.77 kips/ft. The moment is wL^2/8 = 62.77(18)^2/8 = 2540, which is roughly φbMp, again because stability is not an issue at low (though not necessarily continuous) unbraced lengths. I am assuming we can simply overlook whatever rounding or minor mathematical error I managed to introduce along the way.


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## EBAT75 (Nov 18, 2020)

Lest I am considered to have “No Comment”, I give below my last set of comments:

1.        Steel decking in and of itself is not the bracing element unless it is designed and detailed as such. Orientation of the decking i.e. perpendicular or parallel to the girder or beams in a bracing system comes into play. Also is the decking designed as a diaphragm? I am not familiar with the SCM 15 or the 2016 specs. Apparently there is more in them on the topic.

There is no consistency on stiffness, strength requirements in the code(s). Why these checks are generally not done is not because the decked floor is necessarily stiff or strong enough but because the framing layout would be such that beams required at some intervals would be providing that stiffness and strength required. Consider this – a perimeter girder into which beams frame into. Decking spanning across the beams would now be running parallel to the perimeter girder. Is the decking providing the “sufficient” strength and stiffness for this perimeter girder? Wouldn’t there be torsion also on the perimeter girder (loaded only on one side)? Aren’t the beams framing into the girder actually providing torsional stiffness/strength in addition to lateral? Is the Lb=0? Is Lb not the spacing of the framing beams? Now, extend this to the interior girders sans torsion, except the decking being perpendicular to the interior girder would provide more of what was described as “truly continuously braced” condition if the span is such that it can provide the stiffness/strength combination.

If there is no decking with shear studs or welds, is the concrete slab attached to the compression flange as in composite slabs with studs for it to provide the strength and stiffness?

On the one hand, concrete slab (decked or not) is considered sufficient; on the other – use App. 6.3. AISC and SDI or ACI are playing in their own turfs. Does a beam/girder designer also design and specify the bracing elements?

Another item of interest is this. Can one say how much of the reserve strength of the beam/girder is what provides the real, old “Factor of Safety” or as a colleague of mine used to call it “Factor of Ignorance” because a 50 ksi W normally comes with 65 ksi (=/-) yield mill test results. We do not design the 50 ksi yield for 65 ksi yield, but that is the “as built” strength. Can this be a part of the overall bracing, Mn, Mp, Lp, Lp margins in the as-built structure that can mask the bracing issues?

2.       Item 2 in reply – No Comment.

3.       The prime has been mistakenly taken as f.

4.       If Tables 3-6 and 3-10 are not equivalent; should be consistent or should not conflict, the example has shown a relationship. It may not be 1-on-1, direct. Yes, 3-6 is based on Lb&lt;Lp. But the bottom part has the BF listed. It can be used for Mn when Lr&gt;Lb&gt;Lp and triangulation between Max Load, Mp, Lb/Lp is possible. In that sense, there may not be equivalency but there is convertibility.

Ladies and Gentlemen, I apologize for the drawn out discussion on this. I have also been confused at times. As long as we do not get confounded, my hope is that something good also comes out of it.

Please feel free to add your comments too. I do not take these at a personal level. I have no intention to add anymore to this thread unless someone explicitly asks me to. Someone once told me “listening is the better part of the conversation”. I will listen.


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## organix (Nov 19, 2020)

I am confused by your item 3.  The prime isn't shown in the tables.  If you are referring to the screenshot below, that's just a comma to separate the adjacent units.  Otherwise, the prime is shown on page 3-5.


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## thedaywa1ker (Nov 19, 2020)

Thanks for following up EB75

1. I believe most practicing engineers would consider metal decking to be sufficient brace the beam without a second thought, considering it will be attached with welds or TEK screws as a diaphragm.  The perpendicular/parallel flutes question is one I have seen debated before...and theoretically there probably is a difference in bracing capability, even though we don't design the diaphragms as having different capacities in different directions.  But I haven't seen anything compelling enough to make me deviate from what I've been comfortable with for years, barring any special circumstances like excessively large beams in braced frames for example

4. Another example of where 3-6 and 3-10 converge is in my post from 10/12:



> In the 3-10 charts, the horizontal portion of each beams line matches the moment given by taking (loads from 3-6)/(L)*L^2/8 - and the 3-10 charts start sloping at Lp because that is when LTB starts to apply...once the line in the 3-10 charts are sloping, the chart and table no longer match.


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## EBAT75 (Nov 19, 2020)

Thank you for the screenshot. I mistook it for a prime. As it was in color print I associated them as one. The fonts also did not help me.


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