Live Load Reduction 1

[StructuralAddict]

Hello,

I have a question related to the calculation of the live load reduction factor (ASCE 7 Procedure).

L = (Lo){0.25+15/sqrt[(KLL)(AT)]}

With reference to the attached frame:
(1) What (KLL) and (AT) should we consider to calculate the reduced live load of Beam B1? And how many floors is Beam B1 supporting?
(2) What (KLL) and (AT) should we consider to calculate the reduced live load of Column C3? And how many floors is Column C3 supporting?

Thank you.

 

[StructuralAddict]

Further to my question above, please consider the frame to be an interior frame. So, all beams and all columns are interior members.

 

[r13]

See if the linked page helps. Link

 

[Agent666]

Live load reduction is all about the total tributary area being supported.

So it is everything live load wise being supported by those elements typically.

However transfer structures are a special case where some codes and guides require further factoring up of the loads, which is opposite to the live load reduction philosophy. Look into disproportionate collapse.

FYI, there have been a number of threads in the past that hash out LLRFs and their use. So might be of some use as has probably been covered before to one degree or another.

 

[StructuralAddict]

Thank you for your prompt response. Yes, I am a little not sure about how to calculate the LLRFs for transfer girders.

Should I consider the (KL)g and (AT)g of the girder for one floor only (where the girder is located)? And consider the (KLL)c and (AT)c for the column supported by the girder (including all floors supported by the column)? And then use the following expression:

L = (Lo){0.25+15/sqrt[(KLL)g(AT)g+(KLL)c(AT)c]}

Subscripts (g) and (c) refers to "Girder" and "Column", respectively.

 

[KootK]

My vote is to do it like this.

With the ASCE method, it's important to note that it's really about Influence Area (IA) rather Tributary Area (TA) per se. And much confusion would surely be avoided if they just went straight to the influence area rather than having you futz around with the K_LL business.

IA = K_LL x TA = Every square foot that, when loaded, would add some increment of load to the member being considered.

Do your brain a favor and just skip the middle bit and go straight to the influence area.

Continuity results in further confusion and most engineer will just pretend the members ares simple spans for the sake of the live load reduction calculation.

 

[StructuralAddict]

Thank you very much KootK. I totally agree with you. I believe using the tributary area concept is because it's generally easier to determine the tributary area than the influence area. Thus, calculating "(IA)calculated = KLL x TA" will result in a smaller value than "(IA)actual"; and thus more conservative when calculating the live load reduction factor.

Thanks for taking the time to mark the sketch. I assume the yellow highlight represents the influence area of beam B1 (Left sketch) and column C3 (Right sketch).

You teased my brain with the idea of considering continuity to determine the influence area. I believe it's better to ignore continuity as it will complicate the calculations significantly. Ignoring the continuity will result in reducing the influence area (Thus towards the conservative side when calculating the live load reduction factor).

 

[JoshPlumSE]

Two thoughts on this:

1) Theoretically correct way of doing this based on influence area:
Influence area of column C1 = 4*Trib Area of C1 = 4*A1
Influence area of beam B1 (due solely to the floor on which it's located) = 2*Trib Area of B1 = 2*A2
Total influence area of B1 = (4*A1+2*A2).
Reduction factor for B1 = (0.25+ 15/(sqrt (4*A1+2*A2)) > 0.4 (since it supports more than one floor)

2) Following the letter of the code:
Reduction factor fo B1 = (0.25+15/(sqrt(2*(A1+A2))) > 0.4


Regarding Continuity:
That's not really addressed in the code provisions. So, we mostly ignore continuity for influence area calculations. Though it could get a little murky when we start talking about cantilevers.

 

[r13]

While it is easily understood that K_LL for interior beams = 2, I am lost on "K_LL = 2 for edge beams without cantilever slabs", and "K_LL = 1 for edge beams with cantilever slabs". Can anybody explain? Thanks.

 

[JoshPlumSE]

Retired13 -

Remember KLL relates influence area to tributary area. So, the trib area of an edge slab is half the end bay area, right? Therefore, 2* that area is still the overall influence area.

Now, if you've got a slab cantilevering over the beam. The trib area of the cantilever is equal to the influence area in that direction.

 

[r13]

Josh,

Is this correct?

 

[r13]

I think I got it. Please correct me if wrong. Thanks.