ACI Code : Analysis 2

[pgnair1]

Hi,

I have a question regarding the Design of Frame members using ACI 318.

As per section 10.11 , for compression members design, an elastic first-order frame analysis with reduced moment of Inertia to take into account effect of cracking can be used as an alternative to using second order analysis for design of the compression members in the frames, for deciding sway or non-sway columns/ stories, moment magnification , etc.

My question is do we also have to use the Moments from the above analysis for the design of Beams in the Frames or do we use the results from another elastic first-order frame analysis without reduced moment of Inertia for beam design.

Does the ACI code say anything speciifcally about design of frame beams.

Thanks

 

[JAE]

pgnair1,

I think per ACI Chapter 10, you have the following two choices:

1. Use a rational analysis taking into account second order effects, cracked stiffnesses, etc. (the first part of the column section). Basically a full blown Pdelta analysis and design.

2. Use the reduced sections to account for cracked properties and perform a first order analysis and then use the delta factors (approximate moment magnification factors) to increase your first order moments to replicate second order moments.

In both of these you need to use the magnified moments for both the columns and the beams if they work interactively.

So for example, a beam-column frame along a column line would use all the magnified moments (for both beam and column design) but the repetitive concrete joists within the bays wouldn't need any magnification as they are not intended to resist the lateral/gravity moments.

 

[mitchelon]

The purpose of conducting a first-order analysis with reduced moment of inertia and so forth is to account for second-order effects, or P-Delta effects. The beams will not experience P-Delta effects, so therefore this method is intended only for the columns.

 

[JAE]

The beams do get affected by the second order analysis of the frame. While mitchelon is correct that there is minimal P[Δ] effects (the beams usually have minimal axial compressive forces), the second order effects do increase the beam end moments and this should be considered in design.

 

[mitchelon]

I understand the question know better. In accordance with 10.11.1, you need to modify the moment of inertia of all columns, beams, walls, flat plates, and flat slabs in your first order analysis. You only need to magnify the moments in the columns. You can increase/decrease the areas, material properties, moment of inertia, etc. of all members in a first order analysis, and your moments would still be the same. The moment of inertia and material properties will affect your deflections, which will mostly increase/decrease your second-order effects. This second order effects should not affect your beams connected to interior column, as your columns, depending on beam/column stiffness ratios, should carry most of the additional moment. But, I would worry about exterior column-beam connections where unbalanced moments are more likely to occur. Remember, “we are not making watches.”

 

[dawn836]

well thanks all for your valueable replies, i have been discusing this issue with some engineer today, but there is a point i wonder about.
what kind of analysis can i do to account for cracked sections instead of using modification factors directtly?

 

[mitchelon]

A non-linear analysis taking into account second-order effects. SAP or ETABS has these capabilities.

 

[hagi10]

Could you please clarify the followings?

- What stiffnesses for beams, columns, walls, and slab should used to check the building drift and design?

- ACI318 10.11.1: Is it for strength design?
- Can you use full stiffness of beams, columns, walls, and slab for drift check?

thanks much,
O.

 

[WillisV]

Read the entire commentary to section 10.11.1 (R10.11.1). It answers all of those questions.

 

[hagi10]

It is not clear to me when to use 1/0.70=1.43 times the moment of inertias given in 10.11.1 commentary. Is there anyway to get clarification from ACI committee?

I have a 3D model in Etabs and I need to define the cracked moment of inertias? What do you think the correctness of the following statements;

- For strength design, I used the following cracked moment of inertias;
beams 0.35Ig
columns 0.70Ig
walls 0.35Ig cracked
slabs 0.25Ig

*** For drift check, should I increase the values given above by 1.43 in first order analysis or x1.43 is only applicable for second order (P-delta) analysis?

Any help or suggestions are appreciated. Please help me to clarify when to use 1.43 factor (is it a factor that can also be used in first order drift check)?

Thanks much,
O.

 

[WillisV]

1.43 factor is generally applied to the moments of inertia you listed for use in serviceability checks. It is equally applicable to first or second order drift checks. Results in 0.5Ig for beams and 1.0Ig for columns.

Now however that these values are not mandatory per code and many engineers use different and less conservative assumptions.

 

[hagi10]

Could you please comment and explain the theory behind the crack moment of inertias and x1.43 factor for service loads?

What I understand from the earlier posts (JAE - 6 Aug 06);

We have 2 options for strength design;
1- first order analysis w/cracked moment of inertias and magnification factors to columns to account for second order (P-delta) effect, or directly
2- second order analysis w/cracked moment of inertias

Therefore; cracked inertias given 10.11.1 must be used for strength design unless there is a more accurate estimate (tests etc).

So far so good...

If I reduce moment of inertias of all structural members (beams, columns, walls, slabs...) with same percetange, there will be no change in strength design (since loads are distributed equally, member forces do not change).

My interpretation: In strength design, only the relative difference btw crack moment of inertias of structural members decides the difference in design (because relative difference changes the load distribution and member forces).

QUESTION: If I multiply those cracked moment of inertias given in 10.11.1 with 1.43 for deflection check/service loads (which results in 0.5Ig for beams and 1.0Ig for columns), WHAT IS THE POINT OF USING CRACKED MOMENT OF INERTIAS?

Do not we reduce the effect of cracked moment of inertias to minimal in strength design and service design/drift check?

I am confused, I was not expecting to increase cracked moment of inertias by 1.43 to check drift?
O.

 

[WillisV]

As concisely as possible the theory is this: At ultimate strength load levels concrete cracks - a lot, at smaller service level loads it is assumed to not crack as much. So the factors in 10.11.1 are a "best guess" of what cracking values occur at ultimate load levels and the 1.43 factor is a "best guess" of what cracking occurs at service levels.

You are correct that for a 1ST ORDER ELASTIC ANALYSIS, you will get the exact same load distribution rather you use ultimate cracking: 0.35Ig for beams and 0.7Ig for columns, or service cracking: or 0.5Ig for beams and 1.0Ig for columns, as the relative ratio is the same. In fact, sometimes for structures where I judge that 2nd order effects will be relatively minor, I do just use the service cracking values so that I can directly use the deflections and still design the building using the load distribution provided. Where second order effects are not minor, this is an invalid assumption as described in point 2 below.

To answer your question of what is the point of using cracked moments of inertia, it is many fold:

1. The moment distribution is different than if full moments of inertia were used for all members. Note that in both the service and ultimate load cases the columns are assumed to be cracked less than the beams. This affects the load distribution differently than not assuming any cracking.

2. When a 2nd order analysis is carried out, the magnitude of building sway deflection affects the "Delta" portion of the P-Delta moment magnification effects. So you WILL get different load distributions depending on if you use service or ultimate level cracking, because those values affect the lateral sway magnitude of the building. At ultimate loads, the builing is cracked more, will sway more, and will experience increased P-delta effects.

3. The seismic drift limits in the IBC are based upon an ultimate analysis (as earthquakes are already ultimate loads). Therefore you need to use ultimate load crack factors to determine the building drift for comparison.

4. Wind drift values are normally taken based on a 10-year wind (0.7W) - which is a service level load and therefore based on building drift using service level crack factors.

Hope this helps clear things up a bit.

 

[hagi10]

Thanks WillisV for information and your valuable time. That helps a lot.
O.

 

[JAE]

hagi10 - to add one little bit to WillisV's great post, keep in mind that the "full blown 2nd order analysis" of a concrete frame should include not only P[Δ] moments (moments due to frame sway) but also P[δ] moments (moments due to compression member curvature). The small [δ] are deflections along the length of members such as columns.

Using cracked section properties will have an influence on second order moments (as WillisV pointed out) but even more so when you include P[δ] effects.

To do this you can model your frame using lots of joints/nodes along the length of compression members (say at 1 ft. increments) to allow the solved matrix in your structural program to take into effect these second order effects. This is a lot of work so most use the ACI moment magnification factors)

 

[WillisV]

On a tangent: JAE - what is your interpretation of provision 10.13.5?

In general I have interpreted this provision to allow slenderness effects to be ignored for members in my 2nd order model meeting that provision. I have found this to be true the majority of the time and therefore generally just run a 2nd order analysis for sway effects without using ACI magnification factors.

Gravity columns have a much more restrictive limit per 10.12.2 and therefore I do design those for slenderness effects where appropriate.

 

[JAE]

The commentary for 10.13.5 seems to be pretty good. It seems to me to say this:

1. For sway frames - you add non-magnified nonsway moments to magnified sway moments per 10.13.3.

2. This assumes that the largest moment is at one of the ends of the column.

3. If the l/r of your column is LARGER than the value shown in Eq 10-20, then there is the potential for the largest moment to occur not at the ends...but somewhere along the length of the member.

4. If the l/r exceeds that of Eq 10-20, then find Mc from 10.12.3.

 

[hagi10]

WillisV,

Thanks again for your great help. Can you give the sections in IBC, ACI, or ASCE to support the statement you have given (see below)?

I think to be consistent, EQ drift has to be checked with ultimate cracked moment of inertias (0.35Ig and 0.7Ig) as you say. However, someone may disagree saying that all the deflections should be checked with service cracked moment of inertias.

Is that clearly stated in the code, book, etc. that ultimate crack moment of inertias should be implemeneted to check seismic drift?

YOUR STATEMENT:
"3. The seismic drift limits in the IBC are based upon an ultimate analysis (as earthquakes are already ultimate loads). Therefore you need to use ultimate load crack factors to determine the building drift for comparison."

Thx,
O.

 

[WillisV]

hagi10 - Check ASCE 7-05 Section 12.8.6 - the wording makes it clear strength level forces should be used for drift determination. It is up to your judgement for the rest.

JAE - I agree - which is why I was suprised by your statement regarding having to use 1ft increments for analysis and "most people" using ACI moment magnification factors for 2nd order analysis. The slenderness provisions rarely kick in from what I've seen.

 

[opa123]

well hi all
i checked ACI-318 and read 10.10.1+ its commentry nothing is said directing me to use stiffnes reduction factors 0.7 and 0.35 when doing P-delta analysis, only i found in commentry that i should use stiffnes reduction factor for columns as per R10.12.3
can someone clarify this for me according to ACI