Moment Distribution in Continuous Concrete Members 3

[trekkie]

I'm designing an underground rectangular concrete tank using Moody Tables and I have a condition where the fixed end moment of a wall is 60 ft-kips and the FEM of the adjoining wall is 20 ft-kips. After I redistribute the moments, my balanced moment ends up being 42 ft-kips. Now my question is that in ACI318-02 Section 8.4 the section talks about not increasing or decreasing moments by redistribution by any more than 20% max...does this section refer to my case where my 42 ft-kip moment is obviously more than 20% from 60 or 20. If not could someone please clarify what the section is referring to? Thanks in advance

 

[rowe]

You're determining the moments in a rectangular frame using "moment distribution". You're balanced moment is 42 ft-kip.

The "redistribution of negative moment" in ACI 8.4 allows you to decrease that 42 ft-kip moment if the criteria is met. The decrease accounts for the change in the actual distribution of moment (assumed by elastic behavior) when plastic deflection occurs. If you can decrease that negative moment, you must increase the positive moment at (near) midspan.

good luck.

 

[JAE]

trekkie:
Section 8.4 has nothing to do with moment distribution analysis. What 8.4 is talking about is the technique of slightly reducing the negative moments in a continuous member and adding that reduction to the positive moments.

Your moment distribution would provide you with final design moments (your 42 ft-kips). Section 8.4 lets you take those specific moments and borrow some of the negative moment and "move" it to the positive moment regions.

The 20% limit is limiting how much of the negative moment you can redistribute.

 

[rowe]

I believe that JAE and I have given you the same answer. After further consideration, and if our answers were not very illuminating consider the following:

your rectangular frame is similar to a continuous beam (without end beams).

a continuous beam typically exhibits negative moments over the supports (or the corners of your frame), and positive moments near the midspan. Depending on the beam (or frame), the negative moment might be much higher (absolute value) than the positive moment. The negative moment might be so much higher that you require 2 or 3 times as much rebar for the negative moment than for the positive moment. If so, you can design more economically by allowing the "partial" development of a plastic hinge at the negative moment. In effect, you're in between a truly "continuous" beam and a "simply supported" beam.

Lastly, I would not take any advantage of the allowed reduction in the negative moment for an underground structure. Anyway, the required serviceability (cracking) may control the required reinforcement. Sorry for being long winded, and

good luck.

 

[JAE]

Yes, rowe, I posted and then noticed that you had arrived right before my own post. I agree with your comments.

 

[hernma]

rowe:

Since the characteristic of a plastic hinge – that is not supposed to reach at- is maintain the full capacity of resistant moment, please can you develop your idea that it is "in between a trully "continuous" beam and a "simply supported" beam"?

 

[rowe]

Hernma,

Factored loads are not usually intended to satisfy serviceability, but usually to ensure that the structure is adequate to sustain the load without failure.

If the criteria for failure is collapse, then you should be able to design for the development of a plastic hinge due to some extreme event (like an earthquake).

Some structures, like critical bridges, hospitals, etc. require some extent of serviceability even under these types of extreme events, so that some plastic deflection is allowed, but limited (closer to elastic than to strain hardening).

As far as the original question concerning ACI 8.4, suppose you have a fixed-fixed member with a uniform load:
wL^2/12 = end moments
wL^2/24 = moment at mid-span
Total difference = wL^2/24 - (-)wL^2/12 = wL^2/8

wL^2/8 is max moment at mid-span for a simply-supported beam (W/ A UNIFORM LOAD)

Therefore, the uniform load causes the same distribution of moment along the beam - only the "end" conditions are different.

ACI allows you to consider allowing SOME plastic deformation at locations of continuity (like the negative moments of a continuous beam), but since the load is not changed, you must apply that reduction of the negative moment to the positive moment area of the span.

 

[koodi]

Rowe's main point being:
The 20% limit will maintain elasticity during service loading--but the code will allow redistribution for ultimate loading.

In 1930 Von Emperger stated, "To design a beam with uncertain fixity it is only necessary to assume an arbitrary moment diagram in equilibrium with external loads."

Well written responses Rowe and Jae,
I love reinforced concrete