MULTI-SPAN (CONTINUOUS) CONCRETE BEAM DESIGN

[gotlboys]

I usually compute moment of continuous concrete beams using MDM (moment distribution method). This gives larger moments at supports (neg. moments)and smaller moments at mid-spans(pos. moments). While this may be a common practice to many, a senior designer advised me to consider it as simple beams where max. moment is at mid-span for safety purpose.
He argues that it is economical to consider as continuous beam but, in reality, if one span gives up due to high earthquake magnitude, others capacity become insufficient to carry redistributed loads.

Please share your advice based on some theoretical and practical information.

 

[KootK]

There is some logic in your colleague's recommendation. When designing continuous beams, one span's capacity is dependent on the neighbouring span's integrity and, to an extent, even the presence of the neighbouring span's live load. Designing for computed negative moment and simple span positive moment will produce a more conservative design. Too conservative, in my opinion, considering that:

1) most codes include patterned live load cases that will reduce dependency on the presence of adjacent span live loads.

2) vertical seismic loads on gravity beams are relatively small. They, and the seismic drift, can be designed for so as to greatly minimize the risk of adjacent span damage.

3) Continuity is a fundamental characteristic of cast in place concrete construction. Disregarding the benefits of that continuity altogether is unacceptably wasteful in my opinion.

4) Most codes include integrity reinforcement detailing provisions that will increase the robustness of all spans within a continuous beam and reduce dependence on adjacent span live loads and capacity.

I myself practice a much less conservative version of your colleague's strategy. I often redistribute a portion of the beam negative moment to the positive moment region and I never design for a positive moment less than wL^2/20 no matter what value is computed in the analysis process.







I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JAE]

KootK's list is good and I would emphasize his first point.

Patterned loading is the key here and typically for any series of continuous spans you will have six different pattern combinations:

Full Live Load
Live load on Odd spans
Live load on Even spans
Live load on adjacent spans (pattern 1) Load/Load/zero/load/load/zero/load/...
Live load on adjacent spans (pattern 2) Zero/Load/load/zero/load/load/zero/...
Live load on adjacent spans (pattern 3) Load/zero/load/load/zero/load/load/...

Also with patterned loads you need to consider whether the "zero" loaded spans above are more correctly some percent of the live load (i.e. some of the live load is sustained)
This might make the zero load more like 25%LL.



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[BUGGAR]

For heavy marine structures (Navy piers, etc.), we usually design all spans as both simple and fixed and detail the top and bottom steel for the worst case. These things have to be highly redundant and the additional steel is not that much. It makes the detailing incredibly simple.

 

[gotlboys]

Thank you Kootk and JAE for taking some time to share with me.
I seem to have been more confident with my design after reading both 1st and 3rd points. I am curious about wl^2/20. I think this could have a relation to ACI code provision: "The pos. moment strength at the joint faces should not be less than half of the neg. moment. Neither the pos. or neg. moment strength at any section be less than one-fourth of the max. moment strength provided".

By the way, what is the common practice to compute moments for steel frame building (SMRF). My colleague uses wl^2/8 (simply supported) for all steel beams where no moments are transferred to steel columns. This definitely results in larger steel beam section but will economize column section and footing pad as they only carry seismic moment.

BUGGAR, I take note of what you shared.

Sorry for asking many questions. I am a newbie in design practice.

 

[Akeee]

Hello guys,
I think you are too conservative regarding this subject. Just think about that steel and concrete strenght are divided by safety factors. The real strength is the medium one and for steel is 1.15*value in desing and for concrete + 8 mpa. So only from steel you have 15% bigger bending capacity. The second point is in loading big values from codes. That live load for example is very very big and has 95 % probability in reality to be less. So the values that we work with in design are very very not reality like, ultra conservative so in my opinion you dont have to more conservative....

 

[rapt]

Aketr,

The real material strength is not the medium one, it is accepted as the lower 5 percentile figure as you could get the material with the lower percentile value in your building, so the medium one will not help keep your building standing if it is not there.

Load factors and material factors have been developed over many years to provide the necessary risk/safety factors that are considered to be acceptable for structures of different importance levels. And buildings still fall down. We are not being overly conservative.

Yes, Buggar's concept of designing for the worst possible case of continuity is not required for most structures. But may be logical for structures that are likely to face damage from severe accidental actions e.g. a very large ship colliding with it and causing something that is continuous to all of a sudden become simply supported. It is a method of providing Robustness for a special structure that requires it as the port could be out of action for years if badly damaged.

All of the other comments above simply suggested following defined Design Code requirements. They are not overly conservative.

 

[Akeee]

When i meant with real strenght is the most probable values are the medium ones not the 5% fractile. I didnt sad that we should use them i just wanted to show a point, although if you want to make a pushover analysis ( not liniar one) the design code recommands that you work whith the mediums. So this is 1 thing. Another, when you calculate the sectional efforts M,V,N in your load combinations you have load factors. In europe zone for live load the factor for gravitational design is 1.5 so you increase it with 50%. The loads from the minimum requirements are already big, make them 50% bigger its kinda too much. Lets say for example a simple home, live load is 150 kg/m2 ( 1.5 kn/m2), this is like on every meter square you will have at least 2 people of 75 kgs (maybe reduce them due to the other loads like furniture who stand under live) but is something very unlike to happen. For a usual one or two familly homes of 200 m2 that means you have to have around 300 ppls at the same time in the building. And this not to mention you have to add 50% more from combination so 450 people ? This is way off reality. So to recap, the probability to have 450 people in a usual house at the same time and to have materials that goes under that 5% fractile its like none. So to this thing to add another conservative assumption in the moment diagram to be safe its for nothing. This was my point. And i didnt mention that the bending capacity of a beam is 35% bigger, we work with yell values for strengths but at the failure the ultimate ones count.

 

[gotlboys]

Kootk, JAE, Aketr and rapt, is the use of subframes an acceptable method to calculate moments, shears, and axial forces of gravity loads on moment resisting frames?
My colleague uses 'continuous beam' analysis for such frames but I am not convinced since those girders or beams are monolitic with lower and upper columns.

 

[KootK]

Not if those sub-frames would have fixed end columns above and below the beams under consideration as you would typically do for equivalent frame gravity design. Methods like Portal, Cantilever, and Spur are the way to go for hand calcs. You know, unless you've got the stamina for a hand calc'd stiffness matrix analysis or a two-cycle moment distribution.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.