Concrete Beam End Moments

[carnahanad]

Hello,

I'm evaluating an existing structure that has a 1-way slab supported by concrete beams and concrete walls. The existing documents indicate a Live Load for the room. I'm using the concrete beam reinforcement schedule to double check the beams for some new equipment in the room. I have a 3 span beam condition. Unfortunately, I don't meet the beam length or uniform loading requirements of 8.3 (ACI 318-08) to use the moment calcs in 8.33. I put my beams and loading into RISA to get load diagrams. From the reinforcement in my beam, which is an end beam, the only way I can get the positive moment reinforcement to work is if I fix the end of the beam at the wall. The reinforcement at the top of the beam at the end is hooked into the wall and there is enough reinforcement to develop the end moment assuming a fixed end. Is this a valid assumption, or do I need to determine the rigidity of the beam and use that for developing a moment at the end?

I look forward to the discussion.

 

[PicoStruc]

Are you ready to accept cracking ?

Are-you sure that the negative moment (fixed in wall) is right. By experience, it should be A LOT higher that the positive moment and generally, not enough top steel are present !!

Anyway what you are doing is called Plastic Design, soo check the requirement for that type of design in you local code.

 

[spats]

Is the wall able to resist the beam end moment? Are you properly modeling the wall stiffness to calculate the end moment? You can't just assume full fixity.

 

[carnahanad]

OK,

So when I assumed anything less than fixed at the beam end the reinforcement at the middle of the beam is not acceptable for the listed Live load on the drawing. The building was built in 66 and I am using 40ksi steel which was backed up by the specs (can't believe they still had the spec book from then). I'm not sure how to move forward with the study if I can't even verfy the existing loading.

 

[JAE]

acarnah2, what spats suggests is the right direction. The supporting walls have a set stiffness which would be based upon the wall thickness, axial load, and bending moment.

The RISA model you are creating would want to use the wall as a member element in the model and if you use the proper stiffnesses (beam and wall) you should get fairly close to the true moments in the beam.

Also - per code you should alter the live loading since you have a continuous 3 span situation. Full dead load on all spans plus the following live load combinations:
1. Odd spans loaded only
2. Even spans loaded only
3. Spans 1 and 2 loading
4. Spans 2 and 3 loaded
5. All spans loaded

The beam and wall stiffnesses can be calculated in two ways -
Option A - use ACI suggested stiffnesses per section 10.11.1 where beams are 0.35 x Ig and cracked walls are 0.35 x Ig. If there is a lot of axial load in the walls (say from a wall above) then walls could be 0.7 x Ig.

Option B - analyze the beams and walls using second order effects and altering their EI values to account for cracking - in other words - use 1 ft. segments of wall (additional joints along the wall) and step-by-step calculate the Ie (see ACI 9.5.2.3) of each 1 ft. segment to model the cracking/stiffness response of the wall.

 

[carnahanad]

In RISA I did set up skip loading, I apologize for leaving that out.

 

[JAE]

How long ago was the structure design/built? Many older concrete structures did not use skip loading.
Might be why you have problems with this one.

 

[spats]

If it doesn't work unless you have full fixity at the wall, it doesn't work... period.

 

[dik]

Is the wall parallel or perpendicular to the span. I often design beams that frame into walls as being fully fixed and reinforce accordingly. As long as the supporting member is greater than twice the depth of the beam or slab... generally behaves as fixed if constructed accordingly.

Dik

 

[DST148]

@acarnah2: Since you are verifying adequacy of the structure built in 1966 for the existing loading conditions, then check with the relevant provisions of the code used in the sixties rather than 2008 version.
Many times we do have similar situation - a beam framing into wall with a sizable top reinforcing. However, in most cases the wall is not wide enough(thickness) to develop the beam top bars. (fy 60 ksi)
You may also check with gross properties (1.0 Ig) for all the elements as a starting point. Then do refinement with cracked properties.

 

[dhengr]

You are adding new equipment loads to the beam, in a room? Obviously, they replace the old LL’s, or at least modify them. It sounds like there may be a wall above and below the beam, in which case the beam end moment would be distributed btwn. the two wall sections. Have you considered that?

 

[JedClampett]

1966 was a little before my time. But my assumption is always that the designer knew what he (very unlikely she) was doing. Add to that the fact that working stress design was typical in that era and a natural conservatism due to less precise design tools, and usually vintage designs work quite well when checked. And it's very unlikely that the wall was designed to take any moment.
Have you checked the effective width of the slab to take advantage of a "T" effect? Sometimes this helps for positve bending. And have you tried using hand calculations rather than RISA?
As far as section 8.3, I never use it. I'd prefer just running my own numbers then using those.

 

[EricCA]

You may want to try and redistribute your moments. I wouldn't push much to the wall, but you could move the diagram up 20% at the continuous end (prvided there is enough steel).

 

[JAE]

JedClampett brings up some good points. I agree with the suggestion that older designs many times were a bit conservative.

However, for "vintage designs" (love that phrase) usually were not conservative for shear.

T-beam design is also a good suggestion if you aren't doing that for the positive moments.

Also - for vintage designs, the analysis was probably done by hand using manual calculation techniques (think moment distribution) so my earlier post regarding wall moment participation probably wasn't used in the original design effort.

 

[hokie66]

Thanks, Jed. Actually, 1966 was a vintage year, so the phrase is appropriate.

1966 was in the transition period from Working Stress Design to Ultimate Strength Design. ACI318-63 was the first to formally introduce USD, and was included in the engineering curricula then. That was also in the transition period from Grade 40 to Grade 60 reinforcement, so even though the specification said 40, it could well have been built with Grade 60. Sorry if that adds more complexity to your problem...

 

[dhengr]

Hokie:
You beat me to it.

“older designers”? What the heck kind of talk is that? I was actually pretty young then, designing in concrete, nonetheless. As for “vintage designs,” like vintage wines and engineers they get better with age. And, as for conservative designs, the rebar people got all uppity every time we called out 5 & ½ - #8s, so we almost always called out 6 - #8s in that case. Never had any shear problems either, undoubtedly sheer luck. We did start using Ultimate Strength Design at about that time, I actually taught/helped teach courses in USD at about that time at the U of MN. And, my buildings are still standing and functioning just fine, all 20 some stories of them, and the whole design process was a good deal less cumbersome in those old, vintage, days.

 

[JAE]

dhengr - were you a vintage wine or a vintage moonshine?

 

[frv]

Just a note: if it helps, I think it would be perfectly reasonable to omit Live Load over the area where the equipment rests. Just use the equipment load over the footprint of the equipment, plus live load all around. Can you reduce the Live Load? I know a lot of "vintage" engineers who nearly always reduce LL's.

 

[hokie66]

Back to the original question...the beam would almost certainly have been designed with a knife support at the wall, but with nominal top bars. We didn't have the analysis programs or the computing capacity which is available today, so we used moment distribution and other methods to arrive at design reactions and moments, with a lot of simplifying and conservative assumptions.

Even now, a beam end supported on a wall is not "fully fixed". The concrete doesn't know whether it has been designed by a computer or not.

 

[carnahanad]

Wow, we got a pretty good discussion on this thread.

I have thought about replacing the LL on the floor with the actual. However, there is a pretty big boiler and cooling tower in the room as well. I back calculated from my concrete beam the max LL on the floor to get the positive moment reinforcement to work I had to reduce my LL by about 60%. So, at this point, I'm less concerned about adding the new load and more concerned about the original design.