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# Out Of Plane Shear in Two Way Slab

## Out Of Plane Shear in Two Way Slab

(OP)
Hello,

I would appreciate some of your opinions regarding a two way slab with heavy loads and how to hand the out of plane shears:
- Typical Bay = 6m x 6m
- Floor Live Load = 20 kPa
- Equipment Live Load = 200 kN

I have run a finite element model on RISA 3D and while the bending steel is easy to design, I am a bit unsure how to interpret out of shear forces. Because of the equipment placed in various places across the slab, the shear contours are spread out, but mostly located at column and beam locations.

I can handle the shear in 3 ways:
1. Thicken the slab until Vc > Shear force
2. Add shear reinforcement (not desirable)
3. Use shear friction: By this I mean, once I calculate the As for bending and membrane forces in the slab, I calculate the shear friction As and add it, so hypothetically lets say As for bending+tension = 1000mm2 and As for shear friction is 400mm2, then the total As would be 100mm2 + 40mm2 = 140mm2.

Another question is how to interpret the shear forces: for one way shear do we check for Qx alone or Qy alone or use something like ( Qx^2 + Qy^2)^0.5?

The client is insisting that 250mm slab will work as they have other buildings very similar, however I am a bit skeptical about the 20kPa floor live load.

### RE: Out Of Plane Shear in Two Way Slab

I don't think I've ever seen anyone using shear friction like this, so I can't comment on whether its appropriate or not, is it allowed under your code for proving shear capacity?

Either option 1 or 2 seem more valid/standard approaches to the issue of lack of shear capacity. It's hard to say which would be more valid in your situation as you don't really state how short you are in terms of capacity and how much you need to make up to get it to work.

Increasing primary reinforcement also increases Vc. Though some codes have for thinner slabs with d<200mm another formula that recognises the increased level of aggregate interlock that is mobilised in thinner slabs and this is independent of the longitudinal reinforcement ratio. What code are you actually working to?

The way most codes seem to state it, you just check one way shear independently in each direction I believe, same situation applies to column design for example under biaxial loading. Due to having a different effective depth in each othogonal direction the capacity will obviously differ for each direction.

Were these existing buildings designed under the same codes, using the same finite element method, or did they use the simplified rules for 2 way slabs that are in most codes. You might be picking up the peaks, whereas these hand methods seem to do a fair bit of averaging across a 'design column or middle' strip. How do your numbers compare to the simplified hand methods in your code?

### RE: Out Of Plane Shear in Two Way Slab

If you are reliant on concrete shear capacity, increasing the concrete strength is another method to get a bit more out of a slab.

Also spreading out the point loads via a grillage of beams above the slab, like an equipment skid, might even out some of the hot spots if its due to simply applying a 200kN point load to a slab locally. Turn it into a line load over the full length + beyond the equipment if you need to, rather than say 4 point loads at the leg locations.

### RE: Out Of Plane Shear in Two Way Slab

You check shear in each direction for the shear loads going in that direction.

Where the potential shear failure wraps around columns/walls/point-loads you check according to punching shear.

Shear friction is inappropriate to get you over the line. It is not typically the critical shear failure mode in a slab. Slab shear failure (one way shear and punching shear) is typically diagonal tension failure.

Where is the slab failing in shear? Can you show diagram?

Also, are you applying 20kPa and the equipment load concurrently?

### RE: Out Of Plane Shear in Two Way Slab

Definitely no on the shear friction proposal. Shear friction isn't a valid solution to diagonal tension shear problems. Add some drop panels or get cozy with some stud rail reinforcement.

### RE: Out Of Plane Shear in Two Way Slab

Surely your max shear is around columns right? 200kN concentrated load will punch through a 250mm slab, but 20kPa live will definitely have pinching shear issue.

### RE: Out Of Plane Shear in Two Way Slab

#### Quote:

3. Use shear friction: By this I mean, once I calculate the As for bending and membrane forces in the slab, I calculate the shear friction As and add it, so hypothetically lets say As for bending+tension = 1000mm2 and As for shear friction is 400mm2, then the total As would be 100mm2 + 40mm2 = 140mm2.

never seen it done that way. don't think it's a good idea.

#### Quote:

Another question is how to interpret the shear forces: for one way shear do we check for Qx alone or Qy alone or use something like ( Qx^2 + Qy^2)^0.5?

Check them alone.

#### Quote:

The client is insisting that 250mm slab will work as they have other buildings very similar, however I am a bit skeptical about the 20kPa floor live load.

Usually (with the software I use), I am comparing shear stresses to allowables. (φ2√f'c or φ4√f'c) That's just how the output typically is.

You also have to remember (using the method I am talking about, unless you modeled the slab thinner than the whole) to factor up the shear stress to account for the fact your thickness is actually "d".....as far as shear stress goes. If you modeled a 12" slab.....and the "d" is 9.5".....that's a significant difference in shear stress.

### RE: Out Of Plane Shear in Two Way Slab

(OP)
Thank you to everyone that responded to my post (first one). Your recommendations are what I was thinking in the back of my head that shear friction may not be the way to go, although there was an engineer at our firm (quite experienced) that had used this methodology, thus the reason I looked into it.

Just to give you all an update: After being told multiple times that they already have a building that is very similar that had a 250mm thick slab with the same equipment and slabs, I requested that they send me their drawings. Turns out they have secondary beams underneath their 250mm slab, but in my building they do not want any beams! This will make my life a lot easier and I will either thicken the slab or tell them that I need the secondary beams.

Regarding the shear itself, I have both high punching shear, where I can add shear reinforcement without much issue and I also have high "zones" of one way shear on equipment that lets say is sitting right in the middle of a 7m x 7m slab for instance and along the length of the beams.

#### Quote (Were these existing buildings designed under the same codes, using the same finite element method, or did they use the simplified rules for 2 way slabs that are in most codes. You might be picking up the peaks, whereas these hand methods seem to do a fair bit of averaging across a 'design column or middle' strip. How do your numbers compare to the simplified hand methods in your code? )

This is a new building per ACI 318-14, the hand calcs seems to support the shear loads

#### Quote (Also spreading out the point loads via a grillage of beams above the slab, like an equipment skid, might even out some of the hot spots if its due to simply applying a 200kN point load to a slab locally. Turn it into a line load over the full length + beyond the equipment if you need to, rather than say 4 point loads at the leg locations. )

I have done exactly what you mentioned.

#### Quote (Where is the slab failing in shear? Can you show diagram? Also, are you applying 20kPa and the equipment load concurrently? )

The building is an industrial building so in addition to heavy equipment, there are also large openings on the floor, thus the shear zones are all over the place so to speak. 20kPa is defined as live load and the equipment is defined as dead load, thus I have to use both in conjunction.

#### Quote (Surely your max shear is around columns right? )

In general this is correct, max is around the columns, but as stated I am also getting high shear around other areas due to odd loading/openings.

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