## Shear studs design with FEM (How to do it in a right way?)

## Shear studs design with FEM (How to do it in a right way?)

(OP)

Hello. Our last project - 4-span continuous overpass with composite section (two box-shaped main girders and monolitic RC slab). My job was check ULS and SLS for main girders and design shear studs map. Somehow I've managed to do this, but now I have several questions about this stuff.

I'll explain my way of thoughts, hope you help me with critics and advices. How it should be done? Was I right in my suggestions? And so on.

1. Find diagram of Shear flow (between steel and concrete parts)

2. Find limit force on one stud

3. Divide beam on short segments, integrate shear flow diagram on segment - find shear force for segment, divide it on limit force

and get the number of struts for segment - countinue...

My main question is -

Here is the problem. We have 2 formula for shear flow:

1) S_flow = (V * S_moment)/I_moment

S_fl - shear flow

V - shear force in beam

S_moment - first moment (static)

I_moment - second moment

2) S_flow = (N_2 - N_1)/ L

S_fl - shear flow

N_2 = σ_c2 * A_c+σ_r2 * A_r - summary force in slab on right end of slab segment

N_1 = σ_c1 * A_c+σ_r1 * A_r - summary force in slab on left end of slab segment

L - length of segment

1) formula is pretty good, but we can use it only for section with elastic behaviour (we can't find influence of primary part of creep or shrinkage)

2) formula is more accurate, we can use it for all situations, but we have problems with live load

What is the problem? In FEM soft for Live load we can get envelope diagram (min and max force in every section). And here is the problem - if we take 2) formula with values from envelope diagram - we doesn't get maximum (minumum) value of S_flow, because we need to maximize abs value of (N_2-N_1), not N_2 or N_1 separately.

So we need use both formula, extract separately V - shear force for live load (and for any other envelope diagram) and N_force for the rest. Is it good practice? Or we can do something else? (

One more thing about using formula 2). From FEM soft we can get values of internal forces for I-end, J-end of finite element (1/4, 2/3 and 3/4 of element length too, for some software). So - it is really easy - take N_2 value in J-end, N_1 value in I-end of element and divide (N_2-N_1) on element length (pretty easy make it in Excel). But in this project, I've found some difficulties. Our slab will pouring in stages: 1, 2, 3, 4 stages - pouring in the middle of each span, 5,6,7 - pouring in pier zones (zones of hogging/negative moment), to decrease tension stresses in slab. I'va modelled all stages - and in the end get this axial force diagram in slab

Look at gap near support zone - it appears right in the place between slab stages. I've thought it was error or something, checked it twice. But it's right thing. And problem is that this thing did't exist in real structure. I mean - in real structure - in this place during construction we have open end of slab, so there is no stresses(forces) there. But in FEM here we have changing of element properties and math is correct. In real life - stresses in this place should smoothly increase (due to smooth interraction between steel-slab connection). So - we have to change values in diagram, because it doesn't reflect real perfomance of structure, but how? Do you have such problem? Have you got any algorithm for extraction and processing data from FEM soft in this case? (

P.S. For those who wants to know, how I've managed to find Shear flow diagram. I've found value of N in the middle of element - then - used formela 2). In that way I've got those spikes on graph, but so they was shifted from real position - bad thing, good thing - they was there.

I'll explain my way of thoughts, hope you help me with critics and advices. How it should be done? Was I right in my suggestions? And so on.

**Design process for shear studs consists from 3 steps:**1. Find diagram of Shear flow (between steel and concrete parts)

2. Find limit force on one stud

3. Divide beam on short segments, integrate shear flow diagram on segment - find shear force for segment, divide it on limit force

and get the number of struts for segment - countinue...

My main question is -

**how we should do step #1 in right way?**Here is the problem. We have 2 formula for shear flow:

1) S_flow = (V * S_moment)/I_moment

S_fl - shear flow

V - shear force in beam

S_moment - first moment (static)

I_moment - second moment

2) S_flow = (N_2 - N_1)/ L

S_fl - shear flow

N_2 = σ_c2 * A_c+σ_r2 * A_r - summary force in slab on right end of slab segment

N_1 = σ_c1 * A_c+σ_r1 * A_r - summary force in slab on left end of slab segment

L - length of segment

1) formula is pretty good, but we can use it only for section with elastic behaviour (we can't find influence of primary part of creep or shrinkage)

2) formula is more accurate, we can use it for all situations, but we have problems with live load

What is the problem? In FEM soft for Live load we can get envelope diagram (min and max force in every section). And here is the problem - if we take 2) formula with values from envelope diagram - we doesn't get maximum (minumum) value of S_flow, because we need to maximize abs value of (N_2-N_1), not N_2 or N_1 separately.

So we need use both formula, extract separately V - shear force for live load (and for any other envelope diagram) and N_force for the rest. Is it good practice? Or we can do something else? (

**First question**)One more thing about using formula 2). From FEM soft we can get values of internal forces for I-end, J-end of finite element (1/4, 2/3 and 3/4 of element length too, for some software). So - it is really easy - take N_2 value in J-end, N_1 value in I-end of element and divide (N_2-N_1) on element length (pretty easy make it in Excel). But in this project, I've found some difficulties. Our slab will pouring in stages: 1, 2, 3, 4 stages - pouring in the middle of each span, 5,6,7 - pouring in pier zones (zones of hogging/negative moment), to decrease tension stresses in slab. I'va modelled all stages - and in the end get this axial force diagram in slab

Look at gap near support zone - it appears right in the place between slab stages. I've thought it was error or something, checked it twice. But it's right thing. And problem is that this thing did't exist in real structure. I mean - in real structure - in this place during construction we have open end of slab, so there is no stresses(forces) there. But in FEM here we have changing of element properties and math is correct. In real life - stresses in this place should smoothly increase (due to smooth interraction between steel-slab connection). So - we have to change values in diagram, because it doesn't reflect real perfomance of structure, but how? Do you have such problem? Have you got any algorithm for extraction and processing data from FEM soft in this case? (

**Second question**)**Thank you in advance.**I'm not really good at composite section bridges, thankfull for any reply.P.S. For those who wants to know, how I've managed to find Shear flow diagram. I've found value of N in the middle of element - then - used formela 2). In that way I've got those spikes on graph, but so they was shifted from real position - bad thing, good thing - they was there.

## RE: Shear studs design with FEM (How to do it in a right way?)

1.Why are you checking shear studs for service loading? Isn't it just just strength and fatigue?

You are discussing pouring sequences. Shear studs ensure the deck acts composite. You check beams for non composite with DC loads and the composite with DC2. Checking the deck in a pour sequence is a separate service check and usually just involves placing the deck in positive moment regions only and checking stresses in the negative moment regions, which usually involves adding some additional steel in the deck to control cracks.

2. You don't "need" shear studs in a negative moment region, but there will be some minimum spacing requirement. For positive moment you are relying on the composite section in compression to move the neutral axis to better resist the moment, in negative bending the tension is taken up in the top flange, you don't "need" a composite section here. Unless you are relying on steel in the deck for helping resist negative moment (which you really shouldn't).

If you have a constant depth section, this whole process is relatively simple, you just looks at 10 points along the span and project out the stud spacing requirements . Variable depth member get a little more complex in that you have to look at each section and the forces there.

You don't need FEM, you can calculate the shear in the studs by knowing the shear and moment at the locations you are evaluating.

## RE: Shear studs design with FEM (How to do it in a right way?)

## RE: Shear studs design with FEM (How to do it in a right way?)

Actually, you might as well make it fully composite to take advantage of the small gain in capacity from the reinforcing in the deck at the Strength limit state and the capacity of the concrete in the negative moment regions at the service and fatigue limit states. If it's composite in the spans adjacent to the negative moment region, you have to consider the moment of inertia of the entire section, including the deck, in determining the stiffness of the negative moment region. Gone are the days when you could ignore the deck over the piers because it was "noncomposite".

Actually, you don't even need the moments, just the range of fatigue shear for the points of interest along the girder. Calculate the force along the slab to girder interface (VQ/I), divide by the fatigue capacity of a stud, to determine the spacing of the studs required at each of those points.

For Strength, you take the compression capacity of the slab within the effective width, or the tension capacity of the girder, whichever is smaller, and divide the yield capacity of a stud. That will tell you the minimum number of studs needed between points of max and min moments (typically, from midspan to interior supports) and also between points of max moment and discontinuities (typically, between the max moment location in the end spans and the ends of the bridge).

The requirements for fatigue typically control, so the usual process is to design for fatigue and check for Strength.

Rod Smith, P.E., The artist formerly known as HotRod10

## RE: Shear studs design with FEM (How to do it in a right way?)

To be honest, I don't live in America, so I don't use AASHTO to design. If you find something strange in my words, in some cases it's because we have different basis. But I think, than in common all codes for composit briges have a lot of same stuff.

about this part:

I have a deal with static indeterminate stucture. So we have to take in accout infuence of creep and shrinkage (both primary - redistribution of stress in composite section, and secondary - redistribution of forces in statically indeterminate structure due to additioanal deformations from creep and shrinkage).

Therefore I use construction stage analysis (with real construction sequence). I use for CS analysis SLS loads, but then I separate different parts of resulting internal forces apply design coefficients and make ULS shear flow diagram. I guess here we have main difference (we don't have fatigue check for studs, only strength).

about this part:

I agree with you that it's a bad idea to rely on steel in the deck for helping resist negative moment. But I think, than shear connection in this zone is nessecery. We have to satisfy SLS for concrete slab (crack opening) - therefore we need a good connection between slab segments without cracs and girder - to transfer stress flow in reinforcement.

## RE: Shear studs design with FEM (How to do it in a right way?)

Hope I understand it right, correct me if I wrong.

You mean that, fatigue check ( I don't have such check in my country code) in most cases define design of studs. So we can use V*S/I to find shear force in some points (as you say 10 points along beam) and define distance between studs. For ULS - we define maximum force in slab F_slab_MAX=(f_cd*A_c+f_rd*A_r)

f_cd - design strength of concrete, A_c - area of concrete (consider effective width), f_rd - design reinforcement strength, A_r - area of reinforcement.

Then we divide on stud strength - here we get number of studs in region of interest (as you say between points with maximum an minumum moments, or maximum moment and the end of beam).

As I say (in post above), I've tried to consider creep and shrinkage in my shear flow diagram (I think than in fatige analysis redistribution of shear between studs due to shrinkage in particular should be considered - as it mentiond in my country code for ULS check).

I'm not familiar with AASHTO, so something that clear for you, I can see in first time (as it often happens, I'm not the experienced guy).

## RE: Shear studs design with FEM (How to do it in a right way?)

## RE: Shear studs design with FEM (How to do it in a right way?)

That's how it is in AASHTO.

I'm not sure about the nomenclature, but we use V*Q/I. V = range of shear (live load max - live load min) for each point of interest (typically 10th points of each

span), Q is the first moment of the area (AKA the statical moment), and I is the moment of inertia. Both I and Q are calculated at top of the top flange, using the short term composite section (concrete transformed using the modular ratio "n").I don't see how shrinkage produces force on the studs, and creep would reduce the force on the studs, as the deck conforms to the deflected shape of the superstructure under permanent load, and the stress in the concrete is reduced as a result.

I don't know what your code does. All I can tell you is AASHTO doesn't have any adjustments for shrinkage or creep, at either the Strength or Fatigue limit state.

Rod Smith, P.E., The artist formerly known as HotRod10