Hi friends,

On last week's newsletter, we learned how to calculate and design two-way reinforced concrete slabs (flat slabs) by hand. As I mentioned, the slab had a relative simple geometry (=same spans in x- and y-direction). In that scenario, it's somewhat OK to design the slab by hand.

For more complex slabs where the supports (columns and walls) are more irregular, the hand calculations are getting quite inaccurate. And it also takes much more time.

So today, I'll show you how I actually design rc slabs. → with FE software (FE = Finite Elements)

I am very happy and proud that SkyCiv sponsors this episode of the Structural Basics newsletter.

As a Structural Basics reader, you also get a special deal. You get a 30-Day free trial, instead of a 14-Day free trial, if you sign up for a free trial by using the Structural Basics referral link: https://skyciv.com/laurin/ (← click here)

This partnership is great, because I can show and teach you how to use finite element software.

In this newsletter, I’ll show you how to use the SkyCiv Structural 3D program to design and verify reinforced concrete slabs. We first, input geometry parameters like the cross-sectional dimensions, material parameters of the concrete, plates, supports, beams and then loads. Finally, we check out the results and evaluate them.

Let's get into it...

The 13 Steps to Design Reinforced Concrete Slabs with SkyCiv

Here's the slab that we are going to design and verify.

Step #1: Sign-up and Open the Structural 3D Module

SkyCiv is a web-based software, which makes it easy and fast to get started, because we don't need to install anything.

→ Sign up here and claim your 30-Day free trial. ←

Sign up with your Google account. Or if you don't want that, just with your e-mail.

Next, in the dashboard, open the Structural 3D module.

Now, you should see an empty canvas with input options on the left side.

Step #2: Define the Material Properties

First, let's define the material properties of our slab. I usually use C30 for in-situ concrete slabs.

1. Click on Materials
2. Click on Database
3. Metric → Concrete → EN 1992-1-1 (for Eurocode) → C30/37
4. Submit
5. Apply

Step #3: Insert the Nodes

Modelling the slab (=plate) in SkyCiv works with nodes. We enter the coordinates of the corners but also start and endpoints of line supports (=walls) and columns as nodes.

Let's do that for our example slab.

1. Click on Nodes
2. We can enter the x, y and z coordinates of each node and click apply or use a datasheet which works in my opinion quicker.
3. When using the datasheet, don't forget to click Apply at the end.
4. Click on Back

Step #4: Model the Plates

Once the nodes are modelled, we can model the slab(s). We model the slab as a plate. In SkyCiv we actually model our example as 3 slabs, because you will later see that area loads can only be applied to one slab.

But as we learned in last week's newsletter, the positive bending moment is biggest if we apply the live load only on every second span. Therefore, we'll later create 3 load cases for the live load.

To model the slab as a plate, we'll do the following steps:

1. Click on Plates
2. Type in the Node ID's of the corners of a plate. We define the first slab with nodes 1, 2, 7, 5.
3. Plate Thickness is 280 mm
4. Material ID: Select the material that we created in step #2.
5. Click Apply
6. The next slab is defined as 2, 3, 11, 8
7. And the last slab as 3, 4, 12, 11
8. Click on Back

Step #5: Model the Beams

First, we need to create a section for the beam. The beam will have the dimensions 24x50cm. So let't create it.

1. Click on Sections
2. Click on Builder
3. Shape Templates → Rectangular → Material: EN 1992-1-1 - C30/37
4. Dimensions: Depth: 500 mm, Width: 240mm
5. Submit

Next, we'll model the beams..

1. Click on Members
2. Click on Truss. Reinforced concrete beams which are integrated into the slab can be calculated as T-beams, but their moments are 0 kNm at the start and end support. They act as continuous beams. That's why we define them as Truss and not as Frame.
3. Node A = 2
4. Node B = 7
5. Type = Continuous
6. Section ID: Click on 1 - 500 x 240 - EN 1992-1-1 - C30/37 (the section we just created)
7. Node A and Node B Fixity = Pin (if you selected Truss in step #2 this is grayed out)
8. Click Apply
9. Repeat the steps for the beam from Node 3 to Node 11

Step #6: Define the Supports

We model the walls as line supports and the columns as point supports. You could also add a spring stiffness to the supports, which makes the reaction forces a bit more realistic. But from my experience, the difference isn't too big, and I only use a spring stiffness if I really need to optimize my results.

Line supports

1. Click on Supports on the left panel
2. Click on Advanced
3. Type: Line
4. Node IDs: 1, 5
5. Support: Horizontal Roller
6. Click on Apply
7. Repeat for the other walls

Point supports

We basically follow the same steps for the point supports.

1. Type: Node
2. Node IDs: 1, 9, 10
3. Support: Horizontal Roller
4. Click on Apply

Step #7: Apply the Loads

Next, we'll apply the characteristic loads.

• Characteristic dead load: g_k = 3.0 kN/m²
• Characteristic live load: q_k = 4.0 kN/m²

If you want to learn how to calculate the dead load of slabs of residential buildings or how to find the right live load, then check out Loads on Residential Buildings.

First, let's add the self-weight.

1. Click on Self Weight
2. Click on ON
3. Click on Apply

Now, let's add the dead load.

1. Click on Pressures (this might be confusing for Eurocode users, but in SkyCiv, we can only apply pressures on plates. Area Loads can only be applied to Members).
2. Plate ID: 1, 2, 3
3. Load Distribution: Uniform
4. Z Magnitude: - 3 kPa (this another confusing thing for us Eurocode users, but 1 kPa = 1 kN/m2)
5. Load Group: gk (for dead load)
6. Apply
7. Rotate to see the load

Live load:

For the live load, we create 3 different load cases where we apply the live load on the different spans.

Step #8: Define the Load Combinations

In this step, we'll define the ULS and SLS load combinations. We could also let SkyCiv create the load combinations automatically, but I prefer to do it myself when I don't have that many load cases.

ULS load combinations

1. Click on Load Combos
2. Name: LC1 - ULS
3. Criteria: Strength
4. gk Factor: 1.35
5. qk - 1 Factor: 1.5
6. qk - 2 Factor: 0
7. qk - 3 Factor: 0
8. SW1 Factor: 1.35
9. Apply
10. Repeat for the other 2 ULS load combinations

SLS load combinations

Verifying the long-term deflection of reinforced concrete slabs is a topic we could talk about for hours. The deflections are calculated with SLS characteristic load combinations. However, to account for the long-term effects like creep and shrinkage, advanced methods need to be used. Or what I do for most slabs, I use a factor of 3 for the dead loads and a factor of 1 for all variable loads. From my experience, this method comes very close to the "real" results and speeds up the calculation process a lot.

Remember, structural engineering is based on assumptions and simplifications. But it's important that you understand these simplifications and that you are aware of the consequences!

1. Name: LC SLS
2. Criteria: Serviceability
3. gk Factor: 3
4. qk - 1 Factor: 0
5. qk - 2 Factor: 0
6. qk - 3 Factor: 1
7. SW1 Factor: 3
8. Apply

Step #9: Meshing

Before running the calcs, we need to mesh our plate(s). I am not getting into meshing, because this is an online course itself.

1. Edit
2. Plates
3. Auto-Mesh Model
4. Mesh Size: Default
5. Proceed

Step #10: Run the Calculation, Check the Deflection Shape and Verify the Deflection Limit

Next, we run the calculation and check the deflection shape to see if the model is correct. After that, I always check that the deflection is within the defined limits.

1. Click on Solve
2. Linear Static
3. Select LC SLS
4. Go to Plates → Select Displacement Z, and we can see that deflection looks correct. The plates deflect downwards in the spans, and they are 0 at the supports.

Checking the deflection

The deflection limits depend on your country, your client and the usage of the structure. In Germany, we usually design the deflection for buildings with partition walls as < span/500. That way, we make sure the partition walls won't crack because of the slab deflection. I don't want to discuss whether these deflection criteria are good.

We can see that the biggest deflection happens in the center span where we have a span of 7m. The max. deflection is therefore:

7m/500 = 14mm

The deflection is verified because the biggest deflection of the slab is 4.1mm < 14mm.

Step #11: Verify the Internal Forces (Bending Moments and Shear Forces)

Next, let's look at the internal forces like bending moments and shear forces.

I typically skip this step as I look at the calculated reinforcement area. It's kind of the same, just with the information that we need to create reinforcement drawings.

But let's have a quick look at the internal forces.

1. Plates
2. Wood-Armer Results (the longitudinal reinforcement is designed based on the bending moments but also due to torsional moments, the Wood-Armer method takes them into account. Don't just look at the moments in x- or y-direction)
3. Plate ID(s) to Calculate: 1, 2, 3
4. Click on Submit
5. Select Envelope Absolute Max
6. Wood Armer Moment Dir 1
7. Stress at: Top (bending/ Wood-Armer moments in x-direction in the top of the slab = negative moments)

Now, based on these results you can now calculate the required longitudinal reinforcement in the top of your slab in x-direction.

We did that in last weeks newsletter and won't show it today.

Step #12: Design the Reinforcement with the Reinforced Concrete Plate Module

1. Click on Design
2. Select the Reinforced Concrete (RC) Plate Module
3. Select EN 1992-1-1:2004
4. Click on Start
5. Click on Polygon Selection and select the slab
6. Give your slab a name like First floor
7. Click on Add
8. Add the ULS load combinations to Strength Check
9. Add the SLS load combination to Serviceability Check
10. Interprete the required area reinforcement

Area reinforcement in x-diretion at the top of the slab:

Click on Rebar → ID: 1 → Assign Reinforcement Data Based on Optimization Result.

Now, we can see the required area of reinforcement in the top and bottom of the slab and in x- and y-direction.

Required area of reinforcement in x-direction in the top of the slab

In this example, I would use d=12/100, which means rebar of diameter 12mm every 100mm for the entire slab. This has a reinforcement area of 11.3 cm2/m and covers all blue areas (<9.03 cm2/m). For the other areas, I would add rebars. For example for the red area we can add d=20/100 → 31.4 cm2/m. In total we would have 42.7 cm2/m > 40.6 cm2/m.

Now, there's alot more to the design of reinforced concrete slabs and how you get from your engineering results to reinforcement drawings. We can't cover all of it in this newsletter but that's something I will teach you in module #3 of the E-book series Structural Design of Residential Buildings. I am hoping to publish it until the end of the year.

Required area of reinforcement in y-direction in the bottom of the slab

Now for the reinforcement in the y-direction in the bottom of the slab, I would go for d=10/100 → 7.85 cm2/m. This covers all areas except orange and red. For the red and orange areas I would either add some rebars or do a section cut and integrate the bending moments over 1-1.5m and see if I could reduce the bending moments. Again, something I will teach you in the upcoming book.

More checks to consider:

There's are many more things we need to check before the verification is complete. But this newsletter is already now the longest I have ever written. Here are checks we also need to consider:

• Reinforcement checks in y-direction in the top of the slab
• Reinforcement checks in x-direction in the bottom of the slab
• Shear capacity checks
• Design of the reinforcement of the beams
• Reinforcement for possible openings due to installations
• Crack verification of the slab

Step #13: Create a Structural Report

Now, our structural design wouldn't be complete without a structural design report.

Here's how we do it in SkyCiv:

1. Click on Output
2. Analysis Report
3. Select all the data and results you want to include in your report
4. Click on Create Report
5. Download and you will have a very nice report which you can share with your client, architect, etc.

Final Words

Now you have designed your first in-situ concrete slab with a finite element program and created a report of the results.

Let me know how you like SkyCiv's Structural 3D module. I personally like it alot. It's intuitive, and you get all of the results you need as a structural engineer.

I hope you like these guides about how to use software in structural engineering. This is how structural engineers really do their work 90% of the time.

Thank you, SkyCiv, for sponsoring this episode of the Structural Basics newsletter.

See you next Wednesday my friends.

Let’s design better structures together,

Laurin.

P.S.: In case you missed the SkyCiv trial link, here’s another chance to claim your 30-day free trial and get started with a FE-program today.

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