**Updated on 08/12/2016: Illustration of the 2nd method of computing Long Term Deflection**

In case you missed the Step by Step series, Check it up below. It’s a MUST !

- [Part 1] Step by Step Analysis Procedure of Seismic Loads Based on IBC2012/ASCE7-10
- [Part 2] Step by Step Analysis Procedure of Seismic Loads Based on IBC2012/ASCE7-10
- Step by Step – Deflection Analysis Using CSI SAFE

With reference to ACI 435R, §4.4:

“*Because of the complexities involved in calculating two-way slab deflections, engineers have preferred to control deflections by giving minimum slab thickness as a function of span length. Equations such as those in section 9.5 of ACI318, as shown in Table 4.2, are based on experience gained over many years. The ACI 318 equations express minimum thickness in terms of clear span between columns, steel yield strength, and flexural stiffness of edge beams. The minimum thickness values are modified for the effects of drop panels and discontinuous edges. ACI 318 permits to use of thinner slabs if deflections are computed and found to satisfy the specified maximum permissible values.*“

In this post, I’ll try to explain step by step how two way slabs deflections shall be computed using SAFE software:

- Immediate Deflections – No Shrinkage & No Creep
- Long Term Deflections – Sustained Load with Shrinkage &Creep

## 1-Immediate Deflections – No Shrinkage & No Creep

Here we have a simple slab of:

- 10.0m span in each direction
- 40 cm solid slab thickness
- 25 Mpa concrete compressive strength
- 0.5 ton/m2 uniform loading under Super Imposed Dead load & 1 ton/m2 uniform loading of Live load
- Supported on 4 edges by 80x80cm square columns.

This example is meant only to clarify how to compute the deflection using SAFE. However, there is more economical solutions for such spans as post tension, hollow core slabs, etc.

Under Define – Load cases, we will define one load case called IMMEDIATE – ALL LOADS, where we will include of load patterns ( Dead , Live & Super Imposed Dead loads) in one load case under Nonlinear (Cracked) analysis type.

And in term of comparison, we will define a load combination that include all load patterns (Dead+Live+Super Imposed Dead load).

It will be linear (Non-Cracked) Elastic load combination.

Now we’ll define the cracking analysis options under the Run menu, here we have 3 options to choose from:

- User Specified Rebar
- From Finite Element Based Design
- Quick Tension Rebar Specification

In this example, we will choose “From Finite Element Based Design”.

After running the analysis, here below are the results that we get under:

IMMEDIATE – ALL LOADS case = Maximum Deflection is equal to 5.6cm

Elastic Load Combination = Maximum Deflection is equal to 2.8cm

Here we can notice that the deflection under Non-Linear Crack analysis is around 2 times the deflection under Elastic Linear load combination.

## 2. Long Term Deflections – Sustained Load with Shrinkage &Creep

Now, we will elaborate the deflection for Long Term cracked Deflection – Sustained Load with Shrinkage &Creep.

**Long-term cracked deflection**, in which analysis is divided into the following two categories:

**Non-sustained portion**, in which cracked-section analysis considers only the non-sustained portion of LIVE load, solving for incremental deflection.**Sustained portion**, in which long-term cracked analysis considers the sustained loading from DEAD, SDEAD, and a portion of the LIVE load. Creep and shrinkage are included only in this sustained portion of analysis because these effects are only applicable under sustained loading.

Here I draw your attention that:

- Short-term concrete modulus = Elastic concrete modulus Ec(to)
- Long-term concrete modulus = Age-adjusted concrete modulus Ec(t,to), given as:

For example, assume that 25% of the LIVE load is sustained. Analysis proceeds as follows:

- Case 1: Cracked analysis for short-term load with short-term concrete modulus is given as DEAD + SDEAD + Ψ
_{s}LIVE, in which Ψ_{s}= 1.0 - Case 2: Cracked analysis for permanent load with short-term concrete modulus is given as DEAD + SDEAD + Ψ
_{L}LIVE, in which Ψ_{L}= 0.25 (Ψ_{L}= 0 if 100% of the LIVE load is non-sustained)

- Case 3: Long-term cracked analysis (with creep and shrinkage) for permanent load with long-term concrete modulus is given as DEAD + SDEAD + Ψ
_{L}LIVE, in which Ψ_{L}= 0.25

The value of total long-term deflection is then the combination of **Case 3 + (Case 1- Case 2).**

The difference between Case 1 and Case 2 represents the incremental deflection (without creep and shrinkage) due to non-sustained loading on a cracked structure.

And here below how becomes our load combination under which will be conducted the long term cracked deflection result.

And the maximum deflection will be around 7.8cm

So now as a summary, here below are the maximum deflection results that we got for the time being:

**Elastic (Linear) = 2.8cm****Immediate Deflections – No Shrinkage & No Creep = 5.6cm (50% increment from Elastic)****Long Term Deflections – Sustained Load with Shrinkage &Creep = 7.8cm (40% increment from Immediate Deflections)**

The procedure indicated above (Long Term Deflections) results on total long term deflection over time. Most engineers simply check this values against ACI 318 Table 9.5(b), since this will always result in safe and conservative design. In order to remove portion of dead load deflection occurring before attachment of nonstructural elements, the following procedure can also be used:

Case 4= Cracked analysis for permanent load with short-term concrete modulus is given as DEAD + Ψ_{D}SDEAD, in which Ψ_{D} = percentage of super imposed dead load present before attachment of non structural elements

Or Case 4= Cracked analysis for permanent load with long-term concrete modulus creep and shrinkage is given as DEAD + Ψ_{D}SDE

D, in which Ψ_{D} = percentage of super imposed dead load present before attachment of non structural elements, and say using a creep factor for 3 months.

The value of total long term deflection to occur after attachment of nonstructural elements is then the combination of Case 3 + (Case 1- Case 2)- Case 4

In our case we will define Case 4 like the following:

The deflection load combination will become like the following:

And we get the following final deflection result:

Maximum deflection will be equal to around 5.8cm

Updated on 08/12/2016: Illustration of the 2nd method of computing Long Term Deflection

Even though this method is not recommended by the CSI, but I’ll explain it and we will check together the results:

A single load pattern is applied in a load case, then another case is set to continue From State at End of Nonlinear Case.

- Add a DEAD load case using the Nonlinear (Cracked) option, starting with a Zero Initial Condition.

- Add a SDEAD load case using the Nonlinear (Cracked) option, starting From State at End of Nonlinear Case DEAD.

- Add a LIVE load case using the Nonlinear (Cracked) option, starting From State at End of Nonlinear Case SDEAD.

The DEAD load case predicts cracking from a zero initial condition, in which no load is present, then computes cracking due to DEAD load-pattern application. Adding SDEAD then uses the stiffness at the end of DEAD load case, and contributes additional deflection.

And the maximum deflection will be conducted under the load case Live-LT = 5cm

But with reference to CSI this method is not recommended since the deflection result reports the total deflection from both DEAD and SDEAD cases, however, the increase in DEAD load deflection due to additional cracking from SDEAD load application is not recognized.

Summary:

**Elastic (Linear) = 2.8cm****Immediate Deflections – No Shrinkage & No Creep = 5.6cm (50% increment from Elastic)****Long Term Deflections – Sustained Load with Shrinkage &Creep**

(Case1 +Case3 -Case2) = 7.8cm (40% increment from Immediate Deflections)**Long Term Deflections – Sustained Load with Shrinkage &Creep**

(Case1 +Case3 -Case2 -Case4) = 5.8cm (less than 5% increment from Immediate Deflections)**Long Term Deflections – Sustained Load with Shrinkage &Creep**

(2nd Method)= 5.0cm

Hopefully we could clarify properly how to compute the long term cracked analysis. If you have any question please do not hesitate to drop it by comment below.

## And in case you have any query in the structural engineering, drop it by the Handy Forum and we’ll assist you as soon as possible !

## 8 thoughts on “Step by Step – Deflection Analysis Using CSI SAFE”

## Murali

(December 12, 2016 - 7:48 PM)Dear all, I would like to receive all posts from this site. Thanks in advance.

## Step by Step – How to Compute P-Delta effect using ETABS according to ASCE7-10 | KickMyBrain

(December 12, 2016 - 9:31 AM)[…] Step by Step – Deflection Analysis Using CSI SAFE […]

## Faris

(December 11, 2016 - 12:33 AM)Hello Zahi,

Thanks for posting this article. Where does CSI mention that the other method is not recommended? I’ve always used that method with no issues. If it’s not recommended, I don’t see a reason why they have the “continue from state at end of non-linear case” option to begin with.

Regards,

Faris

## Zahi Baroudi

(December 11, 2016 - 12:40 AM)Hello Faris,

It’s stated here :https://wiki.csiamerica.com/display/safe/Cracked-section+analysis

However, this does not mean that the results are wrong. It only does not reflect properly the real case scenario because the increase in DEAD load deflection due to additional cracking from SDEAD load application is not recognized.

And the option of “continue from state at end of non-linear case” it’s not limited only for deflection computation. It may be useful for other purposes.

## Faris

(December 11, 2016 - 1:05 AM)Thanks for your quick reply, Zahi!

I just read what they wrote and I agree that the way they did it does not recognize the additional super-imposed DL. The way I typically do it is different and I believe it does encompass all deflections, I wish I can share an image. Thanks again for sparking the discussion.

## Zahi Baroudi

(December 11, 2016 - 1:12 AM)Your Welcome Faris.

Sure you may explain/ Illustrate your method to admin@kickmybrain.com and we’ll review it accordingly.

## Engr. Ahmed

(December 8, 2016 - 9:42 AM)Hi , thanks for the illustration , its very helpful .

I have a question about why you didn’t use the option “Continue from state at end of non-linear case ” instead of subtracting the deflection values manually as you did .

Sincerely ,

## Zahi Baroudi

(December 8, 2016 - 7:03 PM)Hello Ahmed,

Good to hear that you found this article helpful.

However, We did not use this method because it’s not recommended from CSI. As the deflection results reports the total deflection from both DEAD and SDEAD cases, however, the increase in DEAD load deflection due to additional cracking from SDEAD load application is not recognized.

Anyway, upon your query, We have updated the post above and illustrate this second method of computation for long term deflection. You may check it above.