Method 1: Simplified Event Sequence + Simplified Combined Creep and Shrinkage Allowance
In this approach the simplest method suggested in ACI 318 is emulated. All creep and shrinkage effects are introduced as a single amplification factor and a cracked section analysis is run on a simplified event sequence without addressing the possibility of early age loading.
Download and open the tutorial model
Establish some slab reinforcement
Prior to running a Slab Deflection Analysis, a reasonable level of slab reinforcement should already be provided. This can be achieved by designing all slabs and patches as follows:
- From the Analyze toolbar, click Analyze All (Static)
- From the Design toolbar, click Design Slabs
- From the Design toolbar, click Design Patches
Set up the Simplified Combined Creep and Shrinkage Allowance (ignoring ACI 435)
You can increase the Allowance for Shrinkage Effects multiplier to allow for both creep and shrinkage based on the multipliers from ACI 435 Table 4.1.
Using the ACI code recommendation (highlighted in the below table), multipliers are immediate 1.0, creep and shrinkage 2.0. Total = 3.0.
Thus a creep and shrinkage contribution = 2.0/3.0 = 0.66 is to be applied which equates to 66% of the total deflection.
Table 4.1 - Multipliers recommended by different authors
| Source | Modulus of rupture, psi | Immediate | Creep λc | Shrinkage λsh | Total λt |
|---|---|---|---|---|---|
| Sbarounis (1984) | 7.5 √fc' | 1.0 | 2.8 | 1.2 | 5.0 |
| Branson (1977) | 7.5 √fc' | 1.0 | 2.0 |
1.0 1.0 |
4.0 |
| Graham and Scanlon (1986b) |
7.5 √fc' 4 √fc' |
1.0 1.0 |
2.0 1.5 |
2.0 1.0 |
5.0 3.5 |
| ACI Code | 7.5 √fc' | 1.0 | 2.0 | 3.0 | |
- The automatic procedure using Technical Report 58 is not considered - this is ensured by setting the Aging coefficient to User defined.
- Creep is not also accounted for in the analysis - it can be excluded by setting the Number of Exposed Faces to Zero in the event sequence.
To adopt the above ACI 318 Code multipliers for simplified creep and shrinkage:
-
Ensure the Aging
Coefficient is set to User defined and the Allowance for
shrinkage effects in total deflection is set to 0.66.
The above factor allows for both creep and shrinkage, (i.e. creep and shrinkage effects will account for 66% of the total deflection).
To exclude additional creep effects from the analysis
As creep is already being catered for by the amplification factor, we have to exclude additional creep effects from the analysis. This can be done by setting the number of exposed faces in each event to zero as follows:
-
For each listed event in the
model sequence, ensure the Number of Exposed Faces is set to
0.
If the number of faces = 0 then the creep coefficient Ct = 0 . See: Aging Coefficient - User Defined or Automatic?
Review the Individual Events in the Model Event Sequence
A simplified event sequence has been defined that does not include any construction stage propping events.
Various guidance documents discuss slab deflection analysis without addressing the possibility of significant early age loading events such as propping loads.
An early start event should always be created
since time is measured from this start event. In this example we have assumed a
start event of 10 days and allowed self weight only.
You will also note that:
- Each event has a load start time. The Final load event is set to the normal ACI requirement of 5 years.
- ACI requires that instantaneous deflection due to live loads only should be considered based upon a span/360 limit. To account for instantaneous deflection due to live load only, an end event has been included with the same load start time as the preceding event but only including live load.
- Ultimate Creep Coefficient, Cu is set with the default value of 2.350. This value can be set separately for each event.
- Aging Coefficient is set at the default value of 0.8. This value can be set separately for each event. It may be more logical to set higher values for the earlier event times, however, if your primary concern is differential deflection between later events then it will be conservative to use the same value everywhere.
- Number of exposed Faces is set to 0 - this has been done to exclude additional creep effects from the analysis, (as explained in the previous section).
Discussion:
- You need to think about the accumulation of deflection through time and hence the checks that you ultimately wish to consider.
- As an example, if you are interested in differential deflection between the final load event and the start of finishes (deflection at end of event 1), if you underestimate deflection to the end of event 1 then this check becomes more onerous.
- Is it reasonable to assume no construction load and no self weight from finishes during this period?
- How much load is reasonable to assume at this starting event is ultimately the responsibility of the engineer.
After reviewing the Event
Sequence, click OK to close the dialog.
Set up the Restraint Constant
The modulus of rupture is set using the Restraint Constant slab deflection parameter. Since we are using the ACI code multipliers from Table 4.1 above this should be set to 7.5.
To specify an appropriate restraint constant
-
Select all the slab items in the model and via the Properties Window,
ensure the Restraint Constant is set to 7.5
Perform Iterative Slab Deflection Analysis
To establish some initial results:
-
Review the deflections for
the events
Deflections can be reviewed for each event by making selections from the Event droplist in the ribbon. You are able to review:
- Total deflection at the end of any event.
- Differential deflection between any two events (Start of Event and End of Event).
- Instantaneous deflection.
The Total deflection at the final load event for the chosen location is 1.3”
Tip: If slab patches are obscuring the above deflection contours, these can be switched in Scene Content.
Consider the Sustained Load Multiplier Effect from ACI 435
ACI 435 Clause 4.3.4.2 needs to be reviewed carefully at this stage, as this suggests that the above deflection estimation is unconservative.
-
It states that if the restraint stresses are expected to be insignificant, (so that the restraint constant is set at 7.5) then:
-
“the multiplier for sustained-load deflection should be increased from 2 to 4, as recommended by Sbarounis (1984) and Graham and Scanlon [1986(b)]”
Table 4.1 - Multipliers recommended by different authors
Source Modulus of rupture, psi Immediate Creep λc Shrinkage λsh Total λt Sbarounis (1984) 7.5 √fc' 1.0 2.8 1.2 5.0 Branson (1977) 7.5 √fc' 1.0 2.0 1.0
1.0
4.0 Graham and Scanlon (1986b) 7.5 √fc'
4 √fc'
1.0
1.0
2.0
1.5
2.0
1.0
5.0
3.5
ACI Code 7.5 √fc' 1.0 2.0 3.0 Hence the combined creep and shrinkage contribution = 4.0/5.0 = 0.8 (i.e. 80% of the total deflection).
-
-
Alternatively, if the restraint stresses are likely to have a significant effect then Clause 4.3.4.2 states that:
-
a reduced restraint constant of 4 can be used, along with a long-term sustained-load multiplier of 2.5.
Source Modulus of rupture, psi Immediate Creep λc Shrinkage λsh Total λt Sbarounis (1984) 7.5 √fc' 1.0 2.8 1.2 5.0 Branson (1977) 7.5 √fc' 1.0 2.0 1.0
1.0
4.0 Graham and Scanlon (1986b) 7.5 √fc'
4 √fc'
1.0
1.0
2.0
1.5
2.0
1.0
5.0
3.5
ACI Code 7.5 √fc' 1.0 2.0 3.0 In this case the combined creep and shrinkage contribution should be reduced to 2.5/3.5 = 0.714 (i.e. 71.4% of the total deflection).
-
To adopt the ACI 435 recommendation for insignificant restraint stresses:
-
From the Slab Deflection toolbar, click Analyze Current
Using this value, the revised deflection prediction increases to 2.2”
To adopt the ACI 435 recommendation when restraint stresses are expected to be significant:
-
Select all the slabs in the
model and via the Properties Window, adjust the Restraint Constant to
4.0
-
From the Slab Deflection toolbar, click Analyze Current
Using this value, the revised deflection prediction increases further to 3.1”
Generate Composite Modulus Report
An effective composite modulus report can be obtained by right clicking a slab and choosing Export Eff. modulus report to Excel. The report details the composite modulus Ec determined for each event.
To display the Composite Modulus Report:
-
Right click the slab between
gridline D-E/1-2 and Export Eff Modulus report to Excel > For the
current slab item
We can see from the report that the short term composite modulus, Ec is used.
Summary of Results
Using the Simplified event sequence + simplified combined creep and shrinkage allowance method, the results can be tabulated below:
| Approach | Restraint Constant for Modulus of Rupture | Assumed Creep and Shrinkage combined allowance % |
Total deflection (Final load event) |
|---|---|---|---|
| ACI 318 (ignoring ACI 435) | 7.5 | 66% | 1.3” |
| ACI 435 (simple approach - insignificant restraint) | 7.5 | 80% | 2.2” |
| ACI 435 (simple approach - significant restraint) | 4.0 | 71.4% | 3.1” |
Next steps
- In Method 2 we will re-use the same model, but edit the simplified event sequence so that creep is considered in the cracked section analysis. The multiplier will also be edited so that it only considers shrinkage effects.
- In Method 3 a modified version of the model using a detailed event sequence is investigated.
- Having obtained results for all three methods, observations on the different methods are discussed.
- Finally, using results from one of the methods, deflection checks are performed using check lines and an output report is generated.