Observations on the Different Methods
Combined Table of Results
|Approach||Restraint Constant for Modulus of Rupture||Creep approach||Assumed Creep and Shrinkage combined allowance %||Assumed Shrinkage %||
(Final load event)
|Method 1: Simplified Event Sequence + Simplified Combined Creep and Shrinkage Allowance||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”|
|Method 2: Simplified Event Sequence + Rigorous Creep + Shrinkage Allowance||ACI 435 (creep included in analysis)||4.0||Cu = 2.35, h = 2 and χ = 0.8||25%||1.5”|
|7.5||Cu = 2.35, h = 2 and χ = 0.8||25%||1.0”|
|Method 3: Detailed Event Sequence + Rigorous Creep + Shrinkage Allowance||ACI 435 (creep included in analysis)||4.0||Cu = 2.35, h = 2 and χ = automatic based on TR58||25%||1.5”|
|7.5||Cu = 2.35, h = 2 and χ = automatic based on TR58||25%||1.0”|
When the guidance in ACI 435 about the use of a combined allowance for creep and shrinkage is taken into account, the simplified approach using a combined creep and shrinkage multiplier seems to determine very conservative deflection estimations.
Looking at table 4.1 in ACI 435, it is clear that the creep contribution is the most significant part of the overall deflection estimate. It is also the area where there seems to be greatest variation in opinion on the contribution level.
The creep contribution can be dealt with more rigorously by including it in the analysis. So rather than using a short term E value and then amplifying the result to account for creep, the analysis at the end of each event uses an effective E value which includes for creep up to that point. This impacts on the analysis properties of every shell in the FE analysis and even on the extent of cracking.
It is suggested that when the creep is included in the analysis the use of a modulus of rupture which assumes low restraint (restraint constant = 7.5) be used cautiously.
The option to calculate the effective E value based on some UK guidance in TR58 makes little difference in this example. It should be borne in mind that the aging coefficient χ is user defined and 0.8 is just a default for “normal” situations. In situations such as a transfer slab where load will accrue more slowly over time 0.8 is likely to be conservative and it may be of interest to consider the TR58 alternative.
Overall, it is expected that most engineers would use the settings highlighted in bold in the table above as a default starting point and then make refinements if necessary.
Extent of Cracking
It is clear from the Combined Table of Results, that the Restraint Constant and hence the Modulus of Rupture has a huge impact on the predicted deflections. This is due to the impact the modulus of rupture has on the extent of cracking that develops. This is illustrated below where the extent of cracking for the final load event is displayed for the Method 2 model.
You can clearly see the majority of the slabs have cracked where the restraint constant is 4.0.
The majority of the slabs remain uncracked where the restraint constant is 7.5.
- Using results from one of the methods, deflection checks are performed using check lines and an output report is generated.