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Concrete Slab Long-term Deflection Calculation using Finite Element Method

Posted on in MasterFrame

Long-term deflection in slabs is the deflection or deformation that occurs over time due to creep, shrinkage and concrete cracking. This is an important consideration in the design of reinforced concrete structures.

The calculation of the deflection of a concrete slab involves the assessment of the time-dependent properties of the concrete itself, to account for the variation in the material over time, along with an assessment of the variations in loading during the structure’s serviceable life, particularly during the construction phase when the concrete is still curing.

The analysis, therefore, needs to be done in time steps to match significant time-dependent events such as changes in the loading when the slab formwork is struck. The use of an iterative solution allows for the non-linear material properties to be taken into account during the analysis.

At each stage of the analysis, the stress state of the structure will determine whether or not cracking will occur. Cracking at a cross-section will reduce the stiffness of the structure and this will result in a redistribution of the forces in the structure which can lead to further cracking.

Crack ration calculation in MasterSeries 2021
Crack ration calculation in MasterSeries 2021

Process of the iteration
  1. The stresses in each finite element are checked and if the stresses are such that the cracking limit is exceeded, then the properties of the element are modified to model the cracked section
  2. The next iteration of the analysis is then carried out using the modified element properties and further cracking is determined
  3. Step 2 is repeated until no further cracking is determined to occur
  4. After the analysis is complete for all loading events, the final deflection of the slab is calculated based on the cracked stiffness

At each of the time steps, the iterative solution is carried out for each time-dependent events. The final deflection is a cumulative calculation over time.

The deflection of the slab is significantly influenced by the reinforcement from the ULS design. Hence, the ULS design must be completed as a first stage in the calculation of the deflection of the structure. This means that any modification of the ultimate limit state design (reinforcement) requires recalculation of the deflection analysis.

Concrete slab long-term deflection in MasterSeries 2021
Concrete slab long-term deflection in MasterSeries 2021

Deflection calculation accuracy

The calculation of the deflection of a structure depends on a number of factors. These factors include:

  • Elastic modulus
  • Tensile strength of the concrete
  • Creep
  • Shrinkage
  • Amount of reinforcement
  • Restraint to the structure
  • Aggregate properties
  • Age of concrete when loaded
  • Etc.

All of these factors are subject to inherent variability and many are also subject to variance with time. The elastic modulus, creep coefficient and tensile strength of the concrete have the most significant influence on the final deflections.

Many of the above factors are also influenced by the others and so the factors are not independent. As a result of the variability of the various factors, the calculation of the deflection remains an estimate. The Concrete Centre Technical Report TR58 advises that actual deflection may vary from calculated deflections in a range of +15% to -30%

MasterSeries 2021: Concrete Slab Long-term Deflection Calculation & Crack Control

Last year we introduced our brand-new FE Slab Design module for accurately specifying and designing slab reinforcement. MasterSeries 2021 brings one of the most frequently requested developments, the calculation of long-term deflections including load sequences, creep, cracking & shrinkage.

Join us in the Preview Webinar to get an exclusive view into the new version 2021.

Wed, 26 May 2021, 1:00 PM – 2:30 PM BST

Register now - MasterSeries 2021 Preview Webinar

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