Structural Modelling and Analysis of concrete Floor Slabs based on AS3600 using SPACE GASS

Introduction

This article briefly discusses the use of SPACE GASS software to analyses and design floor slab based on the Australian Standard AS3600. It outlines the design process for concrete slabs, followed by analysis options, and provides insightful details how the software arrives at the design values internally.

There are two methods for slab design in SPACE GASS, namely, Strip-based and FEA methods. Despite of their names, both rely on the finite element method to calculate internal forces to use for the design process.

The strip-based method is close to the way one would normally employ to design a reinforced concrete beam manually. The program automates the process of integrating design forces at many sections along the strip. Thus, it is easy to verify the design solution using beam theory. 

FEM method, on the other hand, is harder to check since the slab is subdivided into hundreds or thousands of discrete elements, and it is impossible to verify the design result for every single one of them. However, FEM method, as shown later in the article, is good for an overview of how the reinforcement should be distributed over the entire slab. In either method, there is an option to whether consider Wood-Armer effect, which takes the twisting moment of slab into account. 

Linear or Nonlinear Analysis?

The choice of analysis type is always a hot spot for debate and may depend on users’ preferences and softwares’ capabilities. Linear analysis is the simplest analysis type and is commonly used in structural analysis for everyday design, provided that the material behaves well below its yield strength and the structures subjects to small deflection, where no geometrical nonlinearity occurs. Nonlinear analysis, in contrast, is quite sophisticated and requires a comprehensive understanding to use properly. 

For typical reinforced concrete slab analysis, personally, I would prefer the linear analysis for the below reasons:

A linear analysis is more than adequate for carrying out a design at the ultimate limit state. The serviceability limit state can be checked using “deemed to satisfy” span-to-effective-depth ratios or by using a conservative value for the elastic modules and slab stiffness.

In general, 85% of structural elements are designed using the span-to-effective-depth rules and this is perfectly adequate for most designs. The remaining 15% probably require nonlinear analysis. However designing elements using nonlinear analysis (material and geometrical nonlinearity) is often highly time consuming. For example, the FE model to investigate the already happened accident where a truck impacted with the barrier on the Bolt Bridge in Melbourne, took a decent multi-core CPU computer 2 weeks to complete. This sort of analysis should only be done by engineers who have highly skill in it.

For nonlinear analysis of reinforced concrete slabs, one should be clearly aware that the use nonlinear analysis for reinforced concrete slab is only useful when the software used is capable of analysing cracked behaviour of concrete. Once concrete has cracked, its stiffness changes. A proper process would be as follows: the program starts with uncracked (gross) sectional properties. It then increments load and determines where the slab has cracked. The program adjusts the sectional properties at locations where concrete has cracked, and then performs the analysis again with new sectional properties until no changes of sectional properties occurs between iterations. The program then repeats the whole process for next load step until the load reaches the user -specified load. This process requires significant computational time as compared to linear analysis but does not necessarily always produces a better result. Some authors have claimed that “even the most sophisticated nonlinear analysis solver will only give an estimate of deflection in the range +15% to -30%” (1).

Estimate slab thickness and deflection 

The first step is to estimate the slab thickness. The thickness is chosen mainly on the basis of deflection control purpose, although there are cases where strength governs the slab depth. Steel reinforcement could help to reduce deflection, however increasing slab depth would be a more effective solution than adding more reinforcement.

As a rule of thumb, the actual deflection is about 3-5 times the elastic deflection. This is because the cracked moment of inertia is usually about 0.2 to 0.6 the gross uncracked value. Thus, if elastic deflection is, says, 2-3 mm in a load case, the actual deflection would be roughly 10-15mm in that load case.

SPACE GASS has a facility to assist the estimation of the slab depth based on “Deem to comply span-to-depth ratio for reinforced slabs” method based on Clause 9.3.4 AS3600-2009. The slab deflections shall be deemed to comply with the requirements of the code if the ratio of the effective span to the effective depth satisfies the following:

Details of each parameter can be found in Clause 9.3.4.1 AS3600.

In the right figure, a set of input sample leads to a required slab depth of 151 mm. This depth (says, 150 mm) could then be used to the next design steps without the designer worrying about the deflection requirements set out by the code.

Alternatively, for the strip-based method, SPACE GASS also provides a detailed deflection calculation taking the effects of concrete creep and shrinkage into account. The designer would then have to compare the calculated deflection with the deflection limits as required by the code. If we consider a constant strip width, the deflection can be calculated using the moment curvature method. For example, in the below figure, deflection of the right-hand support, B, with respect to the tangent at the left-hand support, A, termed delta B|A, has the linear relationship with the rotation at A, assuming small angle theory:

delta B|A = L * ThetaA

where: ThetaA is rotation at A.

SPACE GASS automatically calculates the curvatures at many intermediate nodes (x) between end spans. The calculation of these curvatures also considers the creep and shrinkage effects and whether the section has cracked by comparing the crack moment and the applied one. The program then calculates the deflection of the intermediate nodes off this tangent. This is equal to the first moment of area of the curvature diagram between A and x, about point x. The actual deflection is then equal to : 

delta x=Theta A * Lx - delta x|A

Figure above shows short term, long term and total deflections for a 3-span strip based on the deflection calculation method.

Meshing

SPACE GASS provides a convenient tool to mesh the entire floor quickly and easily. The auto-mesher makes any restraint lines (sometimes called hard lines) within the mesh boundary compatible with mesh elements. In addition, any co-planar nodes, such as the top of column nodes or nodes defining the boundary of the drop panels, will be automatically compatible with the mesh.

Pattern Loading

Apart from normal set of load cases such as dead, live, and wind load and their combinations required by AS3600. We need also to consider the pattern loadings. Pattern load cases can be automatically generated quickly using tool provided. The following is demonstration of one of a typical pattern automatically generated by SPACE GASS:

Strength Design and Crack Control

For strip-based method, SPACE GASS calculates the required reinforcement based on the envelope of bending moment and shear force load cases

The program calculates the steel required for top and bottom of all sections along the strip as well as suggests the reinforcing bars and their layouts. It also suggests the minimum steel and bar spacing for crack control requirements.

For FEM method, the required reinforcement is displayed directly by the contour of reinforcement in each principle direction of the plates. For this reason, all plates should be aligned with the same direction before running the model analysis.

Conclusion

This article is a brief overview of the capability of SPACE GASS software for modelling, analyzing and designing floor slab. It mentioned deem-to-comply deflection tool, mesh tool, the strip-based and finite-element based method for the users to consider when designing RC slabs.