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Influence of Pylon Layout on Reinforcement Demand in Floor Slabs

 

by Dubko M., m.dubko@promcore.io.

 

 

1. Introduction

 

Structural engineers frequently adjust column grids to optimize material use while maintaining serviceability. Modern computational tools like FEMnet 2.0 allow rapid assessment of numerous pylon layouts. This paper investigates how the average span between pylons (L) affects:

• Specific reinforcement demand (A_s), defined as kg of steel per cubic meter of concrete.
• Mid-span deflection (\delta), an indicator of serviceability.

Two distinct architectural floor plans (Plan A and Plan B) are evaluated. Each plan includes 50 different pylon arrangements, resulting in 100 total simulations.

 

2. Model Description

 

Parameter                                       Value                                                                        

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Concrete                                          C30/37, modulus E \approx 6, GPa

Reinforcement Steel                      A500, yield strength R_s = 435, MPa

Slab Thickness                               h = 180, mm (constant)

Design Load                                    q = 10.8, kN/m^2 (self-weight + live load)

Boundary Conditions                     Rigid Fixity: zero rotation (\varphi = 0) and zero translation (u = 0) at pylon                                                                connections

Solver                                               FEMnet 2.0,

Mesh size                                        50, mm

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Each simulation provided:

• Mean span length (L) (calculated as the average approximate value of all distances between pylons)
• Mean reinforcement quantity (A_s) (output by FEMnet 2.0 based on structural analysis)
• Mean deflection (\delta) (calculated for Plan B only, based on FEMnet 2.0 deflection results)

Figures 1–6 and Table 1 present the results.

Fig. 1 - Plan A

 

Fig. 2 - Plan B

• On the plans, the grey walls are the load-bearing walls of the stairwell-elevator unit. The green walls are the architectural walls in which the pylons were located.

 

Table. 1 - Results of 100 experiments

 

Fig. 3 - Reinforcement consumption depending on the span on plan A

 

Fig. 4 - Reinforcement consumption depending on the span on plan B

 

Fig. 5 

 

Fig. 6 

 

3. Theoretical Background

 

3.1. Fixed-End Beam under Uniform Load

A beam rigidly fixed at both ends under a uniform load (q) experiences moments and deflection described by standard structural analysis formulas:

3.2. Reinforcement Calculation

Steel area:

4. Detailed Step-by-Step Regression Analysis

4.1. Calculation for Linear Regression Parameters

Given data points (L_i, A_{s,i}), linear regression:

Step 1: Calculate basic sums

• \sum L_i, \sum A_{s,i}, \sum L_i^2, \sum L_i A_{s,i}

Step 2: Solve for slope (a)

Explicitly substituting all sums (from dataset):

Step 3: Solve for intercept (b)

Explicit substitution:

4.2. Calculation for R^2 (Coefficient of Determination)

The quality of the linear fit:

Where:

• A_{s,i}: actual values
• \hat{A}_{s,i} = aL_i + b: predicted values
• \bar{A}_s: mean of actual values

Explicit calculations from dataset yield:

This indicates 97% of reinforcement variance is explained by span length.

Fig. 7 - Reinforcement Vs Span With Linear Regression

 

4.3. Quadratic Regression (Deflection Plan B)

Model:

Step 1: Basic sums for quadratic regression

\sum L_i^2, \sum \delta_i, \sum L_i^4, \sum L_i^2\delta_i

Step 2: Solve for quadratic coefficient (c)

Step 3: Solve for intercept (d)

Step 4: Calculate R^2 for quadratic model

A nearly perfect fit (99.5% of deflection variance explained).

 

Fig. 8 - Deflection vs Span with Quadratic Regression

 

5. Conclusions

 

5.1. Dependence of reinforcement on the average span.
Based on the results of 100 calculations carried out on two building plans (50 variants for each plan), a stable and almost linear relationship was found between the average span of floor slabs and the required reinforcement consumption. It was found that with an increase in the average span by 1 meter, the specific reinforcement consumption increases by approximately 14.2 kg/m³. This allows design engineers to quickly and accurately estimate the required reinforcement at the early stages of design, based only on the architectural scheme and the average column grid.

 

5.2. Evaluation of the reliability and practical usefulness of the FEMnet 2.0 neural network.
The coefficients of determination (R²) of the regression models (0.97 for reinforcement consumption and 0.995 for deflections) indicate the high accuracy and reliability of the calculation results performed using the FEMnet 2.0 neural network. This confirms that the use of neural network calculation methods at the early stages of design is justified and can significantly simplify the process of preliminary analysis and optimization of building design schemes, providing accuracy close to the traditional finite element method (FEM), but with much less time.