Section Design

Section Design v3.0.0 is now available on Play Store and the aim of this post is to demonstrate its ability to design Reinforced Concrete sections alongside with the theoretical background necessary for this task. 

In particular, Section Design is capable of :

1. Dimensioning the longitudinal reinforcement of rectangular and flange sections under flexure (useful for the design of beam sections).
2. Dimensioning the vertical reinforcement of rectangular sections under biaxial bending with axial force (useful for the design of column sections)
3. Finally, dimensioning the steel reinforcement of rectangular sections under flexure and axial force (useful for the design of ductile walls)

1. Beam Design

• Rectangular Sections

We assume that the distance between the compressive and tensile force equals to z = 0.9d and the reinforcement yields at the Ultimate Limit State (ULS) as illustrated below [1] :

The necessary cross-sectional area of the steel reinforcement is :

• Flange Sections

If the standard parabolic-rectangular σ-ε law of concrete is adopted, then the mechanical ratio of the tension reinforcement (ω) is [2] :

During the process, it also checked whether the dimensionless acting moment (μsd) reaches its upper limit when the ultimate strain of concrete is exhausted. This upper limit equals to [2] :

 εcu2 : concrete's ultimate strain (0.0035 for fck<50 MPa)

Es : steel's modulus of elasticity (200GPa)

fyd : steel's yield stress

So, knowing the value of ω, we can easily calculate the necessary cross-sectional area of the tension reinforcement, solving the below equation [1] :

2. Column Design

A practical, yet approximate, computational method is adopted. This method can be implemented only in case of symmetrically reinforced rectangular sections. The approach is that the dimensioning of the vertical reinforcement is done separately for flexure and axial force at x-axis (Mx-N) and y-axis (My-N) and such are the necessary cross-sectional areas calculated [2]

Dimensioning procedure [2]

Furthermore, another assumption for the ULS design is that the steel is an elastic-perfectly plastic material and both tension and compression reinforcement yield at section's ultimate state. The mechanical ratio of the tension reinforcement for x and y direction equals to [2] :

νd : dimensionless acting force

εc2 : concrete's corresponding strain to its design strength(0.002 for fck<50 MPa)

d1,i : cover of steel reinforcement at i direction

dx : column's dimension parallel to x-axis (b)

dy : column's dimension parallel to y-axis (h)

Finally the cross-sectional area of the tension reinforcement at each direction equals to [1] :

3. Ductile Wall Design

 The Ductile Wall sections are designed under flexure and axial force. In this case, we also assume that the tension and compression reinforcement yield at the section's ultimate limit state and that the web reinforcement has a uniform mechanical ratio ωvd equal to :

ρν : ratio of vertical web vertical reinforcement, equal to 0.002 which is the minimum value according to Eurocode 2 (which is a conservative assumption).

As a result the mechanical ratio of tension reinforcement(ω) and the necessary cross-sectional area are [1] , [2]  :

εsyd : corresponding strain to the steel's design strength fyd

d : effective depth of the tension steel reinforcement

b : width of the wall section

h : length of the wall section

4. Steel Reinforcement

• Beams and Ductile Walls

 The user must insert the number and diameter of the steel bars and then verify that their cross-sectional area is enough, taking into consideration the required cross-sectional area calculated during the design process.

• Columns

 In this case, due to the implemented method at the design process, the user must insert the diameter of the corner bars, the number and diameter of the total bars at x-direction and similarly at y-direction and afterwards verify that these bars have sufficient cross-sectional area.

References

[1] Zararis Prodrommos (2002), "Μέθοδοι Υπολογισμού Σιδηροπαγούς Σκυροδέματος" (in Greek), Thessaloniki : Kyriakidi

[2] Fardis Michael, Carvalho Eduardo, Fajfar Peter, Pecker Alain (2015), "Seismic Design of Concrete Buildings to Eurocode 8", New York : CRC Press 

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