# Design of Concrete Columns Subjected to Axial Compression with RF-CONCRETE Columns

## Technical Article on the Topic Structural Analysis Using Dlubal Software

### Technical Article

This article compares the design to the one in the referenced article: Design of Concrete Columns Subjected to Axial Compression with RF-CONCRETE Members. It is, therefore, about taking exactly the same theoretical application carried out in RF-CONCRETE Members and reproducing it in RF-CONCRETE Columns. Thus, the objective is to compare the different input parameters and the results obtained by the two add-on modules for the design of column-like concrete members.

#### Theoretical Application

Axial compression applies if it is assumed that second-order effects (imperfections, asymmetry, etc.) can be neglected while respecting in particular the slenderness criterion, which depends on various parameters (slenderness coefficient, limiting slenderness, effective length).

Then, under the single loading of a normal force NEd, the force that can be balanced by the concrete cross-section corresponds to its maximum load-bearing capacity for compression, which directly depends on its section and its design resistance. The reinforcement will balance the rest of the axial compressive load.

#### Application of the Theory with the RF-CONCRETE Columns add-on module

In this article, we will analyze the results obtained automatically for the reinforcement calculation.

The parameters remain the same and are listed below:

• Permanent loads: Ng = 1 390 kN
• Variable loads: Nq = 1,000 kN
• Column length: l = 2.1 m
• Rectangular cross-section: width b = 40 cm / height h = 45 cm
• Self-weight of the column negligible
• Column not integrated into bracing
• Concrete strength class: C25/30
• Steel: S 500 A for inclined graph
• Diameter of longitudinal reinforcement: ϕ = 20 mm
• Diameter of transverse reinforcement: ϕt = 8 mm
• Concrete cover: 3 cm

#### Real Cross-Section to Be Calculated

Since it is impossible in RF-CONCRETE Columns to optimize the cross-section height, the section's real height h is directly modified and set to 45 cm.

Image 02 shows the steps to change the height of the rectangular cross-section in RF-CONCRETE Columns.

#### Material Properties

The formulas for the materials' strength and strain are described in detail in the technical article mentioned above.

Total area of pure concrete section

Ac = b ⋅ h = 0.40 ⋅ 0.45 = 0.18 m²

Design value of the compressive strength of concrete

fcd = 16.7 MPa

Relative compression strain for maximum stress

εc2 = 2‰

Design yield strength of reinforcing steel

fyd= 435 MPa

Limit strain in reinforcement

εud = 2.17‰

Stress in reinforcement

σs = 400 MPa

In order to verify the material settings in RF-CONCRETE Columns, Image 03 shows the expected stresses and strains for the concrete and the required reinforcement.

#### Ultimate Limit State

NEd = 1.35 ⋅ Ng + 1.5 ⋅ Nq

NEd = 1.35 ⋅ 1390 + 1.5 ⋅ 1000 = 3.38 MN

NEd ... design value of acting axial force

#### Second-Order Effects not Taken into Account in ULS

As the model is identical for this article and the one that serves as a basis for comparison, we have modeled the same column restrained at the base and free at the head to be able to apply the load correctly at the column head. However, we consider that the column is still fixed at the head to the beams. To do this, we have applied an effective length factor to the column, which allows us to modify the slenderness value of the column.

Effective length factor according to EN 1992-1-1 - 5.8.3.2 (3) - Formula 5.15

kcr = 0.59

Slenderness according to EN 1992-1-1 - 5.8.3.2 (1) - Formula 5.14

λz = 10.73 m

Limiting slenderness according to EN 1992-1-1 - 5.8.3.1 (1) - Formula 5.13N

n = 1.125

λlim = 20 ⋅ 07. ⋅ 1.1 ⋅ 0.7 / √1.125 = 10.16 m

λz > λlim → The condition is not fulfilled.

However, we are still going to calculate in simple compression because, the 'difference being small, we will see later that' with the mechanical ratio d ' reinforcements, the condition will be respected. For this, Image 05 describes how to deactivate the possibility of having buckling around each axis of the cross-section in RF-CONCRETE Columns.

Equilibrium force of concrete

Fc = Ac ⋅ fcd = 0.40 ⋅ 0.45 ⋅ 16.7 = 3 MN

Equilibrium force of reinforcement

Fs = NEd - Fc = 3.38 - 3 = 0.38 MN

We deduce the corresponding reinforcement area:

Reinforcement area

As = Fs / σs = 0.38 / 400 ⋅ 104 = 9.5 cm²

Having configured steels with a diameter of 20 mm in RF-CONCRETE Columns, the reinforcements provided and determined automatically by the module are 4 members, with a distribution in the corners, as requested, i.e. 1 HA 20 per corner. Therefore, the result of the 'cross-sectional area d' reinforcement is as follows:

As = 4 ⋅ 3.142 = 12.57 cm²

Mechanical reinforcement ratio

ω = (As ⋅ fyd) / (Ac ⋅ fcd) = 0.182

Final check of limiting slenderness

λlim = (20 ⋅ 0.7 ⋅ √(1 + 2 ⋅ 0.182) ⋅ 0.7) / √1.125 = 10.79 m

λz < λlim → The slenderness criterion is fulfilled.

#### M.Eng. Milan Gérard

Sales & Technical Support

Milan Gérard works at the Paris site. He is responsible for sales and provides technical support to our French-speaking customers.

#### Reference

 [1] Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings; EN 1992-1-1:2011-01 [2] Roux, J. (2007). Pratique de l'eurocode 2 - Guide d'application. Paris: Groupe Eyrolles.

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• Updated 17 January 2022

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