Alasdair’s Engineering Pages © A. N. Beal 2024 www.anbeal.co.uk
www.anbeal.co.uk
Concrete, May 2019, pp. 52
Concrete column design: simplifying Eurocode 2
Alasdair N Beal, BSc CEng FICE FIStructE, Thomasons Ltd, Leeds, UK
Introduction
The analysis of slender columns is a long
Code design rules for concrete columns have tended to rely heavily on the fact that most real reinforced concrete columns are stocky and very slender columns are rare. Code of practice CP 114 [1] allowed columns to be designed at full stress up to Le/h = 15, which covered most real columns; above this, the allowable column load was reduced linearly (Le is the column effective length and h is its overall depth).
Its successor CP 110 [2] allowed full stress up to Le/h = 12 and beyond this additional moments were applied to allow for buckling effects. The additional moments were calculated on the assumption that at failure the concrete strain would be at its short
Research
In 1986, the author proposed a new graphical analysis method for slender pin
This method was used to analyse the behaviour of slender columns for both short
Following publication of this initial paper [4], a comprehensive programme of research, including load tests and detailed analysis of column behaviour, was carried out at Leeds University. This included analysis of the load capacity of pin
Although this graphical analysis method allows a range of columns to be analysed rapidly once the relevant moment
Simple column design methods generally allow for the effects of slenderness on load capacity by either applying reduction factors to the load capacity or else by requiring additional moments to be allowed for in the design. The 1999 Beal/Khalil paper showed that by using additional moments, which have been set to give results which match those from accurate analysis, it is possible to produce design rules which are more accurate than BS 8110 and also simpler to use. The present article shows how the same approach can be used to simplify Eurocode 2.
Eurocode 2
The present Eurocode 2 recommendations are based on research by the Swedish engineer Bo Westerberg, who carried out a detailed computer analysis of slender column behaviour taking into account the relevant effects [6]. Comparison of the results from the Beal
Like BS 8110, the Eurocode 2 design rules [7] allow slenderness effects to be ignored in some situations (Cl. 5.8.3.1(1) and Cl. 5.8.3.3). However, the calculations that are required limit the value of this simplification. When slenderness effects cannot be ignored, EC2 offers the engineer a choice of three design methods: the ‘general method’ (Cl. 5.8.6), the ‘nominal stiffness method’ (Cl. 5.8.7) and the ‘nominal curvature method’ (Cl. 5.8.8). The ‘general’ and ‘nominal stiffness’ methods are rarely used in the UK because of their complexity; engineers generally use the ‘nominal curvature’ method.
The EC2 ‘nominal curvature method’ superficially appears similar to BS 8110 but it is more complex in practice: first, in addition to calculating the nominal curvature, the engineer must also calculate and add the load eccentricity due to imperfections (Cl. 5.8.8.2(2)). The calculated nominal additional moment is then modified by a correction factor for axial load (Cl. 5.8.8.3(3)) and this in turn is modified for reinforcement arrangement (Cl. 5.8.8.3(2)), creep (Cl. 5.8.3(4)), effective creep ratio (Cl. 5.8.4) and slenderness ratio (Cl. 5.8.3.1). Although this is the simplest column design method offered by EC2, it is still very complicated.
Simplifying EC2
The 1999 Beal
Most real columns carry predominantly long
As cracking affects the stiffness of a column, the effect of slenderness on load capacity will vary with the load eccentricity. The Beal
The proposed additional load eccentricities for design are shown in Table 1. They are calculated from the formula eadd/h = 0.005Le/h + 0.00065(Le/h)². Le = effective length, h = section overall depth.
Table 1 Additional load eccentricities for column design
Comparison
The graphs in Figures 1
Figures 1 and 2 show results for an axially loaded C32/40 300 × 300mm column with 0.8% or 4% steel. As can be seen, the proposed design rules give conservative results; existing EC2 design rules are unconservative for Le/h between 5 and 20 and also for 4% steel.
Figures 3 and 4 show the results for 0.8% reinforcement and load eccentricities of 0.1h and 0.5h; Figures 5 and 6 show the corresponding results for 4% reinforcement. As can be seen, the proposed new rules and the existing EC2 design rules both agree closely with the results from the accurate analysis: the proposed new rules are generally slightly conservative, whereas the EC2 rules are slightly unconservative for 4% steel and at low values of Le/h. For load eccentricities 0.1h, 0.3h and 0.5h, the average capacity (proposed/theory) is 0.95, with a minimum of 0.67 and maximum of 1.06; in the important range Le/h 5–20, the average capacity (proposed/theory) is 0.98, with a minimum of 0.91 and maximum 1.03.
Figures 7 and 8 show the results for a C65/80 column with 0.8% steel respectively and 4% steel and applied load eccentricity e = 0.1h. Again, the results agree closely with the accurate theoretical analysis and comparisons for higher load eccentricities up to e = 0.5h give similar results. For load eccentricities 0.1h, 0.3h and 0.5h, the average capacity (proposed/theory) is 0.90, with a minimum of 0.47 and maximum of 1.08; in the important range Le/h 5–20, the average capacity (proposed/theory) is 0.94, with a minimum of 0.82 and maximum of 1.07.
Therefore the proposed additional load eccentricities are suitable for design of all columns with between 0.8% and 4% reinforcement and for all concrete strengths up to C65/80.
Proposed amendments to Eurocode 2
The following clause may either be inserted as a replacement for the present Cl. 5.8.8 ‘Method based on nominal curvature’ or as a possible alternative design method.
Simple ‘additional moment’ design method for columns
1. In this method, an additional moment to allow for imperfections and slenderness effects is added to the first
2. The design moment is:
MEd = (M0Ed + Madd), or M02, whichever is greater, where:




3. If the column is unbraced, M0Ed is the maximum first
4. The additional eccentricity eadd to allow for the effects of slenderness and imperfections is shown in Table 2. Intermediate values may be interpolated.
Table 2
Simple ‘additional moment’ design method: additional load eccentricity eadd
eadd /h = 0.005Le/h + 0.00065(Le/h)²
where Le = effective length, h = overall section depth in direction of buckling
Acknowledgements
Thanks are due to James Massey for assistance with the calculations and to Charles Goodchild and Paul Gregory at The Concrete Centre for assistance with interpretation of some points in EC2.
References
1. BRITISH STANDARDS INSTITUTION, CP 114. The structural use of reinforced concrete in buildings. BSI, London, 1969.
2. BRITISH STANDARDS INSTITUTION, CP 110. Code of practice for the structural use of concrete. Part 1 – design, materials and workmanship. BSI, London, 1972.
3. BRITISH STANDARDS INSTITUTION, BS 8110. Structural use of concrete. Part 1 
4. BEAL, A.N.The design of slender columns. Proceedings of the Institution of Civil Engineers Part 2, Vol. 81, September 1986, pp.397–414, available at: www.anbeal.co.uk
5. BEAL, A.N. and KHALIL, N. Design of normal
6. WESTERBERG, B. Second order effects in slender concrete structures. KTH (Royal Institute of Technology in Stockholm), Civil and Architectural Engineering, Department of Concrete Structures, Report 77, 2004.
7. BRITISH STANDARDS INSTITUTION, BS EN 1992