ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT
AZOJETE, June, 2019. Vol. 15(2):470-478

Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria.
Print ISSN: 1596-2490, Electronic ISSN: 2545-5818

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470

ORIGINAL RESEARCH ARTICLE

LOADING ECCENTRICITY ISSUE ON THE PERFORMANCE OF REINFORCED CONCRETE
COLUMNS

Kachalla Mohammed
(Civil and Water Resources Engineering Department, University of Maiduguri,

Maiduguri, Borno State, Nigeria)
*Corresponding author’s e-mail address: engrkachalla@unimaid.edu.ng

ARTICLE INFORMATION

Submitted 29 March, 2018
Revised 20 April, 2019
Accepted 23 April, 2019

Keywords:
RC Column
Loading
Eccentricity
Short and Slender Columns
Abaqus

ABSTRACT
Column is a structural element that transmits floor and beam loads to
the foundation safely if properly designed. It is mostly loaded axially or
eccentrically at the column-beam interface. Although several research
articles are available on column performance (both eccentric and axial),
but there is a behavioural challenge on a column loading position
parallel to the axis in relation to the flexural reinforcement requirement
for Reinforced Concrete (RC) column. This paper looks inward to
address the challenge by providing an understanding on the complete
behaviour of RC Column flexural requirement in relations with load and
its point of application for both short and slender columns. This study
uses a numerical data for the column analysis under varied loads and
eccentricities values, and numerical deformation and stresses
determination using ABAQUS. The Finite Element analysis (FEM) result
indicates that increasing column axial load leads to an anticipated
higher flexural reinforcement to enhance the column capacity, and is
rational. Additionally, the established behaviour between the flexural
reinforcement requirement and loading eccentricity for a rectangular
column can be predicted easily using established linear relations for
both column types considered in this study. Moreover, the Finite
Element Method analysis result for the short column similarly indicates
an interesting relationship where 16 % change in load value will
translate to about 16 % change in deformation value irrespective of
either axial or eccentrically loaded points.

© 2019 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved.

1.0 Introduction
Column is a structural element that transmits loads via itself to the foundation. Reinforced
Concrete Column (RCC) plays a very vital role in transferring the structural loads from beams or
slabs to the foundation. The RCCs are primarily compression members that could be categorised
into either short or slender columns. There are several scholarly articles that covers areas such as
ductility, slenderness ratio and buckling effects for rectangular RCC (Zeghiche and Chaouti,
2005). However, most columns are loaded either axially or eccentrically at the column beam
interface, but there exists very little information on its behaviour at that interface; for example
column load position in relation to the flexural reinforcement requirement. Hence, this makes it
imperative to investigate how column load and its positions with respect to the column-centroid
and its reinforcement requirement for stability relates to each other. Although previous research

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Arid Zone Journal of Engineering, Technology and Environment, June, 2019; Vol. 15(2):470-478. ISSN 1596-2490;
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471

findings reveal that increases in load eccentricity results in decreasing load carrying capacity
(Zeghiche and Chaouti, 2005), but not much was covered on how the variations influences the
flexural capacity requirement.
It is known that eccentric loadings in the same direction causes the largest deflection, so also
local buckling plays a very vital role and Euler’s buckling is of little importance while dealing with
short column (Chen and Liew, 2003). In related work conducted by Barrera et al. (2011) on
reinforced concrete column subjected to constant axial load, the result suggests that failure due
to compression is more pronounced when axial load, concrete strength and both transverse and
longitudinal reinforcement ratios are increased. Similar experimental work on concrete-filled
stainless-steel tubular columns was also carried out, but the column was loaded with either fibre
reinforced concrete (Ehab and Mariam, 2012) or steel jacketed column (Cavaleri et al., 2016; Eze-
Eldeen, 2016). This shows that there is a missing gap on the loading position parallel to the
column axis as well as the flexural column reinforcement. This paper looks inward to present the
missing link. The study results will aid the understanding of the complete behaviour of RCC
flexural requirement in relations with load and its point of application for both short and slender
columns. Moreover, most reinforced concrete sections could either be subjected to either axial
loads or biaxial bending characterised by the structure (Bonet et al., 2011), that’s
notwithstanding, the load contour method emphasis bending moment separately in either
direction (Bresler, 1960). Additionally, this study addresses both short and slender column types,
and their numerical performance with the use of ABAQUS software.

2.0 Materials and Method
2.1 Short column
A braced short column type was adopted for this study. The adopted short column design
details followed the provision in accordance with the BS 8110 (1997). Hence, the column
effective height, el is from the use of eq. (1)

e ol bl (1)
where b is an column ends condition determinant factor and the values are obtained from
tables 3.19 and 3.20 of BS 8110 (1997). The parameter ol in eq. (1) stands for the actual column
height. Hence, for an axially loaded column, the design ultimate load, N relation to the flexural
reinforcement area, scA is

0.45 0.95cu sc yN f bh A f  (2)

The parameters cuf and yf are the respective concrete and steel characteristic strength. Similarly,
*b h defines the column cross sectional area (Figure 1). For an eccentrically ( )e loaded column

carrying an axial force, N , the increased moment, aM as shown by Eq.
2( 2 )aM M N h d   (3)

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Kachalla Mohammed: Loading eccentricity issue on the performance of reinforced concrete columns. AZOJETE,
15(2):470-478. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: engrkachalla@unimaid.edu.ng 472

Axial Load (kN)

x x
Y

X

Section x-x

30
0

450

Column section

Column Reinforcement

Figure 1. Short column dimensions

Hence, the flexural reinforcement requirements are obtained through designing the member to
withstand aM using

2 ' '

'

0.156 0.95 ( )

0.95 0.2 0.95
a cu y s

y s cu y s

M f bd f A d d

f A f bd f A

  

  (4)

In Eq.
'
sA stands for the area of reinforcement at the tension zone. This implies that

'0.2 0.95
0.95

cu y s
s

y

f bd f A
A

f



(5)

The resulting output value in Eq. will be reduce by 0.95 yN f

Slender Column
Slender column (Figure 2) are designed to withstand not only the axial load, but increased
moment, iM as shown using Eq. as found in BS 8110 (1997).

i uM N (6)

The column deflection  u akh  , where the coefficient

2

'

1
2000

e
a

l
b

    
  and 'b is the least

column dimension. Similarly, k stands for a deflection reduction factor computed from

1.0uz

uz al

N Nk
N N


 

 (7)
where uzN and alN are from:

0.45 0.95
0.25

uz cu y sc

al cu sc

N f f A
N f A

 



However, subjecting the column to an eccentric load will result in additional moment, addM , and
this is from

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min

min

*
where / 20 or 20

addM N e
e h mm


 (8)

Axial Load (kN)

x x
Y

X

Section x-x

35
0

600

Column section

e

Column Reinforcement

Figure 2. Slender Column dimensions

Therefore, the total moment, t i addm M M  . For the purpose of this analysis, three different
axial loads (1500 kN, 1750 kN and 2000 kN) values are considered under both short and slender
columns. Similarly, the initial eccentricity value was 25 mm, and subsequent 100% increments
that translate to respective 50 mm and 75 mm. Figure 2 shows the column dimensions and
loading position. Those values chosen have high likely of occurrence in the real life situation.

3.0 Numerical Model
This study uses ABAQUS software application to mimic the behaviour of the RC concrete column.
The finite element model considers both the non-linearity behaviour of the concrete and
reinforcement medium. The concrete part was deformable solid element while the reinforcement
part is also deformable-wire element. Figure 3 shows the typical parts-merged and meshed.

Figure 3. Meshed Specimen type

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Kachalla Mohammed: Loading eccentricity issue on the performance of reinforced concrete columns. AZOJETE,
15(2):470-478. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: engrkachalla@unimaid.edu.ng 474

This study concrete behaviour was modelled using the concrete damage plasticity, where the
failure mechanism is by crushing and cracking. This model requires the use of elastic modulus,
poisons ratio, the plastic damage parameters and the description of the tensile and compressive
behaviour. The stress-strain relationship presented in Hamza and Mohannad (2018) was adopted
to construct the concrete uniaxial compressive stress-strain curve, and this is by

2 3

1 ( 2) (2 1)

c c
C

c c c
e

o o o

E

R R R R


  
  


               
      (9)

1
2

0

( 1)where 
( 1)
e o

e
e

c
e

c
o

o

R RR R
R

ER
E

fE



 






(10)

The constant parameters  and o eR R have a value of 4, while the concrete elastic modulus and its

corresponding strain vales are 4700c cE f and
4(0.2 13.06).10o cuf   , respectively. The

parameter cf represents the characteristics concrete strength.
Similarly, the strain-stress relationship for the steel element was in accordance with the method
proposed by literature (Hamza and Mohannad, 2018). To simulate the behaviour of the concrete
and the reinforcement steel, the embedded region function in ABAQUS was used. Additionally,
for the purpose of this numerical analysis, only two axial loading cases (1500 kN and 1750 kN)
are used and the loading eccentric (e) considered was 25 mm. The reason for such values
selection is based on their likely of occurrence in real life situation. However, because of
similarity in the flexural behaviour for the two columns considered in this study, only the flexural
reinforcement characteristics for the short column were used for the ABAQUS analysis. The Von-
misses stresses and deformation values were recorded for interpretation.
Results and discussion
Figure 4 show the flexural behaviour of short column under the different parametric conditions
stated above.

Figure 4. Short Column Flexural requirement behaviour

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In Figure 4, gradual increase of the loading eccentricity from 25 mm to 50 mm results in 44%
surge in flexural requirement (A) with 1500 kN axial load. However, surging load yields to
flexural reinforcement decreases to about 30% with further 250 kN load increment from 1750 kN.
Similar scenario happens when the e values changes to 75 mm from 50 mm and the
corresponding values are 30 and 23%, respectively. The analysis of the short column behaviour
reveals that, increasing the axial load value from 1500 to 1750 kN ( 25 )e mm results in about
32% surge in flexural reinforcement. However, further load increment result in much lesser value
than the previously reported surge (24%).
This study result indicates that increasing column axial load leads to an anticipated higher
flexural reinforcement to shore up the column capacity, and is rational. Additionally, the
established behaviour between the flexural reinforcement requirement and loading eccentricity
for a rectangular column could be easily described with linear relation. For example, consider an
axial load value of 1500 kN, its linear equation of best fit is 330 423y x  , where y is the
dependent variable (short column).

Figure 5. Slender Column Flexural requirement behaviour
There is no doubt, the slender column requires more steel than the short column (see Figure 5).
Similar to the behaviour shown with the short column, the flexural requirement linearly increases
with increasing eccentricity. Generally, eccentrically loaded column exhibits a conservative
flexural requirement especially with increasing eccentricity and similar characteristic behaviour
are found in literature (Ehab and Mariam, 2012). However, reducing this high level of
conservatism could be interesting research areas that need to be explored.

3.1 Finite Element Analysis result
Figure 6 and 7 presents the finite Element Method (FEM) analysis outcomes for the Von-Misses
stress values for both the axial and eccentrically loaded condition, but for short column. The axial
stress resistance values increase with increasing axial load value. This behaviour could be
attributed to the additional flexural reinforcement that enhances the concrete resistance.

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Kachalla Mohammed: Loading eccentricity issue on the performance of reinforced concrete columns. AZOJETE,
15(2):470-478. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: engrkachalla@unimaid.edu.ng 476

Figure 6 Von Misses Stress values under axial load (a) 1500 kN axial load (b) 1750 kN axial load

Figure 7. Von Misses Stress values on 25 mm-eccentric loading (a) 1500 kN (b) 1750 kN
Figure 8 shows the deformation behaviour for the column analysed. As expected, the
deformation values increase with increasing column load (Figure 8 a and b). Interestingly, 16 %
change in axial load will result in 16 % change in deformation value irrespective of point of load
application either axial or eccentrically loaded (Figures 8 a-d), because the 25 mm loading
eccentricity have no influence on the deformation capacity. In general, Stewart and Rosowsky
(1998) showed that the serviceability condition is mostly influenced by the concrete strength
ckf rather than other deformation influencing factors (Kachalla et al., 2018).

(a) (b)

(a) (b)

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Arid Zone Journal of Engineering, Technology and Environment, June, 2019; Vol. 15(2):470-478. ISSN 1596-2490;
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477

Figure 8. Deformation behaviour (a) 1500 kN, (b) 1750 kN, (c) 1500 kN @ Eccentricity of 25 mm
(d) 1750 kN @ Eccentricity of 25 mm

4.0 Conclusion
This paper looks inward to address the missing link on the loading position parallel to the
column axis as well as the flexural reinforcement requirement for RC column in order provide an
understanding on the complete behaviour of RC Column flexural requirement in relations with
load and its point of application for both short and slender columns. Numerical data were used
for the study analysis for both the short and slender columns under varied loads and
eccentricities condition. The study result indicates that increasing column axial load leads to an
anticipated higher flexural reinforcement to enhance the column capacity, and is rational.
Moreover, FEM analysis result for the short column similarly indicates an interesting relationship
between the deformation and loading eccentricity function. Additionally, the established
behaviour between the flexural reinforcement requirement and loading eccentricity for a
rectangular column can be predicted easily by the use established linear relations for both short
and long column types. However, the study results indicate that eccentrically loaded column
exhibits a conservative flexural requirement especially with increasing eccentricity. Hence,
reducing this high level of conservatism could be an interesting field that needs further
explorations.

(b)(a)

(d)(c)

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Kachalla Mohammed: Loading eccentricity issue on the performance of reinforced concrete columns. AZOJETE,
15(2):470-478. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: engrkachalla@unimaid.edu.ng 478

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