Slenderness Criterion for Isolated Confined Compression Member

based on EC2

Tee Horng Hean, Kousay Al-Sanjery and Jeffrey Choong Luin Chiang

Civil Engineering and Architect, Segi University, Malaysia

Keywords: Spiral, Confinement, Column, Slenderness, Eurocode.

Abstract: Clause 5.8.3.1. of the Eurocode 2 (EC2) recommends a slenderness limit (λ

lim

) for compressive members

where second order effects can be ignored. This equation shall be used to study the effects of lateral

reinforcements in the compressive member. The effects of spiral-shaped steel confinements on the reinforced

concrete columns of 9 numbers of 125mm×125mm×500mm reinforced concrete columns, all exceeding λ

lim

were investigated with one control column i.e. without any reinforcements, another four were confined with

single spiral of 50mm pitch and the last four were confined with double spiral of 100mm pitch. This result in

having the same volume of confinements introduced for all the confined concrete columns. The confinement

used for the concrete were mild steel rebars of 6mm diameter. It was found that with the introduction of

spiral-shaped steel confinements, the ultimate failure load of these columns exceeded the control sample and

hence there is a possibility of increasing the λ

lim

factor of EC2 by considering concrete confinements.

1 INTRODUCTION

For circular shaped reinforced concrete (RC)

columns, it is common for some countries to adopt

continuous spiral links. When closely spaced spiral

links are adopted, it can be considered as

confinements for concrete. Confinements enhance

reinforced concrete structural elements in

compression reducing the Poisson’s effect. The Code

of Practice, ACI 318-14 (ACI Committee 318, 2014)

recommends the provision of spiral reinforcements’

volume to approximately the strength of the column

cover / shell.

There had been researches carried out on confined

concrete elements which are normally short or also

known as stocky. For RC columns, researches

commonly carried out include adopting materials

such as fibre reinforced plastic / polymer (FRP),

carbon fibre reinforced polymer (CFRP), glass fibre

reinforced polymer (GFRP) and concrete-filled steel

tubes. There had not been many researches carried

out on the effects of confinements using ordinary

steel reinforcement bars on slender reinforced

concrete columns. More common would be

researches carried out to strengthen slender

reinforced concrete columns.

In Eurocode 2 (EC2) Clause 5.8.3.1 Slenderness

criterion for isolated members, it is recommended

that when the slenderness, λ is less than λ

lim

any

second order effects can be ignored. This research is

to investigate the effects of introducing confinements

in the form of spiral shaped mild steel in reinforced

concrete columns that exceeded the slenderness

criterion as per EC2 (Mosley et al., 2007; Bhatt et al.,

2014).

2 LITERATURE REVIEW

As early as mid-1890s, reinforcement in the form of

helical / spirals were adopted in concrete elements

and it was found that these elements have better

resistance compared to concrete with longitudinal

bars and lateral ties (Cusack, 1981). It is well noted

that increased compressive strength for confined

concrete would be expected since hooping actions

prevent the swelling of concrete and thereby able to

resist higher pressure (Considere, 1908). Stress-

strain relationship for plain concrete had been

developed by researchers Carreira and Chu (Carreira

and Chu, 1985) while Mander, Priestley and Park

developed the stress-strain relationship of confined

concrere in compression (Mander et al., 1988).

Horng Hean, T., Al-Sanjery, K. and Choong Luin Chiang, J.

Slenderness Criterion for Isolated Conﬁned Compression Member based on EC2.

DOI: 10.5220/0009007701510157

In Proceedings of the 7th Engineering International Conference on Education, Concept and Application on Green Technology (EIC 2018), pages 151-157

ISBN: 978-989-758-411-4

151

Table 1: Samples and corresponding variables used for EC2 Clause 5.8.3.1.

No. of

Rebars

Area of Long.

Rebar (mm

)



B N

(kN)





as per EC2

(unconfined)

Actual λ

used





as per EC2

(confined)

0 0 0 1 180.731 10.626 13.86 10.626

3 84.82 0.0665 1.0644 180.963 11.304 13.86 11.059

4 113.10 0.0887 1.0851 180.967 11.523 13.86 11.2

5 141.37 0.1109 1.1053 180.972 11.738 13.86 11.34

Yong, Nour and Nawy carried out experiments on

24 square columns with the dimensions of 150mm ×

150mm × 457mm and compressive strengths of

between 83.6 to 93.5N/mm2 and rectilinearly

confined with lateral ties spacing varied from 25mm

to 75mm. In general, the concrete columns were

ductile with the introduction of the links. The peak

stress and strain for both high and normal strength

concrete and especially the ductility increased when

more lateral steel were provided but however this was

not in proportionally. However, it was found that

lateral steel confinement was not as effective in low

and normal strength concrete. The authors

formulated an empirical model for stress-strain

relationship. (Yong et al., 1988).

Mangat & Azari investigated columns of

150mm×150mm×750mm with link pitches of

125mm, 187mm and 375mm with steel fibres

between 0 and 3%. The theoretical ultimate strength

of the column was calculated based on the expression

= 0.85×σ

×A

+ σ

×A

which is proportional to

the concrete characteristic strength, area of concrete,

steel characteristic strength and area of steel, without

taking into consideration of the partial safety factor

for materials. Their research results indicated that

their theoretical and experimental ultimate load only

varied between 0 to 9%. They concluded that the

strength of the compression members is unaffected by

the link spacing or steel fibre volume (Mangat and

Motamedi Azari, 1985)

Experiments on high strength concrete columns

confined with single spirals and also two opposing

spirals were conducted to study the axial behaviour of

such elements. Monotonic axial loads were applied

to the specimens. Twenty one 350mm diameter ×

1000mm tall high strength concrete circular columns

with different number of longitudinal rebars and four

different confinement ratios were tested. It was found

that the specimen with 12 longitudinal diameter

16mm rebars possessed an ultimate load of 5257kN

while the specimen with 8 longitudinal diameter

16mm rebars possessed an ultimate load of 5305kN.

The researchers concluded that the variation in the

longitudinal rebars had not establish a trend on the

effects in the confined compressive strength and

strain capacity (West et al., 2016; Marvel et al.,

2014). The purpose of having two opposing spirals

was to facilitate easy concreting whereby if

conventional single steel confinements were adopted,

two opposing spirals would create the same results

even if its pitch is twice that of the conventional one

since the confinement volume to concrete core

volume would be the same (Hindi, 2013).

BS 8110 (BSI, 1997) does not include confined

concrete whereas the current code of practice, EC2

included equations for increased characteristic

strength and strains (British Standards Institution,

2008). The strength of slender reinforced concrete

columns under uniaxial load had been evaluated

numerically using the simple transformed section

concept (Chuang and Kong, 1998). In this present

research, the capacity of columns exceeding the

slenderness limit as per EC2 had been evaluated using

the EC2’s expression for confined concrete strength.

3 RESEARCH METHODOLOGY

The λ

lim

as per EC2 Clause 5.8.3.1 is 





20/

√



and for this experiment, A and C had

been taken as 0.7.

Table 1 shows the values of the variables adopted.

Samples with confinements were used and all

exceeded the 



as shown in Table 1 in order to

study the effects of exceeding



A total of 12 prism samples were prepared and

tested under axial compression. The concrete mix

was designed to have a mean 28-day compressive

strength of 25N/mm

. The cement, sand, aggregate

proportion was 1:1:2 and the water cement ratio was

0.5. The influence of specimen slenderness was

investigated by preparing specimens with slenderness

ratios as per EC2 of 3.46, 9.24, 11.55 and 13.86 where

the last slenderness ratio exceeded the limit i.e. λ

lim

If the older code of practice, i.e. BS 8110 were

adopted, the corresponding height to least column

dimension would be 1, 2.67, 3.33 and 4 respectively

and since these are less than 10, it would had been

classified as short based on Clause 3.8.1.3 of BS

8110. The details of the test specimens are as shown

EIC 2018 - The 7th Engineering International Conference (EIC), Engineering International Conference on Education, Concept and

Application on Green Technology

152

Table 2: Specimen Properties.

Specimen (mm) Spiral Longitudinal Diameter 6 Rebar Slenderness

Ratio

Confinement

Pitch (mm)

L / Smallest

Dimension

C1 (150×150×150) None 0 3.46 1

C2 (150×150×400) None 0 9.24 2.67

C3 (150×150×500) None 0 11.55 3.33

C4 (125×125×500) None 0 13.86 4

C0R-SS Single 0 13.86 50 4

C3R-SS Single 3 13.86 50 4

C4R-SS Single 4 13.86 50 4

C5R-SS Single 5 13.86 50 4

C0R-DS Double 0 13.86 100 4

C3R-DS Double 3 13.86 100 4

C4R-DS Double 4 13.86 100 4

C5R-DS Double 5 13.86 100 4

Figure 1: Single and Double Spiral Confinements Used.

in Table 2 where C1 to C4 are pure concrete control

specimens but with different dimensions in order to

have different slenderness ratios. The dimensions of

C1 is 150mm × 150mm × 150mm, C2 is 150mm ×

150mm × 400mm, C3 is 150mm × 150mm × 500mm

and C4 is 125mm × 125mm × 500mm. The

slenderness ratios of these are 3.46, 9.24, 11.55 and

13.86 respectively. The specimens with the suffix SS

represents samples with single spiral confinements

while the specimens with the suffix DS represents

samples with double spiral confinements. The

samples denoted with C and followed by a number

and R indicates that there is additional longitudinal

reinforcement bars as per the number. Diameter 6mm

reinforcement bars with nominal yield stress of

250N/mm

were used to form both the single and

double spiral confinements. The pitch of the single

spiral confinements was 50mm whereas for the

double spiral confinements, the pitch was 100mm. All

the spirals had an outer diameter of 75mm and all

samples had a concrete cover of 25mm. These

confinements and main rebar configurations are as

shown in Figure 1.

All samples except for C1 to C3 were installed

with electronic foil strain gauges in the longitudinal

and lateral directions as shown in Figure 2. All the

samples were tested with an Automatic Compression

Testing Machine with a maximum loading capacity

of 600kN and loading was applied with a rate of

0.1kN/s. The readings of the applied load and also

the strains were recorded with a data logger. The

setup of the experiment is as shown in the Figure 3.

Figure 2: Installation of Strain Gauges on Concrete

Specimens.

Slenderness Criterion for Isolated Conﬁned Compression Member based on EC2

153

Figure 3: Experimental Setup.

4 ANALYSIS AND DISCUSSION

For Table 3, column (1) indicates the Specimen, (2)

the characteristic cylindrical strength, (3) the

characteristic confined concrete strength based on

EC2, (4) the experimental failure load, (5) the

theoretical failure load based on unconfined concrete

strength, (6) the theoretical failure load based on

confined concrete strength with the assumption that

the column is short and (7) the slenderness ratio.

4.1 Ultimate Load

The ultimate load of a compressive member is highly

dependent on the slenderness ratio that is the ultimate

load is inversely proportional to the slenderness ratio.

C1 for instance which was used as cube test, had a

slenderness ratio of 3.46 and could achieve an

ultimate load of 573.75kN while C2 with a

slenderness ratio of 9.24 achieved an ultimate load of

280.13kN. C3 had a slenderness ratio of 11.55 while

C4 had a slenderness ratio of 13.86. Both C3 and C4

achieved very similar ultimate loads that is 263.20kN

and 273.60kN respectively.

The control specimens C2 to C4 which were plain

concrete with slenderness ratios of between 9.24 and

13.86. Samples with slenderness ratio approximately

above 9 and below 14 had its ultimate load reduced to

approximately 50% compared to samples with

slenderness ratio of approximately 3.46.

For the group of samples with single confinement

having a pitch of 50mm, it was found that all

specimens exceeded the control specimen’s ultimate

load (C4) except for specimen C4RSS which was

0.74% lower than the control specimen which should

not be. C0RSS i.e. the specimen with no rebars,

managed to achieve an ultimate load of 392.2kN.

C3RSS, C4RSS and C5RSS reached the ultimate load

of 320.7kN, 271.6kN and 388.6kN respectively.

For the group of samples with double confinement

with a pitch of 100mm, it was found that all

specimens exceeded the control specimen’s ultimate

load. C0RDS, C3RDS, C4RDS and C5RDS achieved

an ultimate load of 323.2kN, 345.9kN, 443kN and

342.9kN respectively.

Column 5 of Table 3 adopted the characteristic

cylindrical strength of concrete i.e. without taking

into account of the confinement effects. Therefore, if

a comparison of the experimental ultimate load with

column 5 were to be made, it would be seen that the

values of theoretical load in column 5 will

underestimate the actual failure load. On the other

hand, if Clause 3.1.9 of EC2 (Confined Concrete)

were to be adopted, the ratio of the experimental

ultimate load (column 4) to the theoretical ultimate

load (column 6) varies from 5% below the theoretical

value to 30% above the theoretical value (see column

10). However, it should be noted that the formulas

adopted in Table 3 are based on short columns but in

actual fact the columns exceeded the slenderness ratio

limit as per EC2 yet was able to perform similar to a

short column.

The theoretical ultimate strength from the

provision of longitudinal rebars would increase as

more longitudinal rebars are introduced. It would had

been expected that with the increase in the number of

rebars for samples C0RSS, C3RSS, C4RSS and

C5RSS, a corresponding higher experimental

ultimate load would be obtained. However, for

C5RSS, it possessed a lower ultimate load compared

to the sample with no reinforcement bars i.e. C0RSS.

Similarly, it would had been expected that C5RDS

possesses a higher ultimate load compared to the

sample C3RDS and C4RDS. However, both C3RDS

and C4RDS exceed C5RDS’s ultimate load.

This is similar to the experiment carried by

Johnathan West, Ahmed Ibrahim and Riyadh Hindi,

Analytical compressive stress-strain model for high

strength concrete confined with cross spiral whereby

for their single spiral specimen with 12 longitudinal

diameter 16mm rebars had a lower ultimate load

compared to the sample with 8 longitudinal rebars.

4.2 Axial and Lateral Strain vs. Stress

The following show the axial and lateral strain vs.

stress curve of all the of the control sample C4,

C0RSS, C3RSS, C5RSS, C0RDS, C3RDS and

C5RDS. All strain units are multiplied by ×10

-6

. The

strain gauge reading of C4 indicated that the

longitudinal strain as positive i.e. tension and the

lateral strain as negative i.e. compression. It is likely

that the applied load had not been perfectly

concentric.

EIC 2018 - The 7th Engineering International Conference (EIC), Engineering International Conference on Education, Concept and

Application on Green Technology

154

Table 3: Test results of column specimens.

Specimen

(N/mm

)

ck, conf

(N/mm

)

Experimental

Theoretical

0.85f

Theoretical

= 0.85

ck,conf

conf

0.85f

gross

- A

conf

)

Slenderness

Ratio

(4) / (6) Poisson's

Ratio (at

60%

Ultimate

Load)

(1) (2) (3) (4) (5) (6) (7) (8) (9)

C1 20.4 573.75 - - 3.46

C2 20.4 280.13 390.15 - 9.24

C3 20.4 263.20 390.15 - 11.55

C4 20.4 273.60 270.94 270.94 13.86 0.14

C0RSS 20.4 32.37 392.2 270.94 315.89 13.86 1.24 0.24

C3RSS 20.4 32.37 320.7 292.14 337.09 13.86 0.95 0.16

C4RSS 20.4 32.37 271.6 299.21 344.16 13.86 0.78 -

C5RSS 20.4 32.37 388.6 306.28 351.23 13.86 1.11 0.16

C0RDS 20.4 32.37 323.2 270.94 315.89 13.86 1.02 0.13

C3RDS 20.4 32.37 345.9 292.14 337.09 13.86 1.03 0.07

C4RDS 20.4 32.37 443 299.21 344.16 13.86 1.30 0.83

C5RDS 20.4 32.37 342.9 306.28 351.23 13.86 0.98 0.25

From the graph of C4RSS it was noticed that

when the specimen experienced a stress of

approximately 11N/mm2, the reading then reduced to

about 8.5N/mn2. Also, the specimen C4RDS had

both longitudinal and lateral strains as tension. These

graphs were not included.

For rest of the curve, it can be seen that a V-shape

curve is formed. In general, it can be seen that the

horizontal distance from the peak of the axial strain

curve to the vertical axis is larger than the horizontal

distance from the peak of the lateral strain curve to

the vertical axis. Column 8 of Table 3 show the

Poisson’s Ratio of the control and the samples.

4.3 Slenderness Limit λ

lim

and Actual

Slenderness λ

Even though the samples with confinements had exceeded

the slenderness limit as per EC2, their theoretical loads

had been calculated as shown in Column (5) of Table 3

and ignoring the partial factors of safety (1.5). The

compressive design strength, N

= 0.85×f

×A

×f

If no longitudinal reinforcements were adopted, the

equation now becomes N

= 0.85×f

×A

= 270.94 kN for

specimen C4. If the similar ultimate load is obtained

based on BS 8110, it would be N

= 0.67×f

×A

266.96 kN. Columns C2, C3 and C4 achieved failure

loads of 280.13, 263.20 and 273.60kN respectively which

was ±3.3% of the control’s ultimate load. C3 and C4

possess the slenderness ratios of 11.55 and 13.86

respectively which exceeded their slenderness limits of

10.626. Sample C2 possess a slenderness ratio of 9.24

which is below the slenderness limit. However, the

experimental ultimate loads of C2, C3 and C4 were very

close suggesting that even though the slenderness limit is

10.626, it could actually be increased to 13.86.

Furthermore, it could be seen in

Table 3 that if confined concrete strength together

with the assumption of a short column, the

experimental values were close to the theoretical

values suggesting that the actual slenderness ratio of

13.86 would be safe to be considered as short column.

The average 



for the 3 rebars, 4 rebars and 5

rebars is 11.52. Based on the equation 





20/

√



, the product of the variables ABC gives

0.532 (B was taken as an average). Since the samples

exceeded the control C4’s ultimate load, the factor 20

in the equation can be increased to 24 or 





24/

√



when closely spaced confinements of

50mm were adopted.

When concrete confinements in the form of single

spiral with a pitch of 50mm were introduced to a 125

× 125 × 500 concrete sample C0RSS with no

longitudinal rebars, the failure load achieved

392.2kN. This is more than the expected failure load

of a short column i.e. 270.94kN. In other words, with

the introduction of concrete confinements, it is can be

acceptable to relax the λ

lim

as per clause 5.8.3.1 of

EC2. Similarly, the same limit 



 24/

√



Slenderness Criterion for Isolated Conﬁned Compression Member based on EC2

155

Figure 4: Stress vs. Lateral and Axial Strain for C4. Figure 5: Stress vs. Lateral and Axial Strain for C0RSS.

Figure 6: Stress vs. Lateral and Axial Strain for C3RSS. Figure 7: Stress vs. Lateral and Axial Strain for C5RSS.

Figure 8: Stress vs. Lateral and Axial Strain for C0RDS. Figure 9: Stress vs. Lateral and Axial Strain for C3RDS.

Figure 10: Stress vs. Lateral and Axial Strain for C5RDS.

can be applied for the samples with double

confinements with a pitch of 100mm or with the

equivalent confinement volume.

Clause 3.8.1.3 of BS 8110 adopted a ratio of

height to smallest unbraced column dimension and if

this ratio is below 10, then the column would be

assumed short. The same criteria applies with the

older Code of Practice i.e. CP114. The sample C4

have a height / least dimension ratio of 4 and hence is

classified as short based on the older codes of practice

i.e. BS 8110 and CP114. The failure load of C4 based

on short column assumption is also still valid since

the experimental and theoretical values are the

±2.66kN. However for samples C2 and C3, the

EIC 2018 - The 7th Engineering International Conference (EIC), Engineering International Conference on Education, Concept and

Application on Green Technology

156

theoretical exceeded the experimental values by

110.02kN and 126.95kN respectively which is not

favourable.

4.4 Confined Compressive Strength

with Slenderness Ratio of 13.86

All the samples with confinements exceeded the

limit, 



as recommended by Clause 5.8.3.1 of EC2

and comparing the control sample C4 with the rest of

the samples, all samples except for C4RSS exceeded

the control column C4 by between 17% to 43% for

the single spiral confinement and 18% to 62% for the

double confinement. On average, the experimental

values exceed the control by 25% for the single spiral

confinement and 33% for the double confinement.

5 CONCLUSION

The introduction of confinements especially closely

spaced confinements such as confinements at 25mm

centres will enhance the ultimate strength of the

concrete column even though columns with their

slenderness ratios exceeding the limit as

recommended by EC2. It is proposed that the

slenderness limit 



 20/

√

 be increased to





 24/

√

.

NOMENCLATURE

1/10.2







√

12

1.7







= the effective creep ratio and if this is not known

then A is assumed as 0.7.

 = the ratio of products A

to A

n = the ratio of N

to A

cd .

= design axial load which was taken based on the

amount of longitudinal reinforcement bars and also

concrete cross section

ACKNOWLEDGEMENTS

The authors would like to express appreciation to

final year project students Alex Bwalya, Ibrahim

Alibrahim and Hael Matouk for their hard work and

discipline during the project.

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Slenderness Criterion for Isolated Conﬁned Compression Member based on EC2

157