Stirrup effects on compressive strength and ductility of confined concrete columns

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1 See discussions, stats, and author profiles for this publication at: Stirrup effects on compressive strength and ductility of confined concrete columns Article in World Journal of Engineering December 2013 DOI: / CITATION 1 READS authors, including: Jure Radnić University of Split 88 PUBLICATIONS 141 CITATIONS SEE PROFILE Radoslav Markić University of Mostar 9 PUBLICATIONS 5 CITATIONS SEE PROFILE A. Harapin University of Split 59 PUBLICATIONS 117 CITATIONS SEE PROFILE Goran Baloevic University of Split 23 PUBLICATIONS 53 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Croatian Science Foundation project IP : Seismic base isolation of a building by using natural materials - shake table testing and numerical modeling View project Croatian Science Foundation project UIP : Influence of Creep Strain on the Load Capacity of Steel and Aluminium Columns Exposed to Fire View project All content following this page was uploaded by A. Harapin on 30 October The user has requested enhancement of the downloaded file.

2 STIRRUP EFFECTS ON COMPRESSIVE STRENGTH AND DUCTILITY OF CONFINED CONCRETE COLUMNS Jure Radnic*, Radoslav Markic, Alen Harapin, Domagoj Matesan, Goran Baloevic Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Split, Croatia. Abstract: The results of experimental testing of stirrup effects on compressive strength and ductility of axially loaded confined reinforced concrete columns of rectangular cross-section are presented. Effects of different concrete strengths and different stirrup bar diameters and spacing on column bearing capacity and ductility have been researched. Key words: experimental testing, confined column, compressive strength, stirrup effects. * Prof. Jure Radnić PhD; University of Split, Faculty of Civil Engineering and Architecture, Matice hrvatske 15, Split; Croatia; tel ; fax ; . jure.radnic@gradst.hr

3 1. INTRODUCTION Lateral strain occurs due to longitudinal stress in beam elements. For non-reinforced concrete elements stressed to about 95% of concrete compressive strength, the ratio between free lateral and longitudinal strain is about 0,20 (Poisson's ratio). In reinforced concrete columns with closed stirrups as transverse reinforcement, there is a transverse horizontal pressure of concrete on stirrups, due to concrete strain in that direction. The consequence is tension in stirrups. On the other hand, stirrups resist free lateral strain of concrete i.e. they induce reactive lateral pressure on concrete. Lateral pressure depends on stirrup form and spacing, steel bar diameter, column cross-section, concrete type, longitudinal column reinforcement and other parameters. Lateral pressure on concrete increases longitudinal compressive strength and deformability (ductility) of column. This contribution is usually not taken into account in engineering calculations, unless stirrups are shaped as dense spiral reinforcement. In order for stirrups to take over lateral pressure of concrete, a sufficient bar overlap is needed. Some of the most commonly used forms of standard stirrups in columns of rectangular cross-section are shown in Figure 1. Stirrups formed as shown in Figure 1 (a) are still in use. That is an unfavorable solution since stirrups are not closed. Those stirrups can bear limited tensile force. More favorable are stirrups shown in Figure 1 (b), where bars are overlapped. The best solution is shown in Figure 1 (c), where bars overlap along shorter column side and along short rectangular hooks. Engineering presentation of lateral pressure forming in concrete and forces in stirrups for square cross-section is shown in Figure 2. (a) (b) (c) Figure 1. Some of the most common forms of standard stirrups in rectangular cross-section columns

4 (a) Lateral distribution (b) Longitudinal distribution Figure 2. Engineering presentation of force and deformation transfer in column of square cross-section subjected to compression The state of stresses and deformations in columns of circular cross-section (Figure 3a) is more homogeneous than in columns of square cross-section, while for columns of complex cross-section or complex stirrup form is far more complex (Figure 3b). Many experimental studies of confined concrete columns subjected to compression were performed. Some of them can be found in [1 13]. However, further investigations are always most welcome.

5 (a) Circular cross-section column (b) Columns of complex cross-section or complex stirrup form Figure 3. Distribution of lateral pressure on concrete depending on the column cross-section type and stirrup form This paper presents the results of experimental testing of axially loaded concrete columns of square cross-section subjected to compression without longitudinal reinforcement. Effects of different concrete strength, different stirrup spacing and diameter on the bearing capacity and stress-strain state of tested elements were researched. For each case three identical samples were made and tested. The presented results are the averages of measured values. Description of the performed experiments, obtained results and main conclusions are given hereinafter. The aim of this research was: (i) (ii) Confirmation of the existing and obtaining new knowledge on stirrup effects on compressive strength and ductility of concrete columns. Testing of numerical models for static, dynamic and time dependent analyses of concrete structures, which include the stirrup effects on compressive strength of columns.

6 2. BASIC DATA OF TESTED ELEMENTS Concrete columns of 600 mm height and square cross-section of mm (Figure 4) were tested. Columns were loaded with increasing axial compressive force P up to failure. Longitudinal column shortening depending on the force P was measured. Force increment was 25 kn, while smaller increments were applied after concrete yielding. Column behavior was monitored until its ultimate strength was reached. Behavior of column in so-called ''softening'' zone was not monitored. Longitudinal strain ε (ε = /h) and stress σ (σ = P/a 2 ) of concrete were calculated based on the measured displacement. Diagrams P-, depending on concrete strength, as well as stirrup spacing and diameter, were presented for all samples. h = 600 mm ; a = 100 mm P = longitudinal compressive force = longitudinal column shortening ε = /h = longitudinal compressive strain σ = P/a 2 = longitudinal compressive stress Figure 4. Tested concrete columns Stirrups were made of plain reinforcing steel St 500/560 MPa. Stirrup details are shown in Figure 5. Effect of three different stirrup diameters was analyzed: φ = 4 mm (φ4), φ = 6 mm (φ6) and φ = 8 mm (φ8). Figure 5. Stirrup details Stirrup spacing (e), shown in Figure 6, was also researched. Namely, elements without stirrups were tested, as well as elements with stirrups at the following spacing: e = 150 mm, e = 100 mm, e = 75 mm and e = 50 mm.

7 Figure 6. Analyzed stirrup spacing Three different concrete strengths were analyzed: relatively low (f c = 24,9 MPa), relatively medium (f c = 35,2 MPa) and relatively high (f c = 45,1 MPa), where f c is uniaxial compressive strength of concrete prism of mm in size obtained on the day of column testing. Concretes were prepared using solid limestone aggregate with the maximum grain size φ ag = 8 mm, Portland cement and admixtures. Water/cement ratio for different mixtures ranged between 0,42 and 0,55. Bulk density of concrete ranged between 2350 kg/m 3 and 2420 kg/m 3 on the day of testing. Analyzed cases are given in Table 1. Therefore, a total of 39 different cases were analyzed (with different concrete strength, as well as stirrup spacing and diameter), i.e. a total of 3 39 = 117 columns were made and tested. Table 1: Analyzed cases The following ratios between stirrup spacing (e) and column width (a) for tested columns were analyzed: e/a = ; 1,5; 1; 0,75 and 0,50. Since the maximum grain size of aggregate was φ ag = 8 mm, the ratios between stirrup spacing e and φ ag were as follows: e/φ ag = ; 18,75; 12,5; 9,38 and 6,25. Transverse reinforcement percentage µ s (µ s = 100A s /A c ) is given in Table 2, where A c is column cross-section area (A c = a 2 ) and A s is cross-section area of all transverse stirrups per column length unit (A s =0,25πφ 2 /e). As can be observed, µ s varies from 0 % to 10 %. In practice, µ s usually ranges from 0,3 % to 3 % for columns. For columns with spiral reinforcement, it usually amounts up to about 9%. It should be observed that very high µ s were adopted as limit value, but also that the maximum grain size of aggregate is φ ag = 8

8 mm. Namely, as it was mentioned, the smallest selected e/φ ag ratio is 6,25. In practice, for columns made of standard concrete (φ ag = 32 mm), e/φ ag ratio usually decreases to about 3,0, and even to about 2,0 for columns with spiral reinforcement. It is well known that e/φ ag ratio has a great influence on bearing capacity in compression. Table 2: Transverse reinforcement percentage (µ s ) for columns 3. PRESENTATION AND DISCUSSION OF OBTAINED RESULTS Measured values of force-shortening (P - ) relationship for columns made of concrete f c = 24,9 MPa are shown in Figure 7, for columns made of concrete f c = 35,2 MPa in Figure 8, and for columns made of concrete f c = 45,1 MPa in Figure 9. All three figures show similar behavior: Ultimate strength capacity and ultimate shortening of a column increase with the amount of transverse reinforcement, i.e. by decreasing stirrup spacing (e) and increasing stirrup diameter (φ). For the same transverse reinforcement area (A s = 0,25πφ 2 /e), columns with smaller spacing between stirrups (e) have higher strength capacity and higher ultimate shortening. In many cases, higher ultimate strength capacity and ultimate shortening of a column were achieved for smaller total area of transverse reinforcement (A s ) and smaller stirrup spacing. Namely, stirrups φ4 mm at e = 50 mm spacing (A s = 251 mm 2 /m) are more efficient than stirrups φ8 mm at e = 75 mm spacing (A s = 670 mm 2 /m), or stirrups φ4 mm at e = 75 mm spacing (A s = 168 mm 2 /m) are more efficient than stirrups φ8 mm at e = 100 mm spacing (A s = 502 mm 2 /m), or stirrups φ4 mm at e = 100 mm spacing (A s = 126 mm 2 /m) are more

9 efficient than stirrups φ8 mm at e = 150 mm spacing (A s = 335 mm 2 /m) etc. The stirrup spacing e, i.e. e/a g ratio is the main factor that has influence on ultimate strength capacity and ultimate shortening of a column. An increase of ultimate strength capacity of the column with stirrups φ8 mm at e = 50 mm spacing, in comparison with the column without stirrups, was about 80 % for all three concrete strengths. Namely, the ratio between appropriate strength capacity of the column with the transverse reinforcement and the same one without stirrups, is almost non-dependant on concrete strength. E.g. for stirrups φ4mm at e = 100 mm spacing (µ s = 1,26 %, e/φ ag = 6,25), the increase in ultimate compressive strength capacity was about 22 % for all concrete strengths. In practice, that case approximately corresponds to the column cross-section mm reinforced with φ10/150 mm (µ s =1,30 %, e/φ ag = 4,70). Standard amount of stirrups in practice increase ultimate compressive strength capacity of columns. Usually, that contribution is not taken into account in calculations of column strength capacity. The increase of column shortening, when ultimate strength capacity is achieved for stirrups φ8mm at e = 50 mm spacing in respect to the column without stirrups, was about 60 % for all three concrete strengths. I.e. ratio between shortening of the column with the transverse reinforcement and the same one without stirrups has small effect on concrete strength. Columns made of higher concrete strength have higher ultimate strength capacity and smaller shortening (ductility) than columns made of smaller concrete strength. Relationships between respective strength capacity and ductility of columns are almost non-dependant on transverse reinforcement (stirrups). Elastic behavior of columns without stirrups is up to about 0,35f c for f c = 24,9 MPa, up to about 0,50f c for f c = 35,2 MPa and up to about 0,60f c for f c = 45,1 MPa. Elastic behavior zone also extends with the increase in stirrup diameter. Thus for e.g. e = 50 mm and φ8 mm, it extends to about 0,45f c for f c = 24,9 MPa, to about 0,55f c for f c = 35,2 MPa and to about 0,65f c for f c = 45,1 MPa. Figures show stress-strain (σ-ε) diagrams for analyzed columns, where σ and ε were calculated from measured values of P and (σ=p/a 2, ε= /h). Those diagrams are affine to P- diagrams and also prove previously listed conclusions. As can be observed, at ultimate strength capacity of non-reinforced columns, strain was: for f c = 24,9 MPa about 3,7, for f c = 35,2 MPa about 3,2 and for f c = 45,1 MPa about 2,7. Crushed concrete

10 strains would be greater, but they could not have been monitored with the available equipment after concrete strengths were reached. Obviously, stirrups significantly increase concrete ductility. It can be observed that columns without stirrups have smaller failure stresses than previously determined concrete strengths f c on specimens. As can be observed, failure stresses of columns without stirrups were about: σ = 21,5 MPa for f c = 24,9 MPa, σ = 30,0 MPa for f c = 35,2 MPa, and σ = 38,0 MPa for f c = 45,1 MPa. This decrease in strength in respect to f c is a consequence of greater height and greater slenderness of the column in comparison with 250 mm high prism. In comparison to columns without stirrups, columns reinforced with stirrups φ8mm at e=5 cm spacing have about 80% higher concrete strength for all samples. Thus, concrete strength for columns made of concrete f c = 24,9 MPa is σ = 37,5 MPa, for columns made of concrete f c = 35,2 MPa strength is σ = 52,5 MPa and for columns made of concrete f c = 45,1 MPa strength is σ = 66 MPa. Initial modules of elasticity of concrete for columns with and without stirrups are almost the same. Initial modulus of elasticity for columns made of concrete fc = 24,9 MPa was about 32,2 GPa, for concrete fc = 35,2 MPa was about 34,6 GPa and for concrete fc = 45,1 MPa was about 37,1 GPa. Tangential modulus of elasticity for confined concrete increases with the increase in stirrup amount (primarily with the decrease in stirrup spacing and then with the increase in stirrup diameter). Thus, total shortening of columns, i.e. its ductility, increases with the increase in stirrup amount.

11 Figure 7. Force (P) shortening ( ) relationship for columns made of concrete f c =24,9 MPa Figure 8. Force (P) shortening ( ) relationship for columns made of concrete f c =35,2 MPa

12 Figure 9. Force (P) shortening ( ) relationship for columns made of concrete f c =45,1 MPa Figure 10. Stress (σ) strain (ε) relationship for columns made of concrete f c =24,9MPa

13 Figure 11. Stress (σ) strain (ε) relationship for columns made of concrete f c =35,MPa Figure 12. Stress (σ) strain (ε) relationship for columns made of concrete f c =45,1 MPa

14 Failure mechanism of all columns was caused by concrete crushing at their mid-height, always between two adjacent stirrups. None of the stirrups was broken or significantly deformed. Failure at column mid-height is the consequence of the greatest effect of column slenderness in that zone. Failure was induced at about half of the spacing between the adjacent stirrups, due to the greatest free lateral strain of concrete. Typical column failure mechanisms depended on stirrup spacing are shown schematically in Figure 13. Typical failure zones in columns are shown in Figure 14. Figure 13. Typical column failure mechanisms (concrete crushing zones) Figure 14. Typical failure zone in columns

15 4. CONCLUSION Ultimate strength capacity and ultimate shortening of tested confined concrete columns increase with the amount of transversal reinforcement. Effect of stirrup spacing is greater than the effect of their cross-section area. With the same transversal reinforcement amount per column length unit, columns with smaller stirrup spacing have greater strength capacity and greater ductility. In comparison with the columns without stirrups, the concrete compressive strength of the analyzed columns with the greatest amount of transversal reinforcement was greater by about 80%, while ductility was about 60% greater (listed ductility refers to the state when ultimate strength capacity is reached and not at real failure). Strength capacity and ductility ratios of confined columns with stirrups and those without them are almost non-dependant on concrete strength. Columns made of higher strength concrete have higher compressive strength capacity and smaller ductility than columns made of smaller concrete strength. It is recommended to apply stirrup spacing as small as possible, for the same percentage of reinforcement by stirrups. Smaller diameter stirrups at smaller spacing are more favorable than greater diameter stirrups at greater spacing. It is favorable from the standpoint of increase in concrete compressive strength, decrease in buckling length of longitudinal compressive reinforcement bars and increase in column shear strength capacity. All stirrups shall be sufficiently overlapped to take over the maximum tensile force. ACKNOWLEDGEMENTS This work was supported by the funds of the Ministry of Science, Education and Sport of Croatia. The authors appreciate their financial support.

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