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Response of self-compacting concrete filled tubes under eccentric compression
Journal of Constructional Steel Research 67 (2011) 904–916
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Response of self-compacting concrete filled tubes under eccentric compression Giovanni Muciaccia ∗ , Francesca Giussani, Gianpaolo Rosati, Franco Mola Department of Structural Engineering, Politecnico di Milano, 20133 Milano, Italy
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Article history: Received 7 March 2010 Accepted 8 November 2010 Keywords: SCC Buckling Concrete filled tube Confined concrete
abstract Self-Compacting Concrete (SCC) use is spreading worldwide and it is becoming a regular solution in some special applications, including steel–concrete composite columns. In the particular case of Concrete Filled Tubes (CFT), the main advantage from a practical point of view in the use of SCC consists in employing the steel tube as a formwork to directly cast concrete inside it, without the need of vibration. The study of three different concretes for structural applications as composite elements is presented, each of them designed for a 28-day cylindrical compressive strength of 50 MPa: (i) a Normal Vibrated Concrete, (ii) a Self-Compacting Concrete, (iii) an expansive SCC (with the goal of an increase in bond strength as a consequence of the expansion). CFT with critical length ranging from 131 cm to 467 cm have been experimentally and analytically investigated in uniaxial compression. In each case the steel case presents a cross section of 139.6 mm of external diameter and 4.0 mm thickness and with a fixed eccentricity of the applied load equal to 25 mm. The bond strength at the steel–concrete interface is reported for each of the three mixes. The experimental and analytical results show that the behavior of eccentrically loaded columns is governed by the bending moment–axial load interaction. As a consequence, perfect bond at the interface can be assumed and the axial capacity of the column is only a function of its geometry and of the mechanical properties of the materials. A numerical procedure is proposed to evaluate the increase in the axial capacity of the composite columns consequent to the confinement of the internal concrete in case of zero-eccentricity of the applied axial load with respect to the column’s axis. Finally, the obtained numerical results are introduced into code provisions to evaluate modified axial force N-bending moment M interaction diagrams to predict the axial capacity of the column in the particular test configuration. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Self-Compacting Concrete (SCC) is drawing increasing interest because it allows casting of concrete without the need of trained personnel even in presence of a high congestion of the reinforcement. The applications of SCC are becoming more and more common, although some issues concerning the material characterization, code specifications and quality control still remain unsolved. In general, SCC is used for specific constructions or in precast plants. In some cases, the choice of SCC instead of ordinary concrete depends on other factors besides the absence of vibration, such as dense reinforcement, novel form of construction, economic benefits (i.e. reduced construction time, reduced labor cost)
∗
Corresponding author. Tel.: +39 0223994274; fax: +39 0223994220. E-mail addresses: [email protected] (G. Muciaccia), [email protected] (F. Giussani), [email protected] (G. Rosati), [email protected] (F. Mola). 0143-974X/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2010.11.003
and environmental conditions. Nowadays, many precast plants worldwide are using SCC because of the advantages related to the absence of vibration such as reduced illness of workers, lower maintenance costs and energy consumption. These advantages balance the higher cost of the material. Domone [1] analyzed more than sixty case studies reported in literature and derived that in most cases the use of SCC is due to technical advantages compared to conventional concrete. SCC in situ is used for a wide range of applications: bridges (towers and anchor blocks), filled columns in high rise buildings, tunnel linings and walls. Nevertheless, since the requirements of high workability and segregation resistance have both to be satisfied, the ratio among SCC constituents and, as a consequence, its mechanical properties, differ with respect to NVC. In particular the most significant difference concerns bond behavior [2]. Nonetheless, building codes have not yet been adapted to SCC. Several investigations [3–6] have been performed in order to possibly exploit the applications of Normal Vibrated Concrete (NVC) codes to SCC while a still-open question is related to the procedure adopted to check the concrete at the building site [7].
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Among the special applications in civil buildings, steel–concrete composite columns are beginning to be used more frequently, in particular Concrete Filled Tubes (CFT). From a practical point of view the main advantage is employing the steel tube as a formwork to directly cast concrete inside it, in case a limited amount of ordinary reinforcement is added. Usually, in these applications the beams also converge on the column are composite elements such that one single operation of casting is generally done for both columns and beams. The main concern is thus related to the ability of guaranteeing a proper vibration and of avoiding the absence of segregation, that is a characteristic of a self-compacting concrete, indeed. Nonetheless, some objections have been recently raised concerning the influence of bond between steel and SCC on the global behavior of the columns in presence of long-term or second-order effects. Extensive research on composite columns, in which structural steel sections are encased in concrete, has been carried out. However, in-filled composite columns, and in particular CFT, have received limited attention compared to the first ones (for an extensive review see [8]). In recent years, a few studies have been carried out on stubby SCC Filled Columns [9,10], and very few indications exist on the bond behavior [11,12]. An experimental and numerical investigation of short circular steel tubes filled by means of expansive cement is presented in [12]; furthermore [13] studied the bond capacities of similar short CFT. Nevertheless, to the authors’ knowledge, no previous studies have been performed on the bond of Self-Compacting Concrete Filled Tubes. Referring to the results reported on NVC Filled Tubes, the following factors are relevant:
• L/D ratio: columns with L/D ≤ 11 (for D/t ≤ 60, [14]) and with L/D ≤ 15 (for D/t ∼ = 90, [15]) exhibit a higher capacity
•
•
•
•
due to the increase of concrete strength resulting from triaxial confinement effects; for columns with higher L/D ratios the composite section fails due to column buckling before reaching the strains necessary to induce concrete confinement. D/t ratio: increasing the D/t ratio reduces the axial ductility performance of thin-walled CFST columns [16]; for concretefilled steel tube columns, smaller D/t ratios provide a significant increase in the yield load and exhibit more favorable postyield behavior; these effects diminish for large diameter columns [17]. Shape effect: concrete confinement can be observed in circular and in many octagonal cross sections; square tubes provide very little confinement of the concrete only in corner regions because the wall of the square tube resists the concrete pressure by plate bending, instead of the membrane-type hoop stresses [18,19]. Load transfer: the point of application of the load has a small influence on the overall behavior; nevertheless, when the steel tube and the concrete core are loaded simultaneously, the tube provides confinement only after yielding, while the effects of confinement are visible when the load is applied on the concrete surface only [20]. Failure mode: it is generally found [21] that short columns fail for steel yielding leading to local buckling associated with the crushing of concrete; medium length columns behave inelastically and fail by partial yielding of steel, crushing of concrete in compression and cracking of concrete in tension; slender columns fail according to an overall buckling mode.
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Table 1 Geometry of steel tubes. Tube length L (mm)
Diameter D (mm)
Thickness t (mm)
L/D
D/t
Eulerian slenderness λ
800 2000 3000 4000
139.6 139.6 139.6 139.6
4.0 4.0 4.0 4.0
5.7 14.3 21.5 31.5
39.9 39.9 39.9 39.9
24 48 74 106
Table 2 Mix proportions (kg/m3 ).
CEM IIAL 42.5R Filler Sand Coarse aggregate Water Super-plasticizer Expansive agent Shrinkage inhibitor Volumic mass
NVC
SCC
SCC-E
440 60 1085 585 180 2.5 0 0 2353
420 370 730 610 190 8 0 0 2328
420 340 730 610 190 7.5 33 4.2 2335
Fig. 1. Compressive strength development curves.
The experimental program presented in this paper investigates the effectiveness of Self-Compacting Concrete as an infill of steel tubular columns, the possible increase in the structural performance when introducing expansive SCC and the suitability of the code prescription when referring to SCC. Ordinary steel tube with lengths ranging from 800 mm to 4400 mm were selected. Table 1 reports, for each specimen, the tube geometry, the length to diameter and diameter to thickness ratios and the Eulerian slenderness in the test configuration. The load was applied on the concrete surface only. 2. Experimental program 2.1. Mix design Three different concretes are studied, each of them designed for a 28-day cylindrical compressive strength of 50 MPa:
• a Normal Vibrated Concrete (NVC); • a Self-Compacting Concrete (SCC); • an Expansive SCC (SCC-E, with the intention that the expansion should produce an increase in bond strength). Details of the mix compositions are given in Table 2 (quantities of the constituents are all expressed in kg/m3 ). The strength development curves for the three mixes are shown in Fig. 1. The Eurocode 2 [22] curve for NVC is also plotted according to the equation: fcm (t ) = βcc (t )fcm
where 0.5
βcc = exp{s[1 − (28/t ) ]}
(1) (2)
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Fig. 2. SCC-E, expansion development curve.
where t is the time variable, fcm is the 28-day average compressive strength and ‘‘s’’ is a factor equal to 0.20 for rapid hardening high strength concrete. Fig. 2 reports the restrained expansion development curve of the mix SCC-E measured on a specimen prepared according to [23]. To simulate the environmental conditions of the concrete within the steel tube a modification in the ASTM test procedure was introduced. In fact, in a CFT it can be assumed that the steel tube does not allow moisture exchange between the concrete core and the environment. The specimen was then wrapped with cellophane after the casting, according to Italian standards [24], and the expansion was measured beginning from the initial curing (approximately 13 h after casting). 28-days after casting a significant residual expansion of 3.2 · 10−5 can be noticed. At the time of testing the cylindrical compressive strength of the concrete was 62 MPa for all the mixes, while the steel constituting the tube was characterized by a yield stress of 374 MPa and an ultimate strength of 440 MPa.
Fig. 3. Test setup for Concrete Filled Tubes.
2.2. Preparation of the specimens The sample preparation was performed in two phases: the cutting of the steel tubes and the casting of the concrete. The first phase consisted in cutting from 6.0 m steel tubes specimens of the desired length. The cut tubes were transported to a concrete production plant (Fig. 4) where casting subsequently occurred. The bottom end of each tube was closed by a circular plastic cap of the same diameter as the internal diameter of the steel tube. The cap was embedded for 40 mm. The top end of the tube was not covered to allow the concrete to be cast in. The tubes were accurately filled up to approximatively 40 mm from the top. After curing, the filled tubes were transported back to the laboratory. Bottom caps were removed, so that the final specimens consisted of steel tubes filled with concrete except for a 40 mm length at both ends. This free length worked as a slot for the constraining devices. A series of targets was subsequently glued on each specimen. Each target represents a measurement point of displacement acquired by the photogrammetry technique, as described in Appendix. Fig. 3 shows a picture of the test setup of a 440 cm composite column highlighting the constraints at the end of the columns, the lifting system and the cameras used for photogrammetry. Fig. 4. Tubes previous casting at concrete plant.
2.3. Constraints Particular attention was devoted to the choice of proper constraints. Tests have been carried out on an MTS servohydraulic
closed-loop machine with a 2500 kN capacity, with fixed platens and under vertical displacement control. To reach a stable control after the peak load it was chosen to hinge the column at both ends
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Fig. 5. Constraints, drawings.
thickness) was placed between the concrete surface and the steel plate. 2.4. Lifting The top end of the longest specimen was at more than 6 m of height from the floor (considering also the height of the machine basement). As a consequence, it was not possible to work safely to manually connect the specimen to the testing machine at that height. It was thus chosen to connect the specimen to the upper constraint, driving it to the desired height by directly lifting the same movable head of the machine (Fig. 7). At the scope, two threaded rods were welded on the specimen, one at each end, and along the same directrix (Fig. 5). The top rod passed through a hole in the pestle and a nut was torqued on the rod to lock the specimen in the desired position. The function of the rod consisted in transferring the self-weight of the specimen to the machine during the lifting. The bottom rod had no function during the lifting. Its functions were to assure a proper positioning of the specimen and to prevent undermining of the pestle from the specimen during testing. 2.5. Data acquisition Fig. 6. Constraints, detail.
with a given eccentricity of 25 mm between the axis of the column itself and the ideal line connecting the two hinges. In this way a progressive buckling of the column was guaranteed. Moreover, a big effort was put into the design of the devices connecting the machine platens to the column. At each end two circular slotted steel plates were welded on a third steel plate clumped to the machine platen (Fig. 5). The distance between these two plates allows a third slotted steel plate to pass through them. The three holes can be aligned and a circular steel rod can pass through, acting like a hinge. The third plate is part of a second specific device whose function is to apply the load on the column (Fig. 6) and which will be referred to as the pestle. On the other end of the pestle a circular steel plate with a diameter 2 mm smaller than the column internal diameter has the function of transferring the load to the concrete surface. The columns are loaded in compression with a fixed nominal eccentricity e = 25 mm and a nominal critical length, Lcr , equal to the distance between the two hinges. The specimen ends were not identical. In fact, at one end the concrete presented a very smooth surface, due to the presence of the cap during casting, while the other end was more irregular. To guarantee a regular contact on the latter a lead disk (2 mm
The outputs of the displacement transducer and of the load cell were automatically recorded by the data acquisition system of the same MTS machine on which the load–deformation data were also continuously displayed. During the tests on the 80 cm length specimens both the vertical and the middle-span displacements were monitored by two additional LVDTs. Data were acquired by a HBM Spider8 unit and stored on a personal computer. As previously mentioned, the complete 3D displacement field was monitored by digital photogrammetry. The minimal resolutions for in-plane and out-of-plane displacement have been evaluated in 0.1 and 0.5 mm, respectively. 2.6. Experimental results Table 3 reports, for each test the test code, the peak load, the tube length, L, the distance between the bottom end and the point of maximum lateral deflection detected during testing, Li and the buckling length, Lcr . Fig. 8 (left) reports the load/vertical displacement behavior of the specimen SCC-80-1. The applied load is plotted against the displacements measured by both the machine actuator and by the external transducer and against the displacement computed by the photogrammetry technique as well. It can be noted how the three measurements basically coincide. The conclusion is twofold:
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Fig. 7. Lifting, detail.
• the displacement computed by the photogrammetry technique is reliable also for low absolute values of displacement; Table 3 CFT—results.
• the machine is very stiff with respect to the specimen. As
Code
Load kN
L cm
Li cm
Lcr cm
28 32 92.75 93.25 150 150 220
131 123 212.5 213.5 327 327 467 467
NVC NVC NVC NVC NVC NVC NVC NVC
80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
756.9 874.7 608.2 605.7 555.9 484.11 336.2 333
80 80 185.5 186.5 300 300 440 440
SCC SCC SCC SCC SCC SCC SCC SCC
80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
813.8 835.2 610.3 687.6 540.95 569 342.4 333.9
80 80 185.5 186 300 300 440 440
SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E
80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
807.1 908.7 663.5 784.1 550.6 513 373 377.7
80 79 185.5 185.5 300 300 440 440
220 40 31 47 93 150 150 220 220 40 22 92.75 92.75 150 150 220 220
107 125 304 213 327 327 467 467 107 141 212.5 212.5 327 327 467 467
a consequence, the vertical displacement measured by the machine actuator can be assumed as the vertical displacement of the specimen when direct measurements are not available. Similarly, in Fig. 8 (right) the applied load is plotted against the deflection measured by the external transducer (‘‘LVDT’’) and the displacement computed by the photogrammetry technique (‘‘Photogr’’). It is worth specifying that the horizontal transducer measures the deflection at the midspan of the column, while the ‘‘Photogr’’ displacement is the maximum deflection among all the displacement computed by photogrammetry. Hence, they do not refer to the same point and the two curves progressively detach from one another. Photogrammetry also allows a proper evaluation of the eccentricity of the applied load with respect to the axis of the column. For each specimen the eccentricity is evaluated after the application of the initial contact load (about 2 kN) as the distance between the measurement point that experienced the maximum displacement during the test and the hinge at the fixed end of the column, which corresponds to the zero point of the coordinate system. Fig. 9 reports the eccentricity of the applied load for all the tested specimens. Significant deviations from the nominal eccentricity of 25 mm at the hinges are observed, probably due to imperfections both of the steel tube and of the connecting devices.
Fig. 8. SCC-80-1, axial load versus vertical displacement (left), axial load versus deflection (right).
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Fig. 9. Eccentricity of the applied load for all the specimens.
Fig. 10. Axial load versus vertical displacement (left), axial load versus deflection (right), slenderness λ = 106.
Fig. 11. NVC-440-02 at peak load (left) and details of the plastic hinge (right).
It will be shown that this difference leads to a change in the ultimate load for specimens of the same length. Fig. 10 compares the load vs. vertical displacement (left) and the load vs. deflection (right) behavior for a Eulerian slenderness of λ = 106, for the concretes NVC, SCC and SCC-E. A similarity in the behavior for the different mixes, characterized by the same stiffness, is immediately apparent. A slightly higher value of the peak load was detected for SCC-E. This is assumed to be due to the fact that at the peak load the formation of a plastic hinge in the middle-span section is evident (Fig. 11). Fig. 12
(left) reports a three-dimensional plot of the deformed shape of the specimen NVC-440-1 at different time steps corresponding to: (i) no load applied, ‘‘Initial shape’’, (ii) the maximum load, ‘‘Peak load’’, (iii) the maximum deflection, ‘‘Max displacement’’ and (iv) the total unloading, ‘‘Residual’’. The column axis is parallel to the Z axis. A single plane of bending almost parallel to the XZ plane is clearly detectable. After the peak load an increase in the vertical displacement, and consequently in the lateral deflection, could be taken up by the column only by an increase in rotation over a portion of a certain length at a constant moment
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Fig. 12. Three-dimensional plots of the deformed shapes of specimens NVC-440-1 (left) and SCC-200-1 (right).
Fig. 13. Axial load versus vertical displacement (left), axial load versus deflection (right), slenderness λ = 24 (left) and λ = 48 (right).
(that is a plastic hinge), thus leading to decreasing the load at the end of the column and to an elastic unloading along the portions of the columns outside the plastic hinge. On the descending branch the middle-span deflection, v , is then given by v = Mpl /N where Mpl is the plastic resistant moment of the cross section while N is the load measured by the load cell. Since Mpl is also a function of the axial load N, in a load versus deflection plot the descending branch is not a perfect hyperbole. The same results have been obtained for each slenderness, with slight variations for stubby columns λ = 24, λ = 48 (Fig. 13). For slenderness λ = 48, a different behavior was observed for the two specimens of the SCC mix, Fig. 13 (right). Actually, in the case of SCC-200-01 the bottom constraint did not act as a perfect hinge (due to the very high irregularity of the concrete surface of that specimen) but it provided an end moment to the column. As a
consequence, the plastic hinge was not located in the middle of the column but closer to the bottom end, and it is apparent in the threedimensional plot of the deformed shape reported in Fig. 12 (right). This was taken into account by considering a different buckling length for the column, being equal to twice the distance between the top end and the point of maximum lateral deflection (as listed in Table 3). The reported results indicate that there is no substantial influence of the different bond strengths on the axial capacity of the columns. This can be explained by the following considerations. According to the first order theory the columns are subjected only to an axial load N = const and M = Ne = const along the entire length (e is the initial eccentricity). Shear is null and, as a consequence, no shear stresses act along the interface between concrete and steel.
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Fig. 14. Interaction domains according to Eurocodes 2 and 4.
On the other hand, second order theory predicts a shear distribution along the column having a maximum value at the base of the column (second order shear is assumed to be perpendicular to the column z axis in the deformed shape) and equal to: NV (z , t ) = N sin ϑ(z , t )
(3)
NV ,max (t ) = NV (z = 0, t ) = N sin θ0
(4)
where θ0 is the angle of rotation at the end of the column (z = 0) at time t. In the present case shear exhibits very low values, showing a negligible effect on the global behavior of the columns, as it will be numerically shown in Section 2.7. Furthermore, the identical observed stiffnesses are explained by considering that, besides being characterized by the same geometry, also the elastic moduli of the materials were the same, with a value of 32 000 MPa. The latter is assumed to depend on the similar proportioning of coarse aggregate in the mixes of NVC and SCC (Table 2). 2.7. Numerical analysis and modeling The effects of the interaction between the axial force, N, and the bending moment, M, on the resistance of the cross section can be taken into account, as common, by calculating the N versus M interaction diagram (Fig. 14). In the present investigation two different procedures are adopted:
• the column is considered as an ordinary reinforced concrete element with deformed bars all around the concrete core;
• the cross section is analyzed according to the procedures indicated in Eurocode 4 [26] for composite columns. In the first case, the steel area is considered equivalent to 51 reinforcement bars φ = 4 mm equally spaced and the interaction domain is calculated according to Eurocode 2 [22]. In the second case, the interaction domain is replaced by a polygonal diagram connecting four representative points (for details refer to Eurocode 4 [26, Section 6.7.3]). In the following analysis design values are replaced by average values. Fig. 14 shows the interaction domain of the considered columns calculated according to the two different approaches. It is apparent that they coincide in the four points calculated according to the procedure previously described. The conservativeness of the simplified domain can be reasonably accepted. ANSI/AISC 360 [27] introduces the plastic stress approach as well, assuming that no slip occurs at the steel–concrete interface
and that the width to thickness ratio prevents local buckling from occurring until extensive yielding has taken place. ANSI/AISC 360 [27] also allows for a five-point simplified interaction diagram to better reflect bending of the filled tubes. This approach is not adopted in the present work. As a general remark, it has to be considered that the design method of EC4 for CFT is valid up to a relative slenderness of 2.0 and up to a diameter to thickness ratio d/t = 90 235 . On the other f y
hand ANSI/AISC 360 [27] qualifies as a filled composite tube if the cross-sectional area of the steel is at least 1% of the total composite cross section and the D/t ratio is lower than 0.15E /fy . In the present investigation the maximum relative slenderness is 1.34, d/t = 34, 9 ≤ 56.5 = 90 235 (Eurocode 4 [26] limit) 374
and ≤ 82.2 = 0.15 205000 (ANSI/AISC 360 [27] limit) and the ratio 374 As /(As +Ac ) is equal to 12.5%. The specimens can be thus considered as fully representative of a real design case. The simplified plastic stress approach is very useful if an increase in concrete strength caused by the confinement needs to be taken into account. In fact, while for high eccentricities of the applied load the not uniformity of the confinement does not provide a significant global increase in the concrete capacity, on the other hand, for zero eccentricity the effect of confinement is not negligible. Eurocode 4 [26] suggests the following expressions to calculate the plastic resistance to compression in order to take into account the effects of confinement: Npl,R = ηa Aa fy + Ac fc
1 + ηc
t fy d fc
(5)
where Aa is the steel area, fy is the steel yielding stress, Ac is the concrete area and fc is the concrete compressive strength. For members with e = 0 (uniaxial compression) the values ηa = ηa0 and ηc = ηc0 are given by the following equations:
ηa0 = 0.25(3 + 2λ) ≤ 1.0
(6) 2
ηc0 = 4, 9 − 18, 5λ + 17λ ≥ 0
(7)
valid for an initial eccentricity of the applied load over the diameter ratio e/d = 0, where λ is the relative slenderness defined as:
λ=
Npl,R Ncr
(8)
where Npl,R is the value of the plastic resistance to compression and Ncr is the elastic critical normal force for the relative buckling
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where Nz = N is the axial force acting on the section. Equilibrium in the circumferential direction (Fig. 15—right) results in:
σrc ri = σϑa t .
(13)
One further condition is thus necessary. In the concrete core, loaded by uniform contact pressure, we assume that the following relation exists:
σrc = σϑc .
(14)
Equations from (10)–(14) can be condensed in the following matrix form:
Fig. 15. Stress components in composite columns, [25].
mode, calculated with the effective flexural stiffness (EI)eff given by:
(EI)eff = Ea Ia + Ke Ec Ic
longitudinal stress in steel, σza ; circumferential stress in steel, σϑa ; longitudinal stress in concrete, σzc ; circumferential stress in concrete, σϑc ; radial stress in concrete, σrc .
Since the radial stress in concrete, σrc , can be considered as a contact force at the steel/concrete interface, it is assumed equal to the internal pressure on the steel tube σra . To derive the five unknowns, five relationships are required. Assuming a perfect bond between steel and concrete, at the contact surface the following two compatibility equations can be written: 1
νa
1
νzcϑ
E
E
Ez
Eϑc
σa − a z
νa Ea
σza −
σa = a ϑ
1 Ea
σϑa =
σc − c z
νzrc Ezc
σzc −
1 c
Eϑ
σϑc − σϑc +
νzrc Erc
νzrc Erc
σrc
(10)
σrc
(11)
corresponding to compatibility relations in vertical (z) and circumferential (ϑ ) directions, respectively. Equilibrium in the vertical direction (Fig. 15—left) results in: Ac σzc + Aa σza − Nz = 0
(12)
− −
νa Ea 1
Ea 0 t 0
0 0
(9)
where Ke is a correction factor that Eurocode 4 [26] suggests to take equal to 0.6, Ea and Ec are the elastic moduli of steel and concrete, respectively, and Ia and Ic are the second moments of inertia of the steel section and of the uncracked concrete section, respectively. The tested columns have a relative slenderness of 0.30, 0.60, 0.93, 1.34 and a e/d ratio of 0.18, while Eurocode 4 [26] considers Eq. (5) as valid only up to a relative slenderness of 0.5 and up to an e/d ratio of 0.1. Consequently, according to EC4, no increase in the plastic resistance to compression should be taken into account. Observing ANSI/AISC 360 [27] provisions, the design compressive strength is evaluated similar to Eurocode 4 [26]. However, unlike Eurocode 4 [26], the influence of the geometry and of the material strength on the plastic resistance are not explicitly taken into account. However, a generic numerical procedure has been implemented to calculate the plastic resistance to compression of a CFT cross section that directly takes the non-linearities of the materials into account. A general procedure proposed by Brauns [25] has been initially considered. Assuming a uniform distribution of working stresses, five stress components are taken into account (Fig. 15):
• • • • •
1 Ea a ν a E a A
−
νzcϑ
1
ν
Eϑ 1
A 0 0
Eϑc 0 0 −1
−
νzrc a σz Erc 0 c σ a νzr ϑ 0 c · σz = Nz Erc σ c 0 0 ϑ 0 σrc −r i
c
Ezc c zr Ezc c
(15)
1
that is: Ax = b.
(16)
The effects of confinement are taken into account by adopting the following uniaxial constitutive law for concrete (Eurocode 2 [22]):
σzc = fc ,c
εc 1−1 1− c σr
2
for 0 ≤ εc ≤ εc2,c
σzc = fc for εc2 ≤ εz ≤ εcu2,c
(17) (18)
with:
f c ,c = f c
f c ,c = f c
1000 + 5.0
σϑc
for σ2 ≤ 0.05fc
fc
σ 1.125 + 2.50 ϑ fc c
for σ2 > 0.05fc
εc2,c = εc2 (fc ,c /fc )2
(19)
(20) (21)
εcu2,c = εcu2 + 0.2σϑ /fc c
(22)
where fc is the compressive strength, εc2 is the strain at reaching the maximum strength and εcu2 is the ultimate strain. To take the effects of radial crack formation into account, after reaching the tensile strength value at σϑc , the Poisson ratio is set equal to 0.4 that considers the structural effect of a larger lateral expansion of the concrete after cracking. The Von-Mises yield criterion is adopted for steel:
(σza )2 + (σϑa )2 − σza σϑa − fy2 = 0.
(23)
No hardening is considered. The procedure consists in increasing the applied load, Nz , until the maximum strain, εcu2,c , is reached. At each load step the following operations are performed: 1. 2. 3. 4. 5. 6. 7.
computing the matrix A; solving Eq. (16) for x: x = A−1 b; evaluating strains; computing confined strength for concrete; checking for steel yielding; checking for ‘‘racked concrete Poisson effect’’; updating stiffnesses and checking convergence.
Stress components versus vertical strains obtained are reported in Fig. 16 (left).
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Fig. 16. Stress components versus vertical strains, both NVC and SCC (left) and SCC-E (right).
It is worth noting the change in the sign of σϑa (indicated as ‘‘steel hoop’’ in the plot). The change occurs after σϑc reaches the tensile strength and, as a consequence, the Poisson ratio is set equal to 0.4. In the absence of prestress, the confinement of the concrete provided by the steel is a passive confinement. In the present case, the steel contribution ratio δ = (Aa fy )/(Npl,R ) is very high, such that the confinement is not active until 67% of the plastic resistance of the cross section is reached. It can also be noticed that the maximum vertical stress in concrete is about 92 MPa, which is 53% higher than the unconfined cylindrical compressive strength. Plastic resistance to compression is finally evaluated in 1925 kN, representing an increase with respect to the unconfined plastic resistance of approximatively 45%. Additionally, for SCC-E, the initial expansion (as reported in Fig. 2) can be taken into account by decomposing the total concrete strain into the concrete net elastic strain component, εc , (for stress calculation) and the concrete elastic offset component, εc0 . Since the core concrete is free to expand in the vertical direction, it is assumed that expansion is effective only in the circumferential and radial directions. As a consequence, Eq. (11), representing the compatibility relation in the circumferential direction, ϑ , results in:
νa Ea
σza −
1 Ea
σϑa =
νzrc Ezc
σzc −
1 c
Eϑ
σϑc −
νzrc Erc
σrc + εϑ,exp
(24)
where εϑ,exp accounts for the expansion (elastic offset) of the concrete. The known term of Eq. (15) then modifies into:
0
M (N ) =
(25)
0 Stress components versus vertical strains obtained for the expansive concrete are reported in Fig. 16 (right). It can be noticed how the plastic resistance increases by approximatively 62.8% and 12.5% with respect to the unconfined one and to the confined one not accounting for expansion, respectively. The effect of the expansion is to introduce an initial active confinement in the concrete. As a consequence radial cracking is reached for a higher value of the vertical strain (around 1.79h against 1.49 h in the absence of expansion). This results in a higher value of the concrete circumferential stress and thus in a higher value of both the strain at the maximum strength and of the concrete confined strength (Eq. (19)). A simplified domain taking into account the effects of confinement and of expansion for point A is plotted in Fig. 17. Five additional curves are plotted. The dark dashed line represents a constant ratio between M and N equal to the inertia
β 1−
N Ncr,eff
eN
(26)
where β is an equivalent moment factor taken as 1.1 and Ncr,eff is the critical normal force corresponding to the effective flexural stiffness given in Eq. (9). In computing the effective stiffness, the Ke factor appearing in Eq. (9) is taken equal to 1.0 if M (N ) curves entirely belong to the uncracked concrete field, otherwise equal to 0.6. Ratios of ultimate loads to values calculated according to the several proposed criteria are plotted for the different mixes in Fig. 18 (a value higher than one is conservative). All the values are reported in Table 4 where P indicates the ultimate load. For each specimen the initial eccentricity has been evaluated according to the photogrammetric measurements, as reported in Fig. 9. Provisions according to the Merchant–Rankine criterion are also reported. The Merchant–Rankine (MR) criterion considers a failure by a cinematic mechanism with a plastic hinge in the middle of the column and it evaluates the axial capacity of the column N in: 1 N
εϑ,exp Nz . 0
radius of the homogenized section (φ/4 = 44.1 mm) and divides the field in which no fiber of the section is subjected to a tensile stress, and thus concrete is non-cracked (right), from the field in which tensile stresses are present and then concrete cracks (left). The remaining curves represent the II order M (N ) relationships given by EC4 for the four different slendernesses considered:
=
1 Ncr
+
1 Npl
.
(27)
The axial capacity predicted by the MR criterion is substantially correct for slender columns but dramatically higher for stubby columns, since the criterion does not consider the reduction in Mpl due to the axial force, N. For slender columns Mpl does not significantly vary as a function of N and the provisions according to the four proposed criteria basically coincide. On the other hand, the proposed procedure correctly predicts also the axial capacity of stubby columns, accounting for the effects of either the confinement only or the confinement coupled with the expansion. For each concrete the ‘‘unconfined’’ criterion results in more conservative predictions than the ‘‘confined’’ one. It is also noted that, for SCC-E, the ‘‘confined+expansion’’ criterion gives more accurate results. On the basis of the presented results the observed independency of the axial capacity from the bond properties of the different mixes can be explained. The second order shear at the basis of the column at the limit of formation of the plastic hinge can be evaluated according to Eq. (3) taking the average values of deflection, v , and of the angle of rotation, θ , measured during the tests. Table 6 reports, for each column, the buckling length, Lcr , the
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Fig. 17. Interaction domains and M (N ) curves for different slenderness.
Fig. 18. Ratios of ultimate loads to values calculated according to the proposed criteria.
average values of midspan deflection, v , the angle of rotation at the end of the column, θ , the average value (for each column length) of the II order shear, NV and the corresponding values of the interface shear stress, τ , calculated according to the classical Jourawsky theory, τ = (NV S )/(Ib), where S and b are the static moment and
the chord width, respectively, at a distance from the center of mass of the uncracked homogenized section equal to the internal diameter rint = 65.8 mm of the cross section itself. Bond strength was previously investigated on slices of 50 mm height obtained by steel tubes and subsequently cast with a
G. Muciaccia et al. / Journal of Constructional Steel Research 67 (2011) 904–916 Table 4 Predicted values of peak load. Lcr
Punconf
Pconf
NVC NVC NVC NVC NVC NVC NVC NVC
Code 80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
131.0 123.0 212.5 213.5 327.0 327.0 467.0 467.0
687.1 701.1 593.6 645.9 467.5 477.2 348.4 366.2
733.9 753.3 610.1 672.7 467.5 477.2 348.5 366.2
Pconf.exp
1242.4 1275.8 912.9 909.2 575.8 575.8 346.0 346.0
SCC SCC SCC SCC SCC SCC SCC SCC
80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
107.0 125.0 304.0 213.0 327.0 327.0 467.0 467.0
755.2 726.6 547.4 837.3 593.0 587.8 316.0 300.0
829.7 787.9 552.6 924.0 601.8 596.0 316.0 300.0
1341.2 1267.5 630.5 911.0 575.8 575.8 346.0 346.0
SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E
80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
107.0 141.0 212.5 212.5 327.0 327.0 467.0 467.0
736.4 776.5 645.9 661.0 539.7 477.9 328.9 319.2
803.2 856.0 674.2 693.0 543.3 477.9 328.9 319.2
824.5 877.0 680.9 700.6 545.0 507.5 328.9 319.2
MR
1341.2 1200.3 912.9 912.9 575.8 575.8 346.0 346.0
Table 5 Bond strength results.
915
slenderness ranging from 24 to 106 have been experimentally investigated in eccentric compression with particular attention to the bond behavior between the concrete core and the steel tube. The experimental and analytical results lead to the following conclusions:
• the behavior of eccentrically loaded columns is ruled by bending moment–axial load interaction. As a consequence, a perfect bond at the interface can be assumed; • the axial capacity of the column is only a function of its geometry and of the mechanical properties of the materials; • the axial capacity of the column can be evaluated by adopting the Eurocode 4 approach, with slight modifications related to the effects of the confinement of the internal concrete. In Concrete Filled Tubes the use of Self-Compacting Concrete allows to avoid the vibration process, which is costly and hard to execute for the considered shape. The presented results confirm many previous findings on Normal Vibrated Concrete, in particular regarding the influence of the L/D ratio and the failure mode. It is found that the use of Self-Compacting Concrete, in place of Normal Vibrated Concrete, does not require a different approach in the design procedure of CFT. However, further investigation is required to account for different D/t ratios and for different amounts of coarse aggregate in the concrete mix, which could influence the stiffness of the concrete and, as a consequence, the global behavior of the columns. Acknowledgements
Code
Load kN
Average τm MPa
CoV (%)
NVC 01 NVC 02 NVC 03 SCC 01 SCC 02 SCC 03 SCC-E 01 SCC-E 02 SCC-E 03
12.01 14.48 24.38 26.97 9.75 23.54 128.58 133.41 105.81
1.20
45.4
1.08
48.1
6.15
8.7
The authors wish to extend their gratitude to A. Faccini and M. Corcella for the help concerning the experimental program. Special thanks to D. Spinelli and A. Desteffani for their help in setting up the experimental apparatus and to M. Degliuomini and M. Pini for setting up the photogrammetry apparatus and for data processing. Deep gratitude goes to L. Buzzi for his support in the investigation and for the concrete supply. Appendix. Photogrammetry
Table 6 II order shear and interface shear stress. Lcr
v
θ
NV (kN)
τ (MPa)
107 212.5 327 467
3.3 4.3 5.3 7.5
89.189 89.075 89.064 88.818
12.01 11.52 8.65 6.98
0.59 0.57 0.42 0.34
bonded length of 40 mm. It can be noticed how the maximum interface shear stress (Table 6) is lower than the lower bond strength reported in Table 5 for NVC (τm = 1.08 MPa). As a consequence, brittle failure caused by debonding at the interface is prevented. In fact, no debonding has been observed at the end of the tests. It has been shown that the loading scheme does not induce shear stresses at the steel–concrete interface high enough to exceed the bond strength. As a development of the presented research, in order to evaluate the shear force–bending moment interaction of the composite member, the longer tested columns have been cut in three sectors. The two sectors which underwent an elastic unloading after the peak load will be subjected to four-point bending tests with a proper shear length such to induce high interface stresses. 3. Conclusions A study of SCC for structural applications as composite elements was presented. Concrete Filled Tubes (CFT) with Eulerian
Techniques of digital photogrammetry are suited for tasks requiring a large number of measurement points distributed over an object surface. The use of photogrammetry in material testing experiments generally allows for the simultaneous measurements of displacement at an almost arbitrary number of locations over the camera’s field of view. Data processing is highly automated and fast, allowing for real-time monitoring at the camera image rate. The adopted system consists of two Nikon digital cameras (one D80 model and one D100 model) and one notebook for each camera for image acquisition. Image acquisition is automated and the measurement of the absolute coordinates and the movement of signalized targets on the specimen is solved by the commercial software package Photomodeler Scanner. Camera calibration is achieved by self-calibrating bundle adjustment based on taking multiple images of the same object from different viewing directions and orientations with each camera to be calibrated before the test. Proper horizontal support braces were designed to connect the cameras to existing vertical steel columns. One main issue consisted in determining the camera positions to completely frame the specimens and, at the same time, to reach the desired resolution (the minimal resolution for in-plane displacement has been evaluated as 0.1 mm). Proper horizontal support braces have been designed for each camera to connect them to the existing vertical steel columns.
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Fig. 19. Camera setup.
The position of the columns and of the cameras during the tests are depicted in Fig. 19. In the drawing the test apparatus is located in the lower left corner. For each column length, cameras were located at different height from the ground ‘‘h’’ and distance ‘‘d’’ from the monitored object (the column). References [1] Domone P. A review of the hardened mechanical properties of self-compacting concrete. Cement and Concrete Composites 2007;29(1):1–12. [2] Cattaneo S, Rosati G. Bond between steel and self-consolidating concrete: experiments and modeling. ACI Structural Journal 2008;106(4):540–50. [3] Sonebi M, Bartos P. Bond behavior and pull-out test of self-compacting concrete. In: Proc. of RILEM int. symp. bond in concrete from research to standards. 2002. p. 511–9. [4] Paultre P, Khayat KH, Tremblay S. Structural performance of self-consolidating concrete used in confined concrete columns. ACI Structural Journal 2005; 102(4):560–8. [5] Galano L, Vignoli A. Strength and ductility of HSC and SCC slender columns subjected to short-term eccentric load. ACI Structural Journal 2008;3(3): 259–69. [6] Cattaneo S, Giussani F, Mola F. Flexural behaviour of reinforced, prestressed and composite self-compacting concrete beams. In: Fourth north American conference on the design and use of self-consolidating concrete SCC2010. 2010. [7] Cattaneo S, Giussani F, Mola F. In situ quality control of self-compacting concrete. In: Third north American conference on the design and use of selfconsolidating concrete SCC 2008. 2008. [8] Shanmugam NE, Lakshmi B. State of the art report on steel–concrete composite columns. Journal of Constructional Steel Research 2001;57(10):1041–80. [9] Han L-H, Yao G-H. Experimental behaviour of thin-walled hollow structural steel (HSS) columns filled with self-consolidating concrete (SCC). Thin-Walled Structures 2004;42(9):1357–77. [10] Lin C-H, Hwang C-L, Lin S-P, Liu C-H. Self-consolidating concrete columns under concentric compression. ACI Structural Journal 2008;105(4):425–33. [11] Shakir-Khalil H, Al-Rawdan A. Composite construction in steel and concrete, vol. 3. ASCE; 1994. p. 222–235.
[12] Chang X, Huang C, Jiang D, Song Y. Push-out test of prestressing concrete filled circular steel tube columns by means of expansive cement. Construction and Building Materials 2009;23:491–7. [13] Chang X, Huang CK, Chen YJ. Mechanical performance of eccentrically loaded prestressing concrete filled circular steel tube columns by means of expansive cement. Engineering Structures 2009;31:2588–97. [14] Knowles RB, Park R. Strength of concrete-filled steel tubular columns. Journal of Structural Division, ASCE 1969;95(12):2565–87. [15] Prion HGL, Boehme J. Beam–column behaviour of steel tubes filled with highstrength concrete. In: Fourth international colloquium. SSRC. 1989. p. 439–49. [16] Liang QQ. Strength and ductility of high strength concrete-filled steel tubular beam–columns. Journal of Constructional Steel Research 2009;65:687–98. [17] Schneider S. Axially loaded concrete-filled steel tubes. Journal of Structural Engineering 1998;124(10):1125–38. [18] Tomii M, Yoshimura K, Morishita Y. Experimental studies on concrete filled steel tubular stub columns under concentric loading. In: Proc. int. colloquium on stability of struct. under static and dyn. loads. 1977. p. 718–41. [19] Matsui C, Tsuda K, Ishibashi Y. Slender concrete filled steel tubular columns under combined compression and bending. In: PSSC’95 4th pacific structural steel conference. vol. 3. Steel–concrete composite structures. 1995. p. 29–36. [20] Sakino K, Tomii M, Watanabe K. Sustaining load capacity of plain concrete stub columns by circular steel tubes. In: Proc. int. spec. conf. on concrete-filled steel tubular struct. 1985. p. 112–8. [21] de Oliveira WLA, De Nardin S, de Cresce El Debs ALH, Kalil El Debs M. Influence of concrete strength and length/diameter on the axial capacity of CFT columns. Journal of Constructional Steel Research 2009;65(12):2103–10. [22] Eurocode 2: design of concrete structures EN 1992. Brussels (Belgium): European Committee for Standardization; 2004. [23] ASTM C878. ASTM Standard C878/C878M. 2009. Standard test method for restrained expansion of shrinkage-compensating concrete. West Conshohocken (PA): ASTM International, 2003; 2009. [24] UNI 8148. UNI 8148:2008: agenti espansivi non metallici per impasti cementizi—determinazione dell’espansione contrastata del calcestruzzo. Ente Nazionale Italiano di Unificazione. 2008. [25] Brauns J. Analysis of stress state in concrete-filled steel column. Journal of Constructional Steel Research 1999;49(2):189–96. [26] Eurocode 4: design of composite steel and concrete structures EN 1994. Brussels (Belgium): European Committee for Standardization; 2004. [27] ANSI/AISC 360. Specification for structural steel buildings. Chicago (IL, USA): American Institute of Steel Construction, One East Wacker Drive 700; 2005.
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Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr
Response of self-compacting concrete filled tubes under eccentric compression Giovanni Muciaccia ∗ , Francesca Giussani, Gianpaolo Rosati, Franco Mola Department of Structural Engineering, Politecnico di Milano, 20133 Milano, Italy
article
info
Article history: Received 7 March 2010 Accepted 8 November 2010 Keywords: SCC Buckling Concrete filled tube Confined concrete
abstract Self-Compacting Concrete (SCC) use is spreading worldwide and it is becoming a regular solution in some special applications, including steel–concrete composite columns. In the particular case of Concrete Filled Tubes (CFT), the main advantage from a practical point of view in the use of SCC consists in employing the steel tube as a formwork to directly cast concrete inside it, without the need of vibration. The study of three different concretes for structural applications as composite elements is presented, each of them designed for a 28-day cylindrical compressive strength of 50 MPa: (i) a Normal Vibrated Concrete, (ii) a Self-Compacting Concrete, (iii) an expansive SCC (with the goal of an increase in bond strength as a consequence of the expansion). CFT with critical length ranging from 131 cm to 467 cm have been experimentally and analytically investigated in uniaxial compression. In each case the steel case presents a cross section of 139.6 mm of external diameter and 4.0 mm thickness and with a fixed eccentricity of the applied load equal to 25 mm. The bond strength at the steel–concrete interface is reported for each of the three mixes. The experimental and analytical results show that the behavior of eccentrically loaded columns is governed by the bending moment–axial load interaction. As a consequence, perfect bond at the interface can be assumed and the axial capacity of the column is only a function of its geometry and of the mechanical properties of the materials. A numerical procedure is proposed to evaluate the increase in the axial capacity of the composite columns consequent to the confinement of the internal concrete in case of zero-eccentricity of the applied axial load with respect to the column’s axis. Finally, the obtained numerical results are introduced into code provisions to evaluate modified axial force N-bending moment M interaction diagrams to predict the axial capacity of the column in the particular test configuration. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Self-Compacting Concrete (SCC) is drawing increasing interest because it allows casting of concrete without the need of trained personnel even in presence of a high congestion of the reinforcement. The applications of SCC are becoming more and more common, although some issues concerning the material characterization, code specifications and quality control still remain unsolved. In general, SCC is used for specific constructions or in precast plants. In some cases, the choice of SCC instead of ordinary concrete depends on other factors besides the absence of vibration, such as dense reinforcement, novel form of construction, economic benefits (i.e. reduced construction time, reduced labor cost)
∗
Corresponding author. Tel.: +39 0223994274; fax: +39 0223994220. E-mail addresses: [email protected] (G. Muciaccia), [email protected] (F. Giussani), [email protected] (G. Rosati), [email protected] (F. Mola). 0143-974X/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2010.11.003
and environmental conditions. Nowadays, many precast plants worldwide are using SCC because of the advantages related to the absence of vibration such as reduced illness of workers, lower maintenance costs and energy consumption. These advantages balance the higher cost of the material. Domone [1] analyzed more than sixty case studies reported in literature and derived that in most cases the use of SCC is due to technical advantages compared to conventional concrete. SCC in situ is used for a wide range of applications: bridges (towers and anchor blocks), filled columns in high rise buildings, tunnel linings and walls. Nevertheless, since the requirements of high workability and segregation resistance have both to be satisfied, the ratio among SCC constituents and, as a consequence, its mechanical properties, differ with respect to NVC. In particular the most significant difference concerns bond behavior [2]. Nonetheless, building codes have not yet been adapted to SCC. Several investigations [3–6] have been performed in order to possibly exploit the applications of Normal Vibrated Concrete (NVC) codes to SCC while a still-open question is related to the procedure adopted to check the concrete at the building site [7].
G. Muciaccia et al. / Journal of Constructional Steel Research 67 (2011) 904–916
Among the special applications in civil buildings, steel–concrete composite columns are beginning to be used more frequently, in particular Concrete Filled Tubes (CFT). From a practical point of view the main advantage is employing the steel tube as a formwork to directly cast concrete inside it, in case a limited amount of ordinary reinforcement is added. Usually, in these applications the beams also converge on the column are composite elements such that one single operation of casting is generally done for both columns and beams. The main concern is thus related to the ability of guaranteeing a proper vibration and of avoiding the absence of segregation, that is a characteristic of a self-compacting concrete, indeed. Nonetheless, some objections have been recently raised concerning the influence of bond between steel and SCC on the global behavior of the columns in presence of long-term or second-order effects. Extensive research on composite columns, in which structural steel sections are encased in concrete, has been carried out. However, in-filled composite columns, and in particular CFT, have received limited attention compared to the first ones (for an extensive review see [8]). In recent years, a few studies have been carried out on stubby SCC Filled Columns [9,10], and very few indications exist on the bond behavior [11,12]. An experimental and numerical investigation of short circular steel tubes filled by means of expansive cement is presented in [12]; furthermore [13] studied the bond capacities of similar short CFT. Nevertheless, to the authors’ knowledge, no previous studies have been performed on the bond of Self-Compacting Concrete Filled Tubes. Referring to the results reported on NVC Filled Tubes, the following factors are relevant:
• L/D ratio: columns with L/D ≤ 11 (for D/t ≤ 60, [14]) and with L/D ≤ 15 (for D/t ∼ = 90, [15]) exhibit a higher capacity
•
•
•
•
due to the increase of concrete strength resulting from triaxial confinement effects; for columns with higher L/D ratios the composite section fails due to column buckling before reaching the strains necessary to induce concrete confinement. D/t ratio: increasing the D/t ratio reduces the axial ductility performance of thin-walled CFST columns [16]; for concretefilled steel tube columns, smaller D/t ratios provide a significant increase in the yield load and exhibit more favorable postyield behavior; these effects diminish for large diameter columns [17]. Shape effect: concrete confinement can be observed in circular and in many octagonal cross sections; square tubes provide very little confinement of the concrete only in corner regions because the wall of the square tube resists the concrete pressure by plate bending, instead of the membrane-type hoop stresses [18,19]. Load transfer: the point of application of the load has a small influence on the overall behavior; nevertheless, when the steel tube and the concrete core are loaded simultaneously, the tube provides confinement only after yielding, while the effects of confinement are visible when the load is applied on the concrete surface only [20]. Failure mode: it is generally found [21] that short columns fail for steel yielding leading to local buckling associated with the crushing of concrete; medium length columns behave inelastically and fail by partial yielding of steel, crushing of concrete in compression and cracking of concrete in tension; slender columns fail according to an overall buckling mode.
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Table 1 Geometry of steel tubes. Tube length L (mm)
Diameter D (mm)
Thickness t (mm)
L/D
D/t
Eulerian slenderness λ
800 2000 3000 4000
139.6 139.6 139.6 139.6
4.0 4.0 4.0 4.0
5.7 14.3 21.5 31.5
39.9 39.9 39.9 39.9
24 48 74 106
Table 2 Mix proportions (kg/m3 ).
CEM IIAL 42.5R Filler Sand Coarse aggregate Water Super-plasticizer Expansive agent Shrinkage inhibitor Volumic mass
NVC
SCC
SCC-E
440 60 1085 585 180 2.5 0 0 2353
420 370 730 610 190 8 0 0 2328
420 340 730 610 190 7.5 33 4.2 2335
Fig. 1. Compressive strength development curves.
The experimental program presented in this paper investigates the effectiveness of Self-Compacting Concrete as an infill of steel tubular columns, the possible increase in the structural performance when introducing expansive SCC and the suitability of the code prescription when referring to SCC. Ordinary steel tube with lengths ranging from 800 mm to 4400 mm were selected. Table 1 reports, for each specimen, the tube geometry, the length to diameter and diameter to thickness ratios and the Eulerian slenderness in the test configuration. The load was applied on the concrete surface only. 2. Experimental program 2.1. Mix design Three different concretes are studied, each of them designed for a 28-day cylindrical compressive strength of 50 MPa:
• a Normal Vibrated Concrete (NVC); • a Self-Compacting Concrete (SCC); • an Expansive SCC (SCC-E, with the intention that the expansion should produce an increase in bond strength). Details of the mix compositions are given in Table 2 (quantities of the constituents are all expressed in kg/m3 ). The strength development curves for the three mixes are shown in Fig. 1. The Eurocode 2 [22] curve for NVC is also plotted according to the equation: fcm (t ) = βcc (t )fcm
where 0.5
βcc = exp{s[1 − (28/t ) ]}
(1) (2)
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Fig. 2. SCC-E, expansion development curve.
where t is the time variable, fcm is the 28-day average compressive strength and ‘‘s’’ is a factor equal to 0.20 for rapid hardening high strength concrete. Fig. 2 reports the restrained expansion development curve of the mix SCC-E measured on a specimen prepared according to [23]. To simulate the environmental conditions of the concrete within the steel tube a modification in the ASTM test procedure was introduced. In fact, in a CFT it can be assumed that the steel tube does not allow moisture exchange between the concrete core and the environment. The specimen was then wrapped with cellophane after the casting, according to Italian standards [24], and the expansion was measured beginning from the initial curing (approximately 13 h after casting). 28-days after casting a significant residual expansion of 3.2 · 10−5 can be noticed. At the time of testing the cylindrical compressive strength of the concrete was 62 MPa for all the mixes, while the steel constituting the tube was characterized by a yield stress of 374 MPa and an ultimate strength of 440 MPa.
Fig. 3. Test setup for Concrete Filled Tubes.
2.2. Preparation of the specimens The sample preparation was performed in two phases: the cutting of the steel tubes and the casting of the concrete. The first phase consisted in cutting from 6.0 m steel tubes specimens of the desired length. The cut tubes were transported to a concrete production plant (Fig. 4) where casting subsequently occurred. The bottom end of each tube was closed by a circular plastic cap of the same diameter as the internal diameter of the steel tube. The cap was embedded for 40 mm. The top end of the tube was not covered to allow the concrete to be cast in. The tubes were accurately filled up to approximatively 40 mm from the top. After curing, the filled tubes were transported back to the laboratory. Bottom caps were removed, so that the final specimens consisted of steel tubes filled with concrete except for a 40 mm length at both ends. This free length worked as a slot for the constraining devices. A series of targets was subsequently glued on each specimen. Each target represents a measurement point of displacement acquired by the photogrammetry technique, as described in Appendix. Fig. 3 shows a picture of the test setup of a 440 cm composite column highlighting the constraints at the end of the columns, the lifting system and the cameras used for photogrammetry. Fig. 4. Tubes previous casting at concrete plant.
2.3. Constraints Particular attention was devoted to the choice of proper constraints. Tests have been carried out on an MTS servohydraulic
closed-loop machine with a 2500 kN capacity, with fixed platens and under vertical displacement control. To reach a stable control after the peak load it was chosen to hinge the column at both ends
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907
Fig. 5. Constraints, drawings.
thickness) was placed between the concrete surface and the steel plate. 2.4. Lifting The top end of the longest specimen was at more than 6 m of height from the floor (considering also the height of the machine basement). As a consequence, it was not possible to work safely to manually connect the specimen to the testing machine at that height. It was thus chosen to connect the specimen to the upper constraint, driving it to the desired height by directly lifting the same movable head of the machine (Fig. 7). At the scope, two threaded rods were welded on the specimen, one at each end, and along the same directrix (Fig. 5). The top rod passed through a hole in the pestle and a nut was torqued on the rod to lock the specimen in the desired position. The function of the rod consisted in transferring the self-weight of the specimen to the machine during the lifting. The bottom rod had no function during the lifting. Its functions were to assure a proper positioning of the specimen and to prevent undermining of the pestle from the specimen during testing. 2.5. Data acquisition Fig. 6. Constraints, detail.
with a given eccentricity of 25 mm between the axis of the column itself and the ideal line connecting the two hinges. In this way a progressive buckling of the column was guaranteed. Moreover, a big effort was put into the design of the devices connecting the machine platens to the column. At each end two circular slotted steel plates were welded on a third steel plate clumped to the machine platen (Fig. 5). The distance between these two plates allows a third slotted steel plate to pass through them. The three holes can be aligned and a circular steel rod can pass through, acting like a hinge. The third plate is part of a second specific device whose function is to apply the load on the column (Fig. 6) and which will be referred to as the pestle. On the other end of the pestle a circular steel plate with a diameter 2 mm smaller than the column internal diameter has the function of transferring the load to the concrete surface. The columns are loaded in compression with a fixed nominal eccentricity e = 25 mm and a nominal critical length, Lcr , equal to the distance between the two hinges. The specimen ends were not identical. In fact, at one end the concrete presented a very smooth surface, due to the presence of the cap during casting, while the other end was more irregular. To guarantee a regular contact on the latter a lead disk (2 mm
The outputs of the displacement transducer and of the load cell were automatically recorded by the data acquisition system of the same MTS machine on which the load–deformation data were also continuously displayed. During the tests on the 80 cm length specimens both the vertical and the middle-span displacements were monitored by two additional LVDTs. Data were acquired by a HBM Spider8 unit and stored on a personal computer. As previously mentioned, the complete 3D displacement field was monitored by digital photogrammetry. The minimal resolutions for in-plane and out-of-plane displacement have been evaluated in 0.1 and 0.5 mm, respectively. 2.6. Experimental results Table 3 reports, for each test the test code, the peak load, the tube length, L, the distance between the bottom end and the point of maximum lateral deflection detected during testing, Li and the buckling length, Lcr . Fig. 8 (left) reports the load/vertical displacement behavior of the specimen SCC-80-1. The applied load is plotted against the displacements measured by both the machine actuator and by the external transducer and against the displacement computed by the photogrammetry technique as well. It can be noted how the three measurements basically coincide. The conclusion is twofold:
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Fig. 7. Lifting, detail.
• the displacement computed by the photogrammetry technique is reliable also for low absolute values of displacement; Table 3 CFT—results.
• the machine is very stiff with respect to the specimen. As
Code
Load kN
L cm
Li cm
Lcr cm
28 32 92.75 93.25 150 150 220
131 123 212.5 213.5 327 327 467 467
NVC NVC NVC NVC NVC NVC NVC NVC
80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
756.9 874.7 608.2 605.7 555.9 484.11 336.2 333
80 80 185.5 186.5 300 300 440 440
SCC SCC SCC SCC SCC SCC SCC SCC
80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
813.8 835.2 610.3 687.6 540.95 569 342.4 333.9
80 80 185.5 186 300 300 440 440
SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E
80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
807.1 908.7 663.5 784.1 550.6 513 373 377.7
80 79 185.5 185.5 300 300 440 440
220 40 31 47 93 150 150 220 220 40 22 92.75 92.75 150 150 220 220
107 125 304 213 327 327 467 467 107 141 212.5 212.5 327 327 467 467
a consequence, the vertical displacement measured by the machine actuator can be assumed as the vertical displacement of the specimen when direct measurements are not available. Similarly, in Fig. 8 (right) the applied load is plotted against the deflection measured by the external transducer (‘‘LVDT’’) and the displacement computed by the photogrammetry technique (‘‘Photogr’’). It is worth specifying that the horizontal transducer measures the deflection at the midspan of the column, while the ‘‘Photogr’’ displacement is the maximum deflection among all the displacement computed by photogrammetry. Hence, they do not refer to the same point and the two curves progressively detach from one another. Photogrammetry also allows a proper evaluation of the eccentricity of the applied load with respect to the axis of the column. For each specimen the eccentricity is evaluated after the application of the initial contact load (about 2 kN) as the distance between the measurement point that experienced the maximum displacement during the test and the hinge at the fixed end of the column, which corresponds to the zero point of the coordinate system. Fig. 9 reports the eccentricity of the applied load for all the tested specimens. Significant deviations from the nominal eccentricity of 25 mm at the hinges are observed, probably due to imperfections both of the steel tube and of the connecting devices.
Fig. 8. SCC-80-1, axial load versus vertical displacement (left), axial load versus deflection (right).
G. Muciaccia et al. / Journal of Constructional Steel Research 67 (2011) 904–916
909
Fig. 9. Eccentricity of the applied load for all the specimens.
Fig. 10. Axial load versus vertical displacement (left), axial load versus deflection (right), slenderness λ = 106.
Fig. 11. NVC-440-02 at peak load (left) and details of the plastic hinge (right).
It will be shown that this difference leads to a change in the ultimate load for specimens of the same length. Fig. 10 compares the load vs. vertical displacement (left) and the load vs. deflection (right) behavior for a Eulerian slenderness of λ = 106, for the concretes NVC, SCC and SCC-E. A similarity in the behavior for the different mixes, characterized by the same stiffness, is immediately apparent. A slightly higher value of the peak load was detected for SCC-E. This is assumed to be due to the fact that at the peak load the formation of a plastic hinge in the middle-span section is evident (Fig. 11). Fig. 12
(left) reports a three-dimensional plot of the deformed shape of the specimen NVC-440-1 at different time steps corresponding to: (i) no load applied, ‘‘Initial shape’’, (ii) the maximum load, ‘‘Peak load’’, (iii) the maximum deflection, ‘‘Max displacement’’ and (iv) the total unloading, ‘‘Residual’’. The column axis is parallel to the Z axis. A single plane of bending almost parallel to the XZ plane is clearly detectable. After the peak load an increase in the vertical displacement, and consequently in the lateral deflection, could be taken up by the column only by an increase in rotation over a portion of a certain length at a constant moment
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Fig. 12. Three-dimensional plots of the deformed shapes of specimens NVC-440-1 (left) and SCC-200-1 (right).
Fig. 13. Axial load versus vertical displacement (left), axial load versus deflection (right), slenderness λ = 24 (left) and λ = 48 (right).
(that is a plastic hinge), thus leading to decreasing the load at the end of the column and to an elastic unloading along the portions of the columns outside the plastic hinge. On the descending branch the middle-span deflection, v , is then given by v = Mpl /N where Mpl is the plastic resistant moment of the cross section while N is the load measured by the load cell. Since Mpl is also a function of the axial load N, in a load versus deflection plot the descending branch is not a perfect hyperbole. The same results have been obtained for each slenderness, with slight variations for stubby columns λ = 24, λ = 48 (Fig. 13). For slenderness λ = 48, a different behavior was observed for the two specimens of the SCC mix, Fig. 13 (right). Actually, in the case of SCC-200-01 the bottom constraint did not act as a perfect hinge (due to the very high irregularity of the concrete surface of that specimen) but it provided an end moment to the column. As a
consequence, the plastic hinge was not located in the middle of the column but closer to the bottom end, and it is apparent in the threedimensional plot of the deformed shape reported in Fig. 12 (right). This was taken into account by considering a different buckling length for the column, being equal to twice the distance between the top end and the point of maximum lateral deflection (as listed in Table 3). The reported results indicate that there is no substantial influence of the different bond strengths on the axial capacity of the columns. This can be explained by the following considerations. According to the first order theory the columns are subjected only to an axial load N = const and M = Ne = const along the entire length (e is the initial eccentricity). Shear is null and, as a consequence, no shear stresses act along the interface between concrete and steel.
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Fig. 14. Interaction domains according to Eurocodes 2 and 4.
On the other hand, second order theory predicts a shear distribution along the column having a maximum value at the base of the column (second order shear is assumed to be perpendicular to the column z axis in the deformed shape) and equal to: NV (z , t ) = N sin ϑ(z , t )
(3)
NV ,max (t ) = NV (z = 0, t ) = N sin θ0
(4)
where θ0 is the angle of rotation at the end of the column (z = 0) at time t. In the present case shear exhibits very low values, showing a negligible effect on the global behavior of the columns, as it will be numerically shown in Section 2.7. Furthermore, the identical observed stiffnesses are explained by considering that, besides being characterized by the same geometry, also the elastic moduli of the materials were the same, with a value of 32 000 MPa. The latter is assumed to depend on the similar proportioning of coarse aggregate in the mixes of NVC and SCC (Table 2). 2.7. Numerical analysis and modeling The effects of the interaction between the axial force, N, and the bending moment, M, on the resistance of the cross section can be taken into account, as common, by calculating the N versus M interaction diagram (Fig. 14). In the present investigation two different procedures are adopted:
• the column is considered as an ordinary reinforced concrete element with deformed bars all around the concrete core;
• the cross section is analyzed according to the procedures indicated in Eurocode 4 [26] for composite columns. In the first case, the steel area is considered equivalent to 51 reinforcement bars φ = 4 mm equally spaced and the interaction domain is calculated according to Eurocode 2 [22]. In the second case, the interaction domain is replaced by a polygonal diagram connecting four representative points (for details refer to Eurocode 4 [26, Section 6.7.3]). In the following analysis design values are replaced by average values. Fig. 14 shows the interaction domain of the considered columns calculated according to the two different approaches. It is apparent that they coincide in the four points calculated according to the procedure previously described. The conservativeness of the simplified domain can be reasonably accepted. ANSI/AISC 360 [27] introduces the plastic stress approach as well, assuming that no slip occurs at the steel–concrete interface
and that the width to thickness ratio prevents local buckling from occurring until extensive yielding has taken place. ANSI/AISC 360 [27] also allows for a five-point simplified interaction diagram to better reflect bending of the filled tubes. This approach is not adopted in the present work. As a general remark, it has to be considered that the design method of EC4 for CFT is valid up to a relative slenderness of 2.0 and up to a diameter to thickness ratio d/t = 90 235 . On the other f y
hand ANSI/AISC 360 [27] qualifies as a filled composite tube if the cross-sectional area of the steel is at least 1% of the total composite cross section and the D/t ratio is lower than 0.15E /fy . In the present investigation the maximum relative slenderness is 1.34, d/t = 34, 9 ≤ 56.5 = 90 235 (Eurocode 4 [26] limit) 374
and ≤ 82.2 = 0.15 205000 (ANSI/AISC 360 [27] limit) and the ratio 374 As /(As +Ac ) is equal to 12.5%. The specimens can be thus considered as fully representative of a real design case. The simplified plastic stress approach is very useful if an increase in concrete strength caused by the confinement needs to be taken into account. In fact, while for high eccentricities of the applied load the not uniformity of the confinement does not provide a significant global increase in the concrete capacity, on the other hand, for zero eccentricity the effect of confinement is not negligible. Eurocode 4 [26] suggests the following expressions to calculate the plastic resistance to compression in order to take into account the effects of confinement: Npl,R = ηa Aa fy + Ac fc
1 + ηc
t fy d fc
(5)
where Aa is the steel area, fy is the steel yielding stress, Ac is the concrete area and fc is the concrete compressive strength. For members with e = 0 (uniaxial compression) the values ηa = ηa0 and ηc = ηc0 are given by the following equations:
ηa0 = 0.25(3 + 2λ) ≤ 1.0
(6) 2
ηc0 = 4, 9 − 18, 5λ + 17λ ≥ 0
(7)
valid for an initial eccentricity of the applied load over the diameter ratio e/d = 0, where λ is the relative slenderness defined as:
λ=
Npl,R Ncr
(8)
where Npl,R is the value of the plastic resistance to compression and Ncr is the elastic critical normal force for the relative buckling
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where Nz = N is the axial force acting on the section. Equilibrium in the circumferential direction (Fig. 15—right) results in:
σrc ri = σϑa t .
(13)
One further condition is thus necessary. In the concrete core, loaded by uniform contact pressure, we assume that the following relation exists:
σrc = σϑc .
(14)
Equations from (10)–(14) can be condensed in the following matrix form:
Fig. 15. Stress components in composite columns, [25].
mode, calculated with the effective flexural stiffness (EI)eff given by:
(EI)eff = Ea Ia + Ke Ec Ic
longitudinal stress in steel, σza ; circumferential stress in steel, σϑa ; longitudinal stress in concrete, σzc ; circumferential stress in concrete, σϑc ; radial stress in concrete, σrc .
Since the radial stress in concrete, σrc , can be considered as a contact force at the steel/concrete interface, it is assumed equal to the internal pressure on the steel tube σra . To derive the five unknowns, five relationships are required. Assuming a perfect bond between steel and concrete, at the contact surface the following two compatibility equations can be written: 1
νa
1
νzcϑ
E
E
Ez
Eϑc
σa − a z
νa Ea
σza −
σa = a ϑ
1 Ea
σϑa =
σc − c z
νzrc Ezc
σzc −
1 c
Eϑ
σϑc − σϑc +
νzrc Erc
νzrc Erc
σrc
(10)
σrc
(11)
corresponding to compatibility relations in vertical (z) and circumferential (ϑ ) directions, respectively. Equilibrium in the vertical direction (Fig. 15—left) results in: Ac σzc + Aa σza − Nz = 0
(12)
− −
νa Ea 1
Ea 0 t 0
0 0
(9)
where Ke is a correction factor that Eurocode 4 [26] suggests to take equal to 0.6, Ea and Ec are the elastic moduli of steel and concrete, respectively, and Ia and Ic are the second moments of inertia of the steel section and of the uncracked concrete section, respectively. The tested columns have a relative slenderness of 0.30, 0.60, 0.93, 1.34 and a e/d ratio of 0.18, while Eurocode 4 [26] considers Eq. (5) as valid only up to a relative slenderness of 0.5 and up to an e/d ratio of 0.1. Consequently, according to EC4, no increase in the plastic resistance to compression should be taken into account. Observing ANSI/AISC 360 [27] provisions, the design compressive strength is evaluated similar to Eurocode 4 [26]. However, unlike Eurocode 4 [26], the influence of the geometry and of the material strength on the plastic resistance are not explicitly taken into account. However, a generic numerical procedure has been implemented to calculate the plastic resistance to compression of a CFT cross section that directly takes the non-linearities of the materials into account. A general procedure proposed by Brauns [25] has been initially considered. Assuming a uniform distribution of working stresses, five stress components are taken into account (Fig. 15):
• • • • •
1 Ea a ν a E a A
−
νzcϑ
1
ν
Eϑ 1
A 0 0
Eϑc 0 0 −1
−
νzrc a σz Erc 0 c σ a νzr ϑ 0 c · σz = Nz Erc σ c 0 0 ϑ 0 σrc −r i
c
Ezc c zr Ezc c
(15)
1
that is: Ax = b.
(16)
The effects of confinement are taken into account by adopting the following uniaxial constitutive law for concrete (Eurocode 2 [22]):
σzc = fc ,c
εc 1−1 1− c σr
2
for 0 ≤ εc ≤ εc2,c
σzc = fc for εc2 ≤ εz ≤ εcu2,c
(17) (18)
with:
f c ,c = f c
f c ,c = f c
1000 + 5.0
σϑc
for σ2 ≤ 0.05fc
fc
σ 1.125 + 2.50 ϑ fc c
for σ2 > 0.05fc
εc2,c = εc2 (fc ,c /fc )2
(19)
(20) (21)
εcu2,c = εcu2 + 0.2σϑ /fc c
(22)
where fc is the compressive strength, εc2 is the strain at reaching the maximum strength and εcu2 is the ultimate strain. To take the effects of radial crack formation into account, after reaching the tensile strength value at σϑc , the Poisson ratio is set equal to 0.4 that considers the structural effect of a larger lateral expansion of the concrete after cracking. The Von-Mises yield criterion is adopted for steel:
(σza )2 + (σϑa )2 − σza σϑa − fy2 = 0.
(23)
No hardening is considered. The procedure consists in increasing the applied load, Nz , until the maximum strain, εcu2,c , is reached. At each load step the following operations are performed: 1. 2. 3. 4. 5. 6. 7.
computing the matrix A; solving Eq. (16) for x: x = A−1 b; evaluating strains; computing confined strength for concrete; checking for steel yielding; checking for ‘‘racked concrete Poisson effect’’; updating stiffnesses and checking convergence.
Stress components versus vertical strains obtained are reported in Fig. 16 (left).
G. Muciaccia et al. / Journal of Constructional Steel Research 67 (2011) 904–916
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Fig. 16. Stress components versus vertical strains, both NVC and SCC (left) and SCC-E (right).
It is worth noting the change in the sign of σϑa (indicated as ‘‘steel hoop’’ in the plot). The change occurs after σϑc reaches the tensile strength and, as a consequence, the Poisson ratio is set equal to 0.4. In the absence of prestress, the confinement of the concrete provided by the steel is a passive confinement. In the present case, the steel contribution ratio δ = (Aa fy )/(Npl,R ) is very high, such that the confinement is not active until 67% of the plastic resistance of the cross section is reached. It can also be noticed that the maximum vertical stress in concrete is about 92 MPa, which is 53% higher than the unconfined cylindrical compressive strength. Plastic resistance to compression is finally evaluated in 1925 kN, representing an increase with respect to the unconfined plastic resistance of approximatively 45%. Additionally, for SCC-E, the initial expansion (as reported in Fig. 2) can be taken into account by decomposing the total concrete strain into the concrete net elastic strain component, εc , (for stress calculation) and the concrete elastic offset component, εc0 . Since the core concrete is free to expand in the vertical direction, it is assumed that expansion is effective only in the circumferential and radial directions. As a consequence, Eq. (11), representing the compatibility relation in the circumferential direction, ϑ , results in:
νa Ea
σza −
1 Ea
σϑa =
νzrc Ezc
σzc −
1 c
Eϑ
σϑc −
νzrc Erc
σrc + εϑ,exp
(24)
where εϑ,exp accounts for the expansion (elastic offset) of the concrete. The known term of Eq. (15) then modifies into:
0
M (N ) =
(25)
0 Stress components versus vertical strains obtained for the expansive concrete are reported in Fig. 16 (right). It can be noticed how the plastic resistance increases by approximatively 62.8% and 12.5% with respect to the unconfined one and to the confined one not accounting for expansion, respectively. The effect of the expansion is to introduce an initial active confinement in the concrete. As a consequence radial cracking is reached for a higher value of the vertical strain (around 1.79h against 1.49 h in the absence of expansion). This results in a higher value of the concrete circumferential stress and thus in a higher value of both the strain at the maximum strength and of the concrete confined strength (Eq. (19)). A simplified domain taking into account the effects of confinement and of expansion for point A is plotted in Fig. 17. Five additional curves are plotted. The dark dashed line represents a constant ratio between M and N equal to the inertia
β 1−
N Ncr,eff
eN
(26)
where β is an equivalent moment factor taken as 1.1 and Ncr,eff is the critical normal force corresponding to the effective flexural stiffness given in Eq. (9). In computing the effective stiffness, the Ke factor appearing in Eq. (9) is taken equal to 1.0 if M (N ) curves entirely belong to the uncracked concrete field, otherwise equal to 0.6. Ratios of ultimate loads to values calculated according to the several proposed criteria are plotted for the different mixes in Fig. 18 (a value higher than one is conservative). All the values are reported in Table 4 where P indicates the ultimate load. For each specimen the initial eccentricity has been evaluated according to the photogrammetric measurements, as reported in Fig. 9. Provisions according to the Merchant–Rankine criterion are also reported. The Merchant–Rankine (MR) criterion considers a failure by a cinematic mechanism with a plastic hinge in the middle of the column and it evaluates the axial capacity of the column N in: 1 N
εϑ,exp Nz . 0
radius of the homogenized section (φ/4 = 44.1 mm) and divides the field in which no fiber of the section is subjected to a tensile stress, and thus concrete is non-cracked (right), from the field in which tensile stresses are present and then concrete cracks (left). The remaining curves represent the II order M (N ) relationships given by EC4 for the four different slendernesses considered:
=
1 Ncr
+
1 Npl
.
(27)
The axial capacity predicted by the MR criterion is substantially correct for slender columns but dramatically higher for stubby columns, since the criterion does not consider the reduction in Mpl due to the axial force, N. For slender columns Mpl does not significantly vary as a function of N and the provisions according to the four proposed criteria basically coincide. On the other hand, the proposed procedure correctly predicts also the axial capacity of stubby columns, accounting for the effects of either the confinement only or the confinement coupled with the expansion. For each concrete the ‘‘unconfined’’ criterion results in more conservative predictions than the ‘‘confined’’ one. It is also noted that, for SCC-E, the ‘‘confined+expansion’’ criterion gives more accurate results. On the basis of the presented results the observed independency of the axial capacity from the bond properties of the different mixes can be explained. The second order shear at the basis of the column at the limit of formation of the plastic hinge can be evaluated according to Eq. (3) taking the average values of deflection, v , and of the angle of rotation, θ , measured during the tests. Table 6 reports, for each column, the buckling length, Lcr , the
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Fig. 17. Interaction domains and M (N ) curves for different slenderness.
Fig. 18. Ratios of ultimate loads to values calculated according to the proposed criteria.
average values of midspan deflection, v , the angle of rotation at the end of the column, θ , the average value (for each column length) of the II order shear, NV and the corresponding values of the interface shear stress, τ , calculated according to the classical Jourawsky theory, τ = (NV S )/(Ib), where S and b are the static moment and
the chord width, respectively, at a distance from the center of mass of the uncracked homogenized section equal to the internal diameter rint = 65.8 mm of the cross section itself. Bond strength was previously investigated on slices of 50 mm height obtained by steel tubes and subsequently cast with a
G. Muciaccia et al. / Journal of Constructional Steel Research 67 (2011) 904–916 Table 4 Predicted values of peak load. Lcr
Punconf
Pconf
NVC NVC NVC NVC NVC NVC NVC NVC
Code 80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
131.0 123.0 212.5 213.5 327.0 327.0 467.0 467.0
687.1 701.1 593.6 645.9 467.5 477.2 348.4 366.2
733.9 753.3 610.1 672.7 467.5 477.2 348.5 366.2
Pconf.exp
1242.4 1275.8 912.9 909.2 575.8 575.8 346.0 346.0
SCC SCC SCC SCC SCC SCC SCC SCC
80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
107.0 125.0 304.0 213.0 327.0 327.0 467.0 467.0
755.2 726.6 547.4 837.3 593.0 587.8 316.0 300.0
829.7 787.9 552.6 924.0 601.8 596.0 316.0 300.0
1341.2 1267.5 630.5 911.0 575.8 575.8 346.0 346.0
SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E SCC-E
80 80 200 200 300 300 440 440
1 2 1 2 1 2 1 2
107.0 141.0 212.5 212.5 327.0 327.0 467.0 467.0
736.4 776.5 645.9 661.0 539.7 477.9 328.9 319.2
803.2 856.0 674.2 693.0 543.3 477.9 328.9 319.2
824.5 877.0 680.9 700.6 545.0 507.5 328.9 319.2
MR
1341.2 1200.3 912.9 912.9 575.8 575.8 346.0 346.0
Table 5 Bond strength results.
915
slenderness ranging from 24 to 106 have been experimentally investigated in eccentric compression with particular attention to the bond behavior between the concrete core and the steel tube. The experimental and analytical results lead to the following conclusions:
• the behavior of eccentrically loaded columns is ruled by bending moment–axial load interaction. As a consequence, a perfect bond at the interface can be assumed; • the axial capacity of the column is only a function of its geometry and of the mechanical properties of the materials; • the axial capacity of the column can be evaluated by adopting the Eurocode 4 approach, with slight modifications related to the effects of the confinement of the internal concrete. In Concrete Filled Tubes the use of Self-Compacting Concrete allows to avoid the vibration process, which is costly and hard to execute for the considered shape. The presented results confirm many previous findings on Normal Vibrated Concrete, in particular regarding the influence of the L/D ratio and the failure mode. It is found that the use of Self-Compacting Concrete, in place of Normal Vibrated Concrete, does not require a different approach in the design procedure of CFT. However, further investigation is required to account for different D/t ratios and for different amounts of coarse aggregate in the concrete mix, which could influence the stiffness of the concrete and, as a consequence, the global behavior of the columns. Acknowledgements
Code
Load kN
Average τm MPa
CoV (%)
NVC 01 NVC 02 NVC 03 SCC 01 SCC 02 SCC 03 SCC-E 01 SCC-E 02 SCC-E 03
12.01 14.48 24.38 26.97 9.75 23.54 128.58 133.41 105.81
1.20
45.4
1.08
48.1
6.15
8.7
The authors wish to extend their gratitude to A. Faccini and M. Corcella for the help concerning the experimental program. Special thanks to D. Spinelli and A. Desteffani for their help in setting up the experimental apparatus and to M. Degliuomini and M. Pini for setting up the photogrammetry apparatus and for data processing. Deep gratitude goes to L. Buzzi for his support in the investigation and for the concrete supply. Appendix. Photogrammetry
Table 6 II order shear and interface shear stress. Lcr
v
θ
NV (kN)
τ (MPa)
107 212.5 327 467
3.3 4.3 5.3 7.5
89.189 89.075 89.064 88.818
12.01 11.52 8.65 6.98
0.59 0.57 0.42 0.34
bonded length of 40 mm. It can be noticed how the maximum interface shear stress (Table 6) is lower than the lower bond strength reported in Table 5 for NVC (τm = 1.08 MPa). As a consequence, brittle failure caused by debonding at the interface is prevented. In fact, no debonding has been observed at the end of the tests. It has been shown that the loading scheme does not induce shear stresses at the steel–concrete interface high enough to exceed the bond strength. As a development of the presented research, in order to evaluate the shear force–bending moment interaction of the composite member, the longer tested columns have been cut in three sectors. The two sectors which underwent an elastic unloading after the peak load will be subjected to four-point bending tests with a proper shear length such to induce high interface stresses. 3. Conclusions A study of SCC for structural applications as composite elements was presented. Concrete Filled Tubes (CFT) with Eulerian
Techniques of digital photogrammetry are suited for tasks requiring a large number of measurement points distributed over an object surface. The use of photogrammetry in material testing experiments generally allows for the simultaneous measurements of displacement at an almost arbitrary number of locations over the camera’s field of view. Data processing is highly automated and fast, allowing for real-time monitoring at the camera image rate. The adopted system consists of two Nikon digital cameras (one D80 model and one D100 model) and one notebook for each camera for image acquisition. Image acquisition is automated and the measurement of the absolute coordinates and the movement of signalized targets on the specimen is solved by the commercial software package Photomodeler Scanner. Camera calibration is achieved by self-calibrating bundle adjustment based on taking multiple images of the same object from different viewing directions and orientations with each camera to be calibrated before the test. Proper horizontal support braces were designed to connect the cameras to existing vertical steel columns. One main issue consisted in determining the camera positions to completely frame the specimens and, at the same time, to reach the desired resolution (the minimal resolution for in-plane displacement has been evaluated as 0.1 mm). Proper horizontal support braces have been designed for each camera to connect them to the existing vertical steel columns.
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Fig. 19. Camera setup.
The position of the columns and of the cameras during the tests are depicted in Fig. 19. In the drawing the test apparatus is located in the lower left corner. For each column length, cameras were located at different height from the ground ‘‘h’’ and distance ‘‘d’’ from the monitored object (the column). References [1] Domone P. A review of the hardened mechanical properties of self-compacting concrete. Cement and Concrete Composites 2007;29(1):1–12. [2] Cattaneo S, Rosati G. Bond between steel and self-consolidating concrete: experiments and modeling. ACI Structural Journal 2008;106(4):540–50. [3] Sonebi M, Bartos P. Bond behavior and pull-out test of self-compacting concrete. In: Proc. of RILEM int. symp. bond in concrete from research to standards. 2002. p. 511–9. [4] Paultre P, Khayat KH, Tremblay S. Structural performance of self-consolidating concrete used in confined concrete columns. ACI Structural Journal 2005; 102(4):560–8. [5] Galano L, Vignoli A. Strength and ductility of HSC and SCC slender columns subjected to short-term eccentric load. ACI Structural Journal 2008;3(3): 259–69. [6] Cattaneo S, Giussani F, Mola F. Flexural behaviour of reinforced, prestressed and composite self-compacting concrete beams. In: Fourth north American conference on the design and use of self-consolidating concrete SCC2010. 2010. [7] Cattaneo S, Giussani F, Mola F. In situ quality control of self-compacting concrete. In: Third north American conference on the design and use of selfconsolidating concrete SCC 2008. 2008. [8] Shanmugam NE, Lakshmi B. State of the art report on steel–concrete composite columns. Journal of Constructional Steel Research 2001;57(10):1041–80. [9] Han L-H, Yao G-H. Experimental behaviour of thin-walled hollow structural steel (HSS) columns filled with self-consolidating concrete (SCC). Thin-Walled Structures 2004;42(9):1357–77. [10] Lin C-H, Hwang C-L, Lin S-P, Liu C-H. Self-consolidating concrete columns under concentric compression. ACI Structural Journal 2008;105(4):425–33. [11] Shakir-Khalil H, Al-Rawdan A. Composite construction in steel and concrete, vol. 3. ASCE; 1994. p. 222–235.
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