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Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors
Engineering Structures xxx (2016) xxx–xxx
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Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors Yong Liu a, Lanhui Guo a,⇑, Bing Qu b, Sumei Zhang a a b
School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China Dept. of Civil and Environmental Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USA
a r t i c l e
i n f o
Article history: Received 6 May 2016 Revised 16 October 2016 Accepted 18 October 2016 Available online xxxx Keywords: Composite beams U-shaped steel girder Angle connectors Flexural behavior Experimental investigation
a b s t r a c t This paper focuses on a new type of steel-concrete composite beams consisting of U-shaped steel girders and angle connectors. Compared with conventional steel-concrete composite beams consisting of wide flange girders and headed shear stud connectors (or short channel connectors), the composite beams considered in this study have favorable flexural performance while reducing the excessive costs and potential construction challenges due to installation of the stud and/or channel shear connectors. Through four-point bending tests on five specimens, this research team experimentally investigated flexural behavior of the new composite beams. The five specimens were varied to have different angle connector intervals and installation locations. Test results show that composite beams with angle connectors welded to the webs of U-shaped steel girder fail in brittle failure modes while composite beam with angle connectors welded on the top flange of U-shaped steel girder fails in ductile failure mode. Based on the test results, it can be concluded that angle connectors welded on the top flange are more ductile than those welded to the webs. This paper also assesses adequacy of the existing formula for short channel connectors in quantifying the shear transfer capacity of angle connectors and the influence of installation location of angle connectors on the resulting beam response. Moreover, plastic moment resistance of the composite beam with full shear connection predicted by Eurocode 4 and AISC 360 and ultimate flexural strength of the partially composite beams predicted by the interpolation method in Eurocode 4 agree well with the experimental results. Besides, specifications in AS 2327.1 and provisions in AISC 360 neglecting the reduction factor could be used to estimate the initial stiffness of composite beams in this study by using cracked moment of inertia. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Steel-concrete composite beams (referred to herein as composite beams) possess the advantages of both structural steel and reinforced concrete. Although composite beams can take different forms, the most popular version consists of a wide flange girder (i.e., the structural shape with an I-shaped cross-section) supporting a reinforced concrete slab. Through application of appropriate shear connectors between the steel girder and the concrete slab, the two parts can act as one unit in resisting the external loads, i.e., enabling the entire system to form the composite action. Under the same design constraints, composite beams can be more economical than conventional steel beams and lighter than typical reinforced concrete beams. The advantages of composite beams
⇑ Corresponding author.
have been long recognized [1–4] and application of composite beams can be found in many buildings and bridges [5–8]. To date, behavior of composite beams (particularly those with partial shear connections) has been investigated and analytical models have been proposed for quantifying stiffness and deflections of such beams [9–12]. Nevertheless, design challenges still exist, hindering the widespread acceptance of such viable structural components. For example, the most popular shear connectors in composite beams are headed studs and short channels attached to the top flange of the steel girder at prescribed intervals [13–16]. Installation of headed studs requires special automatic tools and skilled operators, for which additional cost may be incurred, offsetting the other advantages of composite beams. Adoption of short channels with their bottom flanges welded to the steel girder can help reduce the cost associated with connector installation, and the top flange can reduce the separation of concrete slab from steel girder. However, the channel connectors may congest the longitudinal
E-mail address: [email protected] (L. Guo). http://dx.doi.org/10.1016/j.engstruct.2016.10.037 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Liu Y et al. Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.10.037
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Y. Liu et al. / Engineering Structures xxx (2016) xxx–xxx
rebars in the concrete slab, resulting in construction difficulties. Therefore, there is a research need to develop alternative shear connectors for composite beams. Moreover, application of composite beams may be impeded in some cases due to the insufficient torsional resistance, e.g., in the exterior beam in a building floor system or a bridge deck system supports the tributary gravity load transferred from one side of the beam [17]. The rotational restraint along the edge of the slab or deck due to the presence of shear connectors can result in a significant torsional demand on the composite beams. The same issue may also occur in an interior beam under unequal gravity loads from both sides of the beam. To resist the torsional demand, a wide flange girder much larger than the one designed for the bending moment demand may have to be used in some cases, leading to a less economical composite beam design. Note that torsional resistance of the composite beam with a wide flange girder is generally lower than the one with a box girder [18–21]. As such, it is necessary to develop alternative girders with torsional performance similar to or equal to that of a box girder for composite beams. This research team explored a practical solution to the above issue, in which a U-shaped steel girder with concrete infills were used as an alternative to the steel girder and equal-leg angles welded along the transverse direction to the girder were used as the shear connectors. Fig. 1 schematically shows the system considered in this investigation. As shown, the angles can be welded either to the top flanges or to the webs of the U-shaped girder. Conceptually, the vertical legs of the angles can resist the longitudinal shear force between concrete slab and steel girder while the horizontal legs can mitigate the separation of the concrete deck from the steel girder. Compared with the widely used short channel connectors, the angles welded to webs reduce the potential of rebar congestions in the concrete slab while retaining the ease of installation. Moreover, the angles help reinforce the U-shaped girder, enabling the girder to exhibit a superior torsional moment resis-
Angle connector Concrete slab
U-shaped girder
Reinforcements
Concrete infill
(a) Angle conectors welded to the top flanges
tance similar to that of a boxed cross-section. Although the infill concrete in the U-shaped girder increases the weight of the girder, it helps mitigate local buckling of the webs of the girder and improve strength and stiffness of the girder. The infill concrete can also enhance fire resistance of the composite beam as it does in other types of composite members. Therefore, it is necessary to study its flexural behavior to promote its application. The objective of this research was to evaluate flexural behavior of such composite beams. Through testing of five specimens, this research team investigated damage progression, failure modes and other aspects of the composite beams under monotonic loading. The test results obtained from this investigation form a basis for a better understanding of the fundamental behavior of such composite beams and help promote their applications in future constructions. The following sections describe in detail specimen design and construction, material properties, test setup, loading program, observations, test results, and assessment of adequacy of existing design models for calculating ultimate flexural resistance of such composite beams. 2. Specimen design and construction Five composite beams, designated as Specimens CB1 to CB5, were tested under 4-point bending. All the specimens were identical except that their shear connectors (including connector type, installation location and connector interval) were varied. As shown in Fig. 2, all specimens had the same length of 8900 mm (measured from beam ends) and span of 8400 mm (measured from beam supports). Depth, flange thickness, web thickness, top flange width and bottom flange width of the steel girder adopted in each specimen were 400 mm, 10 mm, 6 mm, 80 mm and 250 mm, respectively. Based on the Chinese Code for Design of Steel Structures [22], effective width of a concrete slab assumed for a composite beam should be the minimum of L/6, s0/2 and 6hc, where L, s0 and hc represent span of the composite beam, clear distance between the steel girders of adjacent composite beams and the slab thickness, respectively. Accordingly, thickness and width of the concrete slab in each specimen of this investigation were selected to be 120 mm and 1690 mm, respectively. As illustrated in Fig. 2b, two layers of steel rebars with the nominal diameter of 10 mm were spaced at 200 mm and 250 mm along the transverse and longitudinal directions to reinforce the concrete slab, respectively. Steel angles with equal legs (50-mm wide and 5-mm thick) were used as shear connectors in all specimens. It is recognized that no analytical models were readily available for calculating the shear force transfer capacity of each angle connector at the time of the investigation. Alternatively, the formula for calculating shear force transfer capacity of short channel connectors in composite beams was adopted to predict the shear strength of angle connectors in this research. The shear strength Ncv of channel connector can be calculated in the Chinese Code for Design of Steel Structures [22] as following: 0:5
Ncv ¼ 0:26ðt þ 0:5t w Þlc ðEc f c Þ Angle connector U-shaped girder
Concrete slab
Concrete infill
Reinforcements
(b) Angle conectors welded to the webs Fig. 1. Composite beams considered in this research.
ð1Þ
where t and tw respectively represent the thicknesses of channel flanges and webs; lc represents the length of channel connectors; and Ec and fc respectively represent the modulus of elasticity and compressive strength of concrete. In the American Design Code ANSI/AISC 360 [23], the shear strength of one channel connector embedded in a solid concrete slab shall be determined as following:
Ncv ¼ 0:3ðt þ 0:5tw Þlc ðEc f c Þ
0:5
ð2Þ
Please cite this article in press as: Liu Y et al. Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.10.037
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Y. Liu et al. / Engineering Structures xxx (2016) xxx–xxx
T4
P
T5
P
T6
T10
T8 T7
T1
T9 250
700
700
2800
T3
T1
T2
700
1400
700
1400
250
8900
(a) Elevation H1
H2
H3
H4
H5
120
H6 GD1 GC1 GC2 GC3
400 GD2 640
Strain gauges
GC4 GC5
80 250 80 0 1690
Transducers 640
(b) Cross-section Fig. 2. Geometries and instrumentation of tested specimens (unit: mm).
Compared with Eq. (2), Eq. (1) is more conservative in predicting shear strength of the connectors. As such, Eq. (1) was adopted for angle connectors in this research. To quantitatively compare the capacity of a group of connectors in transferring the shear force between the concrete slab and the steel girder, the shear transfer coefficient, ks, was calculated for each specimen based on the following equation:
ks ¼ V c =V n
ð3Þ
where Vc = available strength of the connectors between the point of zero moment and the adjacent point of maximum moment; and Vn = required strength of shear connectors to make the beam fully composite; it is equal to the longitudinal compressive strength of the concrete slab or longitudinal tensile strength of the steel girder, whichever is smaller. According to the definition of ks, a composite beam with its ks value equal to 1.0 or larger is fully composite; otherwise it is partially composite. Based on the nominal resistance of angle connectors calculated using Eq. (1) and the nominal material strength of steel and concrete, the nominal ks value of each specimen was calculated and listed in Table 1. The nominal compressive strength of concrete and yield strength of steel considered in design of the specimens were 30 MPa and 345 MPa, respectively. Specimen CB1 was designed to have a ks value equal to 1.0. Specimens CB2
and CB3 were designed to have reduced ks values. Specimens CB1 to CB3 were designed to investigate the influence of interval of angle connectors on the flexural behavior of composite beams. Specifically, the 238-mm long angle elements were welded to the webs of the U-shaped steel girders and connector intervals were 230 mm, 300 mm and 400 mm in Specimens CB1 to CB3, respectively. Specimen CB4 was the same as Specimen CB1 except that 4 angle connectors were replaced with 14 headed shear studs with the identical nominal shear resistance. Specifically, the headed studs with the diameter and length of 16 mm and 80 mm, respectively, were located at the middle points of the angle connectors at the interval of 600 mm. Two shear studs were provided at each section (one on each top flange). Specimens CB1 and CB4 allow comparison of the responses of the composite beams with angle connectors alone and with both angle connectors and headed studs. Specimen CB5 consisted of 350 mm long angle elements welded to the top flanges of the U-shaped girder. Connector interval in Specimen CB5 was the same as that of Specimen CB2, allowing for comparison of the influence of weld locations of angle connectors on flexural performance of the composite beams.
3. Material properties Material properties of the steel elements and concrete used in the specimens were evaluated through tests of material samples. For steel, coupons were prepared and tested according to the
Table 1 Design of shear connectors in tested specimens.
a
Specimen
Angle sizes (leg width thickness length @ interval) (unit: mm)
Numbers n
Weld location
Nominal ks
CB1 CB2 CB3 CB4 CB5
50 5 238@230 50 5 238@300 50 5 238@400 50 5 238@300a 50 5 350@300
18 14 10 14 14
Web Web Web Web Flange
1.00 0.77 0.55 1.00 0.77
A pair of headed studs of U16 80 (diameter height; unit: mm) were also provided every 600 mm.
Please cite this article in press as: Liu Y et al. Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.10.037
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Table 2 Properties of steel.
a
Type of steel
Thickness/diameter (mm)
Yield strength fy (MPa)
Ultimate strength fu (MPa)
Elastic modulus Es (GPa)
Poisson’s ratio
Flange plate Web plate Angle steel Reinforcement
9.57 5.60 4.44 U10
349.5 380.8 346.6 395.8
514.7 547.2 476.4 541.0
207 196 212 216
0.32 0.31 0.32 –a
Not available.
Table 3 Properties of concrete. Parameter
CB1
CB2
CB3
CB4
CB5
fcu (MPa) f0c (MPa) Ec (GPa)
39.5 30.0 29.0
35.9 27.3 30.8
38.8 29.5 26.8
34.8 26.4 28.3
42.6 32.4 32.4
Chinese Standard GB/T 2975-1998 [24]. Table 2 presents yield strength, fy, ultimate strength, fu, modulus of elasticity, Es, and Poisson’s ratio of each type of steel. For concrete, tests were conducted on both cubes (150 mm 150 mm 150 mm) and prisms (150 mm 150 mm 300 mm). Based on the test procedure, data recording and result processing requirements in the Chinese Standard GBJ81-85 [25], the concrete compressive strength associated with cubes and prisms, fc and f0c , were determined, respectively. Moreover, concrete modulus of elasticity, Ec, was determined based on the test data from prisms. Table 3 reports the concrete material properties for each specimen. The nominal yield and ultimate tensile strengths of the steel in the headed shear studs are 322 MPa and 410 MPa, respectively. However, properties of the headed shear studs were not experimentally verified. 4. Test setup loading scheme and instrumentation Four-point bending tests were performed for all the specimens. Fig. 3 schematically shows the test setup. As shown, each specimen was simply supported at the ends and two identical point loads were applied at its one-third points. For each specimen loaded by such a test setup, the interior beam segment (the portion between the point loads) was under pure bending while the exterior beam segments (the portion from one end of the beam to the adjacent point load) were under constant shear and linearly increasing bending moment. Load on each specimen was monotonically increased through the force control protocol during the test. The load increment
Reaction frame Reaction beam Load cell
Spreader beam
Hydraulic jack
T5
Hydraulic jack
T10
T4
T11
T8 T6 T7
T9
T3 T2
T1
Fig. 3. Test setup.
was selected to be 40 kN per step at speed of 40 kN/min up to the elastic limit of each specimen. Then, the load increment reduced to 20 kN per step till the ultimate state. The load was sustained for 3 min at the end of each loading step to allow observation and recording the progressively developed damages in each specimen. Figs. 2 and 3 present distributions of the displacement transducers and strain gauges attached to each specimen. As shown, each specimen was instrumented to record the following response quantities of interest: strains on concrete slab and steel girder (see Strain Gauges H1 to H6, GD1 and GD2, and GC1 to GC5 in Fig. 2), deflections at the midpoint and two loading points of each composite beam (see Transducers T1 to T3 in Figs. 2 and 3); support settlements (see Transducers T4 and T5 in Figs. 2 and 3), and angle of rotation, slip between concrete slab and steel girder and slip between concrete infill and steel girder at beam ends (see Transducers T6 to T11 in Figs. 2 and 3). 5. Test results Tests of all the specimens were conducted as planned. This section reports the observed specimen behavior and failure modes followed by interpretation of the recorded test data. 5.1. Crack progression and failure mode Overall, the five specimens exhibited similar crack progressions in their concrete slabs with the increases of external loads; however, their failure modes can be differentiated into two categories, depending on if significant slip deformations between concrete slab/infill and steel girder at the beam ends occurred at the strength limit. Here, Specimen CB4 was taken as example to present the progressively developed cracks in the concrete slab. Then, the two types of failure modes are compared in detail. Specimen CB4 exhibited linear behavior at the initial stage of the test (i.e., beam deflection increased proportionally with the external load). When the load reached 410 kN (i.e., 0.66 Pu, where Pu represents the sum of the two point loads resisted by the beam at the strength limit, see in Fig. 3), the strain recorded at the bottom flange of the steel girder (see Strain Gauge GD2 in Fig. 2) reached 1688 le, suggesting that the composite beam reached its yielding limit state. The corresponding deflection recorded at the mid-span of the beam (see Transducer T1 in Fig. 2) reached 31.9 mm (i.e., L/263, where L represents span of the beam). When the load was increased to 460 kN (0.74 Pu), the mid-span deflection reached 43 mm (L/195) and the first crack occurred along the transverse direction on the bottom surface of the concrete slab
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and adjacent to one of the two point loads on the beam. Further increasing the load caused formation of more transverse cracks in the concrete slab over the interior beam segment. When the load reached 500 kN (0.8 Pu), the mid-span deflection reached 55 mm (L/153). Concurrently, on top surface of the concrete slab over the interior beam segment, two longitudinal cracks developed right above the web-to-flange intersections of the steel girder as shown in Fig. 4b. Note that the longitudinal shear in concrete slab reached the maximum along the cracks. When the load reached 600 kN (0.96 Pu), the mid-span deflection reached 150 mm (L/56), and the longitudinal cracks in concrete slab extended from the interior beam segment to the exterior beam segments (i.e., to the regions between the point loads and the adjacent beam supports) (see Fig. 4c). Moreover, extensive transverse cracks concentrated on the bottom surface of the concrete slab as shown in Fig. 4d. At the ultimate load of 624 kN, the mid-span deflection reached 215 mm (L/38) and the concrete slab crushed as shown in Fig. 4e. Permanent deflection of the beam after removal of the external loads is shown in Fig. 4f. Slip deformation of concrete slab relative to steel girder was recorded at the ends of each specimen (See Transducer T8 and T10 in Fig. 2). Similarly, slip deformation of concrete infill relative to steel girder was also recorded (see Transducer T7 and T11 in Fig. 2). Among all the specimens, Specimens CB4 and CB5 did not exhibit significant slip deformations between concrete slabs/infills
(a) Specimen before test
(c) Longitudinal cracks over the exterior beam segments
(e) Crushed failure of concrete slab
5
and steel girders as shown in Fig. 5a. Fig. 6 compares the slip deformations in Specimens CB4 and CB5 (i.e., those without exhibiting large slip deformations at the strength limits). As shown, for these two specimens at the end of the tests, the slip deformation of concrete slab is higher than that of concrete infill at the same end of the beam. Although the maximum slip deformation of both specimens is lower than 0.7 mm, it is found that the maximum slip of Specimen CB4 was larger than that of Specimen CB5. Unlike these two specimens, Specimens CB1 to CB3 developed significant slip deformations between concrete slabs/infills and steel girders under the close-to-ultimate levels of loads. The slip deformations at the ends of Specimens CB1 to CB3 were all higher than 20 mm eventually as shown in Fig. 5b. Fig. 7 compares the load versus slip deformation curves of all specimens. As shown, prior to the ultimate load, all the specimens exhibited very small slip deformations; however, Specimens CB1 to CB3 quickly developed large slip deformations under the maximum applied loads. Specimen CB1 and CB4 which are both design to be full shear connection (ks = 1.0) had significantly different behavior in capacity and ductile, showing that the formula recommended in Chinese Code for Design of Steel Structures [22] cannot properly approximate the shear strength of angle connectors in this study. The nominal shear transfer coefficient ks listed in Table 1 has to be re-evaluated. Taking Specimens CB1 and CB4 as examples of the specimens with and without significant slip deformations, Fig. 8 illustrates
(b) Longitudinal cracks over the interior beam segment
(d) Transverse cracks on bottom surface of concrete slab
(f) Residual deformation in the specimen
Fig. 4. Observations from Specimen CB4.
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Slip deformation
(a) Specimen CB4
(b) Specimen CB1
Fig. 5. Slip deformations at beam ends.
700 700
600 600
Load (kN)
Load (kN)
500 400 300 T8 T9 T10 T11
200 100
0.1
0.2
0.3
0.4
0.5
0.6
400 300 T8 T9 T10 T11
200 100
0 0.0
500
0.7
0 0.00
0.03
0.06
0.09
Slip (mm)
Slip (mm)
(a) Specimens CB4
(b) Specimens CB5
0.12
0.15
Fig. 6. Slip deformations in Specimens CB4 and CB5.
700 600
Load (kN)
500 400 300 CB1 CB2 CB3 CB4 CB5
200 100 0 0
2
4
6
8
10
Slip (mm) Fig. 7. Slip deformations between concrete slabs and steel girders in tested specimens.
their respective crack patterns at the strength limits. Fig. 8a and 8c compares the longitudinal cracks in Specimens CB4 and CB1. As shown, the longitudinal cracks extended along the end of angle connectors because longitudinal shear force in concrete slab reaches its maximum value and exceeded the shear strength of concrete along the end of angle connectors. Then the longitudinal shear force was mainly transferred by the transverse rebars in
the concrete slab. As shown in Fig. 8a and 8c, the longitudinal cracks of Specimen CB4 extended over a larger area (almost along the entire span of the beam) and much more severe than those in Specimen CB1, suggesting that shear connectors in Specimen CB4 are more ductile than those in Specimen CB1. Fig. 8b and 8d compares the transverse cracks over the bottom surfaces of the slabs in Specimens CB4 and CB1. The observed transverse cracks were due to the tensile stresses resulting from the slab bending action. This observation indicates that neutral axes were in the concrete slabs in both specimens eventually. To explore the failure mode of Specimen CB1 to CB3 (in which significant slip deformations occurred at the close-to-ultimate loading levels), the concrete in Specimen CB3 was carefully removed. The distribution of the shear connectors in Specimen CB3 is presented in Fig. 9a. As shown in Fig. 9b and 9c, vertical leg of the first angle connector on the left end of Specimen CB3 severely deformed, resulting in formation of the cracks in the surrounding concrete and significant slip deformations of the concrete slab/infill relative to the U-shaped steel girder. Damage in the first angle connector also triggered redistribution of the shear force along the interface of the concrete slab and steel girder, causing crack of the concrete in the interior portion of the specimen (see Fig. 9d). Comparing with the most exterior angle connector at the left end of the specimen, the interior angle connectors deformed to a much lesser degree (see Fig. 9e), indicating that the longitudinal shear force between the concrete slab and steel girder did not distribute uniformly and it actually reduced gradually from the beam end to the adjacent load point on the beam.
Please cite this article in press as: Liu Y et al. Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.10.037
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7
(a) Longitudinal cracks on top surface of the concrete slab of Specimen CB4
(b) Transverse cracks on bottom surface of the concrete slab of Specimen CB4
(c) Longitudinal cracks on top surface of the concrete slab of Specimen CB1
(d) Transverse cracks on bottom surface of the concrete slab of Specimen CB1 Fig. 8. Comparison of crack patterns of Specimens CB4 and CB1.
5.2. Load-deflection curves Fig. 10 compares development of the deflection recorded at the mid-span of each specimen with the increase of external loads. As shown in Fig. 10, under the load up to 25% of the ultimate strength (around 150 kN), elastic flexural stiffness of the beam, which corresponds to the slope of the initial portion of each curve, remains the same among all the specimens. That is because, during this stage, concrete slab and steel beam behave as a monolithic unit since the angle connectors remains fully elastic and their shear transfer capacity is higher than the shear demand. Additionally, the bond between concrete slab and the steel girder can transfer the longitudinal shear force in the initial stage. Beyond the load associated with 25% of the ultimate strength, these specimens exhibit significant stiffness degradations due to yielding of the steel girders and deformation of the angle connectors. Stiffness values of these specimens during the unloading process are similar to their initial stiffness and all the specimens exhibit significant residual deformations after removal of the external loads. Note that Specimens CB1 to CB3 have the reduced degrees of composite action. As indicated by the curves of these three specimens shown in Fig. 10, the higher degree of the composite action tends to increase the mid-span deflection associated with the strength limit in the composite beams consisting of the angle connectors welded to the webs of the U-shaped girders. It is also shown that Specimens CB1 to CB3 are less ductile in comparison with others. Moreover, it is found that Specimen CB4 exhibits a lar-
ger mid-span deflection associated with the strength limit compared with Specimens CB1 to CB3, suggesting that inclusion of headed studs can improve deformation capacity and delay occurrence of strength degradation in the composite beams with angle connectors welded to the webs of the U-shaped girders. The observed improvement in deformation capacity is primarily due to the following two aspects: (1) the shear studs have better anchorage in the concrete slab due to their headed ends embedded in the concrete slab; and (2) the shear studs were welded to the flanges of the U-shaped girder, which is a more effective location for shear transfer connectors to enable the composite action (this will be further confirmed by the test results from Specimen CB5). Further, it is found from Fig. 10 that Specimen CB5 which includes angle connectors welded on the top flanges of the U-shaped girder has the highest flexural strength and the largest deflection associated with the strength limit, indicating that angle connector welded on the top flanges of the U-shaped girder is more ductile than other type of connectors considered in this investigation. 5.3. Representative strain data Focusing on Specimen CB1, Fig. 11 presents the strain profiles of its mid-span cross-section under different load levels. As shown, up to the close-to-ultimate load (before occurrence of the severe slip deformation along the interfaces of concrete slab/infill and steel girder), the strain profile remains primarily linear, indicating that plane section remained plane during the test. Moreover, as the
Please cite this article in press as: Liu Y et al. Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.10.037
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(a) Distribution of angel connectors
(b) Concrete crack and deformation of the first angle on the left end (before removal of concrete)
(c) Deformation of the first angle on the left end (after removal of concrete)
Angle connectors
Cracks
(d) Cracks in concrete between the interior connectors
(e) Comparison of all connectors
Fig. 9. Angle connectors in Specimen CB3.
400
700 600 500
200
Load (kN)
Load (kN)
300
CB1 CB2 CB3 CB4 CB5
100
400 CB1 CB2 CB3 CB4 CB5
300 200 100
0 0
10
20
30
40
50
Deflection (mm)
0
0
50
100
150
200
250
300
350
400
Deflection (mm)
Fig. 10. Load vs. mid-span deflection curves.
load increases, neutral axis of the beam (see the level associated with zero strain) moves upward and remains in the concrete slab at the strength limit. The neutral axis locations observed at the
higher load levels suggest that the transverse cracks observed at the bottom face of the concrete slab (see Fig. 8) were due to the tensile stress caused by the slab bending action.
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0.85fc’
600
Distance from bottom surface (mm)
c
120kN 280kN 440kN 480kN 520kN 560kN 580kN 600kN 620kN
400
200
fy
NT
(a) Fully composite 0.85fc’
c
-1500
0
1500
3000 4500 Strain ( με )
6000
7500
Ha
s
0
-3000
Nc
fy
9000
fy
Fig. 11. Strain profiles of Specimen CB1.
Nc Nsc
NT
Ha
s
(a) Partially composite Location of neutral axis (mm)
450
Fig. 13. Assumed plastic stress distribution for fully and partially composite beams.
400
350
CB1 CB2 CB3 CB4 CB5
300
250
200 0
50
100
150
200
250
300
Midspan deflection (mm) Fig. 12. Neutral axis locations under different loading levels.
Based on the strain profiles of Specimens CB1 to CB5, movements of their neutral axes during the tests are shown in Fig. 12. As shown, the neutral axes are initially in the steel girders, and then move upward into the concrete slabs. It is found that Specimen CB5 has the highest location of neutral axis at the ultimate strength. Moreover, Specimen CB5 has the highest bearing capacity (see Fig. 10) and the least slip deformation between concrete and steel girder (see Fig. 7). Based on the abovementioned observations, Specimen CB5 is believed to be fully composite while the others are partially composite. As discussed earlier, the shear force transferred by the connectors, FT, should be equal to either the compressive resistance of the concrete slab or the tensile resistance of the steel girder whichever is smaller. Using the material strength presented in Tables 2 and 3, the ultimate tensile resistance of the steel girder was found to be much lower than the compressive resistance of the concrete slab and therefore the tensile resistance of the steel girder was used
to calculate FT. Assuming the steel of the U-shaped girder follows the bilinear strain-stress relationship based on the material properties presented in Table 2. The axial stress and the resultant tension force in the U-shaped girder can be determined based on the girder cross-sectional strain profile (such as the one shown in Fig. 11) for each specimen. Table 4 lists FT, the number of shear connectors, n, and the average shear force transferred by each connector, Fave for each specimen. As shown, Fave of Specimen CB5 is higher than those of Specimens CB1 to CB3, suggesting that the angle connectors welded to the top flanges of the U-shaped girder tend to have higher resistance than those welded to the webs of the U-shaped girder. Replacing Vn in Eq. (3) with the resultant axial force of the U-shaped girder for Specimen CB5 and also setting its ks equal to 1.0 (fully composite), the actual value of ks, denoted as keff, for other specimens could be re-evaluated by Eq. (3). As listed in Table 4, keff varies from 0.677 to 0.942 for Specimens CB1 to CB4. 5.4. Discussion on ultimate flexural resistance In Eurocode 4 [26] and AISC 360 [23], the plastic moment resistance of a composite beam with solid concrete slab and full shear connection can be calculated according to the assumed plastic stress distribution shown in Fig. 13. In Fig. 13, Nc represents the resultant compression in concrete while NT and Nsc respectively represent the resultant tension and compression in steel girder. In addition, Ha represents height of the neutral axis of a composite beam. Moreover, an interpolation method was specified in Eurocode 4 [26] to conservatively predict the flexural resistance of a composite beam with partial shear connection.
Mu ¼ M s þ keff ðM pl Ms Þ
ð4Þ
Table 4 Comparison between experimental and calculated results.
a
Specimens
n
Mut (kN m)
FT (kN)
Fave (kN)
keff
Mu (kN m)
Mu/Mut
CB1 CB2 CB3 CB4 CB5
18 14 10 14/14 14
872.1 789.9 786.9 873.5 958.3
2497.2 2331.1 1989.6 2766.8 2938.7
138.7 166.5 199.0 –a 209.9
0.850 0.793 0.677 0.942 1.000
840.8 795.3 723.1 891.0 949.1
0.964 1.007 0.919 1.020 0.990
Not applicable.
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P
P
Ieff ¼
a
a
a
Fig. 14. Force distribution on composite beams.
where Ms is the plastic flexural resistance of steel beam; Mpl is the plastic flexural resistance of composite beams with full shear connection. Table 4 compares the ultimate moments Mut obtained from the tests with the flexural strengths Mu respectively predicted by Eurocode 4 [26] and AISC 360 [23]. Note that the flexural strengths were calculated using the measured material properties shown in Tables 2 and 3. As compared, the plastic moment resistance of a composite beam with full shear connection calculated according to Eurocode 4 [26] and AISC 360 [23] agrees well with the experimental results of Specimen CB5 (which is fully composite). Focusing on the other specimens that are partially composite (i.e., Specimens CB1 to CB4), the values of Mu/Mut range from 0.919 to 1.020 with the average and standard deviation equal to 0.978 and 0.040, respectively. The observed results suggest that the interpolation method specified by Eurocode 4 [26] overall provides reasonable estimates for the ultimate flexural resistance of the partially composite beams in this research. 5.5. Deflection and initial stiffness The elastic deflection at the midpoint of a simply supported composite beam under the two point loads at its one-third points (see Fig. 14), dc, can be calculated based on the elastic beam theory as:
dc ¼
23Pa3 24Es Ieff
ð5Þ
where Ieff = effective moment of inertia of the composite beam; P = magnitude of the point load; and a = one-third of the beam span. Analysis models considering the influence of the degree of shear connection in current provisions could be applied to predict the initial stiffness of a composite beam. For example, according to Eurocode 4 [26] and the British Standard BS5950-3.1 [27], the deflection of a simply supported partially composite beam can be determined from the following expression for unpropped construction:
d ¼ dc þ 0:3ð1 keff Þðds dc Þ
ð6Þ
where dc is the deflection of a fully composite beam while ds is the deflection of steel girder acting alone. Accordingly, in elastic stage, Eq. (6) can be transformed into:
Is Itr ð0:7 þ 0:3keff ÞIs þ 0:3ð1 keff ÞItr
ð7Þ
where Is is the moment of inertia of steel girder and Itr is the moment of inertia of the uncracked transformed section with the fully composite action (which can be obtained by dividing the width of concrete slab by the ratio of the modulus of elasticity of steel to that of concrete). Alternatively, AISC 360 [23] calculates Ieff as:
qffiffiffiffiffiffiffi Ieff ¼ 0:75 Is þ keff ðItr Is Þ
ð8Þ
The reduction factor (i.e. 0.75) is included in the above equation compared with the recommendation of a former version of AISC 360 [28]. Moreover, the Australian Standard for Composite Structures AS 2327.1 [29] proposes the following equation for Ieff:
Ieff ¼ Itr þ 0:6ð1 keff ÞðIs Itr Þ
ð9Þ
Note that deflection of a composite beam under the prescribed service load should be checked as a required step in design of the beam. Here, the service load on each beam was assumed to be 25% of the load associated with the ultimate resistance of the beam. It should be noted that the concrete slab in tension may be assumed to be either uncracked or cracked when calculating Ieff. For comparison purpose, the moments of inertia of the cracked transformed section, Icr, were also adopted to replace Itr in Eqs. (7)–(9). The beam deflections in accordance with the uncracked and cracked moment of inertia are designated as dtr and dcr, respectively, and compared with the measured deflections, dt, in Table 5. As compared, the mean values of dtr/dt range from 0.611 to 0.808, indicating that predicted deflections using the un-cracked slab properties are unconservative. The mean values of dcr/dt range from 1.013 to 1.341, suggesting that the predicted deflections using the cracked slab properties are conservative. Therefore, it is recommended that the cracked section properties should be used in calculating deflection of the composite beams with U-shaped steel girder under service loads. Moreover, it is found that the results predicted by AS 2327.1 [29] agree better with the experimental results. Note that the values of dcr/dt associated with AS 2327.1 [29] range from 0.942 to 1.166, with the average and standard deviation of 1.013 and 0.080, respectively. It is noteworthy that the values of dcr/dt predicted by AISC 360 [23] including the reduction factor of 0.75 range from 1.242 to 1.533, with the average and standard deviation of 1.341 and 0.102, respectively. Then the average and standard deviation from the former AISC 360 [28] without the reduction factor should be 1.005 and 0.076, respectively. Therefore, the reduction factor should be excluded when AISC 360 is used to calculate the deflection of the composite beam.
Table 5 Comparison of experimental and calculated deflections at a selected service load level. Specimens
CB1 CB2 CB3 CB4 CB5
0.25 Pu
173.0 156.8 156.2 173.3 190.2
dt (mm)
EIs
EItr
EIcr
Eurocode 4
(N mm2)
(N mm2)
(N mm2)
dtr (mm)
dtr/dt
dcr (mm)
dcr/dt
dtr (mm)
AISC 360 dtr/dt
dcr (mm)
dcr/dt
dtr (mm)
AS 2327.1 dtr/dt
dcr (mm)
dcr/dt
12.54 12.03 10.53 11.76 12.86
2.14 108 2.14 108 2.14 108 2.14 108 2.14 108
1.27 109 1.32 109 1.21 109 1.25 109 1.37 109
7.63 108 7.72 108 7.50 108 7.59 108 7.80 108
8.43 7.93 9.52 7.62 7.05 Mean
0.673 0.660 0.904 0.648 0.548 0.686
12.86 11.99 13.14 12.13 12.39
1.025 0.996 1.248 1.031 0.964 1.053
9.84 8.82 10.24 9.60 9.40
0.785 0.733 0.972 0.817 0.731 0.808
16.28 14.94 16.14 15.81 16.52
1.298 1.242 1.533 1.345 1.285 1.341
7.46 6.71 7.80 7.24 7.05
0.595 0.557 0.741 0.615 0.548 0.611
12.32 11.33 12.27 11.91 12.39
0.983 0.942 1.166 1.013 0.964 1.013
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6. Conclusions
References
Based upon the test results obtained from this investigation, the following significant conclusions were drawn:
[1] Nie JG, Fan JS, Cai CS. Experimental study of partially shear-connected composite beams with profiled sheeting. Eng Struct 2008;30(1):1–12. [2] Al-deen S, Ranzi G, Vrcelj Z. Full-scale long-term and ultimate experiments of simply-supported composite beams with steel deck. J Constr Steel Res 2011;67 (10):1658–76. [3] Hsu CTT, Punurai S, Punurai W, et al. New composite beams having coldformed steel joists and concrete slab. Eng Struct 2014;71:187–200. [4] Tesser L, Scotta R. Flexural and shear capacity of composite steel truss and concrete beams with inferior precast concrete base. Eng Struct 2013;49:135–45. [5] Xu C, Su QT, Wu C, et al. Experimental study on double composite action in the negative flexural region of two-span continuous composite box girder. J Constr Steel Res 2011;67(10):1636–48. [6] Ahn IS, Chiewanichakorn M, Chen SS, et al. Effective flange width provisions for composite steel bridges. Eng Struct 2004;26(12):1843–51. [7] Sasaki KK, Paret T, Araiza JC, et al. Failure of concrete T-beam and box-girder highway bridges subjected to cyclic loading from traffic. Eng Struct 2010;32 (7):1838–45. [8] Nakamura S. Bending behavior of composite girders with cold formed steel U section. J Struct Eng 2002;128(9):1169–76. [9] Martinelli E, Faella C, Palma GD. Shear-flexible steel-concrete composite beams in partial interaction: closed-form ‘‘exact” expression of the stiffness matrix. J Eng Mech 2012;138(2):151–63. [10] Faella C, Martinelli E, Nigro E. Shear connection nonlinearity and deflections of steel-concrete composite beams: a simplified method. J Struct Eng 2003;129 (1):12–20. [11] Ranzi G, Zona A. A steel–concrete composite beam model with partial interaction including the shear deformability of the steel component. Eng Struct 2007;29(11):3026–41. [12] Fabbrocino G, Manfredi G, Cosenza E. Analysis of continuous composite beams including partial interaction and bond. J Struct Eng 2000;126(11):1288–94. [13] Chen LZ, Ranzi G, Jiang SC, et al. Behaviour and design of shear connectors in composite slabs at elevated temperatures. J Constr Steel Res 2015;115:387–97. [14] Al-deen S, Ranzi G, Vrcelj Z. Shrinkage effects on the flexural stiffness of composite beams with solid concrete slabs: an experimental study. Eng Struct 2011;33(4):1302–15. [15] Qureshi J, Lam D, Ye J. The influence of profiled sheeting thickness and shear connector’s position on strength and ductility of headed shear connector. Eng Struct 2011;33(5):1643–56. [16] Baran E, Topkaya C. Behavior of steel–concrete partially composite beams with channel type shear connectors. J Constr Steel Res 2014;97:69–78. [17] Sennah K, Kennedy JB, Nour S. Design for shear in curved composite multiple steel box girder bridges. J Bridge Eng 2003;8(3):144–52. [18] Zhang Y, Hou Z, Li Y, et al. Torsional behaviour of curved composite beams in construction stage and diaphragm effects. J Constr Steel Res 2015;108:1–10. [19] Tan EL, Uy B. Experimental study on straight composite beams subjected to combined flexure and torsion. J Constr Steel Res 2009;65(8):1855–63. [20] Ban H, Tan EL, Uy B. Strength of multi-span composite beams subjected to combined flexure and torsion. J Constr Steel Res 2015;113:1–12. [21] Hu SW, Nie JG. Experimental study on composite steel-concrete beams with box sections under combined bending and torsion. Build Struct 2006;36 (8):53–9 [in Chinese]. [22] GBJ17-88. China code for design of steel structure. Beijing, China; 1998. [23] AISC Committee. Specification for structural steel buildings (ANSI/AISC 36010). Chicago, Illinois: American Institute of Steel Construction; 2010. [24] GB/T 2975-1998. Steel and steel products: location and preparation of test pieces for mechanical testing. Beijing, China: Standard Press; 1998 [in Chinese]. [25] GBJ81-85. Test standard for concrete material. Beijing, China: Chinese Planning Press; 1985 [in Chinese]. [26] EN C E N. 1-1, Eurocode 4: design of composite steel and concrete structures. Part 1-1: general rules and rules for buildings 2004; 1994. [27] British Standards Institution (BSI). BS 5950-3.1: 1990 structural use of steelwork in building – Part 3: Design in composite construction – Section 3.1 code of practice for design of simple and continuous composite beams. London: BSI; 1990. [28] American Institution of Steel Construction (AISC). ANSI/AISC 360-05. Specification for structural steel buildings. Chicago: AISC; 2005. [29] Standards Australia. AS 2327.1-2003. Composite structures, Part 1: Simply supported beams. Sydney: Standards Australia; 2003.
1. Composite beams with angle connectors welded to the webs of the U-shaped steel girders (Specimens CB1 to CB3) exhibit significant slip deformations between concrete and U-shaped steel girders. The exterior connectors deform to a higher degree compared with the interior connectors. The experimental results shows that replacing part of angle connectors by welded headed studs is an effective way to improve ductility of the composite beams with angle connectors welded to webs. 2. The composite beam with angle connectors welded on the top flange of the U-shape steel girder (i.e., Specimen CB5) exhibit the fully composite action. It fails in a more ductile manner and develops negligible slip deformations between concrete slab/infill and steel girder. The experimental results show that angle connectors welded on the top flanges of the U-shaped girder have higher shear transfer capacities than these welded to webs of the steel girder. 3. The formula recommended for the channel connectors in the Chinese Design Guidelines overestimates the shear transfer capacity of the angle connectors welded to the webs of the Ushaped girders and underestimates that of angle connectors welded on the top flange of U-shaped steel girder. Further research is needed for developing an improved model quantifying the shear transfer capacity of the angle connectors welded to the different elements of the U-shaped girders. 4. Eurocode 4 and AISC 360 are found to provide reasonable predictions for ultimate flexural resistance of the fully composite beams. Additionally, Eurocode 4 overall provides acceptable results for the ultimate flexural resistance of the partially composite beams. 5. Elastic deflections of the composite beams under service loads may be calculated based on the models recommended in Eurocode 4, AISC 360 and AS 2327.1. The cracked concrete slab properties should be considered in determination of beam deflections. Among all the considered models, the one recommended by AS 2327.1 generate the most accurate beam deflections. An improved prediction of beam deflection can be achieved if the reduction factor recommended in the latest version of AISC 360 is neglected.
Acknowledgements This research was financially supported by the National Natural Science Foundation of China under Awards No. 51578187. The third author was also supported by the Tom and Lucia Chou Fund. The authors wish to acknowledge the sponsors. However, any opinions, findings, conclusions and recommendations presented in this paper are those of the authors and do not necessarily reflect the views of the sponsors. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.engstruct.2016. 10.037.
Please cite this article in press as: Liu Y et al. Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.10.037
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors Yong Liu a, Lanhui Guo a,⇑, Bing Qu b, Sumei Zhang a a b
School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China Dept. of Civil and Environmental Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USA
a r t i c l e
i n f o
Article history: Received 6 May 2016 Revised 16 October 2016 Accepted 18 October 2016 Available online xxxx Keywords: Composite beams U-shaped steel girder Angle connectors Flexural behavior Experimental investigation
a b s t r a c t This paper focuses on a new type of steel-concrete composite beams consisting of U-shaped steel girders and angle connectors. Compared with conventional steel-concrete composite beams consisting of wide flange girders and headed shear stud connectors (or short channel connectors), the composite beams considered in this study have favorable flexural performance while reducing the excessive costs and potential construction challenges due to installation of the stud and/or channel shear connectors. Through four-point bending tests on five specimens, this research team experimentally investigated flexural behavior of the new composite beams. The five specimens were varied to have different angle connector intervals and installation locations. Test results show that composite beams with angle connectors welded to the webs of U-shaped steel girder fail in brittle failure modes while composite beam with angle connectors welded on the top flange of U-shaped steel girder fails in ductile failure mode. Based on the test results, it can be concluded that angle connectors welded on the top flange are more ductile than those welded to the webs. This paper also assesses adequacy of the existing formula for short channel connectors in quantifying the shear transfer capacity of angle connectors and the influence of installation location of angle connectors on the resulting beam response. Moreover, plastic moment resistance of the composite beam with full shear connection predicted by Eurocode 4 and AISC 360 and ultimate flexural strength of the partially composite beams predicted by the interpolation method in Eurocode 4 agree well with the experimental results. Besides, specifications in AS 2327.1 and provisions in AISC 360 neglecting the reduction factor could be used to estimate the initial stiffness of composite beams in this study by using cracked moment of inertia. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Steel-concrete composite beams (referred to herein as composite beams) possess the advantages of both structural steel and reinforced concrete. Although composite beams can take different forms, the most popular version consists of a wide flange girder (i.e., the structural shape with an I-shaped cross-section) supporting a reinforced concrete slab. Through application of appropriate shear connectors between the steel girder and the concrete slab, the two parts can act as one unit in resisting the external loads, i.e., enabling the entire system to form the composite action. Under the same design constraints, composite beams can be more economical than conventional steel beams and lighter than typical reinforced concrete beams. The advantages of composite beams
⇑ Corresponding author.
have been long recognized [1–4] and application of composite beams can be found in many buildings and bridges [5–8]. To date, behavior of composite beams (particularly those with partial shear connections) has been investigated and analytical models have been proposed for quantifying stiffness and deflections of such beams [9–12]. Nevertheless, design challenges still exist, hindering the widespread acceptance of such viable structural components. For example, the most popular shear connectors in composite beams are headed studs and short channels attached to the top flange of the steel girder at prescribed intervals [13–16]. Installation of headed studs requires special automatic tools and skilled operators, for which additional cost may be incurred, offsetting the other advantages of composite beams. Adoption of short channels with their bottom flanges welded to the steel girder can help reduce the cost associated with connector installation, and the top flange can reduce the separation of concrete slab from steel girder. However, the channel connectors may congest the longitudinal
E-mail address: [email protected] (L. Guo). http://dx.doi.org/10.1016/j.engstruct.2016.10.037 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Liu Y et al. Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.10.037
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Y. Liu et al. / Engineering Structures xxx (2016) xxx–xxx
rebars in the concrete slab, resulting in construction difficulties. Therefore, there is a research need to develop alternative shear connectors for composite beams. Moreover, application of composite beams may be impeded in some cases due to the insufficient torsional resistance, e.g., in the exterior beam in a building floor system or a bridge deck system supports the tributary gravity load transferred from one side of the beam [17]. The rotational restraint along the edge of the slab or deck due to the presence of shear connectors can result in a significant torsional demand on the composite beams. The same issue may also occur in an interior beam under unequal gravity loads from both sides of the beam. To resist the torsional demand, a wide flange girder much larger than the one designed for the bending moment demand may have to be used in some cases, leading to a less economical composite beam design. Note that torsional resistance of the composite beam with a wide flange girder is generally lower than the one with a box girder [18–21]. As such, it is necessary to develop alternative girders with torsional performance similar to or equal to that of a box girder for composite beams. This research team explored a practical solution to the above issue, in which a U-shaped steel girder with concrete infills were used as an alternative to the steel girder and equal-leg angles welded along the transverse direction to the girder were used as the shear connectors. Fig. 1 schematically shows the system considered in this investigation. As shown, the angles can be welded either to the top flanges or to the webs of the U-shaped girder. Conceptually, the vertical legs of the angles can resist the longitudinal shear force between concrete slab and steel girder while the horizontal legs can mitigate the separation of the concrete deck from the steel girder. Compared with the widely used short channel connectors, the angles welded to webs reduce the potential of rebar congestions in the concrete slab while retaining the ease of installation. Moreover, the angles help reinforce the U-shaped girder, enabling the girder to exhibit a superior torsional moment resis-
Angle connector Concrete slab
U-shaped girder
Reinforcements
Concrete infill
(a) Angle conectors welded to the top flanges
tance similar to that of a boxed cross-section. Although the infill concrete in the U-shaped girder increases the weight of the girder, it helps mitigate local buckling of the webs of the girder and improve strength and stiffness of the girder. The infill concrete can also enhance fire resistance of the composite beam as it does in other types of composite members. Therefore, it is necessary to study its flexural behavior to promote its application. The objective of this research was to evaluate flexural behavior of such composite beams. Through testing of five specimens, this research team investigated damage progression, failure modes and other aspects of the composite beams under monotonic loading. The test results obtained from this investigation form a basis for a better understanding of the fundamental behavior of such composite beams and help promote their applications in future constructions. The following sections describe in detail specimen design and construction, material properties, test setup, loading program, observations, test results, and assessment of adequacy of existing design models for calculating ultimate flexural resistance of such composite beams. 2. Specimen design and construction Five composite beams, designated as Specimens CB1 to CB5, were tested under 4-point bending. All the specimens were identical except that their shear connectors (including connector type, installation location and connector interval) were varied. As shown in Fig. 2, all specimens had the same length of 8900 mm (measured from beam ends) and span of 8400 mm (measured from beam supports). Depth, flange thickness, web thickness, top flange width and bottom flange width of the steel girder adopted in each specimen were 400 mm, 10 mm, 6 mm, 80 mm and 250 mm, respectively. Based on the Chinese Code for Design of Steel Structures [22], effective width of a concrete slab assumed for a composite beam should be the minimum of L/6, s0/2 and 6hc, where L, s0 and hc represent span of the composite beam, clear distance between the steel girders of adjacent composite beams and the slab thickness, respectively. Accordingly, thickness and width of the concrete slab in each specimen of this investigation were selected to be 120 mm and 1690 mm, respectively. As illustrated in Fig. 2b, two layers of steel rebars with the nominal diameter of 10 mm were spaced at 200 mm and 250 mm along the transverse and longitudinal directions to reinforce the concrete slab, respectively. Steel angles with equal legs (50-mm wide and 5-mm thick) were used as shear connectors in all specimens. It is recognized that no analytical models were readily available for calculating the shear force transfer capacity of each angle connector at the time of the investigation. Alternatively, the formula for calculating shear force transfer capacity of short channel connectors in composite beams was adopted to predict the shear strength of angle connectors in this research. The shear strength Ncv of channel connector can be calculated in the Chinese Code for Design of Steel Structures [22] as following: 0:5
Ncv ¼ 0:26ðt þ 0:5t w Þlc ðEc f c Þ Angle connector U-shaped girder
Concrete slab
Concrete infill
Reinforcements
(b) Angle conectors welded to the webs Fig. 1. Composite beams considered in this research.
ð1Þ
where t and tw respectively represent the thicknesses of channel flanges and webs; lc represents the length of channel connectors; and Ec and fc respectively represent the modulus of elasticity and compressive strength of concrete. In the American Design Code ANSI/AISC 360 [23], the shear strength of one channel connector embedded in a solid concrete slab shall be determined as following:
Ncv ¼ 0:3ðt þ 0:5tw Þlc ðEc f c Þ
0:5
ð2Þ
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Y. Liu et al. / Engineering Structures xxx (2016) xxx–xxx
T4
P
T5
P
T6
T10
T8 T7
T1
T9 250
700
700
2800
T3
T1
T2
700
1400
700
1400
250
8900
(a) Elevation H1
H2
H3
H4
H5
120
H6 GD1 GC1 GC2 GC3
400 GD2 640
Strain gauges
GC4 GC5
80 250 80 0 1690
Transducers 640
(b) Cross-section Fig. 2. Geometries and instrumentation of tested specimens (unit: mm).
Compared with Eq. (2), Eq. (1) is more conservative in predicting shear strength of the connectors. As such, Eq. (1) was adopted for angle connectors in this research. To quantitatively compare the capacity of a group of connectors in transferring the shear force between the concrete slab and the steel girder, the shear transfer coefficient, ks, was calculated for each specimen based on the following equation:
ks ¼ V c =V n
ð3Þ
where Vc = available strength of the connectors between the point of zero moment and the adjacent point of maximum moment; and Vn = required strength of shear connectors to make the beam fully composite; it is equal to the longitudinal compressive strength of the concrete slab or longitudinal tensile strength of the steel girder, whichever is smaller. According to the definition of ks, a composite beam with its ks value equal to 1.0 or larger is fully composite; otherwise it is partially composite. Based on the nominal resistance of angle connectors calculated using Eq. (1) and the nominal material strength of steel and concrete, the nominal ks value of each specimen was calculated and listed in Table 1. The nominal compressive strength of concrete and yield strength of steel considered in design of the specimens were 30 MPa and 345 MPa, respectively. Specimen CB1 was designed to have a ks value equal to 1.0. Specimens CB2
and CB3 were designed to have reduced ks values. Specimens CB1 to CB3 were designed to investigate the influence of interval of angle connectors on the flexural behavior of composite beams. Specifically, the 238-mm long angle elements were welded to the webs of the U-shaped steel girders and connector intervals were 230 mm, 300 mm and 400 mm in Specimens CB1 to CB3, respectively. Specimen CB4 was the same as Specimen CB1 except that 4 angle connectors were replaced with 14 headed shear studs with the identical nominal shear resistance. Specifically, the headed studs with the diameter and length of 16 mm and 80 mm, respectively, were located at the middle points of the angle connectors at the interval of 600 mm. Two shear studs were provided at each section (one on each top flange). Specimens CB1 and CB4 allow comparison of the responses of the composite beams with angle connectors alone and with both angle connectors and headed studs. Specimen CB5 consisted of 350 mm long angle elements welded to the top flanges of the U-shaped girder. Connector interval in Specimen CB5 was the same as that of Specimen CB2, allowing for comparison of the influence of weld locations of angle connectors on flexural performance of the composite beams.
3. Material properties Material properties of the steel elements and concrete used in the specimens were evaluated through tests of material samples. For steel, coupons were prepared and tested according to the
Table 1 Design of shear connectors in tested specimens.
a
Specimen
Angle sizes (leg width thickness length @ interval) (unit: mm)
Numbers n
Weld location
Nominal ks
CB1 CB2 CB3 CB4 CB5
50 5 238@230 50 5 238@300 50 5 238@400 50 5 238@300a 50 5 350@300
18 14 10 14 14
Web Web Web Web Flange
1.00 0.77 0.55 1.00 0.77
A pair of headed studs of U16 80 (diameter height; unit: mm) were also provided every 600 mm.
Please cite this article in press as: Liu Y et al. Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.10.037
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Table 2 Properties of steel.
a
Type of steel
Thickness/diameter (mm)
Yield strength fy (MPa)
Ultimate strength fu (MPa)
Elastic modulus Es (GPa)
Poisson’s ratio
Flange plate Web plate Angle steel Reinforcement
9.57 5.60 4.44 U10
349.5 380.8 346.6 395.8
514.7 547.2 476.4 541.0
207 196 212 216
0.32 0.31 0.32 –a
Not available.
Table 3 Properties of concrete. Parameter
CB1
CB2
CB3
CB4
CB5
fcu (MPa) f0c (MPa) Ec (GPa)
39.5 30.0 29.0
35.9 27.3 30.8
38.8 29.5 26.8
34.8 26.4 28.3
42.6 32.4 32.4
Chinese Standard GB/T 2975-1998 [24]. Table 2 presents yield strength, fy, ultimate strength, fu, modulus of elasticity, Es, and Poisson’s ratio of each type of steel. For concrete, tests were conducted on both cubes (150 mm 150 mm 150 mm) and prisms (150 mm 150 mm 300 mm). Based on the test procedure, data recording and result processing requirements in the Chinese Standard GBJ81-85 [25], the concrete compressive strength associated with cubes and prisms, fc and f0c , were determined, respectively. Moreover, concrete modulus of elasticity, Ec, was determined based on the test data from prisms. Table 3 reports the concrete material properties for each specimen. The nominal yield and ultimate tensile strengths of the steel in the headed shear studs are 322 MPa and 410 MPa, respectively. However, properties of the headed shear studs were not experimentally verified. 4. Test setup loading scheme and instrumentation Four-point bending tests were performed for all the specimens. Fig. 3 schematically shows the test setup. As shown, each specimen was simply supported at the ends and two identical point loads were applied at its one-third points. For each specimen loaded by such a test setup, the interior beam segment (the portion between the point loads) was under pure bending while the exterior beam segments (the portion from one end of the beam to the adjacent point load) were under constant shear and linearly increasing bending moment. Load on each specimen was monotonically increased through the force control protocol during the test. The load increment
Reaction frame Reaction beam Load cell
Spreader beam
Hydraulic jack
T5
Hydraulic jack
T10
T4
T11
T8 T6 T7
T9
T3 T2
T1
Fig. 3. Test setup.
was selected to be 40 kN per step at speed of 40 kN/min up to the elastic limit of each specimen. Then, the load increment reduced to 20 kN per step till the ultimate state. The load was sustained for 3 min at the end of each loading step to allow observation and recording the progressively developed damages in each specimen. Figs. 2 and 3 present distributions of the displacement transducers and strain gauges attached to each specimen. As shown, each specimen was instrumented to record the following response quantities of interest: strains on concrete slab and steel girder (see Strain Gauges H1 to H6, GD1 and GD2, and GC1 to GC5 in Fig. 2), deflections at the midpoint and two loading points of each composite beam (see Transducers T1 to T3 in Figs. 2 and 3); support settlements (see Transducers T4 and T5 in Figs. 2 and 3), and angle of rotation, slip between concrete slab and steel girder and slip between concrete infill and steel girder at beam ends (see Transducers T6 to T11 in Figs. 2 and 3). 5. Test results Tests of all the specimens were conducted as planned. This section reports the observed specimen behavior and failure modes followed by interpretation of the recorded test data. 5.1. Crack progression and failure mode Overall, the five specimens exhibited similar crack progressions in their concrete slabs with the increases of external loads; however, their failure modes can be differentiated into two categories, depending on if significant slip deformations between concrete slab/infill and steel girder at the beam ends occurred at the strength limit. Here, Specimen CB4 was taken as example to present the progressively developed cracks in the concrete slab. Then, the two types of failure modes are compared in detail. Specimen CB4 exhibited linear behavior at the initial stage of the test (i.e., beam deflection increased proportionally with the external load). When the load reached 410 kN (i.e., 0.66 Pu, where Pu represents the sum of the two point loads resisted by the beam at the strength limit, see in Fig. 3), the strain recorded at the bottom flange of the steel girder (see Strain Gauge GD2 in Fig. 2) reached 1688 le, suggesting that the composite beam reached its yielding limit state. The corresponding deflection recorded at the mid-span of the beam (see Transducer T1 in Fig. 2) reached 31.9 mm (i.e., L/263, where L represents span of the beam). When the load was increased to 460 kN (0.74 Pu), the mid-span deflection reached 43 mm (L/195) and the first crack occurred along the transverse direction on the bottom surface of the concrete slab
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and adjacent to one of the two point loads on the beam. Further increasing the load caused formation of more transverse cracks in the concrete slab over the interior beam segment. When the load reached 500 kN (0.8 Pu), the mid-span deflection reached 55 mm (L/153). Concurrently, on top surface of the concrete slab over the interior beam segment, two longitudinal cracks developed right above the web-to-flange intersections of the steel girder as shown in Fig. 4b. Note that the longitudinal shear in concrete slab reached the maximum along the cracks. When the load reached 600 kN (0.96 Pu), the mid-span deflection reached 150 mm (L/56), and the longitudinal cracks in concrete slab extended from the interior beam segment to the exterior beam segments (i.e., to the regions between the point loads and the adjacent beam supports) (see Fig. 4c). Moreover, extensive transverse cracks concentrated on the bottom surface of the concrete slab as shown in Fig. 4d. At the ultimate load of 624 kN, the mid-span deflection reached 215 mm (L/38) and the concrete slab crushed as shown in Fig. 4e. Permanent deflection of the beam after removal of the external loads is shown in Fig. 4f. Slip deformation of concrete slab relative to steel girder was recorded at the ends of each specimen (See Transducer T8 and T10 in Fig. 2). Similarly, slip deformation of concrete infill relative to steel girder was also recorded (see Transducer T7 and T11 in Fig. 2). Among all the specimens, Specimens CB4 and CB5 did not exhibit significant slip deformations between concrete slabs/infills
(a) Specimen before test
(c) Longitudinal cracks over the exterior beam segments
(e) Crushed failure of concrete slab
5
and steel girders as shown in Fig. 5a. Fig. 6 compares the slip deformations in Specimens CB4 and CB5 (i.e., those without exhibiting large slip deformations at the strength limits). As shown, for these two specimens at the end of the tests, the slip deformation of concrete slab is higher than that of concrete infill at the same end of the beam. Although the maximum slip deformation of both specimens is lower than 0.7 mm, it is found that the maximum slip of Specimen CB4 was larger than that of Specimen CB5. Unlike these two specimens, Specimens CB1 to CB3 developed significant slip deformations between concrete slabs/infills and steel girders under the close-to-ultimate levels of loads. The slip deformations at the ends of Specimens CB1 to CB3 were all higher than 20 mm eventually as shown in Fig. 5b. Fig. 7 compares the load versus slip deformation curves of all specimens. As shown, prior to the ultimate load, all the specimens exhibited very small slip deformations; however, Specimens CB1 to CB3 quickly developed large slip deformations under the maximum applied loads. Specimen CB1 and CB4 which are both design to be full shear connection (ks = 1.0) had significantly different behavior in capacity and ductile, showing that the formula recommended in Chinese Code for Design of Steel Structures [22] cannot properly approximate the shear strength of angle connectors in this study. The nominal shear transfer coefficient ks listed in Table 1 has to be re-evaluated. Taking Specimens CB1 and CB4 as examples of the specimens with and without significant slip deformations, Fig. 8 illustrates
(b) Longitudinal cracks over the interior beam segment
(d) Transverse cracks on bottom surface of concrete slab
(f) Residual deformation in the specimen
Fig. 4. Observations from Specimen CB4.
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Slip deformation
(a) Specimen CB4
(b) Specimen CB1
Fig. 5. Slip deformations at beam ends.
700 700
600 600
Load (kN)
Load (kN)
500 400 300 T8 T9 T10 T11
200 100
0.1
0.2
0.3
0.4
0.5
0.6
400 300 T8 T9 T10 T11
200 100
0 0.0
500
0.7
0 0.00
0.03
0.06
0.09
Slip (mm)
Slip (mm)
(a) Specimens CB4
(b) Specimens CB5
0.12
0.15
Fig. 6. Slip deformations in Specimens CB4 and CB5.
700 600
Load (kN)
500 400 300 CB1 CB2 CB3 CB4 CB5
200 100 0 0
2
4
6
8
10
Slip (mm) Fig. 7. Slip deformations between concrete slabs and steel girders in tested specimens.
their respective crack patterns at the strength limits. Fig. 8a and 8c compares the longitudinal cracks in Specimens CB4 and CB1. As shown, the longitudinal cracks extended along the end of angle connectors because longitudinal shear force in concrete slab reaches its maximum value and exceeded the shear strength of concrete along the end of angle connectors. Then the longitudinal shear force was mainly transferred by the transverse rebars in
the concrete slab. As shown in Fig. 8a and 8c, the longitudinal cracks of Specimen CB4 extended over a larger area (almost along the entire span of the beam) and much more severe than those in Specimen CB1, suggesting that shear connectors in Specimen CB4 are more ductile than those in Specimen CB1. Fig. 8b and 8d compares the transverse cracks over the bottom surfaces of the slabs in Specimens CB4 and CB1. The observed transverse cracks were due to the tensile stresses resulting from the slab bending action. This observation indicates that neutral axes were in the concrete slabs in both specimens eventually. To explore the failure mode of Specimen CB1 to CB3 (in which significant slip deformations occurred at the close-to-ultimate loading levels), the concrete in Specimen CB3 was carefully removed. The distribution of the shear connectors in Specimen CB3 is presented in Fig. 9a. As shown in Fig. 9b and 9c, vertical leg of the first angle connector on the left end of Specimen CB3 severely deformed, resulting in formation of the cracks in the surrounding concrete and significant slip deformations of the concrete slab/infill relative to the U-shaped steel girder. Damage in the first angle connector also triggered redistribution of the shear force along the interface of the concrete slab and steel girder, causing crack of the concrete in the interior portion of the specimen (see Fig. 9d). Comparing with the most exterior angle connector at the left end of the specimen, the interior angle connectors deformed to a much lesser degree (see Fig. 9e), indicating that the longitudinal shear force between the concrete slab and steel girder did not distribute uniformly and it actually reduced gradually from the beam end to the adjacent load point on the beam.
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7
(a) Longitudinal cracks on top surface of the concrete slab of Specimen CB4
(b) Transverse cracks on bottom surface of the concrete slab of Specimen CB4
(c) Longitudinal cracks on top surface of the concrete slab of Specimen CB1
(d) Transverse cracks on bottom surface of the concrete slab of Specimen CB1 Fig. 8. Comparison of crack patterns of Specimens CB4 and CB1.
5.2. Load-deflection curves Fig. 10 compares development of the deflection recorded at the mid-span of each specimen with the increase of external loads. As shown in Fig. 10, under the load up to 25% of the ultimate strength (around 150 kN), elastic flexural stiffness of the beam, which corresponds to the slope of the initial portion of each curve, remains the same among all the specimens. That is because, during this stage, concrete slab and steel beam behave as a monolithic unit since the angle connectors remains fully elastic and their shear transfer capacity is higher than the shear demand. Additionally, the bond between concrete slab and the steel girder can transfer the longitudinal shear force in the initial stage. Beyond the load associated with 25% of the ultimate strength, these specimens exhibit significant stiffness degradations due to yielding of the steel girders and deformation of the angle connectors. Stiffness values of these specimens during the unloading process are similar to their initial stiffness and all the specimens exhibit significant residual deformations after removal of the external loads. Note that Specimens CB1 to CB3 have the reduced degrees of composite action. As indicated by the curves of these three specimens shown in Fig. 10, the higher degree of the composite action tends to increase the mid-span deflection associated with the strength limit in the composite beams consisting of the angle connectors welded to the webs of the U-shaped girders. It is also shown that Specimens CB1 to CB3 are less ductile in comparison with others. Moreover, it is found that Specimen CB4 exhibits a lar-
ger mid-span deflection associated with the strength limit compared with Specimens CB1 to CB3, suggesting that inclusion of headed studs can improve deformation capacity and delay occurrence of strength degradation in the composite beams with angle connectors welded to the webs of the U-shaped girders. The observed improvement in deformation capacity is primarily due to the following two aspects: (1) the shear studs have better anchorage in the concrete slab due to their headed ends embedded in the concrete slab; and (2) the shear studs were welded to the flanges of the U-shaped girder, which is a more effective location for shear transfer connectors to enable the composite action (this will be further confirmed by the test results from Specimen CB5). Further, it is found from Fig. 10 that Specimen CB5 which includes angle connectors welded on the top flanges of the U-shaped girder has the highest flexural strength and the largest deflection associated with the strength limit, indicating that angle connector welded on the top flanges of the U-shaped girder is more ductile than other type of connectors considered in this investigation. 5.3. Representative strain data Focusing on Specimen CB1, Fig. 11 presents the strain profiles of its mid-span cross-section under different load levels. As shown, up to the close-to-ultimate load (before occurrence of the severe slip deformation along the interfaces of concrete slab/infill and steel girder), the strain profile remains primarily linear, indicating that plane section remained plane during the test. Moreover, as the
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(a) Distribution of angel connectors
(b) Concrete crack and deformation of the first angle on the left end (before removal of concrete)
(c) Deformation of the first angle on the left end (after removal of concrete)
Angle connectors
Cracks
(d) Cracks in concrete between the interior connectors
(e) Comparison of all connectors
Fig. 9. Angle connectors in Specimen CB3.
400
700 600 500
200
Load (kN)
Load (kN)
300
CB1 CB2 CB3 CB4 CB5
100
400 CB1 CB2 CB3 CB4 CB5
300 200 100
0 0
10
20
30
40
50
Deflection (mm)
0
0
50
100
150
200
250
300
350
400
Deflection (mm)
Fig. 10. Load vs. mid-span deflection curves.
load increases, neutral axis of the beam (see the level associated with zero strain) moves upward and remains in the concrete slab at the strength limit. The neutral axis locations observed at the
higher load levels suggest that the transverse cracks observed at the bottom face of the concrete slab (see Fig. 8) were due to the tensile stress caused by the slab bending action.
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0.85fc’
600
Distance from bottom surface (mm)
c
120kN 280kN 440kN 480kN 520kN 560kN 580kN 600kN 620kN
400
200
fy
NT
(a) Fully composite 0.85fc’
c
-1500
0
1500
3000 4500 Strain ( με )
6000
7500
Ha
s
0
-3000
Nc
fy
9000
fy
Fig. 11. Strain profiles of Specimen CB1.
Nc Nsc
NT
Ha
s
(a) Partially composite Location of neutral axis (mm)
450
Fig. 13. Assumed plastic stress distribution for fully and partially composite beams.
400
350
CB1 CB2 CB3 CB4 CB5
300
250
200 0
50
100
150
200
250
300
Midspan deflection (mm) Fig. 12. Neutral axis locations under different loading levels.
Based on the strain profiles of Specimens CB1 to CB5, movements of their neutral axes during the tests are shown in Fig. 12. As shown, the neutral axes are initially in the steel girders, and then move upward into the concrete slabs. It is found that Specimen CB5 has the highest location of neutral axis at the ultimate strength. Moreover, Specimen CB5 has the highest bearing capacity (see Fig. 10) and the least slip deformation between concrete and steel girder (see Fig. 7). Based on the abovementioned observations, Specimen CB5 is believed to be fully composite while the others are partially composite. As discussed earlier, the shear force transferred by the connectors, FT, should be equal to either the compressive resistance of the concrete slab or the tensile resistance of the steel girder whichever is smaller. Using the material strength presented in Tables 2 and 3, the ultimate tensile resistance of the steel girder was found to be much lower than the compressive resistance of the concrete slab and therefore the tensile resistance of the steel girder was used
to calculate FT. Assuming the steel of the U-shaped girder follows the bilinear strain-stress relationship based on the material properties presented in Table 2. The axial stress and the resultant tension force in the U-shaped girder can be determined based on the girder cross-sectional strain profile (such as the one shown in Fig. 11) for each specimen. Table 4 lists FT, the number of shear connectors, n, and the average shear force transferred by each connector, Fave for each specimen. As shown, Fave of Specimen CB5 is higher than those of Specimens CB1 to CB3, suggesting that the angle connectors welded to the top flanges of the U-shaped girder tend to have higher resistance than those welded to the webs of the U-shaped girder. Replacing Vn in Eq. (3) with the resultant axial force of the U-shaped girder for Specimen CB5 and also setting its ks equal to 1.0 (fully composite), the actual value of ks, denoted as keff, for other specimens could be re-evaluated by Eq. (3). As listed in Table 4, keff varies from 0.677 to 0.942 for Specimens CB1 to CB4. 5.4. Discussion on ultimate flexural resistance In Eurocode 4 [26] and AISC 360 [23], the plastic moment resistance of a composite beam with solid concrete slab and full shear connection can be calculated according to the assumed plastic stress distribution shown in Fig. 13. In Fig. 13, Nc represents the resultant compression in concrete while NT and Nsc respectively represent the resultant tension and compression in steel girder. In addition, Ha represents height of the neutral axis of a composite beam. Moreover, an interpolation method was specified in Eurocode 4 [26] to conservatively predict the flexural resistance of a composite beam with partial shear connection.
Mu ¼ M s þ keff ðM pl Ms Þ
ð4Þ
Table 4 Comparison between experimental and calculated results.
a
Specimens
n
Mut (kN m)
FT (kN)
Fave (kN)
keff
Mu (kN m)
Mu/Mut
CB1 CB2 CB3 CB4 CB5
18 14 10 14/14 14
872.1 789.9 786.9 873.5 958.3
2497.2 2331.1 1989.6 2766.8 2938.7
138.7 166.5 199.0 –a 209.9
0.850 0.793 0.677 0.942 1.000
840.8 795.3 723.1 891.0 949.1
0.964 1.007 0.919 1.020 0.990
Not applicable.
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Y. Liu et al. / Engineering Structures xxx (2016) xxx–xxx
P
P
Ieff ¼
a
a
a
Fig. 14. Force distribution on composite beams.
where Ms is the plastic flexural resistance of steel beam; Mpl is the plastic flexural resistance of composite beams with full shear connection. Table 4 compares the ultimate moments Mut obtained from the tests with the flexural strengths Mu respectively predicted by Eurocode 4 [26] and AISC 360 [23]. Note that the flexural strengths were calculated using the measured material properties shown in Tables 2 and 3. As compared, the plastic moment resistance of a composite beam with full shear connection calculated according to Eurocode 4 [26] and AISC 360 [23] agrees well with the experimental results of Specimen CB5 (which is fully composite). Focusing on the other specimens that are partially composite (i.e., Specimens CB1 to CB4), the values of Mu/Mut range from 0.919 to 1.020 with the average and standard deviation equal to 0.978 and 0.040, respectively. The observed results suggest that the interpolation method specified by Eurocode 4 [26] overall provides reasonable estimates for the ultimate flexural resistance of the partially composite beams in this research. 5.5. Deflection and initial stiffness The elastic deflection at the midpoint of a simply supported composite beam under the two point loads at its one-third points (see Fig. 14), dc, can be calculated based on the elastic beam theory as:
dc ¼
23Pa3 24Es Ieff
ð5Þ
where Ieff = effective moment of inertia of the composite beam; P = magnitude of the point load; and a = one-third of the beam span. Analysis models considering the influence of the degree of shear connection in current provisions could be applied to predict the initial stiffness of a composite beam. For example, according to Eurocode 4 [26] and the British Standard BS5950-3.1 [27], the deflection of a simply supported partially composite beam can be determined from the following expression for unpropped construction:
d ¼ dc þ 0:3ð1 keff Þðds dc Þ
ð6Þ
where dc is the deflection of a fully composite beam while ds is the deflection of steel girder acting alone. Accordingly, in elastic stage, Eq. (6) can be transformed into:
Is Itr ð0:7 þ 0:3keff ÞIs þ 0:3ð1 keff ÞItr
ð7Þ
where Is is the moment of inertia of steel girder and Itr is the moment of inertia of the uncracked transformed section with the fully composite action (which can be obtained by dividing the width of concrete slab by the ratio of the modulus of elasticity of steel to that of concrete). Alternatively, AISC 360 [23] calculates Ieff as:
qffiffiffiffiffiffiffi Ieff ¼ 0:75 Is þ keff ðItr Is Þ
ð8Þ
The reduction factor (i.e. 0.75) is included in the above equation compared with the recommendation of a former version of AISC 360 [28]. Moreover, the Australian Standard for Composite Structures AS 2327.1 [29] proposes the following equation for Ieff:
Ieff ¼ Itr þ 0:6ð1 keff ÞðIs Itr Þ
ð9Þ
Note that deflection of a composite beam under the prescribed service load should be checked as a required step in design of the beam. Here, the service load on each beam was assumed to be 25% of the load associated with the ultimate resistance of the beam. It should be noted that the concrete slab in tension may be assumed to be either uncracked or cracked when calculating Ieff. For comparison purpose, the moments of inertia of the cracked transformed section, Icr, were also adopted to replace Itr in Eqs. (7)–(9). The beam deflections in accordance with the uncracked and cracked moment of inertia are designated as dtr and dcr, respectively, and compared with the measured deflections, dt, in Table 5. As compared, the mean values of dtr/dt range from 0.611 to 0.808, indicating that predicted deflections using the un-cracked slab properties are unconservative. The mean values of dcr/dt range from 1.013 to 1.341, suggesting that the predicted deflections using the cracked slab properties are conservative. Therefore, it is recommended that the cracked section properties should be used in calculating deflection of the composite beams with U-shaped steel girder under service loads. Moreover, it is found that the results predicted by AS 2327.1 [29] agree better with the experimental results. Note that the values of dcr/dt associated with AS 2327.1 [29] range from 0.942 to 1.166, with the average and standard deviation of 1.013 and 0.080, respectively. It is noteworthy that the values of dcr/dt predicted by AISC 360 [23] including the reduction factor of 0.75 range from 1.242 to 1.533, with the average and standard deviation of 1.341 and 0.102, respectively. Then the average and standard deviation from the former AISC 360 [28] without the reduction factor should be 1.005 and 0.076, respectively. Therefore, the reduction factor should be excluded when AISC 360 is used to calculate the deflection of the composite beam.
Table 5 Comparison of experimental and calculated deflections at a selected service load level. Specimens
CB1 CB2 CB3 CB4 CB5
0.25 Pu
173.0 156.8 156.2 173.3 190.2
dt (mm)
EIs
EItr
EIcr
Eurocode 4
(N mm2)
(N mm2)
(N mm2)
dtr (mm)
dtr/dt
dcr (mm)
dcr/dt
dtr (mm)
AISC 360 dtr/dt
dcr (mm)
dcr/dt
dtr (mm)
AS 2327.1 dtr/dt
dcr (mm)
dcr/dt
12.54 12.03 10.53 11.76 12.86
2.14 108 2.14 108 2.14 108 2.14 108 2.14 108
1.27 109 1.32 109 1.21 109 1.25 109 1.37 109
7.63 108 7.72 108 7.50 108 7.59 108 7.80 108
8.43 7.93 9.52 7.62 7.05 Mean
0.673 0.660 0.904 0.648 0.548 0.686
12.86 11.99 13.14 12.13 12.39
1.025 0.996 1.248 1.031 0.964 1.053
9.84 8.82 10.24 9.60 9.40
0.785 0.733 0.972 0.817 0.731 0.808
16.28 14.94 16.14 15.81 16.52
1.298 1.242 1.533 1.345 1.285 1.341
7.46 6.71 7.80 7.24 7.05
0.595 0.557 0.741 0.615 0.548 0.611
12.32 11.33 12.27 11.91 12.39
0.983 0.942 1.166 1.013 0.964 1.013
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11
6. Conclusions
References
Based upon the test results obtained from this investigation, the following significant conclusions were drawn:
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1. Composite beams with angle connectors welded to the webs of the U-shaped steel girders (Specimens CB1 to CB3) exhibit significant slip deformations between concrete and U-shaped steel girders. The exterior connectors deform to a higher degree compared with the interior connectors. The experimental results shows that replacing part of angle connectors by welded headed studs is an effective way to improve ductility of the composite beams with angle connectors welded to webs. 2. The composite beam with angle connectors welded on the top flange of the U-shape steel girder (i.e., Specimen CB5) exhibit the fully composite action. It fails in a more ductile manner and develops negligible slip deformations between concrete slab/infill and steel girder. The experimental results show that angle connectors welded on the top flanges of the U-shaped girder have higher shear transfer capacities than these welded to webs of the steel girder. 3. The formula recommended for the channel connectors in the Chinese Design Guidelines overestimates the shear transfer capacity of the angle connectors welded to the webs of the Ushaped girders and underestimates that of angle connectors welded on the top flange of U-shaped steel girder. Further research is needed for developing an improved model quantifying the shear transfer capacity of the angle connectors welded to the different elements of the U-shaped girders. 4. Eurocode 4 and AISC 360 are found to provide reasonable predictions for ultimate flexural resistance of the fully composite beams. Additionally, Eurocode 4 overall provides acceptable results for the ultimate flexural resistance of the partially composite beams. 5. Elastic deflections of the composite beams under service loads may be calculated based on the models recommended in Eurocode 4, AISC 360 and AS 2327.1. The cracked concrete slab properties should be considered in determination of beam deflections. Among all the considered models, the one recommended by AS 2327.1 generate the most accurate beam deflections. An improved prediction of beam deflection can be achieved if the reduction factor recommended in the latest version of AISC 360 is neglected.
Acknowledgements This research was financially supported by the National Natural Science Foundation of China under Awards No. 51578187. The third author was also supported by the Tom and Lucia Chou Fund. The authors wish to acknowledge the sponsors. However, any opinions, findings, conclusions and recommendations presented in this paper are those of the authors and do not necessarily reflect the views of the sponsors. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.engstruct.2016. 10.037.
Please cite this article in press as: Liu Y et al. Experimental investigation on the flexural behavior of steel-concrete composite beams with U-shaped steel girders and angle connectors. Eng Struct (2016), http://dx.doi.org/10.1016/j.engstruct.2016.10.037