Experimental study on flexural performance of steel-reinforced concrete slim floor beams

Abstract

In long-span floors, the use of composite slim floor beams can effectively improve the flexural stiffness and flexural capacity of the floor system. In order to strengthen the stiffness of the composite slim floor beams and achieve better fire resistance, an innovative steel-reinforced concrete slim floor beams is presented in this article. To investigate the flexural performance of the steel-reinforced concrete slim floor beams, static loading experiments were carried out on six specimens. The parameters of the test were the height of slim floor beams and the type and size of steel shape in the steel-reinforced concrete slim floor beams. On the basis of the experiment, the bending failure modes, flexural stiffness, and flexural capacity of the steel-reinforced concrete slim floor beams were studied comprehensively. The test results indicated that the steel-reinforced concrete slim floor beams exhibited great flexural capacity, large stiffness, and high ductility. The calculation formulas of flexural stiffness and flexural capacity were also proposed in this article. The analysis of flexural performance of the steel-reinforced concrete slim floor beams can provide a significant foundation for further research.

Keywords

bending stiffness experimental study flexural capacity flexural performance steel-reinforced concrete slim floor beams

Introduction

The slim floor originated in Switzerland in the early 19th century. Due to its good construction efficiency, which can increase the clearance of the building and reduce the height of floor, it is rapidly developed and researched (Lawson et al., 1999). The traditional slim floors generally adopt cast-in-place reinforced concrete slabs, nevertheless, with the increasing requirements for greater stiffness and flexural capacity in large-span structures, which the traditional slim floors are difficult to satisfy. Therefore, in recent years, the composite slim floor beams were developed and applied in large-span floor structures such as subways and garages. The ordinary composite slim floor beam usually is composed of steel deck, an embedded asymmetric steel beam, and the concrete slab, resulting in a type of floor construction.

In order to strengthen the stiffness of the composite slim floor beams so that it can be used in transfer story with thick floorslab and heavy load garages, and achieve better fire resistance where the steel shapes are totally embedded in the concrete, an innovative steel-reinforced concrete (SRC) slim floor beams, which are abbreviated here as SRC slim floor beams, is presented in this article, as shown in Figure 1. Although the SRC slim floor beams may cost more than the normal composite steel-concrete beams during construction, the height of normal composite steel-concrete beams section normally increases with the increase in span. The use of SRC slim floor beams can result in a reduction in floor depth, as well as large uninterrupted floor areas and significant fire resistance (Ahn and Lee, 2017; Chung, 2002; Singh et al., 2016). And the SRC slim floor beams can be constructed by precast method which could reduce the construction costs and shorten the construction period (Yang et al., 2017, 2018).

Figure 1.

Schematic diagram of SRC slim floor beams.

In recent years, many studies have been conducted on composite slim floor beams (Gholamhoseini et al., 2018; Hegger et al., 2009; Hicks et al., 2006; Li, 2005; Limazie and Chen, 2015; Nádaský, 2012; Yang et al., 2006; Zhang et al., 2016). Among these researches, experimental tests on nine SRC slim floor beams were conducted in Helsinki University of Technology, the tests mainly studied the bending behavior of composite slim floor beams (Lu and Makelainen, 1995). Meanwhile, the effects of parameters such as reinforcement ratios and types of loading on the mechanical behaviors of composite slim floor beams were investigated by Bernuzzi et al. (1995) from Trento University of Technology. The experimental results showed the reinforcement ratios of the slab had a significant influence on the bearing capacity of specimens.

Wang et al. (2009) conducted static load tests on composite slim floor beams with deep deck. The test results showed that the specimens had good bearing capacity and deformation performance, and the bending capacity of the composite slim floor beams can be calculated according to the plastic stress calculation method. A design guide for composite beams using precast concrete slabs was proposed by the Steel Construction Institute (Hicks and Lawson, 2003). However, this design guide was mainly for the design of T-section composite beams, and it was limited to design composite slim floor beams. In general, most of these flexural performance studies were focused on the ordinary composite slim floor beams, and study on the flexural performance of the SRC slim floor beam is very rare in the literatures.

The composite slim floor beam using castellated steel shape have been studied by many researchers in recent years. Chung and Lawson (2001) combined with Eurocode 4 proposed a design method for composite slim floor beams with large web openings. Chen et al. (2015) have carried out the experimental research on the mechanical properties and shear transfer mechanism of shallow cellular composite floor beams. The results showed that the combination of castellated steel shape and concrete can significantly improve the mechanical performance of the composite members. At the same time, it can also improve the shear capacity, slip capacity, and ductility. However, researches on the bending behavior of the SRC slim floor beams using castellated steel shape are relatively rare.

However, the use of composite slim floor beams should be based on the well understanding of the mechanical behaviors of the entire structural components. The combination of steel shape and concrete is the most important aspect in the design of composite slim floor beams (YB9082-2006, 2006). Nardin and El Debs (2009) had carried out an experimental research on the influence of stud setting in the composite slim floor beams. The research showed that welding studs on the top flange of the steel shape can achieve considerable composite action and elastoplastic performance. Thereafter, Nardin and El Debs (2012) conducted a full-scale experiment of beam–column connections in composite slim floor beams, including bare steel connection and composite connection. The result showed that there were almost no steel–concrete slip at the interface between the composite plate and the steel beam at the free end, indicating that the steel shape and concrete worked together well. However, compared with ordinary composite slim floor beams and other composite members, researches on the bending performance of the SRC slim floor beams are very rare in the literatures, which could result in the application of SRC slim floor beams being limited in practical engineering.

To investigate the flexural performance of the SRC slim floor beams, six specimens were carried out. The main variables of the test were the height of specimens, size and type of the steel shapes. Based on the experimental study, the calculation formulas for predicting the flexural capacity and stiffness of the SRC slim floor beams are presented and revised later in this article.

Test program

Test specimens

Six SRC slim floor beam specimens, SRC-1 to SRC-6, were designed and constructed. The steel shapes in the specimens SRC-1 to SRC-5 are all traditional H-steel shape except for that in the SRC-6, which applied castellated steel shape. The key parameters are summarized in Table 1. The schematic diagram of the SRC slim floor beams is illustrated in Figure 2(a) and (b).

Table 1.

Main parameters of the specimens.

Specimen ID	Specimen size (mm) L × B	Specimen height, H (mm)	Shear span ratio	Type of steel shape	Steel size (mm)	Cubic strength of concrete (MPa)	Test setup
SRC-1	2700 × 900	450	3.0	H-shaped	200 × 100 × 5.5 × 8	53.3	One-point loading
SRC-2	2700 × 900	350	3.0	H-shaped	200 × 100 × 5.5 × 8	53.3	Two-point loading
SRC-3	2700 × 900	260	3.0	H-shaped	150 × 75 × 5 × 7	53.3	Two-point loading
SRC-4	2700 × 900	300	3.0	H-shaped	150 × 75 × 5 × 7	53.3	Two-point loading
SRC-5	2700 × 900	300	3.0	H-shaped	200 × 100 × 5.5 × 8	53.3	Two-point loading
SRC-6	2700 × 900	260	3.0	Castellated	226 × 75 × 5 × 7	53.3	Two-point loading

The numbers in the steel size represent total height, flange width, web thickness, and flange thickness in order.

Figure 2.

Schematic diagram of SRC slim floor beam specimens: (a) H-steel shape and (b) castellateed steel shape.

Cross section

These six specimens were similar in cross section form but different in dimensions. As listed in Table 1, there are four different specimen heights and four different sizes of steel shape. The length and width of the specimens are 2700 and 900 mm, respectively, as shown in Figure 4(a) and (b), and the heights of the specimens are from 260 to 450 mm. The steel shapes in the specimens SRC-1 to SRC-5 are all traditional H-steel shape, except for the SRC-6 which applied castellated steel shape, and the characteristics of castellated steel shape are shown in Figure 2(b). The steel shapes in all specimens are in the middle of the cross sections. Specimens in the test are not reinforced by transverse reinforcement; therefore, the bonding performance is not as good as conventional SRC. High-strength bolts are installed within 250 mm at both ends of the flange plate to ensure the bonding performance between steel shape and concrete.

Materials

For the flange of the steel shape, the tested tensile strengths were 286 MPa at yield and 405 MPa at failure. For the web of the steel shape, the tested tensile strengths were 300 MPa at yield and 404 MPa at peak. The tested tensile strengths of the longitudinal reinforcing bar, A10 bars with a diameter of 10 mm and a grade of HPB300, were 334 MPa at yield and 438 MPa at peak.

For the six specimens, the strength grades of the concrete were identical, which was C40 graded per the Chinese code, and the tested compressive strength was 53.3 MPa at 28 days. The compressive strength f_c, of the concrete was calculated as 0.8 times the cubic strength f_cu in the following discussion. All of the configurations of the specimens and the condition of the reinforcements are summarized in Tables 1 and 2.

Table 2.

Mechanical properties of steel shape and reinforcing bars.

Material	Yield strength $f_{y}$ ( $N / m m^{2}$ )	Ultimate strength $f_{u}$ ( $N / m m^{2}$ )	Elastic modulus $E_{s}$ ( $MPa$ )
Flanges	286	405	2.05 × 10⁵
Web	300	404	2.05 × 10⁵
Reinforcing bar	334	438	2.1 × 10⁵

Test setup and instrumentations

In the experiments, all the specimens were tested on an electro hydraulic servo-testing machine with a maximum capacity of 5000 kN. The loading method includes two-point symmetrical loading and single-point centralized loading. The loading devices are shown in Figure 3(a). The shear span-to-depth ratio was 3.0 for all specimens.

Figure 3.

Schematic diagram and photo of test setup (unit: mm): (a) loading devices, (b) layout of LVDTs, and (c) photo of test setup.

During the experiment process, linear variable differential transformers (LVDTs) were used to measure all of the deflections at the central point, loading point, and two supports. A number of electrical-resistance strain gauges were placed on the flanges and web of the steel shape and the reinforcing bars to monitor the strain response. In order to verify the plane section assumption, two sets of strain gauges were vertically set along the height of the cross section on both sides of the specimens at the mid-span point. Figure 3(b) shows the layout of the LVDTs, and Figure 4 shows the layout of the strain gauges.

Figure 4.

Layout of strain gauges (unit: mm): (a) layout of strain gauges on the concrete, (b) layout of strain gauges at the top surface of concrete, and (c) layout of strain gauges on the steel shape.

Experiment phenomena and result analysis

Experiment phenomenon

The six specimens demonstrated similar loading behavior in the test. Taking specimen SRC-2 as an example, in the initial loading phase of the specimens, it can be observed that the load–deflection curve exhibited linear elasticity. As the load applied reached 30% of the peak load, first vertical cracks emerged near the mid-span of the specimen with a slight sound, and the other vertical cracks began to emerge near the loading point and slowly developed with the increase in load. As the load applied reached 50% of the peak load, no new vertical cracks appeared but the existing cracks widened. When the applied load reached 72% of the peak load, the bottom flange and web of steel shape began to yield. With the load increased, the vertical crack developed rapidly, and lateral cracks appeared in the compression zone. Whereafter, the concrete in the compression zone was partially crushed and the applied load reached the peak load at the same time, then the load slowly decreased as the displacement increased. Finally, when the load decreased to 85% of the peak load, the loading process was over.

All the six specimens showed typical flexural failures. The typical failure modes of the specimens and are shown in Figure 5.

Figure 5.

Typical failure modes and damage patterns of specimens: (a) SRC-2, (b) SRC-4, (c) SRC-5, and (d) SRC-6.

Analysis of test results

Figure 6 shows the strain distribution curves of the steel in the specimens SRC-2, SRC-4, and SRC-5. The result indicated that the Euler–Bernoulli beam theory, which states that plane sections remain plane for beams under loading, was satisfied in these specimens. Figure 7 shows the load–deflection curves of these six specimens. In the initial stage of loading, the curve developed smoothly with the increase in load and showed obvious elastic characteristics.

Figure 6.

Strain distribution curves along the specimen height: (a) SRC-2, (b) SRC-4, and (c) SRC-5.

Figure 7.

The load–deflection curves of the specimens.

With the load increased, the bottom flange and web of steel shape at the tension zone began to yield. As a result, a large deflection occurred on the load–deflection curves, indicating the beginning of the elastic–plastic stage. When the load reached the peak load and began to fall down, the steel shape at the tensile area was completely yielded, and the deflection of the curved segment increased significantly. During the failing stage, the curves continued to maintain a relatively gradual decline until the end of loading, showing good ductility. According to the load–deflection test curves, the final flexural capacity of the specimens can be obtained, as shown in Table 3.

Table 3.

Test results of the specimens.

Specimen ID	Load of the flexuralCracking $P_{cr}$ (kN)	Peak load $P_{y}$ (kN)	Flexural capacity $M_{u}$ (kN mm)	Yielding deflection $Δ_{y}$ (mm)	Ultimate deflection $Δ_{u}$ (mm)	Ductility ratios $Δ_{u}$ / $Δ_{y}$
SRC-1	220	646	536	7.94	42.16	5.31
SRC-2	170	560	465	13.92	63.48	4.56
SRC-3	138	324	269	11.59	52.18	4.50
SRC-4	150	450	374	14.95	79.35	5.31
SRC-5	128	550	438	10.15	80.19	7.90
SRC-6	100	350	291	13.56	64.26	4.74

Based on the above test results, the influence of the main parameters on the bending performance of SRC slim floor beams was analyzed. As implied from the test results listed in Table 3 and illustrated in Figure 8, the flexural capacity of the SRC slim floor beams was obviously affected by the specimen height. The peak load of specimen SRC-4 was 39% higher than that of specimen SRC-3, and the difference of peak load among specimens SRC-5, SRC-2, and SRC-1 were 6% and 15%, respectively. Therefore, the flexural capacity of SRC slim beams increased as the height of specimens increased.

Figure 8.

Influence of the specimen height on flexural capacity.

Steel size also played an important role on the bending performance of the SRC slim floor beams as shown in Table 3 and Figure 9; the peak load of specimen SRC-5 was 22% higher than that of specimen SRC-4. From the comparison, it could be concluded that the flexural capacity of the SRC slim floor beams increased as the size of steel shape increased. Table 3 and Figure 9 also showed that the peak load of specimen 6 was 8% higher than the specimen SRC-3, and the test results indicated that using castellated steel shape in the SRC slim floor beams can achieve better bending performance and make full use of materials.

Figure 9.

Influence of the size and type of steel shape on flexural capacity.

From the load–deflection curves of the specimens shown in Figure 7, the ductility ratios of the specimens were calculated as the ultimate deflection Δ_u divided by the yielding deflection Δ_y; the yield displacements Δ_y of the specimens were calculated by the universal yield bending moment method; and the ultimate deflection Δ_u was defined as the deflection when the load descended to 85% of the peak load during the failing stage. The calculation results are shown in Table 3. As observed from the test results, the ductility ratios of specimens SRC-4 and SRC-5 were 5.31 and 7.90, respectively. The comparison indicated that the ductility of SRC slim beams increased as the size of specimens increased. The effect of different types of steel shape on the ductility of specimens can also be observed from Table 3, the ductility ratios of specimens SRC-3 and SRC-6 were 4.50 and 4.74, respectively. The result indicated that the ductility of specimens can be improved using castellated steel shape, but the effect on the ductility was relatively small.

Flexural capacity calculation method

Basic assumptions

The test results indicated that the steel shape worked together well with concrete, showing sufficiently composite effect. Based on the measured strain results, the plane section assumption was verified to be valid. Meanwhile, the measured strain results indicated the bottom flange and web of steel shape were almost tensed to yield. Therefore, the plastic stress theory can be used to calculate the flexural capacity of SRC slim floor beams. In the plastic stress theory, the basic assumptions used in the plastic stress theory are listed as follows:

The plane section assumption was satisfied;

The steel shape and the reinforcing bars were fully yielded at the tension zone and the compression zone, and all the stresses were taken as yield stress for simplicity;

The tensile strength of the concrete was ignored.

Calculation methods

The flexural capacity of the SRC slim beams varies with the position of the neutral axis. In order to simplify the design process, three different situations can be defined according to the three different positions of the neutral axis: one case with the neutral axis passing over the steel shape, another case with the neutral axis passing through the steel upper flange, and the third case with the neutral axis passing through the web of steel shape. The calculation sketches for flexural capacity are shown in Figure 10.

Figure 10.

Calculation sketch for flexural capacity. (a) Case 1: the neutral axis passing over the steel shape. (b) Case 2: the neutral axis passing through the upper flange of steel shape. (c) Case 3: the neutral axis passing through the web of steel shape.

Case 1: the neutral axis passing over the steel shape

It is assumed that the neutral axis passes over the steel shape and should satisfy the case where the height of the compression zone x is less than $a'_{a}$ , as shown in Figure 10(a). In this case, the calculation can be divided into two cases: one considers the effect of upper flange of the steel shape and the other does not consider the effect of upper flange effect of the steel shape. These two cases are based on the basic assumptions from the equilibrium conditions of the forces in the cross section.

When condition $x \leq \frac{0.8 {a'}_{a}}{1 + (f_{a} / 1.003 E_{ss})}$ is satisfied, the effect of upper flange of steel shape is taken into account, and the flexural capacity M_u can be calculated by equation (1)

\begin{matrix} M \leq f_{y} A_{s} (h - a_{s} - x) + f_{a} A_{ss} (h - x - a_{s} - 0.5 h_{a}) \\ + f_{y} A'_{s} (x - a'_{s}) + 0.5 f_{c} b x^{2} \end{matrix}

(1)

When condition $\frac{0.8 {a'}_{a}}{1 + (f_{a} / 1.003 E_{ss})} \leq x \leq \frac{0.8 (h - a_{a})}{1 + (f_{a} / 1.003 E_{ss})}$ is satisfied, the effect of upper flange of steel shape is not considered, and the flexural capacity M_u can be calculated by equation (2)

\begin{matrix} M \leq f_{y} A_{s} (h - a_{s} - {a'}_{a}) + f_{a} A_{sf} (h - x - a_{a} - t_{f} / 2) \\ + f_{a} t_{w} (h_{a} - 2 t_{f}) ({a'}_{a} - x + h_{a} / 2) + f_{y} {A'}_{s} ({a'}_{a} - {a'}_{s}) \\ + f_{c} bx ({a'}_{a} - x / 2) \end{matrix}

(2)

Case 2: the neutral axis passing through the upper flange of steel shape

It is assumed that the neutral axis passes through the upper flange of steel shape and should satisfy the case where the height of the compression zone x is equal to $a'_{a}$ , as shown in Figure 10(b). Based on the basic assumptions from the equilibrium conditions of the forces in the cross section, the flexural capacity M_u can be calculated by equation (3)

\begin{matrix} M & \leq f_{c} bx ({a'}_{a} - x / 2) + f_{y} A_{s} (h - {a'}_{a} - a_{s}) \\ + f_{y} A'_{s} ({a'}_{a} - a_{s}) + f_{a} A_{ss} h_{a} / 2 \end{matrix}

(3)

Case 3: the neutral axis passing through the web of steel shape

It is assumed that the neutral axis passes through the web of steel shape and should satisfy the case where the height of the compression zone x is greater than $a'_{a}$ , as shown in Figure 10(c). Based on the basic assumptions from the equilibrium conditions of the forces in the cross section, the flexural capacity M_u can be calculated by equation (4)

\begin{matrix} M & \leq f_{a} A_{sf} (h - x - a_{a} - \frac{t_{f}}{2}) + f_{a} t_{w} \frac{(h - x - a_{a} - {t_{f})}^{2}}{2} \\ + f_{a} {A'}_{sf} (x - {a'}_{a} - t_{f} / 2) \\ + f_{a} t_{w} \frac{{(x - {a'}_{a} - t_{f})}^{2}}{2} + f_{y} A_{s} (h - x - a_{s}) \\ + f_{y} {A'}_{s} (x - {a'}_{s}) + f_{c} \frac{b x^{2}}{2} \end{matrix}

(4)

The calculation method of the specimen SRC-6 using castellated steel shape is similar to these methods, and the height of the hole is subtracted when calculating the web height.

Validation

The flexural capacity of the specimens can be calculated by the calculation method established above. At the same time, the flexural capacity of the specimens were calculated based on the YB9082-2006 by equation (5) to (7), and the results obtained by these two calculation methods are listed in Table 4.

M \leq M_{by}^{ss} + M_{bu}^{rc}

(5)

where $M_{by}^{ss}$ represents the flexural capacity of steel shape and $M_{bu}^{rc}$ represents the flexural capacity of the concrete.

Table 4.

Comparisons of the calculated results of the specimens.

SpecimenID	Tested flexural capacity $M_{u}^{e}$ (kN·m)	Calculated results by methods suggested $M_{u}^{c - 1}$ (kN·m)	$M_{u}^{c - 1} / M_{u}^{e}$	Calculated results by methods of Chinese Specification $M_{u}^{c - 2}$ (kN·m)	$M_{u}^{c - 2} / M_{u}^{e}$
SRC-1	536	450	0.84	367	0.68
SRC-2	465	384	0.83	305	0.66
SRC-3	269	236	0.88	188	0.69
SRC-4	374	333	0.89	268	0.72
SRC-5	438	383	0.88	315	0.72
SRC-6	291	247	0.85	201	0.69
Average value			0.86		0.69
Coefficient of variation			0.03		0.03

The flexural capacity of the steel shape is calculated by equation (6)

M_{by}^{ss} = γ_{s} W_{ss} f_{a}

(6)

The flexural capacity of concrete is calculated by equation (7)

M_{bu}^{rc} = A_{s} f_{sy} γ h_{0}

(7)

The calculation method in YB9082-2006 (2006) was simple based on the principle of superposition, and the calculation method proposed in this article was based on the plane section assumption and the plasticity theory. It can be seen from the results in Table 4 that the calculation results based on the calculation method proposed in this article are more reasonable than the results obtained by the method recommended in the YB9082-2006 (2006), which is simple but too conservative. Therefore, the calculation method in this article provides a means of considering safety and conservatism to predict the flexural capacity of SRC slim floor beams in practical engineering.

Flexural stiffness calculation method

Flexural stiffness calculation method taking stiffness center zone into consideration

In SRC slim floor beams, the concrete between the flange and web of steel shape is constrained, resulting in an increase in the strength of the concrete and a slow development of the crack. In the normal use stage, the stiffness of this part is higher than other parts, forming a stiffness center zone (YB9082-2006, 2006). In calculating the flexural stiffness, the section stiffness of SRC slim floor beams can be regarded as consisting of the following three parts:

Stiffness of reinforced concrete part (excluding the stiffness center zone) B_rc;

Stiffness of the steel shape B_ss;

Stiffness of concrete stiffness center zone constrained by steel shape B_c.

The following basic assumptions are used in flexural stiffness calculations:

The plane section assumption was satisfied;

In the use phase, reinforcing bar, steel shape, and concrete all work in the elastic stage;

The crack section does not consider the effect of the tensioned concrete.

The stiffness of the reinforced concrete part of the SRC slim floor beams can be calculated by equation (8)

B_{rc} = \frac{E_{s} A_{s} h_{0}^{2}}{1.15 Ψ + 0.2 + \frac{6 α_{E} ρ}{1 + 3.5 {γ'}_{1}}}

(8)

In this formula, Ψ is defined as the coefficient of non-uniformity of the longitudinally stretched reinforcement between cracks. For components directly subjected to repeated loads, take Ψ = 1.0.

According to the observation and analysis of the crack width and penetration of each specimen, there is indeed a stiffness center zone which is substantially free from cracking. YB9082-2006 (2006) suggests using an equivalent rectangle to calculate the stiffness center zone and suggested that the width of the stiffness center zone is taken to be 1.6 times the narrow width of the flange. Considering that the cross-sectional width of SRC slim floor beams used in this experiment is much larger than the width of the steel flange, combined with the results of crack observation, it is found that the width of the stiffness center zone of the SRC slim floor beams is slightly larger than the width of the narrow flange of 1.6-fold. The conversion width b_c of the rigid zone can be calculated by equation (9)

b_{c} = 1.83 b_{s}

(9)

The stiffness B_c of the concrete in the stiffness center zone can be calculated by equation (10)

B_{c} = E_{c} [\frac{1}{12} b_{c} h_{s}^{3} + b_{c} h_{s} {(\frac{h_{s}}{2} - \bar{x} + {a'}_{s})}^{2}]

(10)

The stiffness B_ss of steel shape can be calculated by equation (11)

B_{ss} = E_{ss} [I_{sso} + A_{ss} {({a'}_{s} + \frac{h_{s}}{2} - \bar{x})}^{2}]

(11)

In summary, the stiffness of SRC slim floor beams can be obtained by equation (12)

B_{s} = B_{rc} + B_{ss} + B_{c}

(12)

Transformed section method

Before the SRC slim floor beams cracked, it can be considered to be in the stage of full elastic deformation, and the section stiffness can be calculated according to the conversion stiffness of the section. From the time of cracking to the stage before steel shape in tensile zone yield, the stiffness of SRC slim floor beams is significantly reduced due to the cracking of the concrete, leading to nonlinear deformation. The stiffness B_s of SRC slim floor beams is composed of reinforced concrete B_c and steel stiffness B_ss.

The following basic assumptions are used in flexural stiffness calculations:

The plane section assumption was satisfied;

The steel shape and concrete meet compatible deformation.

The stiffness of the steel shape can be calculated by equation (13)

B_{ss} = E_{s} I_{s}

(13)

The flexural stiffness of the concrete can be calculated by equation (14) (YB9082-2006, 2006)

B_{c} = \frac{E_{s} A_{s} h_{0}^{2}}{1.15 Ψ + 0.2 + \frac{6 α_{E} ρ}{1 + 3.5 {γ'}_{f}}}

(14)

In summary, the short-term stiffness of SRC slim floor beams can be obtained by equation (15)

B_{s} = B_{SS} + B_{C}

(15)

Summarization and analysis of stiffness calculation

According to the flexural stiffness calculation method and the traditional conversion section method, the displacements of the specimens were calculated, and the results are listed as shown in Table 5.

Table 5.

The contrast of two stiffness calculation methods.

Specimen ID	Tested deflectionf_t (mm)	Calculated results by methods mentioned in section “Flexural stiffness calculation method taking stiffness center zone into consideration”f₁ (mm)	$\frac{f_{1} - f_{t}}{f_{t}}$ (%)	Calculated results by methods mentioned in “Transformed section method”f₂ (mm)	$\frac{f_{2} - f_{t}}{f_{t}}$ (%)
SRC-1	7.32	7.90	7.9	8.17	11.6
SRC-2	12.15	12.55	3.3	13.70	12.7
SRC-3	8.34	8.52	2.1	9.19	10.2
SRC-4	12.93	13.80	6.7	14.73	13.6
SRC-5	9.12	9.72	6.6	10.39	13.9
SRC-6	8.12	8.33	2.6	8.92	9.9

$f_{t}$ adopts the corresponding deflection at 70% ultimate load.

It can be seen from the results in Table 5 that the calculation results based on the calculation method which could take stiffness center zone into consideration are more reasonable than the results obtained by the calculation method of the conversion section method. Therefore, the flexural stiffness calculation method proposed in section “Transformed section method” is more suitable for the SRC slim floor beams.

Conclusion

To strengthen the stiffness of the composite slim floor beams and achieve better fire resistance, an innovative SRC slim floor beams is proposed in this article. In this article, six SRC slim floor beam specimens were tested and studied. Combined with experimental results and theoretical analysis, the flexural capacity and bending stiffness of the SRC slim floor beams were analyzed. The main conclusions drawn from this article are as follows.

The SRC slim floor beams exhibited good flexural performance, and the steel and concrete are well bonded. The cross-sectional strain of SRC slim floor beams conforms to the plane section assumption. When calculating deformation and flexural capacity, the steel shape and concrete can be considered to work together.

The height of the specimens and the size of steel shape directly affected the flexural capacity of the SRC slim floor beams, and the flexural capacity of the specimens increased with the increase in the height of specimen and size of steel shape. The use of castellated steel shape in the SRC slim floor beams is an effective way to improve the flexural capacity and it can also make full use of materials.

The calculation methods for the flexural capacities of the SRC slim floor beams were introduced in this article, which were verified to be valid and more reasonable than the method in YB9082-2006 (2006). It is recommended to use the method suggested in this article to calculate the flexural capacity of the SRC slim floor beams.

Two stiffness calculation methods of the SRC slim floor beams were proposed in this article. By comparing the tested deflection with the calculated deflection obtained by the two methods, the method which took stiffness center zone into consideration was verified to be valid and predicted more reasonable results than the transformed section method did.

Footnotes

Appendix 1 Acknowledgements

The funding, cooperation, and assistance of many people from the organization are greatly acknowledged.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the National Science Foundation of the People’s Republic of China under the grant no. 51778525.

ORCID iD

Bo Wei

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