Investigation on partially concrete encased composite beams under hogging moment

Abstract

In order to investigate the mechanical behavior of the partially concrete encased composite beam under hogging moment, static loading tests were conducted on one conventional composite beam and three partially concrete encased composite beams. The results show that partially concrete encased composite beams have higher stiffness and flexural capacity under hogging moment as compared with conventional composite beams. It is also found that the concrete encasement is able to enhance the local bucking resistance of the steel beam and effectively reduces the propagation speed of crack width under hogging moment. By comparing different partially concrete encased composite beams, it is indicated that the stiffness and flexural capacity of partially concrete encased composite beams increase with the increase in reinforcement ratio of the concrete slab. Also, with the increase in the reinforcement ratio of the concrete slab, the distribution of cracks on the slab is denser and the propagation speed of crack width reduces. In addition, the calculation methods in both European code and Chinese code can well predict the crack width on the concrete slab, and the ultimate flexural capacity predicted from the simplified plastic theory in Eurocode 4 is in good agreement with test results.

Keywords

crack width flexural capacity hogging moment partially concrete encased composite beams static loading tests

Introduction

The application of simply supported steel-concrete composite beams can take full advantage of both materials, as the concrete slab is mainly in compression and the steel profile is in tension. However, a large number of composite beams used in the practical engineering are continuous beams, which aims to improve the overall performance of beams especially in terms of deformation. In the area near the internal supports, large bending moment and shear force exist, and the concrete in tension does not contribute to the bending capacity. Moreover, for the conventional composite beam, the steel profile in compression is sensitive to local buckling and lateral-torsional buckling (Chen and Wang, 2012; Vrcelj and Bradford, 2009).

In the 1970s, for the purpose of fireproofing, the partially concrete encased composite beam (PECB) turned up in Germany (Schleich et al., 1983). In PECBs, concrete is poured between the two flanges of the steel beam, as shown in Figure 1(b). The concrete encasement can effectively prevent the temperature of steel from rising sharply in the fire (Piloto et al., 2011, 2013). Usually, the steel beam and the web encasement are integrated by connectors to ensure working as an integral (De Nardin and El Debs, 2009; Kindmann and Bergmann, 1993). However, as research and application continues, it is further realized that, besides good fire-resistant performance, the web encasement also contributes to the enhancement in the stiffness, and about 20% increase in the bearing capacity without enlarging the overall size of the cross section (He et al., 2014; Kindmann and Bergmann, 1993). When this section form is used in a continuous beam, not only the bending and shear capacity of steel beams around the internal supports increase, the buckling of web and flange in compression can also be prevented (He et al., 2012a, 2012b; Jiang et al., 2016; Nakamura and Narita, 2003).

Figure 1.

Cross sections of beam specimens (unit: mm): (a) specimen SCCB2 and (b) specimens PECB5-7.

So far, there have been some investigations on partially encased beams with or without the concrete slab. Kindmann and Bergmann (1993) performed positive bending tests on 12 PECBs with the span length of 3.6 m. Out of 12 beam specimens, two were integrated with concrete slabs. It was proved that the web encasement contributes to the stiffness and flexural capacity significantly. Nakamura and Narita (2003) suggested the use of partially encased composite I-girders as bridge girders, and proposed analytical methods to calculate the bending and shear strength for the encased composite girders. Hegger and Goralski (2004) evaluated the load-carrying behavior of PECBs under both sagging and hogging moment. The results showed that, under sagging moment, nearly no difference in the load–deformation behavior could be recognized between the beams with and without shear connection in the encasement, and the measured slip between the encasement and the steel profile was always less than 0.2 mm. The friction was enough to transfer the shear force between the steel flanges and the concrete encasement. While under hogging moment, the beam without shear connection showed reduced stiffness, premature yielding and 20% reduction in flexural capacity as compared with the beam with sufficient shear connection. The measured slip in the interface could reach up to 25 mm. Kvočáka and Drab (2012) conducted a comparative study between thin-walled steel beams with and without the web encasement. It was found possible to achieve a material saving by concreting in beam’s web, which is laterally secured against buckling. Jiang et al. (2016) performed static tests on three continuous PECBs, to investigate the law of moment redistribution of this kind of composite beam. In addition, a series of push-out tests on headed stud connectors in the encasement of PECBs was conducted (Zheng et al., 2015).

At present, there are few reports about the mechanical behavior of PECBs under hogging moment. Hegger and Goralski (2004) only focused on the effect of the shear connection on the flexural capacity of PECBs under hogging moment. However, there have been no investigations about the effect of the reinforcement ratio of the concrete slab on the mechanical and the anti-cracking properties of PECBs. In this article, experimental studies and theoretical analyses are conducted to investigate the mechanical behavior of PECBs. Three PECB specimens are tested, and the only variable parameter is the reinforcement ratio of the concrete slab. One conventional composite beam specimen is also tested for comparison. In addition, crack width on the concrete slab and the ultimate flexural capacity under hogging moment are calculated theoretically, and compared with the test results.

Experimental program

Beam specimens

A total of four beam specimens are designed for testing. Beam specimen SCCB2 is a simply supported conventional composite beam, and beam specimens PECB5-7 are simply supported PECBs. The span length of each beam specimen is 3800 mm. The cross sections of beam specimens are shown in Figure 1. In all beam specimens, two rows of studs with 19 mm diameter and 80 mm length are welded on the top flanges, with a transverse spacing of 80 mm symmetric about the centerline of the top flange and a longitudinal spacing of 200 mm. Full shear connection is therefore achieved between the concrete slab and the steel profile, which is determined according to Eurocode 4 (EN 1994-1-1:2004, 2004). For PECB specimens, one row of studs is welded on the central position of the steel web to enhance the connection performance between the steel profile and the web encasement. The studs on the web are in the same type with those on the top steel flange, while with a longitudinal spacing of 340 mm. The spacing of the studs on the web is also determined according to Eurocode 4, to ensure full shear connection between the steel profile and the concrete encasement. The shear force transferred between the steel profile and the concrete encasement can be obtained by the equilibrium equation of axial forces for the cross section. The determination of the value of spacing is based on the stud shear capacity from the push-out tests by Zheng et al. (2015). The three PECBs have a varying amount of longitudinal reinforcement in the concrete slab. Details of the reinforcement for beam specimens are given in Table 1. The material performance for steel in the test is summarized in Table 2, and the cube compressive strengths (the mean value of three 150 mm × 150 mm × 150 mm concrete cubes) for concrete are given in Table 3.

Table 1.

Reinforcement of beam specimens.

Specimen	Reinforcement in the concrete slab		Reinforcement in the web encasement
Specimen	Longitudinal	Transverse	Longitudinal	Stirrups
SCCB2	5B14 (top), 4B14 (bottom)	A10@125	–	–
PECB5	5B14 (top), 4B14 (bottom)		4A8 (top), 4B18 (bottom)	A8@160
PECB6	9B14 (top), 4B14 (bottom)
PECB7	13B14 (top), 4B14 (bottom)

Table 2.

Material performance for steel.

	Type	Yield strength (N/mm²)	Ultimate strength (N/mm²)
Steel profile	Q235	270.0	447.0
Reinforcement	A8	460.2	502.5
	A10	420.4	528.2
	B14	433.0	539.0
	B18	364.0	539.5
Stud	Φ19X80	460.0	515.0

Table 3.

Material performance for concrete.

Specimen		SCCB2	PECB5	PECB6	PECB7
Compressive strength (N/mm²)	Concrete slab	24.8	25.1	26.6	26.2
Compressive strength (N/mm²)	Web encasement	–	24.1	26.6	27.1

Test set-up and measurements

As is shown in Figure 2, all beam specimens were simply supported on rollers, and the load from the hydraulic jack was applied to the steel beam of the specimen by means of a spreader. The length of pure bending zone is 800 mm. The load was monotonically applied in three stages: at the beginning, the load was applied at the rate of 10 kN per step. When reaching approximately 70% of the estimated ultimate flexural capacity of the specimens, the load was reduced to 5 kN per step. After each step, the load was held for 10 min. During the loading process, the test measurements included vertical load, deflection in the mid-span, strains near mid-span section, relative slip between the concrete slab and the steel beam, relative slip between the web encasement and the steel beam (see Figure 2).

Figure 2.

Test set-up and measuring point layout (unit: mm).

Test results and discussion

Crack characteristics and failure mode

The first flexural crack appeared on the top of the concrete slab near mid-span section of specimen SCCB2 at approximately 15.8% of its measured ultimate load. With the increase in the load, additional flexural cracks formed continuously on the surface of the concrete slab. These cracks eventually penetrated to the bottom of the concrete slab. At about 50% of the ultimate load, cracks in the shear span began to incline toward the centerline of the slab under the combined action of negative bending and longitudinal shear. At the ultimate failure state, the compression flange of the steel beam buckled locally.

The three partially encased specimens PECB5-6 varied only in the amount of longitudinal reinforcement in the concrete slab, and their experiment phenomena and failure modes were similar. Take specimen PECB6, for an example, at 13.8% of the measured ultimate load, there exhibited the first flexural crack on the concrete slab near the mid-span section. Like specimen SCCB2, cracks of specimen PECB6 also increased in the number and developed downward as the load increased, eventually penetrating the concrete slab as well (see Figure 3(a)). Afterwards, at approximate 33.8% of the ultimate load, the first vertical flexural crack appeared in the web concrete of the pure bending zone, where the stirrup did not exist. With the increase in load, the amount of cracks increased continuously but developed at slow speed. When approaching the ultimate load, the bottom of the web encasement in the pure bending zone began to crush (see Figure 3(b)), and the flexural failure was observed in specimen PECB6 (see Figure 3(c)). During the loading process, no slip occurred between the steel beam and the web encasement, while small slip appeared between the steel beam and the concrete slab at the beam end (see Figure 3(d)).

Figure 3.

Crack characteristics and failure mode: (a) crack distribution on the concrete slab, (b) crush of the encased concrete, (c) the overall flexural failure, and (d) no slip occurred between encasement and steel beam.

Load–deflection behavior and load-carrying capacity

The relationship between the applied load and the deflection of mid-span of the specimens is shown in Figure 4. The load–deflection behavior can be roughly divided into four stages. From the start of loading to the cracking of concrete slab, beam specimens are at the elastic state, and the load–deflection curves are in completely linearity. After the cracking of concrete slabs, the stiffness of all beam specimens decreases to some degree. From the cracking of concrete slab to the yielding of the bottom steel flange, beam specimens are at the elastic-plastic stage. Although the plastic deformation increase somewhat, load–deflection curves approximately keep a linear relationship. Compared with specimen SCCB2, specimens PECB5-7 have much longer elastic-plastic stage and much larger gradients of the curves at this stage. It is indicated that the web encasement helps to postpone the bottom steel flange from yielding, and to enhance the flexural stiffness of the composite beam under hogging moment. After the yield of reinforcement, crack width of the concrete slab in the mid-span increases obviously. The deflection of specimens increases at a higher speed, and the load curves become flatter gradually. At this stage, specimens PECB5-7 undergo a considerable increase in the load as the reinforcement in the web encasement can also provide bearing capacity. In the end, the load decreases in each beam specimen when failure occurs.

Figure 4.

Load–deflection curves.

The primary test results are summarized and compared in Table 4. It is found that the initial cracking moment, the yielding moment, and the ultimate moment of PECB specimens are obviously larger than those of the conventional beam specimen. The comparison results of the three specimens PECB5-7 indicate that both the yielding moment and the ultimate moment increase as the reinforcement ratio of the concrete slab increases. In addition, the displacement ductility factor µ of partially encased beam specimens is all above 4.0, which indicates that PECB specimens have good ductility performance. For all beam specimens, the maximum relative slips between the steel beam and the concrete slab at beam ends are all no larger than 3.00 mm.

Table 4.

Primary test results of beam specimens.

Specimen no.	M_cr,t (kN m)	M_y,t (kN m)	M_u,t (kN m)	δ_y,t (mm)	δ_u,t (mm)	µ = δ_u,t/δ_y,t	S_max (mm)
SCCB2	46.50	213.56	292.58	7.43	47.47	6.39	2.95
PECB5	54.25	327.63	397.63	10.73	48.35	4.50	1.97
PECB6	62.00	357.03	442.59	10.33	44.76	4.33	2.39
PECB7	62.00	380.78	514.72	10.20	43.86	4.30	2.33

M_cr, M_y, and M_u denote the initial cracking moment, the yielding moment, and the ultimate moment from tests, respectively; δ_y and δ_u denote the tested mid-span deflections corresponding to the yielding state and the ultimate state, respectively; µ denotes the displacement ductility factor; and S_max denotes the maximum relative slip between the steel beam and the concrete slab at the beam end.

Mid-span section strain distribution

The values of strain gauge at mid-span of specimens at each load step are plotted against the height of composite section, and typical curves are shown in Figure 5. The horizontal axis represents the strain value while the vertical axis represents the distance to the bottom steel flange. It is shown that, for both the conventional composite beam specimen SCCB2 and the partially encased composite beam specimen PECB5, the plane cross-section assumption could be considered effective, as cross-section strain distribution along the height was nearly linear. The neutral axis position at each load step of each specimen could also be determined, as shown in Figure 6. At first, as the load increases, the cracks in the concrete slab propagate gradually, which results in the movement of neutral axis position toward the bottom flange of steel beam. Then, the development of the crack numbers remains stable, the neutral axis position of each specimen also remains stable. Apparently, the stable stage of the neutral axis position for partially encased beam specimens is much longer than that for the conventional composite beam specimen. In the final stage, the variation of the neutral axis position of the four beam specimens is different. For specimen SCCB2, the bottom flange of steel beam yields prior to the reinforcements so that the neutral axis moves upward to the concrete slab, and then undergoes a sharp rise near the ultimate load as the consequence of the buckling of the bottom steel flange. For specimen PECB5, the neutral axis position undergoes a slightly rise in the final stage, as the reinforcements in the concrete slab yield prior to the bottom steel flange. For specimens PECB6 and PECB7, the bottom steel flange yields before the reinforcement in the slab, as a consequence of larger reinforcement ratio. Overall, the concrete encasement is able to reduce the height of the web of steel beam in compression. Moreover, the concrete encasement is considered to enhance the local buckling resistant of steel beam effectively.

Figure 5.

Mid-span section strain distributions in vertical direction: (a) specimen SCCB2 and (b) specimen PECB5.

Figure 6.

Neutral axis position versus load curves.

Strain results of bottom steel flange

The load–strain curves of the compression bottom flange at the mid-span are shown in Figure 7. The horizontal axis represents the strain value while the vertical axis represents the load. It is illustrated from the curves that, compared with the conventional composite beam specimen SCCB2, partially encased composite beam specimens PECB5-7 have much slower development speed in the strain of bottom flanges. For specimen SCCB2, the strain of the bottom steel flange increases sharply after the yielding occurred. For specimens PECB5-7, the strain of the bottom steel flange keeps moderate increase until it is near the failure load. In addition, the concrete encasement benefits to restrain the buckling of the bottom flange and the web in compression. It is also indicated from the curves that, increase in the reinforcement ratio in the concrete slab also helps to reduce the development speed in the strain of the bottom flange.

Figure 7.

Load–strain curves of the compression bottom flange.

Strain results of reinforcement in web encasement

The strains of the reinforcement in the web encasement at mid-span were also measured for partially encased beam specimens PECB5-7. As shown in Figure 8, the top layer reinforcement is in tension while the bottom layer reinforcement is in compression, and the neutral axis is located in the web of the steel beam. All the reinforcement in the web encasement achieves yielding strength, which indicates that cohesive force between the encased concrete and the steel beam can ensure the strength of the reinforcement in the encasement to be fully exploited. In addition, with the increase in reinforcement ratio in the concrete slab, the development speed of reinforcement strain in the encasement tends to decrease.

Figure 8.

Load–strain curves of reinforcement in the web concrete.

Cracks in concrete slab

Crack width control is vitally important in the design of composite structure subjected to hogging moment (Jiang et al., 2013). During the test, crack width was observed by electronic crack width instruments.

Crack formation and distribution

For all test specimens, the first crack appeared either near the loading points or the pure bending region. Cracks caused by the dominant hogging moment were almost perpendicular to the longitudinal axis of the concrete slab. When the load increases, a few diagonal cracks were observed in the shear span. When approaching the failure load, a few longitudinal cracks could be observed (see Figure 3(a)). Crack patterns near failure for specimens SCCB2 and PECB5-7 are illustrated in Figure 9. As it is depicted in Figure 9, in the ultimate state, the cracks on the concrete slab are almost uniformly distributed. The average crack spacing in the concrete slab of specimen SCCB2 is very close to that of specimen PECB5, while the average crack spacing in the concrete slab of specimen PECB5, PECB6, and PECB7 (126.5, 116.4, and 100.2 mm, respectively) decreases in turn. It can be concluded that, with the increase in the reinforcement ratio in the concrete slab, the distribution of cracks is denser.

Figure 9.

Crack distributions on the concrete slab: (a) specimen SCCB2, (b) specimen PECB5, (c) specimen PECB6, and (d) specimen PECB7.

Crack width

Figure 10 shows the maximum crack width propagation in the concrete slab of the four beam specimens during the loading process. It is shown that, under the same loading condition, the maximum crack width of specimen PECB5 is obviously smaller than that of specimen SCCB2, which indicates the web encasement effectively reduces the maximum crack width under hogging moment. In addition, by comparing specimens PECB5-7, it is concluded that, the increase in the reinforcement ratio of the concrete slab is able to reduce the maximum crack width and the propagation speed of crack width.

Figure 10.

Maximum crack widths versus load curves.

In the service stage of concrete members, crack width should be limited to an extent to ensure the durability of structures. The limiting value of crack width takes into account the proposed function and nature of the structure and the costs of limiting cracking. However, calculation methods of the actual crack width are not the same in different design codes. The crack width of the specimens measured in the test and the calculation results from three design codes (CEB-FIP:1993, 1993; EN 1994-1-1:2004, 2004; GB 50010:2010, 2010) are listed in Table 5. It can be seen that the results from CEB/FIP are not conservative for both the partially encased and conventional composite beam specimens. The results from EN 1994-1-1 or GB 50010-2010 are in good agreement with the test results.

Table 5.

Comparison of test and theoretic values of crack width.

Specimen	Test		CEB/FIP				EN 1994-1-1				GB 50010-2010
Specimen	(1)	(2)	(3)	(4)	(3)/(1)	(4)/(2)	(5)	(6)	(5)/(1)	(6)/(2)	(7)	(8)	(7)/(1)	(8)/(1)
SCCB2	0.20	0.30	0.11	0.21	0.65	0.77	0.16	0.24	0.90	0.87	0.15	0.24	0.85	0.87
PECB5	0.20	0.30	0.16	0.29	0.80	0.97	0.20	0.31	1.00	1.03	0.19	0.30	0.95	1.00
PECB6	0.20	0.30	0.15	0.26	0.75	0.87	0.18	0.30	0.90	1.00	0.18	0.31	0.90	1.03
PECB7	0.20	0.30	0.17	0.19	0.85	0.63	0.22	0.24	1.10	0.80	0.23	0.26	1.15	0.87

Sectional bending resistance

According to the sectional composition and stress state, four classes of cross sections are defined in Eurocode 3 (EN 1993-1-1:2005, 2005) and Eurocode 4 (EN 1994-1-1:2004, 2004). As for the conventional composite beam specimen SCCB2, both the web plate and the bottom flange plate satisfy the requirements of class 1 section. For partially encased composite beam specimens PECB5-7, both the web plate and the bottom flange plate also satisfy the requirements of class 1 section. It is indicated that the ultimate flexural capacity of specimens SCCB2 and PECB5-7 can be determined by the plastic theory.

The simplified plastic theory in Eurocode 4, based on a series of assumptions, is applied to calculate the ultimate flexural capacity of beam specimens. The plastic stress distribution of the cross section under hogging moment is shown in Figure 11. The test and theoretical values of the ultimate flexural capacity are listed in Table 6. Comparison results show that the calculation results of the simplified plastic theory are in good agreement with the test results.

Figure 11.

Plastic stress distribution of the cross section under hogging moment.

Table 6.

Comparison of test and theoretic values of ultimate flexural capacity.

Source	Specimen	M_u,t (kN m)	M_u,c (kN m)	M_u,c/M_u,t
This article	SCCB2	292.58	309.45	1.06
	PECB5	397.63	396.25	1.00
	PECB6	442.59	452.15	1.02
	PECB7	514.72	506.14	0.98
Hegger and Goralski (2004)	H1	3116.00	3000.60	0.96
Hegger and Goralski (2004)	H3	1850.00	1764.52	0.95

M_u,t and M_u,c denote the tested and the calculated ultimate flexural capacity, respectively.

Concluding remarks

Static loading tests were conducted to investigate the mechanical behavior of PECBs under hogging moment. Some important conclusions are summarized as follows:

The concrete encasement between steel flanges greatly enhances the stiffness and flexural capacity of the composite beams under hogging moment. Moreover, the concrete encasement is able to enhance the local bucking resistance of the compressive part of the steel beam, and effectively reduces the maximum crack width under hogging moment.

Both the stiffness and the flexural capacity increase as the reinforcement ratio of the concrete slab increases. Also, with the increase in the reinforcement ratio in the concrete slab, the distribution of cracks in the slab is denser and the propagation speed of the crack width reduces.

Comparison is made between the crack width measured in the test and that calculated from three design codes. It is indicated that the results from CEB/FIP are non-conservative for both the partially encased and conventional composite beam specimens. While the calculation method in EN 1994-1-1 or GB 50010-2010 can well predict the crack width on the concrete slab.

The ultimate flexural capacity under hogging moment of specimens SCCB2 and PECB5-7 can be determined by the plastic theory. The calculation results from the simplified plastic theory presented in Eurocode 4 are in good agreement with the test results.

The PECB has better mechanical performance under hogging moment, as compared with the conventional composite beam. Study results in this article may provide a design reference for this kind of composite beam.

Footnotes

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) received no financial support for the research, authorship, and/or publication of this article.

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