# Investigation of the Mechanical Behavior of Partially Precast Partially Encased Assembled Composite Beams

Authors: Liufeng Zhang; Yinghua Yang
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

In view of the characteristics of a high floor and the heavy load of logistics buildings, a partially prefabricated partially encased assembled composite beam (PPEC) is proposed in order to achieve the low cost construction of such buildings. In this research, the mechanical properties of PPEC beams were studied experimentally. The effects of the concrete strength grade, steel content, shear span ratio, and fabrication methods on the mechanical properties of the PPEC beams were analyzed. The results showed that the proposed structural form of the PPEC beams was generally feasible. Based on the test results, a practical shear formula for PPEC beams was proposed, and the calculated results were in good agreement with the test results.


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## Body

## 1. Introduction

In China, e-commerce is gradually changing peoples’ lifestyles. With the prosperity of e-commerce, the logistics industry has achieved leapfrog development. The rise of the logistics industry has promoted the concept of logistics buildings. Logistics parks, which are flourishing all over China, which are composed of typical logistics buildings. A remarkable feature of a logistics building is its heavy load. However, under the heavy load of a traditional cast-in-place structure, the design of the horizontal members is often controlled by deflection rather than strength, which will lead to large cross-sections, high reinforcement ratios, and poor economic benefits. In view of this situation, the use of steel-concrete composite beams with high rigidity and high strength is a sensible choice for reducing construction costs. Another characteristic of a logistics building is a high floor height. The traditional cast-in-place structure popular in China needs a large amount of scaffolding and formwork, especially for a relatively high scaffolding project, which is very costly. Therefore, an unsupported construction method is a reasonable way to reduce the cost of construction. In conclusion, an assembled steel-concrete composite structure system is more suitable for the construction of logistics buildings.Some scholars have carried out a series of studies on the assembled steel-concrete composite structure system. The SR-PC (a frame structure composed of steel reinforced precast concrete members) method proposed by the Japanese Prefabricated Building Association [1] and the FSRPC (a frame structure composed of steel beams and concrete columns) structure system of the Fujita Corporation of Japan involve the research and development of these types of construction systems. In China, Li et al. [2] proposed an integrated steel reinforced concrete frame system with a dog-bone connection at the beam end and explored the influence of the beam-end dog-bone connection on the seismic performance of the joint. Song et al. [3, 4] proposed a precast steel reinforced concrete frame system with a steel connection in the beam-column joint area, which simplified the beam-column connection procedure of a precast concrete frame. However, these fully assembled reinforced concrete systems have slightly poor overall performance characteristics, such as slightly less seismic performance than cast-in-place structures to some degree. In addition, the installation accuracy of the fully assembled components is high and the lifting weight is large, which greatly increases the project cost. In order to remedy the above shortcomings, this paper proposes a partially precast partially encased assembled composite beam (PPEC) for a logistics building, in order to achieve the low cost construction of these types of buildings.Before introducing PPEC beams, PEC (partially encased composite) beams and the research for these beams are briefly introduced. Partially encased beams are elements in which the web of the steel section is encased with reinforced concrete [5, 6]. The web encasement not only brings good fire resistance but also improves the stiffness and bearing capacity without increasing the cross section [7–12]. PPEC beams are improved from PEC beams. A PPEC beam consists of precast and cast-in-place parts. The precast parts of PPEC beams are shown in Figure 1. The construction of a logistics park can change the construction sequence of buildings. Toad construction is carried out first, then the site formed by the road is used to make on-site precast parts, and continuous turnover steel formwork is used to make on-site production in order to further save the cost of the transportation of precast components and the cost of precast components production, and to greatly reduce the cost of construction. After the precast section is completed, it is hoisted in place and then poured into the slab concrete to form a complete beam-slab system (Figure 2).Figure 1
Prefabricated partial configuration.Figure 2
Complete beam-slab system.The PPEC beam proposed in this paper can be designed as unsupported construction due to the existence of I-steel, and the integral pouring of beam-slab concrete can increase the integrity. This beam has great potential advantages for simplifying construction technology and reducing project cost, and it has good prospects for promotion. Therefore, it is necessary to study the mechanical properties of this new composite beam and provide a reference for its engineering applications.


## 2. Experimental Program

### 2.1. Beam Specimens

A total of sixteen specimens were designed, including six flexural specimens, eight shear specimens, and two cast-in-place contrast specimens. T-shaped beams with flanges were used in all the specimens. The web width of each T-shaped composite beam was 150 mm, the web height of each flexural specimen was 170 mm, and the web height of each shear specimen was 150 mm. The width and the thickness of the concrete flange slab for each specimen were 650 mm and 80 mm, respectively. Each I-steel beam was welded by Chinese steel (brand Q235), each upper flange width was 100 mm, and each lower flange width was 150 mm. In all the specimens, the distance between the upper flange of the I-beam and the slab surface of the T-shaped composite beam was 50 mm, and all specimens were reinforced with HRB335 steel bars. The diameter of the longitudinal rebar was 12 mm and that of the slab rebar was 8 mm. The diameters of the stirrups in all specimens were 8 mm except for one shear specimen (PPEC-7-S) with 10 mm stirrups. The concrete strength grades of the test beams were C20, C30, and C40. The prefabricated part of the PPEC beam was composed of prefabricatedu-shaped concrete and a steel skeleton, wherein the steel skeleton was composed of I-steel, longitudinal reinforcement, and stirrups. The design parameters of the specimens are shown in Table 1, and the mechanical properties of the concrete and steel are shown in Table 2 (Figure 3).Table 1
Design and test results of the specimens.
No.
Shear span length (mm)
Shear span ratio
Steel ratio (%)
Concrete strength
Stirrup
Ultimate load (kN)
Bearing capacity
Mu
Vu
PPEC-1-M
650
2.6
7.01
C30
B8@150
402.75
130.89
—
PPEC-2-M
650
2.6
8.28
C30
B8@150
463.50
150.64
—
PPEC-3-M
650
2.6
9.55
C30
B8@150
468.13
152.14
—
PPEC-4-M
650
2.6
8.28
C20
B8@150
421.55
137.00
—
PPEC-5-M
650
2.6
8.28
C40
B8@150
453.50
147.39
—
PPEC-6-M
650
2.6
8.28
C30
B8@150
382.40
124.28
—
PEC-7-M
650
2.6
8.28
C30
B8@150
488.75
158.84
—
PPEC-1-S
400
2.0
6.84
C30
B8@200
428.25
—
214.13
PPEC-2-S
400
2.0
7.76
C30
B8@200
527.88
—
263.94
PPEC-3-S
500
2.5
6.84
C30
B8@200
399.38
—
199.69
PPEC-4-S
300
1.5
6.84
C30
B8@200
464.13
—
232.07
PPEC-5-S
400
2.0
6.84
C40
B8@200
513.75
—
256.88
PPEC-6-S
400
2.0
6.84
C20
B8@200
407.25
—
203.63
PPEC-7-S
400
2.0
6.84
C30
B10@200
452.63
—
226.32
PPEC-8-S
400
2.0
6.84
C30
B8@100
476.88
—
238.44
PEC-9-S
400
2.0
6.84
C30
B8@200
478.75
—
239.38
Note. The stirrups of the PPEC-6-M specimens were in the form of welded tie rods between the upper and lower flanges. The shear span length refers to the horizontal distance between the loading point and the adjacent support, and the shear span ratio is the length of the shear span divided by the height of the composite beam.Table 2
Measured value of material mechanical performance index.
Mechanical properties of steel
Mechanical properties of concrete
Steel form
Specifications (mm)
f
y (MPa)
f
u (MPa)
Concrete strength (MPa)
f
cu
,
pr (MPa)
f
cu
,
po (MPa)
Steel plate
4
276.5
453
C20
21.0
20.6
6
287.0
442.0
8
279.2
421.0
C30
23.9
22.6
10
308.0
410.0
Rebar
8
192.0
273.0
C40
36.3
35.0
10
200.8
302.6
12
194.0
234.5
Note. In the specifications, the steel plate refers to the thickness and the rebar refers to the diameter.Figure 3
Cross-sectional feature information of the PPEC beam.
(a)
(b)


### 2.2. Specimen Production

First, the unequal flange I-beam was forged, and then the polystyrene board with the corresponding thickness was adhered to the upper part of the web and so that it clung to the top flange. Second, the prepared semiclosed stirrups were put into the I-steel one at a time. Third, the longitudinal bars are placed in the stirrup hooks along the length of the I-steel and fixed in place. Fourth, the template was supported and the concrete was poured to complete the precast parts. Fifth, when the precast part reached the predetermined strength, the cast-in-place part was made. The supporting template, the binding plate reinforcement, and the pouring concrete were completed in turn. This process is illustrated in Figure4.Figure 4
Construction process of the specimens. (a) Preparation of prefabricated parts. (b) Completed prefabricated parts. (c) Preparation of cast-in-place parts. (d) Completed cast-in-place parts.
(a)
(b)
(c)
(d)


### 2.3. Test Set-Up and Loading Process

The test was completed on a 500t pressure-testing machine. The test used a four-point symmetrical loading method. The distribution beam was placed under the jack to transfer the load evenly to the top of the test piece. The loading device is shown in Figure 5. During the loading process, the vertical load, displacement, and strain of the concrete and steel were mainly monitored. A monotonic static grading loading system was adopted in the test, as follows: First, the load was applied at the rate of 10 kN per step. Then, the load was reduced to 5 kN per step when 90% of the predicted cracking load was reached. After the specimen cracked, the load was taken as 20 kN per step. When approximately 90% of the estimated ultimate capacity was reached for the specimens, the load was reduced to 5 kN per step. When the ultimate load was reached, the specimen was continuously loaded to failure.Figure 5
Test set-up and measuring point layout of beam specimens.


### 2.4. Failure Modes of the Specimens

Under the influence of the shear span ratio, the sixteen beam specimens usually presented bending and shear failure modes. The shear span ratio caused the shear failure to be mainly divided into shear-compression failure and cable-stayed failure. The bending failure was a typical bending failure mode. The failure modes of the specimens are shown in Figure6.Figure 6
Typical failure modes. (a) Bending failure. (b) Shear-compression failure.
(a)
(b)For beams subjected to bending failure, there was no significant difference in the failure modes between the PPEC specimens and the PEC specimens. Figure7 shows the bending moment-rotation curve of the specimens with a bending failure mode, where the bending moment was P/2 multiplied by the length of the shear span, and the rotation angle θ was the midspan displacement divided by the half-span length. As can be seen in Figure 7, the stiffness of the PEC beams was slightly greater than that of the PPEC beams, but they all showed good deformation capacity. For beams with a shear failure mode, considering the difference of the specimen lengths, the shear-rotation curves of the specimens are given in Figure 8. The rotation angle of the specimens was defined as the ratio of the displacement of the loading point to the length of the shear span. The shear span ratio reflected the relationship between the bending and shearing to some degree, which affected the shear failure mode of the PPEC beams. When the shear span ratio was between 1.5 and 2.5, the shear-compression failure of the PPEC beams occurred. When the shear span ratio was greater than or equal to 2.5, the specimens experienced cable-stayed failure. However, unlike the shear brittle failure of the RC (reinforced concrete) beams, the PPEC beams exhibited excellent ductility. The load-rotation curve of the shear specimens is shown in Figure 8.Figure 7
Moment-rotation curves at the midspans of the specimens.Figure 8
Shear force-rotation curves of the specimens.From Figures7 and 8, it can be seen that the specimens showed three distinct stages of failure under loading, which could be roughly divided into three stages: elastic, elastoplastic, and plastic failure. Due to the existence of the I-steel, there was no clear turning in the load-rotation curve before and after the cracks occurred in the specimen. With the yielding and slipping of the lower flange of I-steel, the specimen entered the elastoplastic stage, and the turning angle obviously increased. However, the applied load still has room for further improvement. After loading to the peak load, the flexural specimens were accompanied by concrete crushing in the top compression zone of the slab, the shear specimens were accompanied by concrete crushing in the web, and the specimens were subsequently declared damaged.


## 2.1. Beam Specimens

A total of sixteen specimens were designed, including six flexural specimens, eight shear specimens, and two cast-in-place contrast specimens. T-shaped beams with flanges were used in all the specimens. The web width of each T-shaped composite beam was 150 mm, the web height of each flexural specimen was 170 mm, and the web height of each shear specimen was 150 mm. The width and the thickness of the concrete flange slab for each specimen were 650 mm and 80 mm, respectively. Each I-steel beam was welded by Chinese steel (brand Q235), each upper flange width was 100 mm, and each lower flange width was 150 mm. In all the specimens, the distance between the upper flange of the I-beam and the slab surface of the T-shaped composite beam was 50 mm, and all specimens were reinforced with HRB335 steel bars. The diameter of the longitudinal rebar was 12 mm and that of the slab rebar was 8 mm. The diameters of the stirrups in all specimens were 8 mm except for one shear specimen (PPEC-7-S) with 10 mm stirrups. The concrete strength grades of the test beams were C20, C30, and C40. The prefabricated part of the PPEC beam was composed of prefabricatedu-shaped concrete and a steel skeleton, wherein the steel skeleton was composed of I-steel, longitudinal reinforcement, and stirrups. The design parameters of the specimens are shown in Table 1, and the mechanical properties of the concrete and steel are shown in Table 2 (Figure 3).Table 1
Design and test results of the specimens.
No.
Shear span length (mm)
Shear span ratio
Steel ratio (%)
Concrete strength
Stirrup
Ultimate load (kN)
Bearing capacity
Mu
Vu
PPEC-1-M
650
2.6
7.01
C30
B8@150
402.75
130.89
—
PPEC-2-M
650
2.6
8.28
C30
B8@150
463.50
150.64
—
PPEC-3-M
650
2.6
9.55
C30
B8@150
468.13
152.14
—
PPEC-4-M
650
2.6
8.28
C20
B8@150
421.55
137.00
—
PPEC-5-M
650
2.6
8.28
C40
B8@150
453.50
147.39
—
PPEC-6-M
650
2.6
8.28
C30
B8@150
382.40
124.28
—
PEC-7-M
650
2.6
8.28
C30
B8@150
488.75
158.84
—
PPEC-1-S
400
2.0
6.84
C30
B8@200
428.25
—
214.13
PPEC-2-S
400
2.0
7.76
C30
B8@200
527.88
—
263.94
PPEC-3-S
500
2.5
6.84
C30
B8@200
399.38
—
199.69
PPEC-4-S
300
1.5
6.84
C30
B8@200
464.13
—
232.07
PPEC-5-S
400
2.0
6.84
C40
B8@200
513.75
—
256.88
PPEC-6-S
400
2.0
6.84
C20
B8@200
407.25
—
203.63
PPEC-7-S
400
2.0
6.84
C30
B10@200
452.63
—
226.32
PPEC-8-S
400
2.0
6.84
C30
B8@100
476.88
—
238.44
PEC-9-S
400
2.0
6.84
C30
B8@200
478.75
—
239.38
Note. The stirrups of the PPEC-6-M specimens were in the form of welded tie rods between the upper and lower flanges. The shear span length refers to the horizontal distance between the loading point and the adjacent support, and the shear span ratio is the length of the shear span divided by the height of the composite beam.Table 2
Measured value of material mechanical performance index.
Mechanical properties of steel
Mechanical properties of concrete
Steel form
Specifications (mm)
f
y (MPa)
f
u (MPa)
Concrete strength (MPa)
f
cu
,
pr (MPa)
f
cu
,
po (MPa)
Steel plate
4
276.5
453
C20
21.0
20.6
6
287.0
442.0
8
279.2
421.0
C30
23.9
22.6
10
308.0
410.0
Rebar
8
192.0
273.0
C40
36.3
35.0
10
200.8
302.6
12
194.0
234.5
Note. In the specifications, the steel plate refers to the thickness and the rebar refers to the diameter.Figure 3
Cross-sectional feature information of the PPEC beam.
(a)
(b)


## 2.2. Specimen Production

First, the unequal flange I-beam was forged, and then the polystyrene board with the corresponding thickness was adhered to the upper part of the web and so that it clung to the top flange. Second, the prepared semiclosed stirrups were put into the I-steel one at a time. Third, the longitudinal bars are placed in the stirrup hooks along the length of the I-steel and fixed in place. Fourth, the template was supported and the concrete was poured to complete the precast parts. Fifth, when the precast part reached the predetermined strength, the cast-in-place part was made. The supporting template, the binding plate reinforcement, and the pouring concrete were completed in turn. This process is illustrated in Figure4.Figure 4
Construction process of the specimens. (a) Preparation of prefabricated parts. (b) Completed prefabricated parts. (c) Preparation of cast-in-place parts. (d) Completed cast-in-place parts.
(a)
(b)
(c)
(d)


## 2.3. Test Set-Up and Loading Process

The test was completed on a 500t pressure-testing machine. The test used a four-point symmetrical loading method. The distribution beam was placed under the jack to transfer the load evenly to the top of the test piece. The loading device is shown in Figure 5. During the loading process, the vertical load, displacement, and strain of the concrete and steel were mainly monitored. A monotonic static grading loading system was adopted in the test, as follows: First, the load was applied at the rate of 10 kN per step. Then, the load was reduced to 5 kN per step when 90% of the predicted cracking load was reached. After the specimen cracked, the load was taken as 20 kN per step. When approximately 90% of the estimated ultimate capacity was reached for the specimens, the load was reduced to 5 kN per step. When the ultimate load was reached, the specimen was continuously loaded to failure.Figure 5
Test set-up and measuring point layout of beam specimens.


## 2.4. Failure Modes of the Specimens

Under the influence of the shear span ratio, the sixteen beam specimens usually presented bending and shear failure modes. The shear span ratio caused the shear failure to be mainly divided into shear-compression failure and cable-stayed failure. The bending failure was a typical bending failure mode. The failure modes of the specimens are shown in Figure6.Figure 6
Typical failure modes. (a) Bending failure. (b) Shear-compression failure.
(a)
(b)For beams subjected to bending failure, there was no significant difference in the failure modes between the PPEC specimens and the PEC specimens. Figure7 shows the bending moment-rotation curve of the specimens with a bending failure mode, where the bending moment was P/2 multiplied by the length of the shear span, and the rotation angle θ was the midspan displacement divided by the half-span length. As can be seen in Figure 7, the stiffness of the PEC beams was slightly greater than that of the PPEC beams, but they all showed good deformation capacity. For beams with a shear failure mode, considering the difference of the specimen lengths, the shear-rotation curves of the specimens are given in Figure 8. The rotation angle of the specimens was defined as the ratio of the displacement of the loading point to the length of the shear span. The shear span ratio reflected the relationship between the bending and shearing to some degree, which affected the shear failure mode of the PPEC beams. When the shear span ratio was between 1.5 and 2.5, the shear-compression failure of the PPEC beams occurred. When the shear span ratio was greater than or equal to 2.5, the specimens experienced cable-stayed failure. However, unlike the shear brittle failure of the RC (reinforced concrete) beams, the PPEC beams exhibited excellent ductility. The load-rotation curve of the shear specimens is shown in Figure 8.Figure 7
Moment-rotation curves at the midspans of the specimens.Figure 8
Shear force-rotation curves of the specimens.From Figures7 and 8, it can be seen that the specimens showed three distinct stages of failure under loading, which could be roughly divided into three stages: elastic, elastoplastic, and plastic failure. Due to the existence of the I-steel, there was no clear turning in the load-rotation curve before and after the cracks occurred in the specimen. With the yielding and slipping of the lower flange of I-steel, the specimen entered the elastoplastic stage, and the turning angle obviously increased. However, the applied load still has room for further improvement. After loading to the peak load, the flexural specimens were accompanied by concrete crushing in the top compression zone of the slab, the shear specimens were accompanied by concrete crushing in the web, and the specimens were subsequently declared damaged.


## 3. Main Influencing Factors of the Bearing Capacity

The experimental results showed that the typical failure modes of the PPEC beam members could be divided into bending failure and shear failure. The performances of the PPEC beam members under the two failure modes were quite different. The mechanical properties of the beam members were related to the shear span ratio, concrete strength grade, and steel ratio because they determined the interaction between the I-steel and the concrete to some degree and then they affected the failure mode and the bearing capacity of the members. The concrete strength and the steel ratio had a significant impact on the shear resistance and the bending performance of the beam. The shear properties of the beams were more sensitive to the shear span ratio and the stirrup ratio, and the flexural properties of the beams were more sensitive to the stirrup mode.


### 3.1. Concrete Strength

The influence of concrete strength on the bearing capacity of the PPEC beams is shown in Figure9. The research showed that the shear capacity of PPEC beams increased with the increase of the concrete strength. The flexural capacity increased with the increase of the concrete strength in the C20–C30 stage, but it decreased slightly in the C30–C40 stage. In theory, the flexural capacity should increase with the increase of concrete strength grade, but this needs further test verification.Figure 9
Effect offcu on the specimen capacity.


### 3.2. Steel Ratio

With special instructions, it was shown that the change of steel ratio referred to the change of the flange thickness of the I-steel for the flexural specimens and to the change of the web thickness of the I-steel for the shear specimens. Figure10 shows the effect of the steel ratio on the bearing capacity of the PPEC beams. It can be seen that as the steel ratio increased, its bearing capacity increased gradually. In addition, as the steel ratio increased, the improvement of the flexural capacity of the PPEC beams became smaller and smaller. The reason for this was that as the steel ratio increased, the shear and flexural capacity of the I-steel increased continuously, and then the shear and flexural capacities of the PPEC beam were improved to some degree.Figure 10
Effect of the steel ratio on the specimen capacity.


### 3.3. Shear Span Ratio

Figure11 shows the influence of the shear span ratio on the shear capacity of the PPEC beams. The results show that the shear span ratio had a significant effect on the shear capacity of PPEC beams, and they show an inverse relationship. Specifically, when 1.5≤λ<2.5, shear-compression failure occurred in the PPEC beams, and when 2.5<λ, cable-stayed failure occurred easily in the PPEC beams. In addition, due to the three-sided restraint effect of the I-steel flange on the concrete in the PPEC beams, the compression softening of the concrete in the shear span zone was effectively alleviated, and the shear capacity and the ductility of the PPEC beams were higher than those of the RC beams.Figure 11
Effect ofλ on the shear capacity.


### 3.4. Stirrup Ratio

Figure12 shows the effect of the stirrup ratio on the shear capacity of the PPEC beams. As shown in Figure 11, the order of the shear capacity of the PPEC beams was PPEC-1-S < PPEC-7-S < PPEC-8-S. The shear capacity of the PPEC beams increased gradually with the increase of the stirrup ratio. This showed that the increase of the stirrup ratio could increase the shear capacity of the PPEC beams, and the reason was that the increase of the stirrup ratio led to the increase of the stirrup area, which increased the shear capacity of the stirrups and further improved the shear capacity of the PPEC beams.Figure 12
Effect of the stirrup ratio on the shear capacity.


### 3.5. Stirrup Form

The test results showed that the stirrups had a significant effect on the flexural capacity of the PPEC beams, and the flexural capacity of the semiclosed stirrups was approximately 21.2% higher than that of tie-rod PPEC beams. The details are shown in Figure13. This was most likely due to the weakening of the effective cross-sectional area of the I-steel flange by the welded tie rods, but the effect needs further study.Figure 13
Effect of the stirrup form on the moment capacity.


### 3.6. Construction Technology

Figure14 shows the comparison of the bearing capacity between the integrally cast PEC beams and the partially precast PPEC beams. For shear specimen and the flexural specimen, the bearing capacity of the PEC specimen was slightly higher than that of the PPEC specimen. The flexural capacity of the PPEC beams was 5.16% lower than that of the PEC beams, and the shear capacity of the PPEC beams was 10.55% lower than that of the PEC beams. This was because the PPEC beam concrete was constructed twice, so the integrity of the interface between the new and old concrete was not as good as that of a one-time casting. However, the differences in the flexural capacity or the shear capacity caused by the manufacturing method were less than 11%.Figure 14
Effect of the construction technology on the specimen capacity.


## 3.1. Concrete Strength

The influence of concrete strength on the bearing capacity of the PPEC beams is shown in Figure9. The research showed that the shear capacity of PPEC beams increased with the increase of the concrete strength. The flexural capacity increased with the increase of the concrete strength in the C20–C30 stage, but it decreased slightly in the C30–C40 stage. In theory, the flexural capacity should increase with the increase of concrete strength grade, but this needs further test verification.Figure 9
Effect offcu on the specimen capacity.


## 3.2. Steel Ratio

With special instructions, it was shown that the change of steel ratio referred to the change of the flange thickness of the I-steel for the flexural specimens and to the change of the web thickness of the I-steel for the shear specimens. Figure10 shows the effect of the steel ratio on the bearing capacity of the PPEC beams. It can be seen that as the steel ratio increased, its bearing capacity increased gradually. In addition, as the steel ratio increased, the improvement of the flexural capacity of the PPEC beams became smaller and smaller. The reason for this was that as the steel ratio increased, the shear and flexural capacity of the I-steel increased continuously, and then the shear and flexural capacities of the PPEC beam were improved to some degree.Figure 10
Effect of the steel ratio on the specimen capacity.


## 3.3. Shear Span Ratio

Figure11 shows the influence of the shear span ratio on the shear capacity of the PPEC beams. The results show that the shear span ratio had a significant effect on the shear capacity of PPEC beams, and they show an inverse relationship. Specifically, when 1.5≤λ<2.5, shear-compression failure occurred in the PPEC beams, and when 2.5<λ, cable-stayed failure occurred easily in the PPEC beams. In addition, due to the three-sided restraint effect of the I-steel flange on the concrete in the PPEC beams, the compression softening of the concrete in the shear span zone was effectively alleviated, and the shear capacity and the ductility of the PPEC beams were higher than those of the RC beams.Figure 11
Effect ofλ on the shear capacity.


## 3.4. Stirrup Ratio

Figure12 shows the effect of the stirrup ratio on the shear capacity of the PPEC beams. As shown in Figure 11, the order of the shear capacity of the PPEC beams was PPEC-1-S < PPEC-7-S < PPEC-8-S. The shear capacity of the PPEC beams increased gradually with the increase of the stirrup ratio. This showed that the increase of the stirrup ratio could increase the shear capacity of the PPEC beams, and the reason was that the increase of the stirrup ratio led to the increase of the stirrup area, which increased the shear capacity of the stirrups and further improved the shear capacity of the PPEC beams.Figure 12
Effect of the stirrup ratio on the shear capacity.


## 3.5. Stirrup Form

The test results showed that the stirrups had a significant effect on the flexural capacity of the PPEC beams, and the flexural capacity of the semiclosed stirrups was approximately 21.2% higher than that of tie-rod PPEC beams. The details are shown in Figure13. This was most likely due to the weakening of the effective cross-sectional area of the I-steel flange by the welded tie rods, but the effect needs further study.Figure 13
Effect of the stirrup form on the moment capacity.


## 3.6. Construction Technology

Figure14 shows the comparison of the bearing capacity between the integrally cast PEC beams and the partially precast PPEC beams. For shear specimen and the flexural specimen, the bearing capacity of the PEC specimen was slightly higher than that of the PPEC specimen. The flexural capacity of the PPEC beams was 5.16% lower than that of the PEC beams, and the shear capacity of the PPEC beams was 10.55% lower than that of the PEC beams. This was because the PPEC beam concrete was constructed twice, so the integrity of the interface between the new and old concrete was not as good as that of a one-time casting. However, the differences in the flexural capacity or the shear capacity caused by the manufacturing method were less than 11%.Figure 14
Effect of the construction technology on the specimen capacity.


## 4. Analysis of the Bearing Capacity

### 4.1. Flexural Capacity

Based on the plasticity theory [13] and the assumption of a plane section, the design method of flexural capacity of PEC beams was proposed in [14]. From the previous analysis, it was known that the difference between the flexural capacity of the PPEC beams and that of the PEC beams is small, so the flexural capacity of the PPEC beams could still be calculated by the method proposed in [14]. As shown in Table 3, the calculated results were in good agreement with the experimental results. The theoretical flexural capacity divided by the experimental flexural capacity was 0.95 and the coefficient of variation was 0.05. The calculation accuracy of this method is good, and it can be used as a reference for practical engineering design.Table 3
The theoretical values versus the test values of the flexural capacity.
No.
Theoretical value (kN·m)
Test value (kN·m)
Theoretical value/test value
PECB-1-M
117.10
130.90
0.90
PPEC-2-M
136.72
150.64
0.91
PPEC-3-M
152.20
152.14
1.00
PPEC-4-M
135.94
137.00
0.99
PPEC-5-M
141.73
147.39
0.96
Average value
—
—
0.95
Variation coefficients
—
—
0.05


### 4.2. Shear Capacity

The calculation model of the shear capacity of the PPEC beams is shown in Figure14. Based on Chinese code JGJ138-2016 [15] and the characteristics of PPEC beams, the shear capacity formula for PPEC beams was improved upon. The improvement ideas are described in the following:(1)
In the cross section of the PPEC composite beam, the precast concrete section occupied a considerable proportion. The calculation based on the small cast-in-place concrete strength grade was too conservative, and the shearing effect of the cast-in-place and precast two-part concrete needed to be considered reasonably. Using the area as the weight, the weighted average method was used to obtain the converted concrete strength, as follows:(1)ft,com=Ac1Ac1+Ac2ft1+Ac2Acl+Ac2ft2,whereft,com is the conversion of the concrete tensile strength, Ac1 and ft1 are the cast-in-place concrete area and the tensile strength, Ac2 and ft2 are precast concrete area and the tensile strength, and the tensile strength is ft=0.26fcu2/3.(2)
In the shear specimens, the concrete flange was in a state of shear-compression force. The concrete flange in the compression zone contributed to the shear capacity of the inclined section. This has been proven in paper [16]. Hence, the contribution of the concrete flange needed to be considered in the calculation of the shear capacity of the PPEC beam. The effect of the flange could be achieved with an amplification factor, which can be expressed as follows:(2)γf′=bf′−bhf′fc1Ac1fc1+Ac2fc2,wherebf′ is the width of the concrete flange, b is the PPEC beam width,hf′ is the height of the concrete flange, h is the height of the T beam, hw is the height of the I-steel web, fyv is the yield strength of the stirrup, fy is the yield strength of the I-steel web, and λ is the shear span ratio.Referring to the expression of the shear capacity of a JGJ-138 composite beam, combined with the analysis of the factors affecting the shear capacity described in the previous section, the shear capacity of a PPEC beam can be expressed as(3)Vu=c×γf′+1.0λ+dft,combh+hwtwfy3+fyvAsvsh.The regression analysis was carried out by the shear capacity values obtained by the test, and the values ofc and d were 0.388 and 0.12, respectively. The improved PPEC beam shear capacity calculation method was as follows:(4)Vu=0.388γf′+1.0λ+0.12ft,combh+hwtwfy3+fyvAsvsh.The shear capacity of the PPEC beam obtained according to the above method is shown in Table4. The calculation results showed that the experimental values agreed well with the theoretical values. The theoretical shear capacity divided by the experimental shear capacity was 1.00, and the coefficient of variation was 0.045. This proves that the proposed formula for calculating the shear capacity is effective and it can be used as a reference for practical engineering.Table 4
The theoretical values versus the test values of the shear capacity.
No.
Theoretical value (kN·m)
Test value (kN·m)
Theoretical value/test value
PECB-1-S
208.93
214.13
0.98
PPEC-2-S
275.80
263.94
1.04
PPEC-3-S
195.64
199.69
0.98
PPEC-4-S
230.44
232.07
0.99
PPEC-5-S
252.91
256.88
0.98
PPEC-6-S
222.51
203.63
1.09
PPEC-7-S
221.26
226.32
0.98
PPEC-8-S
228.13
238.44
0.96
Average value
—
—
1.00
Variation coefficients
—
—
0.045In summary, the mechanical properties of the PPEC beams proposed in this paper are excellent. Based on the experimental analysis, the corresponding flexural and shear capacity design methods were proposed. The results showed that the calculated results were in good agreement with the experimental results, which had certain guiding significance for the practical application and popularization of this kind of composite beam.


## 4.1. Flexural Capacity

Based on the plasticity theory [13] and the assumption of a plane section, the design method of flexural capacity of PEC beams was proposed in [14]. From the previous analysis, it was known that the difference between the flexural capacity of the PPEC beams and that of the PEC beams is small, so the flexural capacity of the PPEC beams could still be calculated by the method proposed in [14]. As shown in Table 3, the calculated results were in good agreement with the experimental results. The theoretical flexural capacity divided by the experimental flexural capacity was 0.95 and the coefficient of variation was 0.05. The calculation accuracy of this method is good, and it can be used as a reference for practical engineering design.Table 3
The theoretical values versus the test values of the flexural capacity.
No.
Theoretical value (kN·m)
Test value (kN·m)
Theoretical value/test value
PECB-1-M
117.10
130.90
0.90
PPEC-2-M
136.72
150.64
0.91
PPEC-3-M
152.20
152.14
1.00
PPEC-4-M
135.94
137.00
0.99
PPEC-5-M
141.73
147.39
0.96
Average value
—
—
0.95
Variation coefficients
—
—
0.05


## 4.2. Shear Capacity

The calculation model of the shear capacity of the PPEC beams is shown in Figure14. Based on Chinese code JGJ138-2016 [15] and the characteristics of PPEC beams, the shear capacity formula for PPEC beams was improved upon. The improvement ideas are described in the following:(1)
In the cross section of the PPEC composite beam, the precast concrete section occupied a considerable proportion. The calculation based on the small cast-in-place concrete strength grade was too conservative, and the shearing effect of the cast-in-place and precast two-part concrete needed to be considered reasonably. Using the area as the weight, the weighted average method was used to obtain the converted concrete strength, as follows:(1)ft,com=Ac1Ac1+Ac2ft1+Ac2Acl+Ac2ft2,whereft,com is the conversion of the concrete tensile strength, Ac1 and ft1 are the cast-in-place concrete area and the tensile strength, Ac2 and ft2 are precast concrete area and the tensile strength, and the tensile strength is ft=0.26fcu2/3.(2)
In the shear specimens, the concrete flange was in a state of shear-compression force. The concrete flange in the compression zone contributed to the shear capacity of the inclined section. This has been proven in paper [16]. Hence, the contribution of the concrete flange needed to be considered in the calculation of the shear capacity of the PPEC beam. The effect of the flange could be achieved with an amplification factor, which can be expressed as follows:(2)γf′=bf′−bhf′fc1Ac1fc1+Ac2fc2,wherebf′ is the width of the concrete flange, b is the PPEC beam width,hf′ is the height of the concrete flange, h is the height of the T beam, hw is the height of the I-steel web, fyv is the yield strength of the stirrup, fy is the yield strength of the I-steel web, and λ is the shear span ratio.Referring to the expression of the shear capacity of a JGJ-138 composite beam, combined with the analysis of the factors affecting the shear capacity described in the previous section, the shear capacity of a PPEC beam can be expressed as(3)Vu=c×γf′+1.0λ+dft,combh+hwtwfy3+fyvAsvsh.The regression analysis was carried out by the shear capacity values obtained by the test, and the values ofc and d were 0.388 and 0.12, respectively. The improved PPEC beam shear capacity calculation method was as follows:(4)Vu=0.388γf′+1.0λ+0.12ft,combh+hwtwfy3+fyvAsvsh.The shear capacity of the PPEC beam obtained according to the above method is shown in Table4. The calculation results showed that the experimental values agreed well with the theoretical values. The theoretical shear capacity divided by the experimental shear capacity was 1.00, and the coefficient of variation was 0.045. This proves that the proposed formula for calculating the shear capacity is effective and it can be used as a reference for practical engineering.Table 4
The theoretical values versus the test values of the shear capacity.
No.
Theoretical value (kN·m)
Test value (kN·m)
Theoretical value/test value
PECB-1-S
208.93
214.13
0.98
PPEC-2-S
275.80
263.94
1.04
PPEC-3-S
195.64
199.69
0.98
PPEC-4-S
230.44
232.07
0.99
PPEC-5-S
252.91
256.88
0.98
PPEC-6-S
222.51
203.63
1.09
PPEC-7-S
221.26
226.32
0.98
PPEC-8-S
228.13
238.44
0.96
Average value
—
—
1.00
Variation coefficients
—
—
0.045In summary, the mechanical properties of the PPEC beams proposed in this paper are excellent. Based on the experimental analysis, the corresponding flexural and shear capacity design methods were proposed. The results showed that the calculated results were in good agreement with the experimental results, which had certain guiding significance for the practical application and popularization of this kind of composite beam.


## 5. Concluding Remarks

Through an experimental study of the mechanical properties of fourteen T-shaped PPEC beams and two T-shaped PEC beams, the following conclusions were drawn:(1)
The improved PPEC beam structural form proposed in this paper is generally feasible. The I-steel, cast-in-place concrete, and precast concrete worked well together without obvious slips.(2)
Compared with the cast-in-place PEC beams, the PPEC beams had the same failure mode and a similar bearing capacity. Prefabrication and casting-in-place had little effect on the mechanical properties of the specimens, especially in the elastic stage.(3)
With the increase of the concrete strength, the flexural and shear capacities of the PPEC beams were improved except for the flexural specimen of C40. With the increase of the steel ratio, the flexural and shear capacities of the PPEC beams increased.(4)
With the increase of the shear span ratio, the shear capacity of the PPEC beams decreased gradually. With the increase of the stirrup ratio, the shear capacity of the PPEC beams increased gradually.(5)
Based on the test results, the design method of the shear capacity of the PPEC beams was presented. The results show that the test results were in good agreement with the calculation results, which can be used for reference in practical engineering design.



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*Source: 2762846-2019-08-27.xml*