Mechanical performance test and analysis of prestressed lightweight aggregate concrete hollow slab

Abstract

To investigate the mechanical performance of prestressed lightweight aggregate concrete hollow slabs, a symmetric loading test was performed on eight prestressed concrete hollow slabs categorised into four groups based on their variety of coarse aggregate concrete and span, and their respective failure mode, bearing capacity, deformation performance and crack propagation were analysed. Based on the test data, a simulation model was subsequently established to simulate and analyse the test components. The test results showed that the bending process of the prestressed lightweight aggregate concrete hollow slab goes through three stages: elasticity, elasto-plasticity and plasticity. Furthermore, its bearing capacity and failure characteristics are similar to those of a prestressed ordinary concrete hollow slab. Subsequently, we derived a formula for checking the calculation of crack width by introducing a comprehensive influence coefficient of concrete C_m and combining it effectively with the formula in the current code and verified its efficacy. The calculated value of the formula agrees well with the test results, providing a reference for the application of engineering and a supplementary calculation formula for the crack width of lightweight aggregate concrete hollow slabs.

Keywords

bearing capacity bending test crack width lightweight aggregate concrete prestressed hollow slab

Introduction

With continuous developments in society, people’s demands for better function and quality of buildings are increasing. In addition, the layout of modern houses with column grids and beams has been gradually simplified by increasing the size of the column grid and decreasing the beam size as much as possible. Compared with ordinary concrete hollow slab, lightweight aggregate concrete hollow slabs have the advantages of being lightweight and having good seismic performance and strong structural integrity (Hassanpour et al., 2012; Yang et al., 2013). The application of prestressing technology to such hollow slabs can significantly improve the composite reinforcement ratio of the section, enhance the bearing capacity of the structure and relatively decrease the stress change range of the section under cyclic loading to enhance the anti-fatigue performance of components (Xue and Guo, 2011; Yang et al., 2011). Furthermore, the use of prestressed lightweight aggregate concrete hollow slabs in engineering can reduce the number of beams and columns used in a structure, increase the area of the structure that can be used and facilitate free-space division. While meeting the functional requirements of a building, this type of concrete slab can mitigate the deficiency of the relatively large self-weight and poor economic index of prestressed ordinary concrete slabs (Vázquez-herrero et al., 2013).

The inner mould of the hollow slab can effectively reduce the overall weight of the floor and the amount of concrete used. Simultaneously, low-strength and low-weight materials, such as polystyrene foam, can be used to fill in the hollow for sound and thermal insulation (Tian, 2012). Prestressed lightweight aggregate concrete hollow slabs could play an important role in future social development. Therefore, vigorously promoting the application of lightweight aggregate concrete in prestressed concrete structures will not only generate huge economic benefits but also contribute substantially towards sustainable development of the construction industry (Chun, 2012).

In recent years, scholars worldwide have conducted much research on prestressed concrete hollow slabs and achieved outstanding achievements (Han et al. 2018; Liu et al. 2000; Yang et al. 2008; Zhao et al. 2004). Yang et al. (2010) studied the mechanical performance of steel plate – lightweight aggregate concrete hollow composite slabs and presented research results that showed that the steel pipe in the hollow slab can significantly improve its bearing capacity and anti-deformation performance. Xu et al. (2013) showed that the refractoriness of prestressed concrete hollow slabs at different load-holding levels gradually increases with decreasing load-holding level. Zhao et al. (2002) studied the performance of prestressed high-strength concrete hollow slabs in normal use with respect to factors such as cracking resistance, crack width and ultimate bearing capacity and showed that high-strength concrete can meet design requirements and also has good ductility performance. However, few studies have reported on the mechanical performance of prestressed lightweight aggregate concrete slabs. Existing structural design codes do not have clear requirements for such component design. At both local and global levels, specifications or codes for the mechanical performance of prestressed lightweight aggregate concrete hollow slabs are still lacking. However, as this kind of component can significantly reduce the self-weight of concrete structures, and has broad application prospects in engineering, detailed research is critical.

Performance testing

Mix proportion design and basic mechanical performance

C40 and LC40 concrete were designed according to JGJ55-2011 (2011) and JGJ51-2002 (2002) with P. O 42.5 ordinary Portland cement and medium sand with a fineness modulus of 2.8. The coarse aggregate of the ordinary concrete was stone with a diameter of 5–12 mm, while that of the light aggregate concrete was shale ceramsite with a diameter of 5–12 mm. The shale ceramsite is shown in Figure 1, and its basic performance indices are listed in Table 1. The mineral admixture of C40 and LC40 concrete in this test was fly ash, the equivalent quality substitution rate was 10% and the water-reducer content was 1.2%.

Table 1.

Performance indices of shale ceramsite.

Ceramsite level	Loose bulk density (kg/m³)	Compact bulk density (kg/m³)	Cylinder compressive strength (MPa)	1 h water absorption (%)
900	946	1020	14.5	3.0

Ordinary and lightweight concrete cube test blocks with strength grades of C40 and LC40, respectively, were prepared with mass mix proportion as shown in Table 2.

Table 2.

Mix proportion of C40 and LC40 concrete (kg/m³).

Number	Cement	Fine aggregate	Coarse aggregate	water	Fly ash	Water reducer
C40	400	814	1079	113	44	5.3
LC40	420	715	681	128	47	5.6

LC and C refer to lightweight aggregate concrete and ordinary concrete, respectively.

The C40 and LC40 concrete cube test blocks were subjected to cube-compression, prism-compression and cube-splitting tests. A total of nine test blocks for each test were divided into three groups. Following maintenance for 7 days, the first group of related mechanical performance tests were conducted to test the corresponding mechanical strength. Subsequently, following curing of the test blocks for 28 days, the related mechanical performance tests were conducted on two groups of six test blocks. The basic mechanical properties of C40 ordinary concrete and LC40 lightweight aggregate concrete were finally obtained, as shown in Table 3. Their failure characteristics are shown in Figures 2 and 3, respectively.

Table 3.

Basic mechanical performance of C40 and LC40 concrete (MPa).

Number	Compressive strength of cube, f_cu	Compressive strength of prism, f_c	Splitting tensile strength, f_t,s	Elasticity modulus under pressure, E_c
C40	47.6	39.1	2.92	3.27 × 10⁴
LC40	46.5	39.9	2.97	2.42 × 10⁴

The cubic compressive strength of LC40 concrete is slightly lower than that of C40 concrete, while the prism compressive strength and splitting tensile strength are slightly higher. This is because the nature of compression failure is the tensile failure of concrete. However, owing to the porosity of the ceramsite, the ceramsite of lightweight aggregate concrete has a better bond force with cement mortar than that of ordinary stone with cement mortar. In the prism-compression test and cube-splitting test, the bond force is more obvious.

The related mechanical properties were tested using six spiral ribbed prestressed steel wires of the same batch. Table 4 lists the measured parameters of the materials, and Figure 4 shows the material performance test of the spiral ribbed prestressed steel wires.

Table 4.

Measured parameters of spiral ribbed prestressed steel wire.

Steel type	Density (kg/m³)	f_ptk (MPa)	Young’s modulus (N/mm²)
Φ^H7-1570	7800	1641	2.08 × 10⁵

Φ^H7-1570: Φ^H represents the spiral ribbed prestressed steel wire, 7 represents the diameter (d/mm) and 1570 is the specific standard value of ultimate strength.

Bulk density contrast test of lightweight aggregate concrete

This test was performed to determine the changing rule of the bulk density ratios of lightweight aggregate and ordinary concrete with time (to determine the advantages of lightweight aggregate concrete over ordinary concrete with respect to weight). Equation (1) shows the ratio of the weight difference between lightweight aggregate and ordinary concrete (light rate δ). Six sets of 150 mm × 150 mm × 150 mm concrete standard test blocks were selected to simultaneously test their bulk density every 1, 3, 7, 14 and 28 days. The test results are shown in Table 5

δ = \frac{Bulk density of ordinary concrete - Bulk density of lightweight aggregate concrete}{Bulk density of ordinary concrete}

(1)

Table 5.

Comparison of bulk density between ordinary concrete and lightweight aggregate concrete.

Concrete	Time (days)	Test cube 1 (kg)	Test cube 2 (kg)	Test cube 3 (kg)	Test cube 4 (kg)	Test cube 5 (kg)	Test cube 6 (kg)	Average value (kg)	Bulk density (kg/m³)	δ
LC	1	6.710	6.710	6.725	6.745	6.675	6.850	6.736	2021	17.0%
C	1	8.335	8.315	8.210	8.165	8.130	8.150	8.218	2435	17.0%
LC	3	6.630	6.630	6.645	6.705	6.585	6.810	6.668	1976	17.2%
C	3	8.035	8.115	8.090	8.065	8.030	7.985	8.053	2386	17.2%
LC	7	6.555	6.570	6.580	6.630	6.530	6.755	6.603	1956	17.4%
C	7	7.985	8.070	8.025	8.010	7.965	7.920	7.993	2368	17.4%
LC	14	6.520	6.540	6.555	6.600	6.500	6.720	6.573	1948	17.5%
C	14	7.965	8.040	8.005	7.990	7.945	7.895	7.973	2362	17.5%
LC	28	6.500	6.510	6.520	6.575	6.470	6.695	6.545	1939	17.7%
C	28	7.935	8.020	7.980	7.960	7.920	7.875	7.948	2355	17.7%

LC and C refer to lightweight aggregate concrete and ordinary concrete, respectively.

Table 5 shows that the bulk density of lightweight aggregate concrete is lower than that of ordinary concrete, and with time, the bulk densities gradually become smooth, while the growth of δ is relatively stable. On the 28th day, δ reached 17.7%. In summary, application of lightweight aggregate concrete can significantly reduce the self-weight of concrete structures, and it has a strong advantage in terms of cost and seismic reduction.

Component design

Four groups of eight prestressed hollow slabs were designed and manufactured, and a four-point loading test was conducted. The Φ^H7-1570 spiral ribbed prestressed steel wires were used in this study with spacing of 170 mm, distance of 23.5 mm between the centre point and component base plate, tension control stress of 0.7f_ptk (f_ptk represents the limit strength standard value), and Young’s modulus, E = 2.08 × 10⁵ N/mm². The size of the section is shown in Figure 5, and the design parameters of the component are shown in Table 6.

Table 6.

Parameters of the specimens.

Test group component number	Control group component number	Slab span (m)	Reinforcement	Tension control stress	Thickness of protective layer (mm)
LC-4.2	C-4.2	4.2	4Φ^H7	0.7f_ptk	20
LC-4.8	C-4.8	4.8
LC-5.4	C-5.4	5.4
LC-6	C-6	6

4Φ^H7 represents four spiral ribbed prestressed steel wires with a diameter of 7 mm.

Test loading scheme

The test hollow slab adopted the scheme of symmetric synchronous graded loading, and the test-loading device is shown in Figure 6. The test load was applied by considering the calculated load of the hollow slab as the reference. For each additional load, the load was held for 10 min and the data were collected after the load was stabilised. For a component with a large deformation, if the deformation continued to increase after loading, the load was replenished. The load was considered to be stable when the drop value of the load did not exceed 5% of the load value. The next load was added until the concrete was crushed or the stress relief steel wire reached its ultimate strength. The specific steps are as follows:

First, preloading was performed, the test instrument tested and the load then removed. The reading of the sensor and resistance strain gauge was reduced to zero, and the reading on the displacement meter was recorded.

The hollow slab component was loaded. Before the cracking of the component, the load of each stage was calculated as 0.1F_u approximately (where F_u is the ultimate load), and the load holding time was 10 min.

The load added at each stage after the cracking of the hollow slab was calculated to approximately 0.05F_u, with the load duration of 10 min.

The hollow slab was loaded until the crack width reached 1.5 mm, and then it was unloaded to 0.1F_u to observe the condition of crack closure.

After unloading, the next load was loaded to the load level before unloading and then loaded in the original way (0.05F_u).

When the deflection was close to 1/50th of the calculated span, the displacement control loading method was adopted to load the test hollow slab component, and observation of the change rule of load–displacement in the later stage of the hollow slab was completed.

Analysis of test phenomena and results

Test phenomena

In the process of the four-point loading test of the prestressed lightweight aggregate concrete hollow slabs, data were collected synchronously through pressure sensors, strain collection boxes and other test instruments. Considering an LC-5.4 hollow slab as an example, the state of the specimens before and after loading is shown in Figure 7. Before cracking, the load at each level increased uniformly, the components showed good elasticity, the deflection changed slightly and the load–deflection curve showed a linear relation. Following loading to approximately 0.4F_u, the first vertical cracks appeared in the pure bending section with a slight ‘clicking’ sound; however, the cracks did not extend towards the centre of gravity of the prestressed steel wire, and the crack width was below 0.05 mm. The load–deflection curve does not show an obvious turning point, owing to concrete cracking. With the increase in load, the number of cracks increased, along with the crack width and height extension. Following loading to approximately 0.65F_u, the crack width reached 1.5 mm. It was then unloaded to approximately 0.1F_u, and the maximum crack width decreased to below 0.01 mm, indicating that the specimen has a good closure property. Following loading again to 0.65F_u, the performance was the same as indicated above. With loading to approximately 0.9F_u, the deflection reached approximately 1/50th of the calculated span. At this stage, the load increased gradually, whereas the mid-span deflection increased rapidly. With the continuous increase in load, the number of cracks no longer increased, the crack distribution was more uniform, and the neutral axis continued moving upwards until the concrete in the compression zone was crushed, with a ‘banging’ sound, and the components were completely destroyed.

Figure 8 shows the distribution of crack development in LC-5.4 and C-5.4. As shown in the figure, after cracks appeared in the prestressed lightweight aggregate concrete hollow slab, their development speed is faster than that of those in an ordinary concrete hollow slab. In addition, the cracks are linear, number of cracks is relatively small and the distance between cracks is relatively large. These phenomena could mainly be due to the relatively low tensile strength of shale ceramsite, leading to the formation of a model with cement mortar as skeleton and coarse aggregate as filling. When cracks started forming in the interface of the cement mortar and aggregate, and in the interior of the mortar, shale ceramic particles were encountered in the process of extension and expansion. As these do not block the development and extension of cracks, the cracks will directly pass through the shale ceramsite and expand rapidly. The strength of the coarse aggregate in the prestressed ordinary concrete hollow slab is much higher than that of the concrete; the cracks must bypass the coarse aggregate and develop in the mortar. Coarse aggregate has the effect of inhibiting the development of cracks, and the final fracture surface is serrated with relatively close spaces between cracks.

The external loads of cracking and related states are shown in Table 7, where F_cr is the cracking load, F₁ is the load when the crack width reaches 1.5 mm, F₂ is the load when the deflection reaches 1/50th of the calculated span and F₃ is the load when the components completely lose bearing capacity. In addition, $F_{cr}^{LC}$ and $F_{cr}^{C}$ , respectively, represent the cracking loads of prestressed lightweight aggregate and prestressed ordinary concrete hollow slabs and the other similar signs are as follows.

Table 7.

External loads at each stage of prestressed hollow slab.

Specimen number	F_cr (kN)	$F_{cr}^{LC} / F_{cr}^{C}$	$F_{1}$ (kN)	$F_{1}^{LC} / F_{1}^{C}$	$F_{2}$ (kN)	$F_{2}^{LC} / F_{2}^{C}$	$F_{3}$ (kN)	$F_{3}^{LC} / F_{3}^{C}$
LC-4.2	21.51	0.957	32.39	0.939	41.86	0.928	49.89	0.911
C-4.2	22.48	0.957	34.51	0.939	45.09	0.928	53.69	0.911
LC-4.8	19.58	1.035	30.59	1.048	38.97	1.027	45.97	1.038
C-4.8	18.92	1.035	29.52	1.048	37.93	1.027	44.29	1.038
LC-5.4	15.54	0.959	24.49	0.869	31.91	0.895	37.55	0.977
C-5.4	16.21	0.959	28.18	0.869	35.66	0.895	38.43	0.977
LC-6	13.94	0.947	21.13	0.936	37.63	0.956	32.50	0.959
C-6	14.72	0.947	22.57	0.936	39.32	0.956	33.9	0.959

Test results and analysis

The test phenomena of the prestressed lightweight aggregate and prestressed ordinary concrete hollow slabs are similar. The bending test experiences the three-development stages elasticity, elasto-plasticity and plasticity, as shown in Figure 9.

Elastic stage

From applied load to component cracking. The mid-span deflection of components, steel strain and concrete compressive strain in the mid-span compression zone increase linearly with increasing load. The components present elastic characteristics, strain amplitude is small, load growth rate is fast and the integral stability of the components is good. In this stage, the deflections of both the prestressed lightweight aggregate and prestressed ordinary concrete hollow slabs changed slightly and their load–deflection curves are similar.

Elasto-plastic stage

This stage extends from the start of component cracking to the yielding of prestressed steel wire. The reason for the relatively short duration of this stage is that the spiral ribbed prestressed steel wire used in the test component is tensioned according to 0.7f_ptk. In the bending process of the component, the tensile stress increases continuously, and during cracking, the stress is close to the elastic limit of the spiral ribbed prestressed steel wire. After the concrete cracks, the stress is transferred to the prestressed steel wire owing to the withdrawal of the concrete in the cracking area; the stress is then redistributed, reaches a new equilibrium state and tends to be stable. This stage is also known as the working stage with cracks. The load growth rate is smaller than that in the elastic stage. The medium-span deflection of specimens, strain increment of steel bars and strain growth rate of concrete in the mid-span compressive zone are larger than those in the elastic stage. With the increase in load, new cracks appear constantly and the increasing of crack width and height is relatively slow. At this stage, a difference begins to appear between the curves of prestressed lightweight aggregate and prestressed ordinary concrete hollow slabs. The number of cracks in the prestressed lightweight aggregate concrete is smaller and sparser, and the spacing between cracks is larger than in the ordinary slab, and the vertical cracks are linear.

Plastic stage

This stage extends from the prestressed steel wire yielding to component failure. Such a long duration is because the prestressed steel wire fully exerts its toughness during this stage. Even in the case of large deformation, sufficient deformation capacity and increase in the tensile stress are ensured. Therefore, the component bearing capacity gradually increases and approaches the ultimate bearing capacity. In addition, the mid-span deflection of component, mid-span steel strain and concrete compressive strain increase rapidly at this stage. At this point, the cracks basically come out and continue to develop along the thickness direction of the slab, the neutral axis continues moving upwards, the concrete area in the compression zone continues decreasing and the compressive stress continues increasing until the concrete in the compression zone is crushed. Moreover, the components completely lose the bearing capacity and exhibit good ductility. In this stage, the number of cracks in both the types of hollow slabs stop increasing, the load increases slowly, the crack width increases constantly and the component deflection increases rapidly. Compared with the ordinary slab, the number of cracks in the lightweight aggregate concrete hollow slab is relatively smaller and the crack width is relatively larger. When the component is completely destroyed, some shale ceramic particles in the section are crushed, and the fracture section is relatively flat. However, in the prestressed ordinary concrete hollow slab, when the components are completely destroyed, only a small amount of coarse aggregate in the section is crushed, and the fracture section is relatively rough.

The lateral concrete strain of prestressed concrete slab changes along the height of the slab, as shown in Figure 10. The load–deflection relationship in the mid-span of the prestressed hollow slab is shown in Figure 11, and Figure 12 shows the load–concrete strain relationship at mid-span.

Simulated analysis of the specimens

Constitutive relation model of lightweight aggregate concrete

The stress–strain relationship of lightweight aggregate concrete is similar to that of ordinary concrete. It presents two parts: the ascending and descending sections. Maximum stress value f_c, corresponding strain value ε₀, and ultimate compressive strain ε_cu of concrete are still three characteristic values of the curve. The typical stress–strain relationship of compression failure of lightweight aggregate concrete was adopted for the simulation and analysis of the components.

When $ε_{c} \leq ε_{0}$

σ_{c} = f_{c} [1.5 (\frac{ε_{c}}{ε_{0}}) - 0.5 {(\frac{ε_{c}}{ε_{0}})}^{2}]

(2)

When $ε_{0} < ε_{c} \leq ε_{cu}$

σ_{c} = f_{c}

(3)

where f_c is peak stress (ultimate compressive strength of prism), ε₀ is the compressive strain of lightweight aggregate concrete when its strength reaches f_c and ε₀ = 0.0022, and ε_cu is the ultimate compressive strain of lightweight aggregate concrete and ε_cu = 0.0033.

Establishment of component simulation model

The model of a hollow slab was analysed using ABAQUS software. In the simulated analysis, the concrete and prestressed steel wires adopted different unit types: the concrete adopted the C3D8R hexahedral reduction unit, while the prestressed steel wire adopted the T3D2 truss unit. Furthermore, the prestressed steel wire adopted the isotropic elasto-plastic model, which meets the Von Mises yield criterion, and the concrete used the plastic damage model. The SPRING2 spring units were applied to the joints of the prestressed steel wire and concrete to consider the effect of the interaction between them.

The density of the mesh division in the simulated analysis greatly influences the accuracy of the calculation results. Considering the comprehensive calculation cost and analysis accuracy, the mesh division scheme, as shown in Figure 13(a), was selected. Figure 13(b) shows the model perspective chart.

Analysis of loading capacity of the simulated hollow slab

By considering the LC-5.4 simulated hollow slab as an example, the comparison between the obtained simulated analysis and test results is shown in Figure 14. Figure 14(a) shows the cloud diagram of the deflection change of prestressed lightweight aggregate concrete hollow slab under external load; this is in good agreement with the deformation state of the hollow slab after the test loading in Figure 14(b). Unlike the smearing cracking model, the ABAQUS plastic-damage concrete constitutive model cannot evolve the crack; however, it can show the development region and direction of the crack through the cloud diagram, as shown in Figure 14(c). The mid-span red-light region in the figure is the main crack development region, which is consistent with the test component’s crack development region. Figure 14(d) shows the stress-distribution cloud diagram of the prestressed lightweight aggregate concrete hollow slab in the critical failure state.

The stress process of the simulation model of prestressed lightweight aggregate concrete hollow slab is also divided into three stages: elastic, elasto-plastic and plastic stages. In the elastic stage, the deflection and load change of the four simulated prestressed lightweight aggregate concrete hollow slabs were basically consistent with the test values. In the elasto-plastic stage, as the prestressed steel wires were stretched, the simulated analysis results of the elasto-plastic stage were similar to the test values in terms of deflection change and load growth trend; however, the simulated load values were larger than the test values. In the plastic stage, although both the simulated and test results showed a rapid increase in the deflection, the load increased much slower in the simulation than in the test. Overall, the data and trend of the whole curve coincided with the test results. Moreover, the cracking load, ultimate load test values and simulated results of prestressed lightweight aggregate concrete hollow slab are less different. The load–deflection curves of four groups of prestressed hollow slabs were compared with the results of the simulated analysis, as shown in Figure 15.

The test results were compared with those of the simulated analysis, as shown in Table 8, where the maximum deviation between the analysis value of the cracking load and the test results is 8.5%, which shows good agreement. The deviation between the analysis value and the test result of the ultimate load is within 6%, and the agreement degree is higher. The correctness of the test process and conclusion were verified through a simulation analysis.

Table 8.

Comparison between test analysis and simulation results.

Specimen number	Cracking load			Ultimate load
Specimen number	$F_{cr}^{m}$ (kN)	$F_{cr}^{t}$ (kN)	$F_{cr}^{m}$ / $F_{cr}^{t}$	$F_{u}^{m}$ (kN)	$F_{u}^{t}$ (kN)	$F_{u}^{m}$ / $F_{u}^{t}$
LC-4.2	22.61	21.51	1.051	49.14	49.89	0.985
LC-4.8	20.40	19.58	1.042	44.65	45.97	0.971
LC-5.4	15.97	15.54	1.028	36.97	37.55	0.985
LC-6	15.09	13.94	1.085	29.92	32.50	0.921

$F_{cr}^{m}$ and $F_{cr}^{t}$ represent the simulation and test results of the cracking load, respectively. $F_{u}^{m}$ and $F_{u}^{t}$ represent the simulation and test results of the ultimate load, respectively.

Theoretical analysis and design calculation

Normal section bearing capacity

The bearing capacity of the normal section of the prestressed lightweight aggregate concrete hollow slab was calculated according to the following three basic assumptions:

The plane deformation of the section strain is retained;

The tensile strength of lightweight aggregate concrete is not considered;

The stress–strain relationship curve of lightweight aggregate concrete is considered according to the JGJ12-2006 (2006).

To simplify the calculation under the condition that the section stiffness, height and width remain unchanged, the hollow slab section was converted into an I-shaped section according to the principle of equal area and overlapping centre of gravity of the two graphs, as shown in Figure 16

b_{k} \times h_{k} = \frac{π}{4} D^{2} \times \frac{3}{2}

(4)

\frac{1}{12} b_{k} \times h_{k}^{3} = \frac{π}{64} D^{4} \times \frac{3}{2}

(5)

According to the principle of equal concrete compressive stress resultant C and unchanged applied point position, the bending stress-distribution model of the structure’s section was established, as shown in Figure 17. The calculated values of M_u simultaneously obtained through equations (6) and (7) were compared with their corresponding test values. The specific results are shown in Table 9. The symbolic meanings in the formula can be referenced from Yang et al. (2010)

\sum X = 0 α_{1} f_{c} bx = σ_{p} A_{s}

(6)

\sum M = 0 M_{u} = σ_{p} A_{s} (h_{0} - \frac{x}{2})

(7)

Table 9.

Calculated values and experimental values of ultimate bearing capacity.

Specimen number	$M_{u}^{c}$ (kN m)	$M_{u}^{t}$ (kN m)	$M_{u}^{t}$ / $M_{u}^{c}$	Average value
LC-4.2	58.01	59.87	1.032	1.031
LC-4.8	61.41	64.36	1.048
LC-5.4	58.10	60.08	1.034
LC-6	58.05	58.51	1.008
C-4.2	61.30	64.43	1.051	1.062
C-4.8	59.06	62.01	1.050
C-5.4	57.74	61.49	1.065
C-6	65.40	61.02	1.082

$M_{u}^{c}$ and $M_{u}^{t}$ represent the calculated and experimental values of the bending capacity, respectively.

Table 9 shows that the test values of the bearing capacity of the prestressed lightweight aggregate concrete hollow slab differ only slightly from the calculated values. The test results of ordinary concrete hollow slab are slightly higher than the calculated values; however, the deviation remains approximately 6.2%, which is in good agreement. This shows that the use of the above-mentioned calculation model is reasonable, and the calculation of the ultimate bearing capacity of a prestressed lightweight aggregate concrete hollow slab according to the current formulas is desirable.

Calculation of maximum crack width in prestressed lightweight aggregate concrete

To the best of our knowledge, no calculation of the maximum crack width of prestressed lightweight aggregate concrete hollow slabs has been reported. The formulas in GB50010-2010 (2010) still need further tests and verification. By considering the influence of concrete aggregate variety on the average crack spacing, comprehensive influence coefficient C_m of concrete is introduced. According to GB50010-2010 (2010), maximum-crack-width limit value $ω_{lim}$ of prestressed concrete components in a class-II-A environment is 0.10 mm. Therefore, the binding moment of the maximum crack width of 0.1 mm measured in the test was selected as the M_k value of equivalent stress $σ_{sk}$ of the tensile reinforcement, as shown in equation (8)

σ_{sk} = \frac{M_{k} - N_{p 0} (z - e_{p})}{(α_{1} A_{p} + A_{s}) z}

(8)

The definitions of the symbols in equation (8) can be referenced from JGJ12-2006 (2006) and GB50010-2010 (2010).

For the lightweight aggregate concrete hollow slab, the maximum crack width can be calculated through equation (9)

ω_{\max} = \partial_{cr} ψ \frac{σ_{sk}}{E_{s}} (2.7 c + \frac{0.571 d_{eq}}{ρ_{te}}) ν C_{m}

(9)

For the prestressed ordinary concrete hollow slab, the maximum crack width can be calculated using equation (10)

ω_{\max} = \partial_{cr} ψ \frac{σ_{sk}}{E_{s}} (2.7 c + \frac{0.1 d_{eq}}{ρ_{te}}) ν C_{m}

(10)

In equations (9) and (10), v is the surface characteristic coefficient of tensile reinforcement. For the spiral ribbed prestressed steel wire, v is 0.7. C_m is the comprehensive influence coefficient of concrete, which can be 1.68 for lightweight aggregate concrete and 1.0 for ordinary concrete. Furthermore, $ρ_{te}$ is the reinforcement ratio of tensile reinforcement and its actual value is recommended for use. The other symbol values of the equations can be referenced from JGJ12-2006 (2006).

The calculated and test results of the maximum crack width are shown in Table 10, which shows that the theoretical calculation results of the maximum crack width are in good agreement with the test results. It is feasible to use the above-mentioned formula to calculate the crack width.

Table 10.

Calculation results and test results of the maximum crack width.

Specimen number	$M_{k}$ (kN m)	$ω_{\max}^{t}$ (mm)	$ω_{\max}^{c}$ (mm)	$ω_{\max}^{t}$ / $ω_{\max}^{c}$
LC-4.2	30.647	0.11	0.098	1.12
LC-4.8	31.034	0.1	0.119	0.84
LC-5.4	30.964	0.1	0.115	0.87
LC-6	31.934	0.14	0.165	0.85
C-4.2	32.327	0.14	0.165	0.85
C-4.8	31.933	0.12	0.147	0.82
C-5.4	31.769	0.12	0.139	0.86
C-6	32.465	0.16	0.172	0.93

Conclusion and recommendations

Through symmetric loading tests of the four groups of eight prestressed hollow slabs, their behaviours, such as failure mode, crack and strain development, bearing capacity and deformation performance, were investigated. The results obtained are in good agreement with the analysis results of the simulation model, and the following conclusions are drawn:

The comparison of the bulk densities of the standard cube test blocks of lightweight aggregate concrete and ordinary concrete shows that the average value of $δ$ is 17.36%. Thus, the application of lightweight aggregate concrete can significantly reduce the self-weight of concrete, which is obviously advantageous in terms of cost and seismic reduction.

The application of spiral ribbed prestressed steel wire inhibits the development of cracks, effectively controls the width of cracks, improves the resistance performance of hollow slab component and improves the service performance in the normal operation stage.

Owing to relatively low tensile strength of shale ceramsite, it cannot block the development of cracks during the extension and expansion processes. The cracks will thus pass directly through the shale ceramsite and extend rapidly. Thus, the cracks of lightweight aggregate concrete develop faster than those of ordinary concrete, the number of cracks is relatively smaller and the spacing is relatively larger and more linear. Therefore, it is recommended to adopt high-strength, lightweight aggregate in structural design as it is more favourable for structural safety.

Owing to the characteristics of the deformation performance of this type of hollow slab, when the deflection of the specimen reached 1/50th of the calculated span, the bearing capacity reached approximately 90% of the ultimate bearing capacity. When designing and calculating, the deflection that reached 1/50th of the calculation span can be taken as the deflection limit state; this can not only give full play to the bearing capacity but also have a good safety reserve.

By introducing the comprehensive influence coefficient C_m of concrete and combining it with the formula in the current code, a simple and feasible method has been provided for crack calculation of lightweight aggregate concrete hollow slab, and the consistency of crack width calculation of component was realised. The calculated value of the formula is in good agreement with the test results.

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.

ORCID iD

Shiping Li

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