Structural Behaviour of Reinforced Concrete Beam with Embedded Polystyrene Spheres

: The beam is a structural element in a reinforced concrete structure. However, its weight places additional strain on the columns and foundations.Polystyrene spheres can be used to replace concrete in a beam to reduce its weight. However, this can affect the beam’s structural performance. This study investigated the behavior of beams with embedded polystyrene spheres under loads. The purpose was to determine the feasibility of this technique. Six beam specimens, including a control specimen, were tested under the four-point load setup. The polystyrene spheres’ diameter ranged from 50 mm to 75 mm. The spacing between the spheres varied from 10 mm to 30 mm. By replacing 8.7% of the concrete, the beam's strength increased by 8% per unit of concrete. The polystyrene spheres marginally altered the load capacity but reduced the stiffness, uncracked load, and ductility. The load capacity decreased by 2.6% as the polystyrene sphere’s diameter increased from 50 mm to 10 mm. The strength increased by 0.6% as the spacing increased from 10 mm to 30 mm. For satisfactory performance, the polystyrene spheres with a diameter of 0.57 times the beam’s width may be spaced at 1.2 times the concrete cover.


Introduction
The beam is a crucial structural element in reinforced concrete (RC) structures.It is a part of the skeletal frame system.It resists loads acting perpendicularly to the beam's axis [1].One problem with RC members is their weight.The weight puts extra load on the columns and foundations.Thus, larger columns and foundations are required.The weight of RC beams can be reduced by partially removing the concrete.This can be done by creating voids or embedding lightweight materials in the beam (Table 1).This approach is conceptually viable based on the beam's bending theory.The concrete in the tension zone is expected to convey no load, which may reach 80% of the total concrete volume [2].Even so, that concrete cannot be fully removed, as this can significantly affect the beam's performance.The biggest challenge in removing concrete from beams is achieving structural performance comparable to that of a solid beam.Excessive concrete removal can affect the beam's stiffness, load capacity, and ductility [20,27,28].It may also reduce the shear strength of the beam and result in brittle failure [29].The material's efficiency can also be a concern for these beams.The beam can lose more strength than weight, in percentage [30].Thus, this kind of beam needs to be comprehensively investigated, particularly to uncover the factors governing its structural performance.
Table 1.Previous studies of lightweight beams.

Embedded lightweight materials
Polystyrene spheres [20] Polystyrene block [21][22][23][24] Foamed concrete infill [25] Polypropylene Plastic Sheet [26] There were studies on beams embedded with various lightweight materials, but only a limited number involved polystyrene spheres (Table 1).Most studies compared the beam's strength with that of the solid beams, but not many looked into the material efficiency, which is the strength per unit of concrete.This paper presents an experimental study of beams with embedded polystyrene spheres.The purpose was to investigate the behavior of the beams.The effects of the size of the polystyrene spheres and the spacing between the polystyrene spheres were examined.Then, the feasibility of having polystyrene spheres in RC beams was analyzed.Material efficiency would be one of the evaluation criteria for feasibility.

Materials and Methods
In this study, RC beams embedded with polystyrene spheres were tested under an incremental monotonic load.This was hypothesised that polystyrene spheres would reduce the beams' strength but increase the strength per unit weight.

Specimens.
Six beam specimens were fabricated.This included one control (i.e., CB) and five test specimens (i.e., PB1 to PB5).The control specimen was a solid beam.It represented the beam's response without the influence of the polystyrene spheres.The test specimens had polystyrene spheres embedded in the beams (Figure 1).The polystyrene spheres were placed at the centroid of the beam's cross-section.The sphere's diameter ranged from 50 mm to 100 mm, whereas the spacing between the spheres was between 10 mm and 30 mm (Table 2).The specimens were cast in timber formworks (Figure 2(a)).Before casting, steel reinforcements were prepared.The polystyrene spheres were tied to the reinforcement using galvanised wires (Figure 2(b)).The specimens were cast using C20/25 ready-mix concrete with the designed slump of 100 mm to 180 mm.For curing, the specimens were sprayed with water and covered with plastic sheets.The specimens were tested 28 days after casting.

Test setup.
The specimens were tested under the four-point load test setup (Figure 3).Each specimen sat on two rockers with a clear span of 1500 mm.A hydraulic jack was used to impose force on a distribution beam.The distribution beam then transmitted the force to the specimen through the two steel rockers.The distance between the rockers was 260 mm.A load cell was used to measure the load applied to the specimen.It was placed between the hydraulic jack and the distribution beam.Three Linear Variable Differential Transformers (LVDTs) were used to measure the specimen's deflection.One LVDT was installed in the midspan, and two more were installed below the rockers.All the measuring instruments were connected to a data logger for data acquisition.The equipment and instruments used for testing are given in Table 3.The test was carried out following the procedure described by the previous researchers [20,21,22].The specimen was first preloaded to 10% of the estimated ultimate capacity for about 5 minutes to consolidate the test setup.The preload was then released for 1 minute for recovery.This process was repeated twice to check the test setup and the measuring devices.Then, all the readings were reinitialized to zero.The load was gradually increased at an interval of about 5 kN or 0.5 mm, whichever was achieved first.The purpose was to acquire smooth loaddisplacement plots.The load was held in place for at least one minute.Readings were taken once the load stabilized.Throughout the test, the specimen's surface was inspected to monitor the cracks.The test was stopped after three consecutive drops in the readings given by the load cell.

Results and Discussion
The test results comprised the material properties, geometrical properties, load-displacement responses, failure modes, and mechanical properties of the specimens.Then, the effects of polystyrene spheres on the beams' stiffness, strength, and ductility are discussed.

Material properties.
The properties of the materials used to fabricate the specimens are shown in Tables 4 and 5.
The concrete strengths were higher than the designed cube strength of 25 N/mm 2 .The reinforcements and shear links achieved their nominal strengths of 500 N/mm 2 and 250 N/mm 2 respectively.Hence, the quality of materials was considered acceptable.

Geometrical properties.
The polystyrene spheres partially replaced the concrete in the specimen.An area replacement ratio, Ra, quantified the effective concrete area of the beam's cross-section (Eq.1).
where Ap = Cross-sectional area of polystyrene spheres, mm 2 ; Ac = Cross-sectional area of the solid beam, mm 2 .
The volume replacement ratio, Rv, represented the effective concrete volume of the entire beam (Eq.2).
where Vp = total volume of polystyrene spheres, mm 3 ; Vc = volume of the solid beam, mm 3 .
The volumes of polystyrene spheres Vp, and solid beam Vs, were computed using Eqs. 3 and 4, respectively.
where np = number of polystyrene spheres in the beam; dp = diameter of polystyrene spheres, mm.
where b = width of the beam, mm; h = height of the beam, mm; l = length of the beam, mm.
The effective moment of inertia of the specimen's cross-section was computed using Eq. 5.
The moments of inertia of a solid beam and a polystyrene sphere were calculated based on Eqs. 6 and 7.
where b = width of the beam, mm; h = height of the beam, mm; dp = diameter of polystyrene spheres, mm.
Table 6 summarises the geometrical properties of the specimens.The results reveal that as the diameter of the polystyrene spheres rose, the area and effective moment of inertia of the beam section dropped.When the diameter of the polystyrene spheres increased and the space between the polystyrene spheres decreased, the concrete volume decreased.,261 Ab = cross-sectional area of solid beam (52500 mm 2 ), Vs = volumes of solid beam (84000000 mm 3 ), Ib = moment of inertia of solid beam (393750000 mm 4 ); np and dp refer to Table 2; b = 175 mm, h = 300 mm, l = 1600 mm

Load-displacement responses.
The load-displacement responses of the specimens are shown in Figure 4.The specimens started with the uncracked-elastic stage.At this point, the stiffness was the highest.The concrete and reinforcements were both in good condition, allowing stress to be effectively transferred between them.The specimens entered the cracked-elastic stage after the first crack.
The stiffness dropped slightly as the concrete gave way.The reinforcements then played an important role in resisting the load.The specimens gave an elastic response due to the elasticity of the reinforcements.This elastic stage ended as the reinforcement yielded.This set off the post-yield stage.For the plastic deformation of the reinforcements, significant beam deflection was observed.The failure stage happened at the ultimate state, where the load capacity peaked.The response for each stage is described in Table 7.The earliest stage of the specimen before the first crack.

•
The entire specimen was in good condition.

•
The specimen's stiffness 1 at this stage was the highest.Deflection increased marginally under load.

•
The load-displacement curve was about linear.The deflection was nearly proportionate to the applied load.Elastic (cracked) The stage of the specimen after the first crack and before the yield point

•
The first crack appeared in the middle of the span.As the load increased further, (a) the crack widened and propagated deeper into the beam, and (b) more cracks developed along the specimen.

•
The stiffness decreased slightly.The displacement increased at a faster rate.

•
The load-displacement curve was still close to linear.Thus, the deflection was about proportionate to the applied load.

Post-yield
The later stage of the specimen after the yield point before failure.
• The specimen's stiffness decreased drastically after the yield point.This could be due to the yielding of steel reinforcement 2 and excessive cracking of concrete.

•
The specimen endured plastic deformation.Considerable displacement developed with a slight increase in load.

Failure
The ultimate state of the specimen.

•
The specimen experienced critical damage and thus the applied load peaked. 1 The specimen stiffness was represented by the gradient of the load-displacement curve 2 As strain gauge was not installed on the steel reinforcement, the yield point of the steel reinforcement was not determined.
In this study, strain gauges were not installed on the reinforcements.It was unsure whether or not the reinforcement had yielded during the test.Nevertheless, the beam specimens exhibited signs of yielding.At the post-yield stage, the beam's stiffness degraded dramatically.This was followed by a substantial deflection before reaching the ultimate state.This response was believed to be caused by the yielding process of the reinforcements.

Crack pattern and failure mode.
Cracks developed as the strain limit of the concrete was exceeded.The strain was due to the flexural stress caused by the load applied to the beam.Three types of cracks were found, namely flexural, flexural-shear, and shear cracks.These cracks are shown in Figure 5 and described in Table 8.

•
The first crack noticed on the beam's surface • It started from the beam soffit and slowly propagated upward as the load increased.

•
It was found at the mid-span of the beam, between the two point loads acting on the beam.Flexural-shear crack (FS)

•
The cracks were discovered 1.5 to 2 d away from the beam's support.

•
It spread vertically at first but eventually became diagonal.Shear crack (S)

•
The crack appeared within 1.5 d of the beam's support.

•
The crack was slanted all the way through.The angle of inclination was about 45o from the beam's soffit.d = effective depth of the specimen The flexural crack was first detected at around 1/4 to 1/5 of the ultimate load at the midspan (Figure 5).As the load increased, more flexural cracks were observed.The cracked region spread sideways from the mid-span and towards the supports.Then, flexural-shear cracks appeared.Occasionally, shear cracks develop near the support.These cracks deteriorated the concrete, downgraded the bond with reinforcement, and eventually affected the load capacity of the specimens [20].The failure mode implied critical damage to the specimen.It was determined based on the crack pattern and the severity of the cracks.The severity of the cracks was determined based on the crack length, the crack width, and the highest load achieved by the cracks [1].All the specimens experienced diagonal tension failure (Figure 5 and Table 9).Table 9. Type of failure mode [1].

•
The flexural cracks were dominant.

•
The flexural-shear crack may or may not be present.

•
No shear crack was noticed.

•
The flexural-shear cracks were dominant.

•
Shear crack may or may not be present.

•
The shear crack was dominant.

•
The shear crack may or may not reach the top reinforcement in the beam

•
The top beam may or may not be crushed.

Test results.
Table 10 displays the specimen test results.The computation of these results is briefly described in Table 11 and Figure 6.The test specimens were then compared with the control specimen using performance ratios (Table 12).The beams with embedded polystyrene spheres were generally inferior to the solid beam.They had lower first crack, stiffness, and yield strength than the solid beam.The respective performance ratios in Table 12 were less than 1.0.This finding was in line with the observation by Mohamad et al. (2017) [13].Their beams with HDPE plastic balls also had a lower first crack load than the solid beam.

Description First crack load, Pcr
The load when the first crack was noticed, as acquired from Figure 5.

First crack deflection, δcr
The specimen's deflection when the first crack was noticed.It was obtained from the loaddisplacement curve in Figure 4.

Initial stiffness (uncracked), Si
The stiffness of the specimen before cracking (Figure 6(a)).It was calculated using the equation

Secant stiffness, Ss
The specimen's elastic stiffness.It was calculated as the gradient of the line passing through the point of 0.75Pu (Figure 6(b)).

Yield point (Py, δy)
A point on the load-displacement curve where plastic deformation of the specimen was initiated.It was determined by using the method used by Ling et al. ( 2020) [31], as demonstrated in Figure 6(b).

Ultimate load, Pu
The load capacity of the specimen was the highest point of the load-displacement curve (Figure 4).Ultimate deflection, δu The deflection of the specimen when the load peaked (Figure 4).

Ductility, Δ
An index representing the ductile behaviour of the specimen, which was computed using the equation, Δ =

Effects of polystyrene spheres on beam's stiffness.
The initial stiffness and secant stiffness represent the behavior of the specimen before and after cracking, respectively.The initial stiffness was always greater than the secant stiffness (Table 10).This was regardless of the solid beam or the beams with embedded polystyrene spheres.Before cracking, steel reinforcement and concrete resisted the flexural stress together.The elastic moduli of the two materials contributed to the high initial stiffness.After cracking, the concrete gave way under the tensile stress.As a result, the reinforcements took on all of the stress.This slightly reduced the beam's stiffness.The polystyrene spheres reduced both the initial and secant stiffness of the beam.The performance ratios Si,i/Si,c and Ss,i/Ss,c of specimens PB1 to PB5 were all less than 1.0 (Table 12).The polystyrene spheres reduced the moment of inertia of the section.This had an effect on the beams' ability to withstand bending moments [32].
The beam's stiffness decreased as the polystyrene spheres' diameter increased.This can be seen in specimens PB1, PB2, and PB3.The surface stiffness decreased by 40% from 18.5 kN/mm to 11.1 kN/mm as the polystyrene spheres' diameter increased from 50 mm to 100 mm.As the diameter increased from 50 mm to 100 mm, the concrete replacement increased from 1.9% to 8.7% (Table 6).The moment of inertia decreased when more concrete was replaced.This affected the stiffness (i.e., resistance to bending deformation) of the beam [32].The spacing between the polystyrene spheres also influenced the beam's stiffness.This was proven by specimens PB3, PB4, and PB5.As the spacing increased from 10 mm to 30 mm, the nominal stiffness increased by 30%, from 11.1 kN/mm to 14.5 kN/mm.The spacing between the polystyrene spheres formed a series of ribs in the beam.The ribs provided resistance to the beam's deformation under load.The larger the ribs around the polystyrene spheres, the higher the stiffness of the beam.This finding was in line with the studies by Izzat et al. (2014) [33] and Lim (2020) [34].Their specimens performed better with larger ribs between the lightweight materials.

Effects of polystyrene spheres on beam's strength.
There were three types of strength obtained.The uncracked strength was the beam strength before the first crack.The yield strength marked the beginning of the plastic deformation of the beam.The ultimate strength represented the load capacity of the beam.
As the diameter of the polystyrene sphere increased from 50 mm to 100 mm: (Table 10) • the uncracked strength decreased by 16.2%, from 29 kN to 24.3 kN.
• the yield strength decreased by 1.9%, falling from 103.9 kN to 101.9 kN, and • the ultimate strength was reduced by 2.6%, dropping from 119.8 kN to 116.7 kN.
When the spacing between polystyrene spheres increased from 10 mm to 30 mm: (Table 10) • the uncracked strength increased by 9.8% from 24.3 kN to 26.7 kN.
• the yield strength was influenced marginally within a range of +/-1.1%, and • the ultimate strength increased by 0.6%, rising from 116.7 kN to 117.4 kN.
Based on these observations, the uncracked strength was more severely affected by the polystyrene spheres than the yield strength or the ultimate strength.The spheres substituted for the concrete and altered the geometrical properties of the beam's section.This impeded the distribution of stress in the beam, where higher stress was concentrated near the beam's soffit.Subsequently, the larger concrete strain caused the beam to quickly crack.To delay the first crack, polystyrene spheres may be placed further away from the soffit [22].

Effects of polystyrene spheres on beam's ductility.
Ductility reflects the ability of a beam to deform significantly under excessive load.It provides warnings before the beam failed.The size of the polystyrene influenced the ductility of the test specimens.This can be observed from specimens PB1, PB2, and PB3 (Table 10).When the polystyrene sphere's diameter was 75 mm or less, the ductility was comparable to that of the solid beam.The ductility of the beam was 32% lower than the solid beam when 100 mm polystyrene spheres were used.A similar observation was reported by Lim et al. (2021) [21].Their beams with embedded polystyrene blocks also had a lower ductility than the solid beam.
The ductility was also affected by the spacing between the polystyrene spheres.This was observed in specimens PB3, PB4, and PB5.The ductility increased 27% from 3.25 to 4.14 when the spacing increased from 10 mm to 30 mm.

Feasibility Evaluation
The feasibility of the beam with polystyrene spheres was evaluated in various aspects.This included weight reduction, material efficiency, load capacity, serviceability, ductility, and failure modes.
The evaluation criteria are outlined as follows: a. C1: The polystyrene spheres should replace a large amount of concrete so that the reduction in the specimen's weight is meaningful.The volume replacement ratio, Rv, (Table 6) was preferably at least the mean value of the test specimens, which was 5.94%.b.C2: The beam with polystyrene spheres should be more efficient than the solid beam.The strength per unit of concrete of the test specimen should be greater than that of the control specimen.Thus, the effective strength-volume ratio, Re, should theoretically be at least 1.0 [20].Since all the test specimens had Re greater than 1.0, the mean value of all specimens was benchmarked.
where Eb = strength per unit concrete of the beam with polystyrene spheres, kN/m 3 ; Es = strength per unit concrete of the solid beam, kN/m 3 .
The strengths per unit of concrete (i.e.Eb and Es) were determined by dividing the load capacity by the total concrete volume of the beam.c.C3: The beam with polystyrene spheres should have a larger load capacity than the solid beam.Thus, the strength ratio, Rs, should be at least 1.0.
where Pu,i = ultimate strength of the beam with polystyrene spheres, kN; Pu,s = ultimate strength of the solid beam, kN.
d. C4: The service load of the beam with polystyrene spheres should not be too low compared with its load capacity.Thus, the serviceability ratio, Rsv, should be at least 0.75 [35,36].
where Py = yield strength of the beam with polystyrene spheres, kN; Pu = ultimate strength of the beam with polystyrene spheres, kN.
e. C5: The beam with polystyrene spheres should have adequate ductility for survival purposes.The ductility ratio, Δ, should be at least 4.0 for the application in the low to moderate seismic regions [20,35,37,38].
where δu = ultimate displacement of the beam with polystyrene spheres, mm; δy = yield displacement of the beam with polystyrene spheres, mm.
f. C6: The failure mode of the beam with polystyrene spheres should be similar to that of a solid beam.Substituting the concrete with polystyrene spheres reduced the beam's shear strength.For a typical flexural load test, the specimen was preferred without the shear crack.
Each specimen was evaluated based on criteria C1 to C6 (Table 13).None of the specimens fulfilled all the criteria.Thus, the specimen that met the most criteria was identified.Specimen PB5 satisfied all the criteria except C3.Its strength ratio, Rs, of 0.99 was slightly below the requirement of 1.0.This was considered acceptable.Thus, specimen PB5 could be used for structural application.Its specifications included (a) the size of polystyrene spheres equalled 0.57 times the beam's width, and (b) the spacing between polystyrene spheres was 1.2 times the concrete cover.10, Eb = strength per unit concrete of beam, Re = effective strength ratio, Rs = strength ratio, Rsv = serviceability ratio, Δ = ductility ratio, ns = nos. of shear crack found on beam surface. 2 Nos. of evaluation criteria met out of six 3 A -Applicable, NA -Not applicable It is worth mentioning that this study ignored the weight and strength of polystyrene spheres.The concrete region occupied by the polystyrene spheres was assumed to be void, which carried no stress.The volume of polystyrene spheres in the beam was deemed equal to the weight reduction.This was conditional on the homogeneity of the concrete throughout the beam.As an exploratory study, only one specimen was tested for each design.Out of the limited data, it seemed the beam with polystyrene spheres was more efficient than the solid beam.There have also been studies that show a discernible loss of strength in hollow beam sections [1,30].For some reason, the two types of beams were similar, but the outcome varied.Further studies may be required to find out the reasons.

Conclusions
This study investigated the behavior of beams with embedded polystyrene spheres under loads.This technique can improve the material's efficiency.The beam's strength per unit of concrete increased by 8% when polystyrene spheres replaced 8.7% of the concrete volume.Polystyrene spheres marginally affected the beam's strength.The strength dropped by 2.6% as the diameter of the polystyrene spheres increased from 50 mm to 100 mm.The load capacity increased by 0.6% as the spacing increased from 10 mm to 30 mm.The diameter and spacing of the polystyrene spheres did not appear to have a significant effect on the beam's strength.Compared with the solid beam, the beams with polystyrene spheres generally had lower uncracked strength, stiffness, and ductility.PB5 outperformed the other specimens.It met almost all of the evaluation criteria.Nevertheless, there is no explicit guide for evaluating a beam's feasibility.The evaluation was mainly based on the preferred states of the specimens.Specimen PB5 can be expressed in generic specifications: the size of the polystyrene spheres equals 0.57 times the beam's width, and the spacing between polystyrene spheres is 1.2 times the concrete cover.This might be a reference for future studies with the conditions that the polystyrene spheres are placed at the centroid of the cross-section and the beam's width is smaller than its height.One may need to verify whether or not those specifications apply to beams of other sizes and aspect ratios.

Figure 1 .
Figure 1.Schematic drawing of the test specimen.The specimen size was 175 mm by 300 mm by 1600 mm.The concrete cover was 25 mm thick.High-strength steel bars with a nominal yield strength of 500 N/mm 2 were used as reinforcements.The top bars were 10 mm in diameter, whereas the bottom bars were 12 mm in diameter.The shear links were mild steel bars with a nominal yield strength of 250 N/mm 2 .They were 150 mm apart and 6 mm in diameter.

Figure 3 .
Figure 3. Test setup of the specimen.

Table 2 .
Details of specimens.

Table 3 .
Equipment and instruments used for testing.

Table 5 .
Yield strength of steel bar.

Table 7 .
Stages of load-displacement responses.

Table 8 .
Types of cracks observed.

Table 11 .
Computation of the results.

Table 12 .
Performance of test specimens relative to the control specimen.

Table 13 .
Feasibility evaluation of the test specimen.Rv = volume replacement ratio, Vb = concrete volume of beam (  =   −   ), Pu and Py refer to Table