static behaviour of steel plate-strengthened reinforced

6
1 INTRODUCTION Reinforced concrete (RC) slabs are flexural mem- bers that usually carry the floor loads and transfer it to the beams. When these members are distressed and there is a possibility that the load carrying ca- pacity of the elements will be exceeded, the ele- ments might collapse, if remediation actions are not implemented on time. Collapse of flexural RC ele- ments should be prevented as this may result in heavy loss of properties and lives. The cost of clear- ing and disposal of the resulting debris from collapse sites before re-construction, if funds are available, can also be enormous. Possibility of strengthening distressing or grossly under-reinforced flexural members with steel plates was first reported by L’Hermite & Bresson (1967) and for about five dec- ades research in this area has continued up to date. According to Olajumoke & Dundu (2014) the two widely reported strengthening methods for flexural RC structural elements are externally bonding (EB) and near surface mounting (NSM) using plates or bars. Of these methods, externally bonding (or sur- face bonding) of plates is easier to apply, especially for flexural members with inadequate concrete cover or whose construction history may not be known to the repairing engineer (Olajumoke & Dundu 2014). Jones et al (1982) reported that gluing steel plates onto RC beams surface resulted in good composite properties. However, other authors (Oh et al. 2003, Thanoon et al. 2005, Jurkiewiez & Braymand 2007) have reported the challenges and different levels of success of strength enhancement of the surface bonding strengthening technique (SBST). The three common premature failure modes in SBST agreed to by many authors (Teng et al. 2003, Aykac et al. 2011, Ajeel et al. 2011, Narayanamurthy et al. 2012) are intermediate crack debonding (ICD), delamina- tion (D) or rip-off failure and plate-end debonding (PED). These are premature failures which usually prevent the achievement of full flexural capacity of the strengthened flexural elements. It is noted that most published works on this sub- ject are on RC beams and little information with re- gards to RC slabs is available despite their structural importance. Hence, as standardisation of this strengthening technique is yet to be fully developed, particularly for RC slabs, this study aims to contrib- ute to its achievement, through the adoption of the surface bonding of steel plates, using epoxy glue. Static behaviour of steel plate-strengthened reinforced concrete slabs in bending A.M. Olajumoke & M. Dundu Department of Civil Engineering Science, University of Johannesburg, Auckland Park, Johannesburg, Gauteng, South Africa ABSTRACT: This paper reports on an investigation on a reinforced concrete (RC) strengthening technique carried out by the authors, using surface bonding steel plates (SBSP). To accomplish this investigation, the tension face of one-way spanning RC slabs was scabbled and bonded with one or two sandblasted steel plate(s) of different thicknesses, using epoxy glue. The steel plate thicknesses were varied in order to deter- mine the width-to-thickness ratios that can promote yielding (and not premature debonding) of the RC slabs before failure. A low flexural reinforcement percentage (≈ 0.314% bh) was used in order to prevent over- reinforcement and to ensure that failure of the slabs under static loading was due to flexure. Static two-point line loading was adopted to simulate the worse loading condition. Based on the deformation response of the slabs, the most appropriate parameters of the steel plates, for strengthening distressing reinforced concrete slabs were determined. The SBSP strengthening technique was found to possess effective composite proper- ties as all the strengthened RC slabs failed essentially by flexural yielding before steel plate separation, with enhanced load carrying capacity of at least 89% above that of control slabs.

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Page 1: Static behaviour of steel plate-strengthened reinforced

1 INTRODUCTION

Reinforced concrete (RC) slabs are flexural mem-bers that usually carry the floor loads and transfer it to the beams. When these members are distressed and there is a possibility that the load carrying ca-pacity of the elements will be exceeded, the ele-ments might collapse, if remediation actions are not implemented on time. Collapse of flexural RC ele-ments should be prevented as this may result in heavy loss of properties and lives. The cost of clear-ing and disposal of the resulting debris from collapse sites before re-construction, if funds are available, can also be enormous. Possibility of strengthening distressing or grossly under-reinforced flexural members with steel plates was first reported by L’Hermite & Bresson (1967) and for about five dec-ades research in this area has continued up to date. According to Olajumoke & Dundu (2014) the two widely reported strengthening methods for flexural RC structural elements are externally bonding (EB) and near surface mounting (NSM) using plates or bars. Of these methods, externally bonding (or sur-face bonding) of plates is easier to apply, especially for flexural members with inadequate concrete cover

or whose construction history may not be known to the repairing engineer (Olajumoke & Dundu 2014).

Jones et al (1982) reported that gluing steel plates onto RC beams surface resulted in good composite properties. However, other authors (Oh et al. 2003, Thanoon et al. 2005, Jurkiewiez & Braymand 2007) have reported the challenges and different levels of success of strength enhancement of the surface bonding strengthening technique (SBST). The three common premature failure modes in SBST agreed to by many authors (Teng et al. 2003, Aykac et al. 2011, Ajeel et al. 2011, Narayanamurthy et al. 2012) are intermediate crack debonding (ICD), delamina-tion (D) or rip-off failure and plate-end debonding (PED). These are premature failures which usually prevent the achievement of full flexural capacity of the strengthened flexural elements.

It is noted that most published works on this sub-ject are on RC beams and little information with re-gards to RC slabs is available despite their structural importance. Hence, as standardisation of this strengthening technique is yet to be fully developed, particularly for RC slabs, this study aims to contrib-ute to its achievement, through the adoption of the surface bonding of steel plates, using epoxy glue.

Static behaviour of steel plate-strengthened reinforced concrete slabs in bending

A.M. Olajumoke & M. Dundu Department of Civil Engineering Science, University of Johannesburg, Auckland Park, Johannesburg, Gauteng, South Africa

ABSTRACT: This paper reports on an investigation on a reinforced concrete (RC) strengthening technique carried out by the authors, using surface bonding steel plates (SBSP). To accomplish this investigation, the tension face of one-way spanning RC slabs was scabbled and bonded with one or two sandblasted steel plate(s) of different thicknesses, using epoxy glue. The steel plate thicknesses were varied in order to deter-mine the width-to-thickness ratios that can promote yielding (and not premature debonding) of the RC slabs before failure. A low flexural reinforcement percentage (≈ 0.314% bh) was used in order to prevent over-reinforcement and to ensure that failure of the slabs under static loading was due to flexure. Static two-point line loading was adopted to simulate the worse loading condition. Based on the deformation response of the slabs, the most appropriate parameters of the steel plates, for strengthening distressing reinforced concrete slabs were determined. The SBSP strengthening technique was found to possess effective composite proper-ties as all the strengthened RC slabs failed essentially by flexural yielding before steel plate separation, with enhanced load carrying capacity of at least 89% above that of control slabs.

Page 2: Static behaviour of steel plate-strengthened reinforced

2 EXPERIMENTAL PROGRAMME

2.1 Preparation of reinforced concrete slabs

The RC slabs of 3150 length, 1000 width and 125 mm thickness were designed and reinforced as one-way spanning slabs with low reinforcement percent-age (ρs = 100As/Ac) of 0.314% of high yield steel. The reinforcement bars consisted of 5Nos of 10 mm diameter (5Y10) in the main direction and 11Nos of 10 mm diameter (11Y10) in the transverse direction as distribution bars. This was to ensure that flexural failure of control RC slabs takes place. This rein-forcement percentage is greater than the minimum of 0.13% recommended for rectangular RC solid slabs by code SANS 10100-1 (2000). This code is based on code BS EN 1992-1-1 (2004) provisions. A 25 mm thick cover to reinforcement was provided in all the slabs through ready-made circular plastic spac-ers, which were attached to the steel bars at regular intervals before placing them into the fabricated formworks. Ready mix concrete supplied by Afris-am Company, South Africa was used to cast four-teen tested RC slabs, in two batches, and cured for 28 days. These were later divided into three groups.

2.2 Material properties of steel and concrete

The tensile strength of the steel plates and the 10 mm diameter steel bars were determined in accord-ance with the BS EN ISO 6982-1 (2009) procedure. The steel materials were procured from a supplier in Johannesburg, South Africa. Table 1 shows a sum-mary of some of the physical properties for the steel plates and bars that were tested. In Table 1, parame-ters fy, fu, εy, εu and E) are yield stress, ultimate stress, yield strain, ultimate strain and elastic modu-lus, respectively. SP is the steel plate type of 4, 6 and 8 mm thicknesses and SB is steel bar of 10 mm diameter, respectively.

It can be observed that the yield strength of 4, 6 and 8 mm thick steel plates varied widely, particu-larly that of 8 mm. This may influence the toughness behaviour of the composite slabs at failure. By the values of yield stresses, the 4 and 6 mm thick plates can be classified as mild steel while the 8 mm thick plate and 10 mm diameter bars can be classified as high yield steel. Table 1: Properties of the steel plates and bar

Steel

type

fy

(MPa)

fu

(MPa)

εy

εu

E

(MPa)

SP4 320.26 462.72 0.00214 0.20802 203807

SP6 291.18 397.83 0.00161 0.19912 209737

SP8 564.32 867.81 0.00153 0.20084 211132

SB10 438.47 651.15 0.00238 0.17458 201668

The compressive strength of the concrete at 28-

day and 90-day curing are 32 and 45 N/mm2. This

was determined in accordance with BS EN 12390-3

(2009) procedure. However, since testing of the slabs commenced after about six months of casting, the value for the 90-day curing was used to calculate the theoretical load carrying capacities of both the control and strengthened RC slabs.

2.3 Surface preparation of steel plates and concrete slabs

It should be noted that adequate surface preparation of both the RC slabs and steel plates is central to ef-fective steel plate-strengthening technique in order to achieve good composite actions. Hence, after re-moving the formworks, the one metre wide RC slabs were appropriately marked and scabbled at the ten-sion face using a three-piece tungsten carbide tipped cruciform head pneumatic scabbler. The scabbling commenced after 60 days of casting and was done to an approximate roughness depth of 2 mm over the marked surface of the slabs. This was to remove the weak laitance concrete, expose the small and medi-um aggregates for effective adhesion between the concrete and the steel plate surfaces, using the epoxy as gluing agent (Olajumoke & 2015). Thereafter, the concrete dust on the scabbled RC slab surface was removed by wire-brushing and blowing of air under high pressure.

It is noted that different methods of surface prepa-ration or roughening, such as using hand grinder, chiseling or using other abrasive objects have been reported by researchers (Oh et al. 2003, Thanoon et al. 2005, Afefy & Fawzy 2013). However, the use of a scabbling machine in this study gave a better pre-pared concrete surface. A typical scabbled RC slab surface is illustrated in Figure 1.

Figure 1: Scabbling of reinforced concrete slab surface

Three steel plates of 4, 6 and 8 mm thicknesses

were cut into strip sizes of 100 mm wide by 2750 mm long. This was the epoxy bonded area in each slab. The 2750 mm length of steel plate was arrived at after allowing a gap of 95 mm from each curtail-ment end of the plates to the centre of support of the simply supported slabs. This curtailment end gap to the centre of supports was to simulate field practice where the RC slabs to be strengthened are in most

Scabbler Scabbled RC slab surface

Page 3: Static behaviour of steel plate-strengthened reinforced

cases already constructed. In such cases, scabbling may not be possible beyond the face of the supports.

The surface of one side of the steel plate strips was first roughened by sandblasting to remove any rust or mill scales that may adversely affect bonding. The surface was cleaned with acetone before apply-ing the epoxy glue. These were used in one or two number(s), depending on the specimen. In one strip steel plate-strengthened slabs, the plate was laid and glued along the centre line of the slab while in two strips steel plate-strengthened slabs, the plates were similarly laid and glued to the scabbled surface at one-third spacing across the width of the slabs

The effective epoxy thickness used in these tests was established to be 1.5 mm in some earlier work (Olajumoke & Dundu 2015). This thickness was used throughout the experiment to glue the steel plates onto the concrete surface. Gauging of this epoxy thickness was achieved by gluing small pieces of Perspex glass of 1.5 mm thick over the sandblast-ed surface of the steel plates. These small pieces of Perspex glass were of approximately 5 mm square sizes before fixing them onto the steel plates using small drops of super glue, as shown in Figure 2.

Figure 2: Epoxy thickness gauging on strips of steel plates

2.4 Bonding of steel plates to the concrete surfaces

After preparing the surface of the RC slabs and the steel plates with fixed gauges, the epoxy was spread over the steel plates by using scraper. The primer and the epoxy used in this study were procured from StonCor (Pty) Ltd, South Africa. The scabbled con-crete surface was first primed with PROSTRUCT 618LV. It is a two-mix liquid of ratio 1:2 (activator and base), according to the manufacturer’s instruc-tions. This serves to condition the concrete surface for improved bonding between the steel plate and the concrete surfaces before the epoxy is applied, as well as to fill the micro cracks that might have oc-curred due to scabbling exercise. The epoxy PROSTRUCT 617NS is also a two parts viscous material, which is mixed in ratio 1:1 (activator: base). The steel plates on which the epoxy was

spread were pressed against the primed concrete sur-face while the primer was still wet, using 5-tonne hydraulic jacks arranged at a spacing of 450 mm, as shown in Figure 3.

Figure 3: Plating of the reinforced concrete slabs

As jacking of the steel plates against the concrete

surface was gradually being done and the gauges pressed against the concrete surface, the excess epoxy was squeezed out and scraped off until the 1.5 mm epoxy thickness was achieved. This arrange-ment was left in place for five days in accordance with the manufacturer’s instructions to allow the epoxy to harden properly. At the end of the fifth day, the jacks were carefully removed and the composite RC slabs were properly stacked into position.

2.5 Instrumentation of the composite slabs

Strain gauges were attached to the concrete and steel plate surfaces, below the loading point and at the mid-span of both control and composite slabs. This was done to measure the strain variation in the slabs during loading. Thereafter, the slabs were lifted to testing position, where they were supported at each end by circular steel bars of 50 mm diameter. Mid-span deflection was measured using Linear Vertical Displacement Transducers (LVDTs),

Both the control and steel plate-strengthened RC slabs were subjected to static two-point line loading system. The static loading was applied from a uni-versal Instron testing machine of 250 kN capacity, at a displacement rate of 2 mm per minute. Data of all the measured parameters (strain, deflection and loads) were collected through a computerised auto-mated system. Other parameters observed and rec-orded include, occurrence of first visible crack (≈ 0.3 mm) at serviceability load level, failure mode, zone of ultimate failure, maximum crack width and pat-tern, as well as the distribution and location of the cracks with respect to either end supports.

It should be noted that in some cases the tests were stopped after the formation of extensive cracks and development of excessive deflection. This was

Strengthened RC slab Hydraulic jacks supported

on concrete blocks

Perspex glass pieces fixed on steel plates for epoxy thickness gauging

Page 4: Static behaviour of steel plate-strengthened reinforced

to prevent damaging the LVDTs below the slabs should the slabs collapse. The main variables in this study are the steel plate thicknesses (4, 6 and 8 mm) and the number (one or two) of steel plate strips used to strengthen each slab. Two slabs were tested for each of these variables in addition to that of con-trol slabs.

3 RESULTS AND DISCUSSION

3.1 Strength and failure mechanism of composite slabs

A summary of the static loading test of the slabs is shown in Table 2. In Table 2, Pu, ∆max, Puc(av) and Pc is measured maximum failure load, measured maxi-mum deflection, average measured maximum failure load for control slabs and serviceability limit state crack load, respectively. Also, NP-S is slab with no steel plate (2Nos), SP4-1S is slab of one strip 4 mm thick steel plate (2Nos), SP4-2S is slab of two strips 4 mm thick steel plate (2Nos), SP6-1S is slab of one strip 6 mm thick steel plate (2Nos), SP6-2S is slab of two strips 6 mm thick steel plate (Nos), SP8-1S is slab of one strip 8 mm thick steel plate (2Nos), SP8-2S is slab of two strips 8 mm thick steel plate (2Nos), FY is flexural yielding, PS is plate separa-tion, PED is plate end debonding and RL is reload. Table 2: Physical properties of static loading for control and

strengthened reinforced concrete slabs

The NP-S-1 and NP-S-2 slabs are the control with maximum failure loads of 41.5 and 40.9 kN, respec-tively, which gives an average value (Puc(av)) of 41.2 kN. This average value was used as a base to deter-mine the level of load carrying capacity enhance-ment of the strengthened slabs over the control slabs. A detailed study of Table 2 shows that generally, the steel plate-strengthened slabs supported higher loads than the control slabs. Also, the slabs strengthened with two strips of steel plate sustained higher loads

than those strengthened with one strip of steel plate. In addition, the results of 4 and 6 mm steel plate-strengthened slabs are more consistent than those of 8 mm thick plates. Hence, 4 and 6 mm thick steel plates are recommended for general strengthening work while 8 mm thick steel plate should be used with caution, except where rigidity with high load carrying capacity are of higher priority.

It can be observed from Table 2 that the failure mode for the control slabs was flexural yielding (FY), while the strengthened slabs failed initially by flexural yielding (FY) before steel plate separation (PS), except for SP8-1S-1 and SP8-2S-1 slabs which failed prematurely by plate-end debonding (PED). It was observed that FY with PS occurred mainly in slabs strengthened with 4 and 6 mm thick steel plates, which had width-thickness ratio (b/t) of 25 and 16.7, respectively. It was noted that FY failure mode occurred after extensive cracking and deflec-tion of the slabs. Those that failed by PED were strengthened with 8 mm thick plate and had b/t of 12.5. It is worth noting that failure of the composite slabs by FY with PS was always accompanied by a very sudden loud noise. The most severe noise oc-curred when the SP8-1S-1 (one 8 mm thick steel plate-strengthened) and SP8-2S-1 (two 8 mm thick steel plate-strengthened) slabs failed by PED. In the case of the SP8-2S-1 slab, the force of separation emanating from the PED led to a sudden switching-off of the data acquisition system at about 128 kN which is also about the maximum failure load for SP6-2S-1. After the system was switched-on again, the specimen was reloaded and about 101 kN load (as shown in Table 2) was sustained before the sec-ond plate failed by PED as well. Based on the results in Table 2, it can be conclud-ed that with adequate surface preparation of both concrete and steel plate surfaces, 4 and 6 mm thick steel plates can conveniently be used to strengthen RC slabs. However, strengthening with 8 mm thick steel plates makes the composite slab too rigid. It is therefore not advisable to strengthen RC slabs with steel plate of width-thickness ratio lesser than 16. The load-deflection profiles of the tested slabs were plotted for control, one and two steel plate-strengthened RC slabs as shown in Figures 4(a & b). The graphs show that the slabs possessed adequate elastic properties to promote redistribution of mo-ments. It can also be observed that while first yield-ing of the reinforcing bars occurred at a deflection of about 22 mm for control slabs, yielding of the strengthened (composite) slabs occurred at deflec-tion values ranging between 30 and 33 mm. This shows an appreciable delay of failure and improved load carrying capacity of the strengthened slabs. Similarly, Table 2 shows that while the serviceabil-ity limit state of cracking occurred at about 60% of the ultimate loads for control slabs, it occurred in plate-strengthened slabs at not less than 70% of the

Slab Pu

(kN)

∆max

(mm)

𝑷𝒖

𝑷𝒖𝒄(𝒂𝒗) 𝑷𝒄

(kN)

𝑷𝒄

𝑷𝒖

(%)

Failure

mode

NP-S-1 41.5 169.0 1.01 23.8 57.35 FY

NP-S-2 40.9 102.0 0.99 24.2 59.17 FY

SP4-1S-1 82.3 125.5 2.00 60.3 73.27 FY & PS

SP4-1S-2 77.7 144.9 1.89 60.3 77.61 FY & PS

SP4-2S-1 112.0 137.5 2.72 93.1 83.13 FY & PS

SP4-2S-2 110.8 103.2 2.69 85.5 77.17 FY & PS

SP6-1S-1 90.3 125.7 2.19 66.9 74.09 FY & PS

SP6-1S-2 86.0 156.5 2.09 62.6 72.79 FY & PS

SP6-2S-1 128.8 134.0 3.13 98.2 76.24 FY

SP6-2S-2 122.4 138.2 2.97 92.2 75.33 FY

SP8-1S-1 97.0 56.7 2.35 74.4 76.70 PED

SP8-1S-2 102.9 81.1 2.50 74.4 72.30 FY & PS

SP8-2S-1 128.2

(RL =

101.1)

21.0

44.4

3.11

2.45

89.6 69.89 PED

PED

SP8-2S-2 167.4 88.8 4.06 120.9 72.22 FY & PS

Page 5: Static behaviour of steel plate-strengthened reinforced

Separated steel plate

(a) One steel plate-strengthened reinforced concrete slabs

(b) Two steel plates-strengthened reinforced concrete slabs

Figure 4: Load-deflection profiles of the tested slabs

ultimate loads. For the three steel plate thicknesses, the load carrying capacity of one plate-strengthened slabs over the control slabs increased by between 89 and 135%, while that of two plates-strengthened slabs increased by between 109 and 306%. Also, Figures 4(a & b) shows that the gradient of the plate-strengthened slabs at the elastic range are much higher than that of the control slabs and this is con-stant up about 80 kN in both one and two plates-strengthened slabs. All these are indications of the rigidity of the strengthened slabs compared to the control slabs. The rigidity of the strengthened slabs is noted to increase with the thickness and number of steel plates used. However, 6 mm thick steel plate-strengthened slabs had the highest toughness as can be observed from Figures 4(a & b) for one and two plates-strengthened slabs, respectively.

3.2 Cracking and deflection characteristics of slabs

Figures 5(a-c) show typical cracking characteristics

and the failure modes of both strengthened and con-

trol RC slabs. Generally, the cracks in the slabs

started at the bottom and propagated transversely

and laterally. At maximum loading, some of the

cracks particularly those that occurred around the

mid-span, extended up to the compression face of

the slabs. Also, crushing of the concrete at the top

faces of some of the strengthened slabs occurred due

to the high compressive force as shown in Figures

5(b & c). In addition, Figures 5(a-c) show that the

cracks essentially occurred within the middle third

zone of the slabs that failed by FY with PS while

they occurred at close to end support for those that

failed by PED. It was also noted that the cracks in

FY failure were due to flexure while that of PED

(a) Control slab showing flexural yielding failure

(b) Strengthened slab showing yielding and plate separation

(c) Strengthened slab showing plate-end debonding failure

Figure 5: Typical failure modes and cracking of the tested slab

0

20

40

60

80

100

120

0 50 100 150 200

Lo

ad (

kN

)

Deflection (mm)

NP-S (Control) SP4-1S SP6-1S SP8-1S

SP8-1S

SP6-

SP4-1S

NP-S (control)

0

20

40

60

80

100

120

140

160

180

0 50 100 150

Lo

ad (

kN

)

Deflection (mm)

NP-S (Control) SP4-2S SP8-2S SP6-2S

SP8-2S

SP6-

NP-S

SP4-2S

Plate-end debonding failure

Strain gauges Crack

Flexural cracks

Page 6: Static behaviour of steel plate-strengthened reinforced

were due to shear failure. The cracks initiated gradu-

ally and as the applied load increased, they propa-

gated transversely and laterally with increased

width. The crack width and spread were generally

smaller in steel plate-strengthened slabs than those

in control slabs.

It can be observed from Figures 4(a & b) that de-

flection increased substantially as the magnitude of

the loading marginally increased beyond the first

yielding load up to failure point. Also, for all the

plate-strengthened slabs, the deflection of those of 4

and 6 mm thick steel plates are higher than those of

8 mm thick steel plate at failure loads.

4 CONCLUSIONS

The use of 1.5 mm epoxy thickness coupled with

adequate surface preparation of the RC slabs and the

steel plates, appreciably enhanced the load carrying

capacity of the RC slabs, and reduced the effects of

serviceability limit state factors such as cracking and

deflection before failure set in. While serviceability

limit state cracks occurred at about 60% of the fail-

ure load for control RC slabs, it occurred at not less

than 70% for the steel plate-strengthened RC slabs.

The 4 and 6 mm thick steel plate-strengthened RC

slabs achieved higher toughness than the 8 mm thick

steel plate-strengthened RC slabs. Hence, the 4 and

6 mm thick steel plates can conveniently be used for

general strengthening of RC slabs, while the 8 mm

steel plate is recommended for use with caution and

only for a situation where the rigidity is of higher

priority. Also, the 4 and 6 mm steel plates have

width-thickness ratios (b/t) of 25 and 16 while that

of 8 mm is 12.5, respectively. It can therefore be

concluded that steel plate of b/t of 16 and above can

be used with confidence to achieve flexural failure

in the steel plate-strengthening of RC slabs.

Generally, the steel plate-strengthened RC slabs

sustained higher loads than the control slabs. The

load carrying capacity enhancement ranged from 89

to 135% for one steel plate-strengthened RC slabs

and 109 to 306% for two steel plates-strengthened

RC slabs over the control slabs.

Irrespective of the steel plate thickness, the use of

one or two 100 mm wide steel plate strips per metre

width of RC slabs substantially increased their load

carrying capacity. The number of strips to be used

would depend on the magnitude of the load.

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