Ain Shams Engineering Journal (2013) 4, 1-16

Ain Shams University Ain Shams Engineering Journal

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CIVIL ENGINEERING

Shear behavior of concrete beams externally prestressed with Parafil ropes

A.H. Ghallab a *, M.A. Khafaga b, M.F. Farouk c, A. Essawy a

a Faculty of Engineering, Ain Shams University, 1 Alsarayat Street, Abbasia, Cairo, Egypt b Housing and building National Research Center, 87 El Tahrir St., Dokki, Giza, Egypt c Dar El-Handasa Consultation office, 34/36 Geziret El-Arab Street, Mohandesin, Giza, Egypt

Received 13 September 2011; revised 15 March 2012; accepted 28 May 2012 Available online 13 October 2012

KEYWORDS

Shear;

Prestressed concrete beam; External prestressing; Parafil rope

Abstract Although extensive work has been carried out investigating the use of external prestressing system for flexural strengthening, a few studies regarding the shear behavior of externally prestressed beams can be found. Five beams, four of them were externally strengthened using Parafil rope, were loaded up to failure to investigate the effect of shear span/depth ratio, external prestressing force and concrete strength on their shear behavior. Test results showed that the shear span to depth ratio has a significant effect on both the shear strength and failure mode of the strengthened beams and the presence of external prestressing force increased the ultimate load of the tested beams by about 75%. Equations proposed by different codes for both the conventional reinforced concrete beams and for ordinary prestressed beams were used to evaluate the obtained experimental results. In general, codes equations showed a high level of conservatism in predicting the shear strength of the beams. Also, using the full strength rather than half of the concrete shear strength in the Egyptian code PC-method improves the accuracy of the calculated ultimate shear strength.

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1. Introduction

Corresponding author. Address: Structural Engineering Dept., Faculty of Engineering, Ain Shams University, 1 Alsarayat Street, Abbasia, Cairo, Egypt. Tel.: +2 01066679616.

E-mail addresses: ahghallab@yahoo.co.uk (A.H. Ghallab), makhafa-ga@yahoo.com (M.A. Khafaga).

Peer review under responsibility of Ain Shams University.

External prestressing technique has been widely used in construction of new bridges as well as retrofitting existing ones that need strengthening due to deterioration, changes in use or deficiencies in design or construction. External prestressing is characterized by the features such as: the post tensioning tendons are placed on the outside of the cross-section of the concrete member. The forces exerted by the post-tensioning tendons are only transferred to the member at the anchorages and the deviators. No bond is present between the tendons and the structure.

2090-4479 © 2012 Ain Shams University. Production and hosting by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asej.2012.05.003

Abbreviations

qc and vc cracking shear strength of concrete (MPa) fc characteristic compressive cylinder strength of

n ultimate shear strength (MPa) concrete at 28 days (MPa)

s nominal shear stress of stirrups (MPa) fcp design compressive stress at the centroidal axis due

u ultimate shear stress (MPa) to post-tensioning, taken as positive

i shear stresses due to the nominal shear accompa- fcu characteristic compressive cube strength of con-

nied the maximum moment Mmax that results from crete at 28 days (MPa)

the external loads at the considered section fpcc concrete compressive stress after all losses at the

d shear stress due to the working permanent load section centroid

pv shear stress due to the vertical component of the fyv and fywd yield strength of the reinforcement used as stir-

prestressing force rups

V1 strength reduction factor for concrete cracked in ft maximum design principal tensile stress at the

shear centroidal axis of the section (MPa)

Ac and Ag gross area of concrete section subjected to axial Mc and Mcre flexural cracking moment

stress (mm2) Mo moment necessary to produce zero stress in the

As cross sectional area of longitudinal reinforcement concrete at the extreme tension fiber; in this calcu-

provided in the tension zone. lation only 0.8 of the stress due to prestress should

Ap cross sectional area of tendons in that zone, which be taken into account

will be tensile under ultimate load condition Mu and Mmax ultimate moment occurs simultaneously with

Asv cross sectional area of the shear reinforcement Vu at section considered

(mm2) N axial force in the cross-section due to loading or

s spacing between stirrups in the long direction prestressing in kN ( + ve for compression)

(mm) Vc nominal shear strength provided by concrete (kN)

bw web width (mm) Vn nominal shear resisting force at a considered sec-

d depth from the extreme compression fiber to the tion

centroid of longitudinal steel bars (mm) Vs nominal shear strength provided by shear rein-

dP distance from extreme compression fiber to cen- forcement

troid of prestressing tendon, not less than 0.8 sec- Vu factored shear force at a considered section

tion thickness (mm) VP shear resistance provide by the vertical component

dt depth from the extreme compression fiber either to of prestressing force

the centroid of longitudinal bars or to the centroid Vi factored shear force at section due to externally

of the tendons, whichever is the greater applied loads occurring simultaneously with Mu

h overall depth of a cross section in the plan of bend- Cc strength reduction factor for concrete (=1.5)

ing Cs strength reduction factor for steel (=1.15)

As the tendons are outside of the structure, they are more exposed to the environmental influences and the protection against these detrimental influences is therefore of special concern. However, several bridges built or strengthened by external steel tendons in Germany, France, USA, UK and other countries in the world did not behave satisfactory as most of these externally prestressed structures suffered from corrosion [1]. This problem can be solved by using fiber reinforced plastic tendons (FRPs) based on glass, aramid or carbon fibers as an alternative to high strength prestressing steel due to its high-tensile strength and excellent corrosion resistance. Using FRP in strengthening structures is currently widely used for both reinforced concrete structures [2-7] and prestressed concrete structures [8-11].

Several studies had been conducted to study the flexural behavior of externally prestressed concrete beams, either strengthened using steel tendons [12-14] or strengthened using FRP tendons [15-17]. The shear failure mechanism of bonded prestressed beams, will differ depending on several factors such as ratio between the shear span and the effective depth of the beam, concrete strength, aggregate interlock, concrete in the compressive zone, stirrups ratio, prestressing type, and variation of prestress.

While the shear failure of externally prestressed beams is undesirable because it is a sudden phenomenon and catastrophic in nature, research on the effect of external prestress-ing on the shear behavior of externally prestressed concrete beams is limited, especially for beams strengthened using fiber reinforced polymer (FRP) tendons. Nevertheless, it is well accepted that the presence of prestressing significantly alters the shear behavior of a concrete beam and the bond between the prestressing tendons and concrete has an effect on the shear strength of the beam.

Kordina et al. [18] tested ten prestressed concrete beams with unbounded tendons to elucidate the effect of bond condition upon the load-bearing behavior in shear. Test results show that the shear strength of prestressed beams with unbounded tendons can be determined with a truss model. Also, the web reinforcement in the ultimate stage nearly reached the yield strength.

Bouafia [19] tested two specimens' sets representing four test cases of simply-supported externally prestressed beams with a shear span to effective depth ratio of 2.3 under a mid-span concentrated load. He observed diagonal tension failure in three of the cases and shear-compression failure in the other.

Kondo et al. [20] performed an exploratory investigation on the overall effects of slightly inclined external prestressing steel tendons on the shear behavior of reinforced concrete (RC) beams. From the test results of four beams, they observed that prestressing enhanced the shear cracking load and failure load by 68% and 13%, respectively. Moreover, the external prestressing was found to be effective in shear strength enhancement, even when the prestressing was applied after the RC beam was first cracked in shear. The study concluded that external prestressing can be used in shear strengthening and called for a suitable design method to be developed for such applications.

Ranasinghe et al. [21] studied the effect of bond between reinforcement and concrete on the shear behavior of reinforced and prestressed concrete beams. Seven beams with different bond conditions were tested till failure, while stress-slip relationships for these specimens were obtained from a parallel series of simple pullout tests. A numerical analysis was also conducted to simulate the tested beams. It was found that bond condition of steel bars and prestressing bars highly influences the shear strength and failure mode of RC and PC beams.

Witchukreangkrai et al. [22] tested four concrete beams in studying the effects of external prestressing with steel tendons under large eccentricity on their shear behavior. The test results confirmed that the ultimate shear strength increased with increasing tendon area and prestressing force. Moreover, a tied-arch mechanism was observed in beams with a larger tendon area, leading to higher load-carrying capacity and shear compression failure mode instead of the less desirable diagonal tension failure.

Ng and Soudki [23] tested eight reinforced concrete beams and seven prestressed concrete beams. All beams had a rectangular cross section and were tested under a single concentrated load at the third span, hence, shear action and beam action mechanisms were developed simultaneously. The smaller shear span in the prestressed concrete beams was locally externally strengthened using CFRP rods. The main studied factors were span/depth ratios (a/d), shear reinforcement and external pre-stressing levels. The test results demonstrated that the development of arch and beam action in prestressed beams does not conform to the traditional a/d of 2.5. Instead, the prestressing force reduced the effective a/d and significantly strengthened the concrete beams in shear. Ng and Soudki [23] concluded that this significant shear enhancement cannot be predicted with the current shear design equations in ACI 318-08 [24]. Ng and Soudki [23] based their conclusion on the test results of all beams although only four of them failed in shear.

The carried out literature review indicated that more data are needed to accurately describe the shear behavior of RC beams prestressed with external FRP tendons. Also, the validation of code equations; proposed for bonded prestressed concrete, to calculate the cracking and ultimate shear strength of externally prestressed beams should be checked.

The objectives of the experimental program described in this paper are:

1. Providing data for the shear behavior of RC beams externally prestressed with Parafil rope type G.

2. Studying of the effects of a/d, concrete strength and pre-stressing force on the shear behavior of prestressed concrete

beams.

3. Examining of the shear strengthening potential of external prestressing for RC beams.

4. Examining of the accuracy of the shear design equations in different codes such as ECP-2007 [25], ACI 318-2008 [24], BS8110-1997 [26] and others in predicting the shear capacity of externally prestressed concrete beams with Parafil ropes.

Five simply supported reinforced concrete beams with T-section were tested to failure under two concentrated loads, four beams were strengthened with draped Parafil rope as external tendons while the fifth was tested without external prestressing as a reference beam. Particular attention to crack formation, deflection, variation in external prestressing force, and cracking and ultimate strengths was considered.

The experimental results were used to evaluate the equations proposed by different codes to calculate the shear strength of the beams. Two types of equations were evaluated; the first for ordinary beams subject to compressive stress and the second for ordinary bonded beams.

2. Experimental program

2.1. Details of the test beams

Five beams with the same dimensions and steel reinforcements were used in this study. All beams had a T-section shape and were simply supported as shown in Fig. 1. Four beams were cast with the same concrete strength (the target strength = 35 N/mm2), while the fifth beam was cast with higher concrete strength (the target strength = 55 N/mm2). Therefore, two concrete mixtures were designed and two cement contents; 350 kg/m3 and 450 kg/m3 were used, respectively. Cement type CEM I - 42.5, nature sand, dolomite crushed stone size 10 mm, tap water and high range water reducer were used in the designed mixes. The water-cement ratios were 0.43 and 0.40, respectively. While the dosage of the used admixture was constant for the two designed mixes and equals 1%.

Two high tensile steel bars 12 mm were used as bottom reinforcement while both the top steel bars and stirrups were R6 mild steel. Reinforcement details of the tested beams are shown in Fig. 1, while the properties of steel reinforcement are shown in Table 1.

Before testing, four beams were externally strengthened using two Parafil ropes type G with diameter of 11 mm. Properties of Parafil rope are listed in Table 1. The strength of the Parafil rope exceeds that of high tensile steel, while its elastic modulus represents approximately two thirds that of steel. Table 2 shows the group number and properties of the test beams as well as the concrete strength at test date.

After about 3 months from the casting date of the test beams, external prestressing was applied using two (11-mm diameter) Parafil ropes, located at the same distance from the longitudinal axis of the beam. Before tensioning (using hydraulic jacks), the ropes were greased at the deviators to reduce the friction. The two ropes were tensioned simultaneously using two hydraulic jacks connected to the same pump, while forces are measured by two 100 kN load cells attached to the other end of the ropes as shown in Fig. 2. During prestressing, precautions were taken to prevent increasing prestressing force

SEC. A-A

Figure 1 Typical concrete dimensions and reinforcement details of the test beams.

Table 1 Properties of steel reinforcement and Parafil rope.

Type Mild steel High tensile steel Parafil ropec

Diameter (mm) 6 12 11/(7.6)a

Cross sectional area (mm2) 28.76 110.5 30.55b

Young's modulus (kN/mm2) 200 200 126.5

Yield strength (N/mm2) 310 433 NA

Weight/unit length (kg/m3) 0.224 0.861 .091

Ultimate strength (N/mm2) 434 698 1900

Elongation (%) 24.12 16.24 1.5

a Outside sheath diameter/fiber core diameter.

b Based on area of fibers in the core.

c For single Parafil rope Pult = 58 kN.

Table 2 Main properties of the test beams at test dates.

Beam no. External prestressing force (Pex) (kN) Shear span to depth ratio (a/d) fcua (MPa) Group no.

P ex Pex/ Pult

PS1-1 36 0.31 (733/280) = 2.62 36.3 G1

PS1-2 33 0.284 (300/280) = 1.07 36.3 G1

PS1-3 36 0.31 (450/280) = 1.61 36.3 G1, G2, and G3

RC - - (450/280) = 1.61 36.3 G2

PS2-1 36 0.31 (450/280) = 1.61 58.8 G3

a Concrete compressive strength at test date.

in one rope relative to the other, to avoid biaxial bending of the beam, by closing the connection of the higher force to the pump and increasing the force in the other rope.

After reaching the required force, the ropes were locked by tightening the anchorage nuts against the end plate. The losses due to anchorage draw-in were almost zero.

After applying the external prestressing force, the beams were loaded to failure by a 5000 kN hydraulic compressive machine. A 500 kN load cell with sensitivity of 0.1 kN was used to measure the applied load. A very rigid steel beam mounted on two steel rods was used to transfer the applied load to the test beam as two concentrated loads. The readings of the load cells were recorded automatically by means of a data acquisition system.

Three linear voltage differential transducers (LVDT's) were used to measure the deflection, two under each point load, and the third at the mid span. All LVDT's were connected also to the same data acquisition system.

Steel strains were measured by four electrical strain gauges 6mm, mounted on the steel bars, two in the mid height of the vertical stirrups near supports, the third one in the middle of lower reinforcement and the fourth one in the middle of upper reinforcement. The readings ofthe strain gauges were recorded using the data acquisition system. Fig. 3 illustrates a schematic drawing of the test setup and instrumentation of the tested beams.

Loads were incrementally increased until failure. During loading, all measurements, such as beam deflections, steel strain and force in the external ropes were recorded at each increment.

Figure 2 External prestressing system. 3. Test results and discussion

Results of the tested beams are presented in this section. Analysis and discussions of the test results regarding the effect of the parameters taken into consideration on the structural behavior of the strengthened beams during its life span are also presented. This includes the cracking patterns, cracking and ultimate loads, mode of failure, the load deflection relation, the load reinforcement strain relation and the increase in the external prestressing force at ultimate and cracking loads of the tested beams.

The beams were divided to three groups based on the studied factors as follows:

• Group 1: effect of shear span/depth ratio (a/d).

• Group 2: effect of prestressing force.

• Group 3: effect of concrete strength.

3.1. General behavior

As the load was applied, flexural cracks formed first in the constant moment region between the two concentrated loads and then flexural shear cracks, just outside of each load point, or

web shear cracks, within the shear span, were formed (dependent on the a/d ratio).

During loading, all tested beams showed well distributed cracks, because of the presence of steel reinforcement. Crack widths and crack propagation on the strengthened beams were smaller than those on the un-strengthened beam (RC). This can be attributed to the external compressive force which prevented cracks from opening and reduced propagation and extension of the cracks in the externally strengthened concrete beams. As the load was increased, the number of web shear cracks increased in both the shear spans. These cracks formed adjacent to each other and were generally parallel to the original web shear cracks. Failure of these beams occurred when the web reinforcement failed along one of the diagonal cracks.

The ultimate shear capacity of the strengthened beam was significantly higher than that of the un-strengthened beam due to the additional prestressing force provided by the external prestressing, which reduced the crack propagation and enabled the section to tolerate higher load before failure.

Moreover, by observing the failure of externally prestressed beams, the tested beams failed in shear show limited ductility especially for beams with lower (shear span/depth) ratio.

The first flexural and shear crack loads, ultimate load carrying capacities and mode of failure for the tested beams are listed in Table 3.

Before cracking, the external prestressing force slightly increased, however, after cracking the external prestressing force increased as the load increased and significantly increased at ultimate. Values of external prestressing force as well as its increase ratios at different loading stages are shown in Table 4.

In addition, Fig. 4 shows the load deflection curves for reinforced concrete beam (RC), beam PS1-1 from group G1, and beam PS2-1 from group G3, respectively, as examples of the load-deflection relationships of the tested beams.

As shown in Fig. 4, beam PS1-1 which failed in flexural-shear mode recorded the highest deflection value at ultimate load when compared to the other tested beams those failed in shear. Also, the stiffness of RC beam was lower than those of strengthened beam after cracking due to rapid increase in cracks number and cracks propagation.

Fig. 5 shows the relationships between the applied loads and the measured strains in the stirrups for the tested beams PS1-1, PS2-1 and RC respectively.

As can be seen, in case of the unstrengthed beam and strengthened beam failed in shear; RC and PS2-1, the strain

Figure 3 Schematic drawing for test setup and instrumentation of the tested beams.

Table 3 Summary of recorded data of the test beams.

Beam no. Cracking jack load (kN) Ultimate jack load (kN) Mode of failure

Flexure Shear

PS1-1 60 70 171 Flexural shear

PS1-2 110 110 293 Shear

PS1-3 70 110 263 Shear

RC 25 55 150 Shear

PS2-1 80 120 269 Shear

Table 4 External prestressing force at different stages.

Beam no. External prestressing force at different stages (kN) Increase in external prestressing force (%)a

Cracking Ultimate Cracking Ultimate

PS1-1 38 91 5.6 153

PS1-2 34 56 3 70

PS1-3 37 68 2.8 89

RC - - - -

PS2-1 37 82 2.8 128

a Relative to the initial external prestressing force.

Figure 4 Load-deflection relationship for tested beams.

Stirrups Strain x10-6

Figure 5 Relation between load and stirrup strain of tested beams.

of stirrups located in the maximum shear region rapidly increased after cracking and reached the yielding value at the ultimate stage. Stirrup strain started to increase earlier in case of RC beam than in case of strengthened beam (PS2-1). This proves the advantage of using external prestressing to improve the shear strength of reinforced concrete beams.

The stirrup strain of beam PS1-1 was very small during loading as beam PS1-1 failed in flexure.

It should be noted that the strain of the top and bottom reinforcement bars of beams failed in shear; strengthened beams and reinforced concrete beam, did not reach the yielding value.

3.2. Effect of key variables

3.2.1. Effect of shear span to depth ratio (Group 1) The shear span to depth ratio (a/d) has a significant effect on the structural behavior and structural strength of the strengthened beams. The effect of (a/d) ratio on the cracking pattern, cracking load, ultimate load, mode of failure and the increase in external prestressing force of each beam is discussed below.

3.2.1.1. Cracking pattern. On all beams flexural cracks appeared first between the concentrated loads, and then the cracks in the shear span appeared at a higher load. Flexural cracks on beam with the highest shear span/depth ratio; PS1-1, appeared at a lower load (60 kN) than that on beam PS1-3 and beam PS1-2 (70, 110 kN respectively). This also was noticed in the case of shear cracks, as the diagonal cracks on beam PS1-1 appeared at a lower load (80 kN) than that on beam PS1-3 and beam PS1-2 (110, 140, respectively). As the load increased, both the flexural and shear cracks extended and propagated. Before failure, the width of the shear cracks increased while the flexure cracks slightly increased. Fig. 6 shows the pattern of cracks of the tested beams PS1-1, PS1-3 and PS1-2, respectively.

3.2.1.2. Mode offailure. Shear span to depth ratio (a/d) is one of the most affecting factors on the mode of failure, due to its

Beam PS 1-2

Figure 6 Cracks pattern of beams in group G1.

major influence on the type of the internal forces of the tested beams.

For beam PS1-1 (a/d = 2.62) the mode of failure was flexure-shear failure, it began by the yielding of the tension reinforcement at the concentrated load accompanied by increasing in the deflection before failure occurred, considerable deflection and wide cracks were observed, giving ample warning of the impending failure. At failure, great increase in the mid span deflection occurred while the applied load remained constant. On the other hand, on beams PS1-3 and PS1-2 at failure, shear cracks widened at one side of the tested beams, and then shear failure occurred. At failure, on beam PS1-3 (a/d = 1.61) shear crack extended to the top flange and connected horizontally with the support, while on beam PS1-2 (a/d = 1.07) the shear cracks connected the top flange of the beam and the support as shown in Fig. 7.

As shown above, reducing (a/d) ratio changed the failure mode from flexural-shear failure (PS1-1) to shear-tension failure (PS1-3), and to diagonal tension failure (PS1-2). This is attributed to the increase in the shear stresses compared with the flexure stresses.

3.2.1.3. Cracking and ultimate loads. As can be seen from Table 3, the cracking and ultimate loads for the tested beams of group G1 are inversely proportion with the (a/d) ratio. Beam PS1-1 with the highest (a/d) ratio; (a/d = 2.62), had the least cracking and ultimate strength while beam PS1-2, with the least (a/d) ratio; (a/d = 1.07), had the highest cracking and ultimate strength. This is because the increase in shear span increases the flexural stresses on the beam cross section area, which increased the tensile stresses in the concrete section and consequently speeds cracking.

Fig. 8 shows that the increase in shear cracking strength was less than the improvement in the ultimate shear strength. This is due to reduction in (a/d) ratio. Also, both cracking and ultimate loads almost vary linearly with the shear span to depth ratio.

3.2.1.4. Increase in externalprestressing force. Fig. 9 shows the relation between the applied load and the increase in the external prestressing force up to failure for beams PS1-1, PS1-3 and PS1-2 (a/d = 2.62, 1.61, 1.07), respectively. Before cracking, the increase in the external prestressing force was small and can be neglected. The increase in the external prestressing force relative to the initial prestressing force at this stage of loading ranged from 2.8% in beam PS1-3 to 5.6% in beam PS1-1 as shown in Table 4 and Fig. 10. After cracking, there was a higher increase in the external prestressing force and at ultimate this increase was significant in all beams and ranged from 70% in beam PS1-2 to 153% in beam PS1-1. Fig. 10 shows that the increase in (a/d) ratio significantly affected the increase in the external prestressing force at ultimate. The increase in external prestressing force after cracking can be attributed to the increase in deflection and as the external prestressing force is directly proportional with the beam deflection, hence, beam with higher deflection; beam PS1-1; had higher increase in external prestressing force.

3.2.2. Effect of external prestressing force (Group 2) During loading, both the flexural and shear cracks on the un-strengthened concrete beam; RC, propagated and spread faster than those on the strengthened beam; PS1-3. While the crack widths on beam PS1-3 were smaller and the number of cracks were higher than those on beam RC as shown in Fig. 11.

Figure 7 Failure of beams in group G1.

0.5 1 1.5 2 2.5 3

Shear Span to Depth Ratio (a/d)

Figure 8 Effect of shear span to depth ratio (a/d) on the cracking and ultimate loads in group G1.

Table 3 shows that the shear cracking load of beam PS1-3 was higher than that of beam RC by about 100%, while its ultimate load increased by about 75%.

At failure, shear cracks concentrated on one shear span of both beams and wide cracks were observed. The failure of both beams was brittle failure and failure of beam RC was accompanied by sapling of concrete cover at the support location as shown in Fig. 12.

3.2.3. Effect of concrete strength (Group 3)

Increasing the concrete strength slightly affected both the

cracking and ultimate strength, as beam PS2-1 which had the

175 150 125 100 75 50 25

1 1.5 2 2.5 3

Shear Span to Depth Ratio (a/d)

Figure 10 Effect of shear span to depth ratio (a/d) on the increase in the external prestressing force of beams in group G1.

highest concrete strength (fcu = 58.8 N/mm2) cracked and failed at slightly higher applied loads than PS1-3 (fcu = 36.3 N/mm2). Increasing the concrete strength of beam PS2-1 by about 60% (compared to beam PS1-3) improved the cracking shear load by 9% and ultimate strength by about 2.5% (comparing PS2-1 to PS1-3). The increase in cracking strength can be attributed to the increase in the concrete tensile strength.

Cracks on beam PS2-1 had better distribution than those on beam PS1-3 due to the improvement in the concrete tensile strength as shown in Fig. 13. Also, beam PS2-1 had better failure than beam PS1-3, although both of failure was brittle as shown in Fig. 14.

As can be seen from Fig. 9, the relation between load and the increase in external prestressing force of beams PS1-3 and PS2-1 are almost typical during the loading stages.

4. Analytical investigation

Two types of shear cracking can occur in prestressed concrete beams; flexure-shear cracking and web-shear cracking.

A flexure-shear crack originates as a vertical flexural crack in a member. As the crack penetrates deeper into the cross-section it becomes inclined as a result of the shear stresses. On the other side, web shear cracking initiated in the web, without

Beam RC

Figure 11 Cracking pattern of beams in group G2.

Beam PS1-3 Beam RC

Figure 12 Failure of beams in group G2.

Beam PS 2-1

Figure 13 Cracking pattern of beams in group G3.

previous flexural cracking, when the principal tension in the concrete becomes equal to its tensile strength.

The concrete contribution to shear strength is a function of the type of shear cracking that controls (flexure-shear or web-shear) at a given cross-section. Flexure-shear cracking controls where moment is large and shear exists, and web-shear cracking typically controls in thin web members near the supports where moment is small and shear is large.

The contribution of prestressing to shear resistance results from two components. The vertical component of the pre-

stressing that reduces the shear force and the horizontal component that improves the concrete shear strength.

The ultimate shear resistance of externally prestressed concrete section, Vu, can be calculated from:

Vu = V + V + Vp (1)

where Vc is the shear cracking load calculated by considering the effect of prestressing force, Vs is the shear resistance provided by stirrups and Vp is the vertical component of the pre-stressing force at the critical section.

Beam PS 1-3 Beam PS2-1

Figure 14 Failure of beams in group G3.

Following several equations proposed by several codes are presented and compared with the experimental results of the present research.

Two types of code equations were examined, in the first type the external prestressing force is treated as external compression load as the case of the conventional reinforced concrete beams while the equations in the second type consider the external prestressing force as an internal force, which is the case of the ordinary prestressed concrete beam.

To use these equations, the value of the axial prestressing force; the horizontal component of the external prestressing force was considered as the total prestressing force value due to the small inclination angle of the external prestressing force. The error resulting from this assumption in calculation was negligible. Also, although the external prestressing force increases as the beam is overloaded, it is assumed conservatively equals to the effective prestressing force (Pe). A brief summary of some of these equations follows (for consistency, some symbols in the following equations have been changed from the original).

4.1. Egyptian code of practice [ECP-203-2007] [25]

4.1.1. Method A: conventional RC beam In the Egyptian code (ECP) [25] Eq. (1) is used to predict the cracking shear strength of concrete beams while Eq. (2) is used to calculate its ultimate shear strength. In Eq. (2), the ultimate shear strength of concrete beams depends only on the com-pressive strength and the amount of stirrups. This equation is used for concrete with compressive strength up to 60 MPa and considers that the ultimate shear strength of concrete beams is resisted by the nominal shear strength of stirrups and half of the nominal shear strength of the concrete.

qcu = 0.24^/ Jj

$CU , A 1 ^ ifcu i

qu = -2 + qs = °.12v — +

2 V 'c

nAJ —

The effect of the axial compression force on the concrete shear strength is considered by multiplying Eq. (1) with a specific factor (d):

d = + .07AN) 6 1.5

if a/d 6 2, ECP allows to reduce the shear force by multiplying it by the value a/2d. However, the shear stress before reduction should not be higher than 0.7y/fcu/yc)

4.1.2. Method B: prestressed beam

ECP [25] suggested two methods to calculate the cracking shear strength in members. The first method is simple and less complicated than the second method but used with prestress-ing force higher than 40% of the nominal tensile strength of the prestressing tendons. Using the first method, the cracking shear resistance can be calculated from the following equation:

qcu = 0.045</ — + 3.6

0.24. — 6 qcu 6 0.375. — V'c V'c

where Mu is the maximum moment at the critical section of shear and (Qudp/Mu 6 1).

In the second method; the detailed method, the cracking shear strength is calculated based on the anticipated cracking type. The cracking shear strength (qcu) is taken as the minimum of the values obtained from the following equations:

qa = 0.045,^ + 0.8 qd

qcw = 0.24 t Fu

The ultimate shear stress allowed by ECP (qu) is higher than that in case of the conventional concrete beam and is calculated from:

qu = q2u + qs 6 0.75 f 6 4.5 N/mm2 (9)

4.2. ACI318-2008 [13]

4.2.1. Method A: conventional RC beam For conventional RC beams, the ACI 318-2008 [24] presents the following equations for computing the shear strength of beams with web reinforcement. In these equations the ACI-

2008 [24] considered that the ultimate shear strength (Vn) depends on the nominal shear strength provided by concrete (Vc) and stirrups (Vs). In the factor concerning the nominal strength provided by the concrete, the effect of the axial compression stresses (N/Ag) is taken into consideration as seen in Eq. (12).

/Vn P Vu (10)

Vn = Vc + Vs

Vc = 017 Pfbwd^ 1 + JA^j

Vs = AsVfyd/s

Also, Vc is permitted to be computed by a more detailed calculation as follows:

Vc = (^0.16p/c + 17PwÇMdjbw^j 6 0.29Pfcbwd^1

Mm = Mu - Nu

(4h - d)

4.2.2. Method B: prestressed beam

To calculate the ultimate shear strength of the prestressed beams and for members with effective prestress force not less than 40% of the tensile strength of flexural reinforcement:

Vc = (0.05vf + 4.8 VM^jbwd

0.17 J A-bwd 6 Vc 6 0.42л fbwd

V Ce v Cc

and (Vudp/Mu 6 1) where Mu occurs simultaneously with Vu at the section considered.

For general calculation ACI suggested a detailed method to calculate the concrete shear strength as the minimum of Vci, Vcw where:

Vc, = (^0.05 Vfcbwd + Vp

Vcw = (0.29 yf + 0.3fcpywdp + Vp

Mcre = 1 (0.5y/fc + 0.3fcP)bwdp + Vp

The concrete shear strength is in terms of the percentage area of longitudinal tension reinforcement (100As/bd), effective depth of the section (d), concrete cube strength (fcu) and axial compression.

The ultimate shear strength can be calculated from:

Vu = c + "

0.87fy As

For the design of sections near a support the enhancement of shear strength may be taken into account by increasing the design concrete shear stress c to 2dvc/av provided that at the face of the support remains less than the lesser of 0.8fcu or 5 N/mm2 (this limit includes ym of 1.25).

4.3.2. Method B: prestressed beam

The design ultimate shear resistance of the concrete alone Vc should be considered at sections that are uncracked (M < Mo) and at sections that are cracked (M > Mo) in flexure, as follows.

The ultimate shear resistance of the un-cracked section, Vco, is computed as follows:

Vco = 0.67bh_ (ft + 0.8fcpft) (23)

On the other hand, the design ultimate shear resistance of a section cracked in flexure Vcr may be calculated using the following equation:

Vcr - (1 - 0.55fpe/fpu)cbd + Mo VIM 6 0.1bdfcu (24)

The ultimate shear strength can be calculated from:

Vu = Ve +

0.87fyAsdt

where dt is the depth from the extreme compression fiber either to the longitudinal bars or to the centroid of the tendons, whichever is the greater.

5. Experimental versus theoretical results

The ultimate shear strength as well as the concrete shear strength were calculated for all the studied beams and the pre-stressed beams tested by Ng and Soudki [23] by using all the equations stated above in the considered codes and compared with the experimental results. As previously stated, the effect of the prestressing force is counted in the majority of codes equations but with different factors, and the effect of shear span to depth ratio (a/d) is also taken into consideration. The predicted shear and ultimate shear strengths of the beams were calculated as conventional beams and as prestressed beams.

5.1. Concrete shear strength

4.3. BS 8110-1997 [26]

4.3.1. Method A: conventional RC beam

The design concrete shear stress (c) can be determined from the following equation:

-^nTTTO (2')

As shown from previous equations all the studied codes do not account for the difference between bonded and unbounded tendons, even though a number of studies have shown that unbonded tendons would result in a much greater shear capacity [21,22,27].

In determining the concrete contribution in shear, ECP [25] simple equation and ACI [24] simple equation should be used only for members with effective external prestressing force (Pe) not less than 40% of the nominal tensile strength of prestress-

ing tendons. Hence, the prestressing level is not a factor in the simple method; instead, the prestressing level is a factor in the detailed method in both codes.

The experimental and the predicted shear strengths of concrete for each beam computed using ECP [25], ACI [24] and BS [26] methods are compared graphically in Figs. 15-17. The values of the prestressing force used in calculations were the effective prestressing forces (Pe) which were listed in Table 2. For ECP [25] methods and as can be seen in Fig. 15, the detailed PC (prestressed concrete) method was more conservative than the other methods while the conventional RC (reinforced concrete) method shows less accuracy at lower prestressing force values. However, the conventional RC method is less complicated than the other methods and can be directly used by increasing the concrete factor of safety for design purpose.

In case of ACI [24], both RC simple and detailed equations are conservative and the difference between them is negligible, see Fig. 16. On the other side, the simple PC method shows the least accuracy among all codes, while the detailed PC equation shows reasonable accuracy and estimation of concrete shear strength.

Moreover, the degree of conservatism in case of PC equation of BS was higher than that of RC equation; see Fig. 17.

5.2. Ultimate shear strength

5.2.1. Considering codes' factors of safety The relation between the nominal shear strength and the ultimate shear strength calculated by the studied codes are shown in Figs. 18-20. The experimental nominal shearing loads were always higher than the code predicted values. This is attributed mainly to the code underestimation of the strength contributed by the concrete and the effect of prestressing force in determining the shear strength of the beams. The contribution of pre-stressing force to the shear strength of beams can be calculated by deducting the shear strength of RC from that of beam PS1-3. As indicated in Table 5, the ultimate shear load of Beam PS1-3 (131.5 kN) is about twice the ultimate shear capacity of beam RC.

40 50 60 Vc_actual (kN)

APC_Simple XPC_detai1ed ♦RC_Simple ■RC_Detailed

Figure 16 Relation between actual and calculated concrete shear strength using ACI equations.

40 50 60 Vc_actual (kN)

Figure 17 Relation between actual and calculated concrete shear strength using BS equations.

90 80 70

e 60 ■a

■S 50

* 30 20 10

If—rr ▲ ■ ▲

10 20 30 40 50 60 70 80 90 Vc_actual (kN)

| APC_Simp1e BPC_Detailed »RC |

Figure 15 Relation between actual and calculated concrete shear strength using ECP equations.

80 120 Vult_actual (kN)

»PC_Simp1e BPC_Detai1ed ARC

Figure 18 Relation between actual and calculated ultimate shear strength using ECP equations.

APC_Simple XPC_Detailed»RC_Simple lRC_Detailed

Figure 19 Relation between actual and calculated ultimate shear strength using ACI equations.

■ RC ♦PC

Figure 20 Relation between actual and calculated ultimate shear strength using BS equations.

The ratio between the nominal shear strength to the calculated ultimate shear strength of the studied beams was higher than 1.5 as suggested by many codes. Also, as a/d ratio

reduced the calculated ultimate shear strength are far too conservative. This may be attributed to the inadequacy address the effect of prestressing force on the arch action contribution that control the failure of beam with small a/d ratio.

Values of the actual and predicted ultimate shearing loads as conventional beams and as prestressed beams are summarized in Tables 5 and 6, while comparisons between the experimental and calculated values in both cases were shown in Tables 7 and 8.

Also, it can be observed from Tables 7 and 8 that the accuracy of the predicted values (the ratios between the experimental results and the calculated ultimate shearing loads by the considered codes) for the tested beams in the current work was better than that of the beams tested by Ng and Soudki [23]. This may be due to the mechanism of the test setup used in their experiments; the test beams were externally strengthened in only one shear span using straight tendons.

The comparison between code values for conventional RC beam (shown in Table 7) shows that both methods suggested by ACI [24] are more conservative than those of ECP [25] and BS [26] codes.

Also, considering the total concrete shear strength (qcu) instead of (0.5 qcu) in the ECP [25] conventional RC method shows better accuracy but has a factor of safety less than 1.5. While in case of ECP [25] PC-method, using full concrete strength show better accuracy and factor of safety higher than 1.5.

It can be observed from Table 8 that the PC simple equation proposed by ACI [24] and using full concrete strength in ECP [25] RC simple equation has better accuracy with reasonable factor of safety than the other methods.

5.2.2. Considering codes' factors of safety equal unity To check the codes degree of conservatism, ultimate shear strength of test beams were recalculated by the studied code equations using strength factors of safety equal unity. Table 9 shows the calculated ultimate shear strength using codes conventional RC beams equations while Table 10 shows the calculated ultimate shear strength using codes PC equations.

As can see, the nominal shear strength of the test beams was higher than the calculated ultimate shear strength, and the difference between them increased as a/d ratio increased. Also, all code equations show better accuracy when used to calculate the ultimate shear strength of RC beam than when used to calculate the ultimate shear strength of PC beams.

Table 5 Values of experimental and predicted ultimate shear strength using the considered codes as conventional RC beams.

Beam no. Put (kN) Exp. ult. shear force (kN) Predicted (kN)

ECP ACI simple ACI detail BS ECP total qcu

PS1-1 171 85.5 52.8 43.4 41.7 55.3 70.2

PS1-2 293 146.5 93.7 43.3 42.1 76.4 126.0

PS1-3 263 131.5 64.5 43.4 41.9 62.5 86.1

PS2-1 269 134.5 70.4 48.5 46.5 63.2 97.9

RC 150 75.0 58.5 42.5 41.8 54.6 79.1

Beams from literature (Ng and Soudki [23])

400-SP40% 264.9 176.6 59.5 49.8 44.3 107.3 86.4

550-SP3% 159.1 106.1 49.6 45.6 44.2 67.5 69.9

700-NSP40% 170.5 113.7 24.2 26.3 20.5 55.3 48.3

700-SP40% 157.8 105.2 53.5 49.9 44.2 87.6 77.7

Table 6 Values of experimental and predicted shear strength using the considered codes as prestressed beams.

Beam no. Exp. ult. shear force (kN) Predicted (kN)

ECP simple ECP detail ACI simple ACI detail BS ECPa

PS1-1 80.5 47.9 45.3 58.7 42.5 48.3 64.7

PS1-2 141.9 52.8 46.9 68.9 53.8 51.3 75.0

PS1-3 126.5 53.3 45.3 68.9 46.3 49.4 75.4

PS2-1 129.5 57.5 49.2 78.3 49.9 51.3 84.0

RC 75.0 - - - - - -

Beams from literature (Ng and Soudki [23])

400-SP40% 176.6 56.7 49.5 73.2 58.4 74.6 86.0

550-SP3% 106.1 52.6 46.1 69.2 41.3 55.7 77.9

700-NSP40% 113.7 20.6 18.8 59.9 44.6 33.9 41.2

700-SP40% 105.2 48.0 46.1 59.9 44.8 63.4 68.6

a Shear calculated using full concrete strength.

Table 7 Ratios between experimental and predicted shear strength using the considered codes as conventional RC beams.

Beam no. Experimental/predicted

ECP simple ACI simple ACI detail BS ECP total qcu

PS1-1 1.62 1.97 2.05 1.55 1.22

PS1-2 1.56 3.38 3.48 1.92 1.16

PS1-3 2.04 3.03 3.14 2.10 1.53

PS2-1 1.91 2.77 2.89 2.13 1.37

RC 1.28 1.77 1.79 1.37 0.95

Mean 1.68 2.58 2.67 1.81 1.25

Standard deviation 0.30 0.69 0.72 0.34 0.22

Median 1.62 2.77 2.89 1.92 1.22

Beams from literature (Ng and Soudki [23])

400-SP40% 2.97 3.54 3.98 1.65 2.04

550-SP3% 2.14 2.32 2.40 1.57 1.52

700-NSP40% 4.70 4.31 5.56 2.06 2.35

700-SP40% 1.97 2.11 2.38 1.20 1.35

Mean 2.94 3.07 3.58 1.62 1.82

Standard deviation 1.25 1.04 1.52 0.35 0.46

Median 2.55 2.93 3.19 1.61 1.78

Table 8 Ratios between experimental and predicted shear strength using the considered codes as prestressed beams.

Beam no. Experimental/predicted

ECP simple ECP detail ACI simple ACI detail BS ECPa

PS1-1 1.78 1.89 1.46 2.01 1.77 1.32

PS1-2 2.77 3.12 2.13 2.72 2.85 1.95

PS1-3 2.47 2.90 1.91 2.84 2.66 1.74

PS2-1 2.34 2.74 1.72 2.70 2.62 1.60

RC - - -- -

Mean 2.34 2.66 1.80 2.57 2.48 1.66

Standard deviation 0.41 0.54 0.28 0.38 0.48 0.27

Median 2.40 2.82 1.81 2.71 2.64 1.67

Beams from literature (Ng and Soudki [23])

400-SP40% 3.11 3.57 2.41 3.02 2.37 2.05

550-SP3% 2.02 2.30 1.53 2.57 1.90 1.36

700-NSP40% 5.52 6.06 1.90 2.55 3.35 2.76

700-SP40% 2.19 2.28 1.76 2.35 1.66 1.53

Mean 3.21 3.55 1.90 2.62 2.32 1.93

Standard deviation 1.61 1.78 0.37 0.28 0.75 0.63

Median 2.65 2.93 1.83 2.56 2.14 1.79

Table 9 Values of experimental and predicted ultimate shear strength using the considered codes as conventional RC beams using strength reduction factors equal unity.

Beam no. Exp. ult. shear force (kN) Predicted (kN) Experimental/predicted

ECP ACI simple ACI detail BS ECP ACI simple ACI detail BS

PS1-1 85.5 61.3 62.0 59.6 65.4 1.39 1.38 1.44 1.31

PS1-2 146.5 109.5 61.9 60.2 94.0 1.34 2.37 2.43 1.56

PS1-3 131.5 75.1 62.0 59.8 74.8 1.75 2.12 2.20 1.76

PS2-1 134.5 82.3 69.4 66.4 75.8 1.63 1.94 2.03 1.77

RC 75.0 68.8 60.7 59.8 66.9 1.09 1.24 1.25 1.12

Table 10 Values of experimental and predicted shear strength using the considered codes as prestressed beams using strength reduction factors equal unity.

Beam no. Exp. ult. shear force (kN) Predicted (kN) Experimental/predicted

ECP simple ECP detail ACI simple ACI detail BS ECP simple ECP detail ACI simple ACI detail BS

PS1-1 80.5 52.4 52.4 83.8 60.7 55.2 1.63 1.63 1.02 1.41 1.55

PS1-2 141.9 61.7 52.0 98.4 76.9 57.2 2.37 2.82 1.49 1.91 2.56

PS1-3 126.5 61.3 52.4 98.4 66.1 55.7 2.14 2.51 1.34 1.99 2.36

PS2-1 129.5 62.2 57.1 111.8 71.3 57.7 2.16 2.35 1.20 1.89 2.33

RC 75.0 56.3 47.4 60.7 60.7 NA 1.33 1.58 1.24 1.24 NA

6. Conclusions

Based on the results of the conducted experimental and analytical investigations, the following conclusions were obtained:

- The shear span to depth ratio governed the mode of failure and should be taken into consideration when analyzing and designing externally prestressed simple beams.

- Increasing shear span to depth ratio increased the appearance of shear cracks and increased the cracks propagation.

- Increasing the shear span to depth ratio for the tested prestressed beams from 1.07 to 2.62 decreased the shear cracking load by 75%, and decreased the ultimate shear load by 71%.

- Before cracking, the shear span to depth ratio has no significant effect on the increase of the external prestressing force, due to the small deflection at this stage.

- After cracking, increasing shear span to depth ratio increases the external prestressing force. Increasing a/d from 1.07 to 2.62 increased the percentage of the increase in the external prestressing force from 70.0% to 153.0% at the ultimate stage.

- The presence of the external prestressing force delayed the appearance of diagonal cracks and reduced their widths. The shear cracking load increased up to 200% and the ultimate shear strength by about 75% compared to unstrength-ened beam.

- The gain from increasing the concrete compressive strength was insignificant. Increasing the concrete strength of the tested prestressed beams by about 60% improved the cracking shear load and the ultimate shear strength by only 9.0% and 2.5%, respectively.

- In general, most of the considered codes equations for ultimate shearing force give conservative results.

- For the equation stated in the Egyptian code ECP [25], using the full strength rather than half of the concrete shear

strength in the prestressed method improves the accuracy of the predicted shear strength of the prestressed beams.

- Although the inclination angle of the Parafil rope is too small, considering the external force as prestressed force and using the prestressing equations gives better accuracy, than considering it as axial force only and using the conventional RC equations.

- Simple methods in the considered codes gave better accuracy than the detailed methods when predicting the shearing strength as prestressed beams.

Acknowledgment

The authors are grateful to Linear composite limited (UK) for providing Parafil ropes.

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A. Ghallab, is an associate professor at faculty of Engineering, Ain Shams University. Egypt. Dr. Ghallab received his BSc and MSc from Ain Shams University and his PhD from Leeds University, UK. His research focused on behaviour of externally prestressed concrete beams, fiber reinforced concrete and high performance concrete.

M. A. Khafaga, is a professor of strength of materials at Housing and building National Research Center, Egypt. Dr. Khafaga received his BSc and PhD from Ain Shams University, Egypt. His research focused on properties of construction and innovative materials.

M. F. Farouk, is an Engineer at Dar El-Han-dasa Consultation Office. Eng. Farouk received his BSc and MSc from Ain Shams University. His research focused on behaviour of externally prestressed concrete beams.

A. Essawy, is a professor of concrete Structures at faculty of Engineering, Ain Shams University, Egypt. Dr. Essawy received his BSc and MSc from Ain Shams University and his PhD from MacMaster University, Canada. . His research focused on behaviour of concrete structures.