Experimental and analytical study of strengthening schemes for shear deficient RC deep beams

Construction and Building Materials 216 (2019) 673–686

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Experimental and analytical study of strengthening schemes for shear deficient RC deep beams Abdulrahman Albidah, Aref Abadel, Husain Abbas, Tarek Almusallam, Yousef Al-Salloum ⇑ Chair of Research and Studies in Strengthening and Rehabilitation of Structures, Department of Civil Engineering, King Saud University, Riyadh 11421, Saudi Arabia

h i g h l i g h t s
Studied the performance of schemes adopted for strengthening of RC and FRC deep beams in shear.
Beams were strengthened using welded wire mesh and CFRP U-wraps and horizontal strips.
Strengthening schemes upgraded the shear strength of deep beams to greater than that provided by steel web reinforcement.
FRC showed excellent shear resistance although it caused reduction in the beam deformation capacity.
A methodology is presented to assess the shear strength of concrete (without fibers) and FRC deep beams.

a r t i c l e

i n f o

Article history: Received 13 January 2019 Received in revised form 30 April 2019 Accepted 4 May 2019 Available online 17 May 2019 Keywords: Deep beam Concrete RC Fiber reinforced concrete Strengthening FRP Welded wire mesh Shear Flexure Steel fibers

a b s t r a c t This paper investigates experimentally and analytically the effectiveness of adopted schemes for strengthening of reinforced concrete (RC) and fiber reinforced concrete (FRC) deep beams in shear. Six specimens were cast in two groups of three specimens each. First group was cast in concrete without fibers, whereas the second was cast half in concrete without fibers and the remaining half-length in concrete having steel fibers. The steel web reinforcement was provided in half span of all beams and the other half was strengthened using different schemes. The shear strengthening schemes employed for the first group were: (i) near surface mounted (NSM) carbon fiber reinforced polymer (CFRP) U-wrap strips and externally bonded horizontal CFRP strips, and (ii) welded wire mesh. For shear strengthening of the FRC of the second group in shear, externally bonded CFRP U-wraps and horizontal CFRP strips were used. The strengthening schemes upgraded the shear strength of deep beams to greater than that provided by steel web reinforcement. FRC showed excellent shear resistance although it caused reduction in the beam deformation capacity. A methodology is proposed to assess the shear strength of concrete (without fibers) and FRC deep beams. The shear strength prediction of the tested deep concrete beams was consistent with the test results. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction The reinforced concrete (RC) beams are often exposed to aggressive environment leading to the corrosion of shear stirrups, which are exposed to the outside environment earlier than the longitudinal rebars due to lesser concrete cover. This generally causes loss of shear strength in RC beams and its effect on beam behavior is more evident in RC deep beams due to predominant shear behavior. In fact, deep beams are common structural elements in RC structures such as bridges, parking garages, water reservoirs. The deficiency in shear capacity of RC deep beams arising due to the corrosion of shear stirrups or otherwise is compensated ⇑ Corresponding author. E-mail address: [email protected] (Y. Al-Salloum). https://doi.org/10.1016/j.conbuildmat.2019.05.024 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

through shear strengthening of beams for which different schemes are employed. The response of RC deep beams, strengthened for shear using different schemes including fiber reinforced polymer (FRP), has been studied extensively. Externally bonded FRP systems, commonly employed for shear strengthening of deficient RC beams (e.g. [1–3]), were used by Islam et al. [4] to examine the shear response of RC deep beams. Their test results of different strengthening schemes adopted enhanced the failure load of beam and limited the diagonal cracks propagation. The experimental program of Adhikary and Mutsuyoshi [5] involved testing eight concrete deep beams, which were strengthened using unidirectional carbon FRP (CFRP) laminates. The vertical U-wrapped beams were found to achieve almost double the shear strength observed for counterpart beam without strengthening.

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Li and Leung [6] examined the shear response of deep beams strengthened using full-wrapping FRP strips for a range of shear span a, to depth, d, ratios varying from 1 to 3.5. The authors concluded that enhancement in the shear capacity of concrete deep beams is strongly influenced by the a/d ratio with the a/d ratios in the order decreasing performance were: medium a/d ratios (2  a/d  3), large a/d ratios (>3), and small a/d ratio (<2). Dhahir [7,8] proposed a strut-and-tie model for assessing the shear capacity of FRP reinforced deep beams having no web reinforcement. The model was validated using a database of FRP strengthened deep beams. Hanoon et al. [9] tested RC deep beams, strengthened in shear using FRP. The beams were strengthened in shear using externally bonded CFRP sheets. The test results were employed to develop a simplified strut-and-tie model for shear strength calculation. Besides the aforementioned studies, steel fibers were also employed to enhance the shear resistance of concrete deep beams (e.g. [10–12]). The experimental observations revealed that the incorporation of steel fibers is beneficial for resisting shear stresses and concrete spalling. Test results showed that an addition of 1% steel fibers for specimens having a/d ratio of 1.5 enhanced the deep beam shear strength by 25–30% [10]. For predicting shear capacity of concrete deep beams, strutand-tie models are commonly adopted [13–15]. Similarly, shear strength prediction models for fiber reinforced concrete (FRC) deep beams were also developed using strut-and-tie approach (e.g. [16,17]). Empirical models are also proposed in the literature for FRC deep beams (e.g. [10,18]). Zhang et al. [19] employed modified compression field theory for estimating the shear capacity of FRC beams and verified the prediction with the experiments available in literature. Godat and Chaallal [20] presented analysis and design approach for the CFRP shear-strengthened girders using the strutand-tie model. In the proposed method, tensile forces in the steel stirrups and externally bonded CFRP laminates were combined. The above review illustrates that there is limited research on the behavior of RC deep beams retrofitted using different retrofitting schemes. Although the shear response of FRC deep beams has also been investigated in some studies, the research on studies pertaining to strengthened FRC deep beams is scanty. Moreover, there is no unified approach for the prediction of shear capacity of concrete deep beams that incorporates the contributions of concrete, shear stirrups, fibers as well as strengthening layers of different materials such as FRP and welded wire mesh. This research was taken up with the objective of investigating the effectiveness of different retrofitting schemes in enhancing the shear resistance of concrete and FRC deep beams and to propose a unified approach for predicting the shear capacity of concrete deep beams. Six RC and FRC deep beams were tested under the action of central point load for studying the shear response of different strengthening schemes. The strengthening schemes involved the use of welded wire mesh and FRP for improving the shear resistance of deep beams. It is worth mentioning here that most of the schemes adopted for strengthening have either not been investigated thoroughly or there is limited research for these schemes. A unified methodology is proposed for the estimation of the shear capacity of the retrofitted concrete deep beams. 2. Experimental program 2.1. Test specimens The experimental plan involved the testing of six RC deep beams of rectangular cross-section under a central point load. The size of beams was 100  250 mm in cross-section and 1000 mm long. The beams were supported on steel rollers across

an effective span of 850 mm. The diameter of steel rollers used for supports and for applying load was 75 mm. The flexural tension reinforcement was provided in the form of two layers of 2/10 deformed bars each, giving the percentage of flexural reinforcement as 1.53%. The rebars were fabricated with 90° bend for proper anchorage at beam ends (Figs. 1 and 2). Two rebars of /6 were used as compression reinforcement primarily to support the shear stirrups. The concrete cover to longitudinal rebars (side as well as bottom and top) was 25 mm, which was achieved by using precast concrete blocks of 25 mm thickness. The vertical gap between the two layers of rebars was 20 mm. The beams were used for studying the behavior of different alternate methods for resisting shear. These methods included different strengthening schemes, the use of FRC, and their combinations. The shear reinforcement consisted of two-legged /6 mm stirrups of plain bars at a uniform spacing of 100 mm and horizontal web rebars of 2/6 mm provided at the mid-depth of the beam. The shear reinforcement was provided only in half-span (Figs. 1 and 2). The specimens were classified into two groups, namely Group-1 and Group-2, of three specimens each. The first group (Group-1) of three specimens was cast using concrete without fibers (i.e. plain concrete). Nevertheless, the deep beams of second group (Group-2) were cast using concrete without fibers in their half-length having web reinforcement and the remaining half-length was cast using the same concrete grade but mixed with hooked steel fibers. Susetyo et al. [21] studied the requirement of steel fibers to serve as the minimum shear reinforcement in FRC. They concluded that a fiber volume fraction of 1.0% is adequate for acceptable deformation ductility and shear strength. Thus, the steel fibers added in concrete were 1% by volume (i.e. 3.27% by weight). The two halves of beams of Group-2 (half span without fibers and the other half with steel fibers) were cast at the same time and a separator was used during casting, which was subsequently removed. The separator was in the form of a plastic sheet with vertical slots cut at the location of the longitudinal rebars. Fig. 1(a) was drawn to scale to show the actual positions of rebars. One beam of each group (SF0 and SF1) was tested without strengthening, while the remaining beams were tested by adopting different strengthening schemes, discussed in subsequent section. Some of the strengthening schemes were decided after knowing the behavior of the tested beams, which is described in greater detail in later sections.

2.1.1. Size effect The size effect in RC deep beams has been extensively studied [22–25]. The possible reasons for decrease in shear strength with increase in the depth of RC deep beams are: (i) reduced aggregate interlock (interface shear transfer) in beams of larger depth, (ii) width of bearing plates in deeper beams are proportionately smaller as compared to the width of bearing plates used in smaller tested beams, and (iii) randomness of material strength. It is now well known that the critical path of shear cracks in concrete deep beams is governed by mechanics rather than the randomness of material strength and thus Weibull theory does not apply to beam shear [26]. The effect of width of bearing plates on shear strength of deep beams was eliminated by using rollers for supports as well as for applying the loads. The only parameter that may introduce the size effect is the interface shear transfer. Although its effect is expected to be less due to the use of smaller size of aggregate (i.e. maximum size of aggregate = 10 mm) and the use of steel fibers in some of the specimens because the fibers substantially mitigate the size effect in shear [27], its effect will however be studied in future.

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Fig. 1. Specimens of Group-1: (a) Shear stirrups only in half span (SF0); (b) Half span strengthened using FRP strips (SF0-FRP); and (c) Half span strengthened using WWM (SF0-WWM) (All dimensions are in mm).

2.1.2. Strengthening schemes For the beams of Group-1, two shear strengthening schemes were employed to strengthen the half length of the beam having no shear stirrups. First scheme employed the use of FRP composite in the form of CFRP strips, whereas the second scheme involved the use of welded wire mesh. The purpose of the selection of the two

schemes was to have two different alternatives – first one being non-conventional and requiring specialized knowledge of composites and skilled labor but requiring less alterations in existing structure, whereas the second scheme (i.e. welded wire mesh) was conventional but requiring intensive labor work. Details of the adopted schemes are described below:

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Fig. 2. Specimens of Group-2: (a) Half span cast using FRC (SF1); (b) Half span of specimen SF1 having shear stirrups strengthened using full FRP U-wrap (SF1S); and (c) Half span of specimen SF1S containing FRC strengthened using FRP strips (SF1S- FRP) (All dimensions are in mm).

(i) Shear strengthening using FRP strips (SF0-FRP): This strengthening scheme, adopted in specimen SF0-FRP, consisted of near surface mounted U-wraps of CFRP strips and externally bonded horizontal CFRP strips. The CFRP laminate used was having unidirectional fibers. Two layers of CFRP Uwraps, with fibers along the depth of the beam, were provided in 25 mm wide and 25 mm deep grooves at a center to center spacing of 100 mm. The center line of the CFRP

U-wraps matched with the mirror image position of shear stirrups in the remaining half span of the beam. After the bonding of CFRP U-wraps with concrete using epoxy, the grooves were filled and levelled with Sikadur 31 thixotropic epoxy resin mortar. One layer of 50 mm wide CFRP strip with fibers along the length of the beam was provided at mid-depth of each face of the beam. The horizontal strips extended from the beam end to the mid-span of the beam

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(see Fig. 1(b)). As the CFRP U-wrap was laid in the grooves, the horizontal CFRP strips were bonded to the outside surface of concrete after drying of the CFRP U-wraps. The construction details of this scheme are shown in Fig. 3. (ii) Shear strengthening using welded-wire mesh (SF0-WWM): This strengthening scheme, adopted in specimen SF0WWM, employed near surface mounted U-shaped steel welded wire mesh of /4 mm at a spacing of 50 mm c/c both ways. The mesh was embedded in 25 mm thick (=cover thickness) Sikadur 31 thixotropic epoxy resin mortar, which extended up to the top edge of the deep beam. Thus, whole area of side faces of half-span of the beam was covered by welded wire mesh (See Fig. 1(c)). The construction details of this strengthening scheme are depicted in Fig. 4.

Boom face

(a)

Similarly, two strengthening schemes adopted for Group-2 specimens were designed to study the shear failure in FRC deep beam and FRP strengthened FRC deep beam:

Boom face

(i) Shear strengthening of the beam part having shear stirrups (SF1S): As the beam SF1 failed in shear in the beam part having web reinforcement, this part of the deep beam was retrofitted for enhancing its shear resistance using externally bonded full U-wrap of one layer of CFRP laminate. The enhancement in shear capacity of the beam required upgrading of the flexural capacity also for which two layers of CFRP strips, having fibers along the span of the beam, were externally bonded to the soffit of the beam along the full beam span (see Fig. 2(b)). The CFRP U-wrap was applied

(b) Fig. 3. Steps involved in the strengthening of beam SF0-FRP: (a) placement of vertical CFRP U-wrap strips completed; and (b) filling of grooves with Sikadur 31 thixotropic epoxy resin mortar and bonding of horizontal CFRP strips completed.

Boom face

(a) Boom face

(b) Fig. 4. Steps involved in the strengthening of beam SF0-WWM: (a) placement of the WWM after removing concrete cover; and (b) covering the WWM with the Sikadur 31 Thixotropic epoxy resin mortar completed.

No fibers

No fibers No fibers

No fibers

SF0-WWM

SF1 SF1S

SF1S-FRP

Group 2

No fibers No fibers Group 1

SF0 SF0-FRP

2L-/6@100

None Single layer of externally bonded full FRP U-wrap As above 2L-/6@100 2L-/6@100

FRC

None

2 layers of externally bonded FRP U-wrap strips (25 mm wide) at a c/c spacing of 100 mm and one layer of externally bonded horizontal FRP strip (50 mm wide) at mid-depth on each face

None 2 layers of CFRP strips externally bonded to the soffit of the beam As above None None None None

None No fibers None 2L-/6@100

FRC FRC

None None

None 2 layers of NSM FRP U-wraps (25 mm wide) at a c/c spacing of 100 mm and one layer of externally bonded horizontal FRP strip (50 mm wide) at mid-depth on each face NSM U-wrap of welded wire mesh of /4@50 mm both ways None None None None 2L-/6@100 2L-/6@100

No fibers No fibers

Shear strengthening Shear stirrups Right half span

Concrete type Shear strengthening Shear stirrups Concrete type

Left half span Specimen Class

Table 1 Summary of test specimens.

None

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Flexural strengthening

678

after bonding the longitudinal CFRP strips to concrete. The focus of this strengthening scheme was to examine the shear response of FRC deep beam. (ii) Shear strengthening using FRP strips (SF1S-FRP): This scheme of strengthening was similar to the one adopted in SF0-FRP in the part without shear stirrups with a difference that the CFRP U-wraps were externally bonded because it was not practical to cut the grooves in FRC. This strengthening was done on beam strengthened as in SF1S using externally bonded full U-wrap of single layer of CFRP laminate together with the flexural strengthening of the deep beam (see Fig. 2(c)). The purpose of this strengthening scheme was to investigate the response of FRC strengthened using FRP strips. The welded wire mesh strengthening adopted for Group-1 specimens was not considered for this Group because of the requirement of cutting concrete layer which was not feasible for the FRC. Moreover, the laying of welded wire mesh over the existing surface of FRC could have resulted in considerable increase in beam section. Table 1 summarizes the test matrix of the RC deep beams tested in this study. The vertical stirrups provided in one-half of beam length are numbered starting from the stirrup closest to the support, as shown in Fig. 1(a). As the FRP vertical strips are provided at the locations of the missing vertical stirrups, the numbering of these strips is kept same as that of the vertical stirrups (Fig. 1(b)). 2.1.3. Material properties Plain concrete used to cast the beams was designed for a target compressive strength of 65 MPa using the mix proportion given in Table 2. The same batch of concrete was mixed with steel fibers (1% by volume or 3.27% by weight) for producing FRC required for half-span of Group-2 specimens. The average compressive strength for plain and fiber reinforced concrete obtained by testing standard concrete cylinders was 68.5 MPa and 79 MPa, respectively. The properties of steel fibers employed in the production of FRC are given in Table 3. The average properties of steel rebars are given in Table 4. Table 5 provides the properties of the CFRP sheets and the properties of the bonding agents (epoxy primer and Sikadur 31 thixotropic epoxy resin mortar) adopted for strengthening deep beams. The resin based mortar was used for its desirable characteristics such as: better adhesive properties, hardening without shrinkage, and non-sag, which makes it suitable for vertical and overhead applications. 2.1.4. Instrumentations and test procedure Three-point bending configuration was adopted to test all deep beam specimens. The monotonically increasing point load was applied at the mid-span of the beam using displacement control procedure at a loading rate of 0.5 mm/min. The mid-span deflection was measured using an LVDT and the axial strains in the bottom two layers of longitudinal rebars were measured using strain gauges fixed at mid span. The strains at mid-depth of all vertical shear stirrups were also measured. The development of strains in the strengthening materials were also recorded.

3. Test results and discussion The following sections will discuss the results of the six deep beams in terms of the cracking patterns, failure modes, rebar strains, and load-displacement behavior. Figs. 5 and 6 show the failure pattern of specimens of Group-1, and Group-2, respectively.

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A. Albidah et al. / Construction and Building Materials 216 (2019) 673–686 Table 2 Mix proportions for the plain concrete mix.

Table 5 Properties of strengthening materials.

Material

Weight (kg/m3)

Item

Cement Crush sand Silica sand Coarse aggregate (Nominal size = 10 mm) Water (water-cement ratio = 0.25) Gli-110 (Super-plasticizer)

650 264 528 770 162.5 3 Liters

CFRP composite system (Tyfo SCH-41S) Type of FRP

Table 3 Properties of steel fibers. Item

Value

Type Length (mm) Diameter (mm) Aspect ratio Ultimate tensile strength (MPa)

Hooked ends 60 0.75 80 1270

Table 4 Mechanical properties of steel reinforcement. Mechanical Property

Yield strength (MPa) Ultimate strength (MPa) Modulus of elasticity (GPa)

Bar diameter

Test Standard

10 mm

6 mm

4 mm (WWM)

525 578

280 380

250 355

200

200

200

ASTM A370 (2017)

3.1. Modes of failure of deep beams 3.1.1. SF0 specimen The first flexural crack was detected in the part having no shear stirrups at 48 kN followed by another flexural crack at 57 kN. A diagonal shear crack initiated in the shear deficient portion of the beam when the load reached 80 kN and continued to widen until beam failure. Fig. 5(a) clearly shows that the controlling failure mode of the deep beam is diagonal splitting in shear deficient portion. 3.1.2. SF0-FRP specimen The flexure cracks were first detected at the load levels of 64, 70, and 85 kN in the unstrengthened part of the deep beam, whereas the first diagonal crack in the same part of the beam appeared when the load reached 95 kN. This was followed by diagonal cracks at load levels of 116 kN and 127 KN. Further load enhancement caused the development of additional minor flexural cracks and the extension of existing shear cracks. Fig. 5(b) clearly shows that the diagonal crack extending from the loading point to the right support dominated the beam behavior till failure. Although the majority of cracks formed in the unstrengthened part of the deep beam, a few minor shear cracks were also detected in the FRP strengthened part of the beam. Overall, the mode of failure of the beam was dominated by a mixed mode of shear failure characterized by diagonal splitting and shear compression in the unstrengthened part of beam. 3.1.3. SF0-WWM specimen Almost all cracks were present in the shear stirrups portion of the deep beam, whereas the strengthened side was limited to one minor flexural crack, which was initiated at 100 kN and continued to grow upward but stopped at 152 kN. The flexural cracks formed at 85 kN and 87 kN were followed by shear cracks at

Elastic modulus in primary fibers direction (GPa) Elastic modulus of transverse to primary fiber direction (MPa) Fracture strain in primary fibers direction (%) Ultimate tensile strength in primary fibers direction (MPa) Thickness per layer, tf (mm)

Value Unidirectional CFRP sheet 77.3 40.6 1.1 846 1.0

Epoxy Density (kg /l) Adhesive tensile strength (MPa) Tensile modulus of elasticity (GPa)

1.16 >4.0 (7 days) 3.5 (7 days)

Sikadur 31 Thixotropic epoxy resin mortar Density (kg /l) Adhesive tensile strength (MPa) Modulus of Elasticity (GPa)

1.65 15 4.3

107 kN and 112 kN. The existing shear crack which appeared at 112 kN started to progress upward towards the load point and downward towards the roller support at 140 kN to 145 kN. Further enhancement in load led to the development of new cracks and existing cracks also propagated while one crack became major indicating the development of strut, which led to the beam failure. Cracking behavior of the deep beam is depicted in Fig. 5(c). The diagonal splitting was observed as the dominant shear mode of failure. 3.1.4. SF1 specimen Although the cracks developed in both halves of the beam (steel fiber reinforced half without shear stirrup and the plain concrete half with web reinforcement), cracks were concentrated in the plain concrete side which eventually failed the beam. In the steel fiber side, three flexural cracks developed at load levels of 102, 107, and 112 kN, which were followed by a diagonal minor shear crack at the load level of 142 kN which later extended upward when load increased to 165 kN. In the other half of the deep beam, the first shear crack was observed at load corresponding to 102 kN. Further shear cracks initiated at the load of 142, 168, 169, and 172 kN (Fig. 6(a)). A couple of flexural cracks also appeared but the final mode of failure was characterized by the shear crack initiated at 142 kN, which continued to extend and widen along the line joining the loading point and the support until the beam failure. 3.1.5. SF1S specimen The shear cracks were detected only in the FRC part of the deep beam. The first inclined crack was detected at about 70 kN followed by another crack at 130 kN. A major diagonal crack initiated when the load reached 130 kN and with increasing load, started to progress up towards the load point and down to the support (Fig. 6 (b)). It is evident from Fig. 6(b) that this major crack governed the failure mode, which indicates the occurrence of shear diagonal splitting. No flexural cracks were detected since the beam flexural strength was enhanced by using CFRP strips externally bonded to the beam soffit. 3.1.6. SF1S-FRP specimen As the major portion of this beam was covered with the CFRP sheets and strips, the monitoring of the development of cracks was not possible. At failure, only a few shear cracks were detected in the FRC portion of the deep beam (Fig. 6(c)) indicating shear

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(a)

(b)

Fig. 5. Failure pattern of specimens of Group-1: (a) SF0; (b) SF0-FRP; and (c) SF0-WWM.

failure in this portion. The critical shear crack (CDC) debonding occurs in vertical CFRP strips which causes CDC debonding in horizontal CFRP strip also. 3.2. Load-displacement behavior and rebar/FRP strains The load-displacement curves of different specimens are plotted in Figs. 7–12. For understanding the change in behavior observed in these curves, strains in longitudinal rebars, shear stirrups, and/or FRP strips are also plotted in these figures. The numbering of shear stirrups and FRP strips mentioned in these figures is same as that indicated in Fig. 1. Among the strains recorded for the web reinforcement (shear stirrups and FRP strips), only those values are plotted that play a major role in affecting the load–displacement behavior. The levels of rebar yield strains and FRP fracture strains are also indicated in Figs. 7–12. As the shear stirrup 1 does not cross the diagonal shear crack, the strain in this stirrup was low and thus ignored in the strain plots. The discussion of indi-

vidual specimen behavior, presented in this section, also takes the help of the crack pattern, discussed above. 3.2.1. SF0 specimen The load increases almost linearly with mid-span deflection until a sudden drop in load occurred at about 85.6 kN. This corresponds to the major shear crack formation in the unreinforced side of the beam (Fig. 7). The load continued to increase until a peak load of 134.2 kN was reached. The enhancement in load was accompanied by the widening of shear crack and then there was a drop in load causing the failure of beam through the widening of crack causing separation of shear crack faces. The maximum strain in the bottom layer of longitudinal rebars reached 2440 lm/mm, which did not yield. Moreover, the maximum strain in the upper layer of longitudinal rebars was quite low (595 lm/ mm). The strains in shear stirrups in the other half span were low. The low stirrup strains are expected because the shear cracks were localized in the unreinforced portion of the beam.

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(a)

(b)

Fig. 6. Failure pattern of specimens of Group-2: (a) SF1; (b) SF1S; and (c) SF1S-FRP (CDC: Critical shear crack).

175

3000

150

2000

75

Yield strain of stirrups

1500

2500

50

1000

25

500

125

Load (kN)

100

Yield strain of flexural rebars

150

50

Load-Deflection Strain in tension rebar (lower layer) Strain in tension rebar (upper layer) Strain in stirrup 2 Strain in stirrup 3 Strain in stirrup 4

25

Yield strain of flexural rebars

100 75

26250 22500 18750 15000 11250 7500

Strain in rebars (µm/mm)

3500

30000

Peakstrain = 12%

200

125

175

Load (kN)

4000 Load-Deflection Strain in tension rebar (lower layer) Strain in tension rebar (upper layer) Strain in stirrup 2 Strain in stirrup 3 Strain in stirrup 4

Strain in rebars (µm/mm)

200

3750 Yield strain of stirrups

0

0 0

2

4

6

8 10 12 14 Mid-span deflection (mm)

16

18

Fig. 7. Load versus mid-span deflection of beam and variation of strains in longitudinal rebars and shear stirrups for specimen SF0.

0

0 0

2

4

6

8 10 12 14 16 Mid-span deflection (mm)

18

20

22

Fig. 8. Load versus mid-span deflection of beam and variation of strains in longitudinal rebars and shear stirrups for specimen SF0-FRP.

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15000

200

400 350

Load-Deflection Strain in tension rebar (lower layer) Strain in tension rebar (upper layer) Strain in stirrup 2 Strain in stirrup 3 Strain in stirrup 4

Load (kN)

125 100 75

7500

Yield strain of flexural rebars 3750

50

Yield strain of stirrups

25

0

2

4

6 8 10 12 Mid-span deflection (mm)

14

16

22500

200

15000

Load (kN)

150 Load-Deflection Strain in tension rebar (lower layer) Strain in tension rebar (upper layer) Strain in stirrup 2 Strain in stirrup 3 Strain in stirrup 4

125 100 75

11250 7500

Strain in rebars (µm/mm)

18750 175

50 3750

Yield strain of flexural rebars 25

Yield strain of stirrups 0

0 0

4

8 12 16 Mid-span deflection (mm)

20

Fig. 10. Load versus mid-span deflection of beam and variation of strains in longitudinal rebars and shear stirrups for specimen SF1.

Load-Deflection Strain in tension rebar (lower layer) Strain in tension rebar (upper layer) Strain in stirrup 2 Strain in stirrup 3 Strain in stirrup 4

200 175 150 125

4500 4000 3500 3000 2500

Yield strain of flexural rebars

2000

100 Yield strain of stirrups

75

1500

50

1000

25

500

Strain in rebars (µm/mm)

225

0

0 0

4

8 12 16 Mid-span deflection (mm)

20

Fig. 11. Load versus mid-span deflection of beam and variation of strains in longitudinal rebars and shear stirrups for specimen SF1S.

3.2.2. SF0-FRP specimen Fig. 8 clearly shows that the force was steadily increasing with the beam mid-span deflection until a load of about 154 kN was reached. At this stage, shear stirrups 3 and 4 had already yielded (at 0.76 and 0.81 Pu, respectively) and yielding of the bottom layer of flexural reinforcement occurred at 0.78 Pu (see Fig. 8). The beam continued to gain strength following this stage but with lower stiffness until peak load was achieved at 178.4 kN at which time

17500 15000 12500

200

10000

150

7500 5000

100 Yield strain of flexural rebars Yield strain of stirrups

2500 0

0

Fig. 9. Load versus mid-span deflection of beam and variation of strains in longitudinal rebars and shear stirrups for specimen SF0-WWM.

20000

Fracture strain of FRP

0

18

225

250

50

0

0

300

Load (kN)

11250

150

Strain in rebars (µm/mm)

175

Load (kN)

Load-Deflection Strain in tension rebar (lower layer) Strain in tension rebar (upper layer) Strain in flexural FRP Strain in FRP U-wrap-2 Strain in FRP horiz. strip

Strain in rebars/FRP (µm/mm)

682

4

8 12 16 Mid-span deflection (mm)

20

Fig. 12. Load versus mid-span deflection of beam and variation of strains in longitudinal rebars and shear stirrups/FRP for specimen SF1S-FRP.

strain in the main longitudinal rebar was about 0.6%. Prolonged inelastic behavior with stable strength degradation was achieved following the peak load. Although peak response was dominated by a major shear crack, significant flexural contribution is evidenced by post-peak curve. 3.2.3. SF0-WWM specimen Force versus displacement variation of the deep beam up to the peak can be categorized into three distinct zones: elastic (0– 40 kN), linear but with reduced stiffness (40–150 kN), post yield region of 150 to 185.3 kN (Fig. 9). Strain in bottom layer of flexural rebars reached the yield value at a point corresponding to 118 kN and reached its maximum value of 0.011 when the beam load was 154.5 kN. Following this loading point, strain in the flexural rebars started to reduce till 0.29% at the ultimate load of 185.3 kN. The decrease in the flexural rebar strain following the 154.5 kN load is because of the widening of shear crack. Transverse steel bars, depending on their location, experienced different levels of strains (Fig. 9) e.g. at the ultimate load, strain in shear stirrup #2 exceeded the yielding value while others did not yield. As the failure in this test specimen did not occur in the WWM-strengthened portion, the force-displacement behavior of this specimen is quite similar to Fig. 8. 3.2.4. SF1 specimen Fig. 10 shows that load-displacement response of the deep beam was elastic until 35 kN. Next loading region up to 160 kN was still linear but stiffness got reduced. Yielding of the bottom layer of longitudinal rebars was detected at 139.6 kN. At the same loading level, stirrups S3 and S4 exceeded the yielding point with strains of 0.2% and 0.17%, respectively. Beam continued to gain strength with increase in mid-span deflection until peak load was reached at 202.2 kN. The strain in the vertical shear stirrups was mainly concentrated in stirrup S3 (1%). 3.2.5. SF1S specimen Force increased steadily with the beam mid-span deflection until the peak strength was reached at 214.8 kN (Fig. 11). The flexural rebar stresses were below the yield value. Strains in the vertical stirrups was low even at the ultimate load and none of them experienced yielding because there was no failure in the deep beam portion having shear stirrups (Fig. 11). 3.2.6. SF1S-FRP specimen The force displacement behavior of this specimen (see Fig. 12) was generally increasing at almost the same rate until the peak

A. Albidah et al. / Construction and Building Materials 216 (2019) 673–686

point at 339 kN. The strain in the flexural FRP strip was well below the fracture strain. Yielding of the bottom longitudinal rebar was recorded at 202.6 kN. Strain in the bar continued to increase until reached its maximum value at the peak (1.3%). The strain in vertical U-wrap was more than that in the horizontal FRP strip provided at mid-depth.

However, the use of steel web reinforcement in RC deep beams alters the strut-and-tie model through the development of the horizontal and vertical mechanisms of truss elements [28]. Following the approach adopted by Matamoros and Wong [28], the ultimate shear strength of RC deep beam with web reinforcement can be estimated from:

V u ¼ V strut þ V sv þ V sh þ V f v þ V fh

4. Effectiveness of strengthening schemes Table 6 summarizes the ultimate load of the tested deep beams. For Group-1 specimens wherein no fibers were used, the shear resistance offered by the steel web reinforcement alone is 33% of concrete including dowel action. The two strengthening schemes employed for this group of specimens were helpful in avoiding shear failure of RC deep beams in the strengthened portion and thus the shear failure got shifted to the other half span of the deep beam. Thus, the shear capacity of the strengthening schemes adopted in the study is higher than the shear strength of steel web reinforcement. For Group-2 specimens having FRC in half span, the shear capacity of FRC deep beam with no web reinforcement also exceeds the shear strength of beam having steel web reinforcement. The shear capacity of FRC alone without steel web reinforcement is 20% higher than the shear capacity of deep beam having steel web reinforcement (SF0) due to which the failure did not occur in the FRC portion in the specimen SF1. The enhancement in shear resistance due to the addition of hooked steel fibers in concrete is 60% of the shear resistance of plain concrete (i.e. without steel fibers) with dowel action of the longitudinal rebars. The shear strengthening of FRC using CFRP strips enhanced the shear resistance of FRC by 58%. Although strengthening procedures adopted in SF1S-FRP significantly improved the peak shear strength, it resulted in insignificant enhancement in displacement capacity of the deep beam. 5. Prediction of shear strength of deep beams The basic assumptions of the theory of bending not being applicable for the RC deep beams, strut-and-tie modeling was adopted to estimate the ultimate shear strength of the RC deep beams. The modeling assumes to represent the deep beam behavior at failure by hypothetical pin-jointed truss with the struts joining the roller support and the loading point. The longitudinal rebars are assumed to act as a tie. The truss action and the development of strut is apparent in the failure of RC deep beam, SF0, having no web reinforcement (Fig. 5(a)). As the bearing failure (at the roller supports and under the load) and anchorage failure were prevented, the ultimate shear strength of deep beam with no web reinforcement can be assessed from the compressive strut force.

683

ð1Þ

where Vstrut is the shear strength provided by concrete diagonal strut of RC deep beam having no web reinforcement; Vsh and Vsv are respectively, the shear strength contributions of horizontal and vertical web reinforcements; Vfh and Vfv are respectively, the shear strength contributions of horizontal and vertical FRP web reinforcement. These contributions of horizontal and vertical steel/FRP web reinforcements arise from the horizontal and vertical mechanisms of truss elements [28]. The shear resistance offered by different components of the truss can be estimated from the following equations:

V strut ¼ C e f ce bw wstrut V sv ¼ Asv f sv ¼ qsv bw

ð2Þ
a 3

f sv

V sh ¼ Ash f sh tanhs ¼ qsh bw

Vfv ¼

m1 X

  d f tanhs 3 sh

ð3Þ ð4Þ

Af v ;i f f v ;i

ð5Þ

Afh;i f fh;i tanhs

ð6Þ

i¼1

V fh ¼

m2 X i¼1

where fce is the effective compressive strength of concrete 0 (=0:85bs f c ); bs is a factor to account for the effect of cracking and confining reinforcement on the effective compressive strength of 0 the concrete in the strut [13]; f c is the cylinder compressive strength of concrete; hs is the angle between the concrete strut and the longitudinal axis of the beam (=tan1 ðd=aÞ); a is the shear span; d is the effective depth of the RC deep beam; Asv and Ash are respectively the areas of cross-section of the vertical and horizontal web reinforcement in the effective web areas, which are taken as a/3 along the shear span and d/3 along the depth of the beam, as indicated in Fig. 13 [28]; bw is the width of the beam web; qsv and qsh are respectively the reinforcement ratios for vertical and horizontal web reinforcement; f sv and f sh are respectively the yield stresses of vertical and horizontal web reinforcement; Af v ;i and Afh;i are respectively the cross-sectional areas of the ith vertical and horizontal FRP strips in the effective web area (Fig. 13); m1

Table 6 Experimental test results of shear strength of different beam parts of control and strengthened beams. Description of beam part (half span)
Beam part with no web reinforcement
Beam part having web reinforcement
Beam part with no web reinforcement but strengthened using FRP strips
Beam part with no web reinforcement but strengthened using WWM
FRC beam part with no web reinforcement
FRC beam part with no web reinforcement but strengthened using FRP strips *

Shear strength* (kN)

Remark

67.1 (SF0) 89.2 (SF0-FRP) –

–

Failure did not occur in this portion

–

Failure did not occur in this portion

107.4 (SF1S) 169.5 (SF1S-FRP)

20% enhancement as compared to steel web reinforcement and 60% enhancement as compared to SF0 58% enhancement as compared to SF1

33% enhancement as compared to SF0

Beam ID within brackets is the beam whose test results are reported because the failure occurred in the portion described in first column.

684

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Fig. 13. Strut-and-tie model for RC deep beam having: (a) steel web reinforcement; (b) FRP strengthening.

and m2 are respectively the number of vertical and horizontal FRP strips in the effective web area; f f v ;i and f fh;i are respectively the tensile stress of the ith vertical and horizontal FRP web strips corresponding to the available anchorage length; Ce is the concrete efficiency factor, given by [29]:

 0 1=3 C e ¼ k1 f c

ð7Þ

where, k1 ¼ ð1:8  38 e1 Þ, its value should neither less than 0.85 and nor greater than 1.6; e1 is the principal tensile strain of concrete  0.00008 [30]. The upper limit for the values of k1 was a design cutoff [29] and thus it was not used. The areas of vertical and horizontal FRP strips, Af v ;i and Afh;i , are calculated using:

  Af v ;i or Afh;i ¼ 2 n tf wf

ð8Þ

where n is the number of layers of FRP used in vertical/horizontal strips; t f is the thickness of FRP layer; and wf is the width of vertical/horizontal FRP strip. The accurate determination of the geometry of the struts is usually difficult. However, the struts may be assumed to be prismatic with uniform area of cross-section. The assessment of the width of strut is also difficult for the current study due to the use of two layers of longitudinal rebars and negligibly small width of contact at supports/load (due to the use of roller for support and applying load). In the absence of the width of support and contact width of load, the following formula has been used for the calculation of strut width [13,30]:

wstrut ¼ kd cos hs where,

k ¼ nq þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðnqÞ2 þ 2nq

ð9Þ

ð10Þ

where n is the modular ratio (=Es/Ec); Es and Ec are the moduli of qffiffiffiffi 0 elasticity of steel rebars and concrete respectively (Ec ¼ 4700 f c ; Units: MPa); q is the longitudinal reinforcement ratio. The stresses developed in ith vertical and horizontal FRP strips, f f v ;i and f fh;i , are calculated from the available anchorage length as a proportion of the development length, ldf , required for the development of stress in the FRP strips [31]:

vffiffiffiffiffiffiffiffiffiffiffiffiffi un E t u f f ldf ¼ t qffiffiffiffi 0 fc

ð11Þ

where Ef is the modulus of elasticity of FRP. The above formulation has been used for the prediction of the shear strength of RC deep beams. For the beam with steel web reinforcement, Asv was calculated based on only one vertical stirrup which lies in the effective area (Fig. 13). Similarly, for the beam with FRP web reinforcement, m1 was taken as 1 to represent one vertical U-wrap that lie within the effective web area. Because of only one horizontal web rebar on each face, Ash was obviously the area of these bars thus reinforcement ratios qsh was not required. Similarly, because of the use of only one horizontal FRP strip on each face, m2 was equal to 1. However, for the welded wire mesh, the calculation of V sv and V sh was based on the reinforce0 ment ratios, qsv and qsh . The strength of repair mortar, f cm (=60 MPa for the repair mortar used in this study), used for the installation of welded wire mesh being different from the strength of concrete used for the casting of beam (=68.5 MPa for the concrete used in casting of beams of this study), the compressive strength of strut was calculated using the following equations:

V strut ¼ C ew wstrut f cew bw

ð12Þ

where f cew is the effective compressive strength of repaired section 0 0 (=0:85bs f cw );f cw is the equivalent compressive strength of the repaired beam section (=64.3 MPa for the repaired section of this study) calculated using Eq. (13): 0

f cw ¼

0

0

f c bwp þ f cm bwm b

ð13Þ

where bwp and bwm are the beam widths of parent concrete (=50 mm for SF0-WWM) and repair mortar (=50 mm for SF0-WWM), respectively. The concrete efficiency factor of the repaired beam section 0 0 Cew was calculated using Eq. (7) by replacing f c with f cw . The ultimate shear strength of FRC deep beam with web reinforcement is also calculated using Eq. (1) but the shear strength of diagonal strut of concrete deep beam V strut is replaced by shear strength of diagonal strut of FRC deep beam V fstrut , which is calculated in proportion to the enhancement in split tensile strength of concrete due to the addition of steel fibers:

V fstrut ¼ V strut

f ctf f ct

ð14Þ

where, f ct and f ctf are the split tensile strengths of plain and fiber reinforced concrete respectively; f ct is calculated using ACI 318-

*Beam ID within brackets is the beam for which the experimental value is reported. **value is not reported when failure did not occur in the portion described in column 1 and average value is reported when failure in the portion described in column 1 occurred in more than one test specimens. ***ratio of split tensile strength of FRC to plain concrete calculated using Eqs. (15) and (16).

1.04 0.93 111.6 157.5 – 14.9 – 30.9 Beam with no web reinforcement but having steel fibers (SF1S) Beam with no web reinforcement but having steel fibers and strengthened using externally bonded FRP U-wraps and horizontal FRP strips (SF1S-FRP)

– 4.1 17.8 72.0 0.45 –

Concrete having steel fibers (FRC) fctf /fct = 1.5*** 107.4 – 1.5  74.2 = 111.6 169.5 – 111.6

74.2 97.7 113.7 > 91.0 (OK) 94.0 > 91.0 (OK) – 7.6 14.9 74.2 74.2 74.2 0.44 0.44 0.44 67.1 (89.2 + 92.7)/2 = 91.0 –

Beam with no web reinforcement (SF0) Beam with steel web reinforcement (SF0-FRP, SF0-WWM) Beam with no web reinforcement but strengthened using NSM FRP U-wraps and externally bonded horizontal FRP strips Beam strengthened using welded wire mesh U-wrap

(1)

Eq. (7) Eqs. (2)/(15) (2) (3) (4) Concrete with no steel fibers (Plain concrete)

– 15.8 24.6

(4) + (5) + (6)

1.11 1.07 –

pred/ Vu,exp

Horizontal web reinforcement, V sv orV fh Eqs. (4) and (6) (6) Vertical web reinforcement, V sv orV f v Eqs. (3) and (5) (5) Strut,V strut

Experimental value of shear strength**, Vu,exp (kN) Description of the portion of beam for which calculations are made*

Table 7 Shear strength prediction for different beam parts of control and strengthened beams.

Concrete efficiency factor, Ce

Shear resistance (kN) provided by

Predicted shear strength, Vu,pred

Vu,

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685

14 [13], whereas f ctf is calculated as per Ref. [32] after simplifying for hooked end steel fibers.

qffiffiffiffi 0 f ct ¼ 0:56 f c ðUnits : MPaÞ f ctf ¼ f ct þ 2:92 v f

lf df

ð15Þ ð16Þ

where, vf is the volume fraction of steel fibers, lf and df are the length and diameter of hooked end steel fibers. The strength of FRC being more than the strength of concrete, the development length of FRP strips for the development of stress in the FRP strips, calculated using Eq. (11), also gets reduced. Table 7 provides the details of intermediate calculations in the estimation of the shear strength of RC deep beams tested in the present study using the above equations. The shear strength of beam with steel web reinforcement is taken as the average of the ultimate load of SF0-FRP and SF0-WWM because of the failure of both these beams occurred in the portion having steel web reinforcement. The ratio of experimental to the predicted shear strength of deep beam, given in the last column the table, shows that its value varies from 0.93 to 1.11. This is indicative of the close prediction for all cases (Table 7). 6. Conclusions The following major conclusions are drawn from this study: i) The strengthening schemes adopted in the study (FRP strips and welded wire mesh) were successful in improving the shear strength of the RC deep beams to a level greater than the shear strength of deep beam with steel web reinforcement. ii) The addition of 1% of hooked steel fibers (by volume) in concrete makes the concrete stronger in shear than that of plain concrete with steel web reinforcement. This demonstrates the excellent shear resistance contribution of steel fibers in deep beam. iii) Although the FRP strengthening improves the shear strength of FRC deep beams, the enhancement in deformation capacity is not significant. iv) A unified methodology is proposed for predicting the shear strength of reinforced concrete and FRC deep beams strengthened using FRP strips and welded wire mesh. The equations are based on the modified strut-and-tie model by incorporating the horizontal and vertical mechanisms of truss elements (Matamoros and Wong, 2003). The prediction of shear strength for the concrete and FRC beams tested in the present study shows low errors in the prediction. Declaration of Competing Interest None. Acknowledgement The authors are grateful to the Deanship of Scientific Research, King Saud University, for funding through Vice Deanship of Scientific Research Chairs. References [1] D. Baggio, K. Soudki, M. Noel, Strengthening of shear critical RC beams with various FRP systems, Constr. Build. Mater. 15 (66) (2014) 634–644. [2] V. Colotti, Mechanical shear strength model for reinforced concrete beams strengthened with FRP materials, Constr. Build. Mater. 15 (124) (2016) 855– 865.

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