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Tests of reinforced concrete beams strengthened with wire rope units
Engineering Structures 29 (2007) 2711–2722 www.elsevier.com/locate/engstruct
Tests of reinforced concrete beams strengthened with wire rope units S.Y. Kim a , K.H. Yang b,∗ , H.Y. Byun c , A.F. Ashour d a Institute of BIO Housing, Chonnam National University, Gwangju, South Korea b Department of Architectural Engineering, Mokpo National University, Mokpo, Jeonnam, South Korea c Korea Engineering & Consultant, Inc., Hwasun, Jeonnam, South Korea d EDT1, School of Engineering, Design and Technology, University of Bradford, Bradford, BD7 1DP, UK
Received 20 September 2006; received in revised form 13 December 2006; accepted 17 December 2006 Available online 6 March 2007
Abstract This paper presents a simple unbonded-type shear strengthening procedure for reinforced concrete structures with wire rope units. Fifteen beams were tested to failure in shear, repaired, strengthened using the proposed wire rope units, and then retested. The main variables investigated were the shear span-to-depth ratio, and the prestressing force, orientation and spacing of wire rope units. The shear strength of beams strengthened with wire rope units increased relative to that of the corresponding original beams. Reinforced concrete beams strengthened with inclined wire rope units exhibited higher shear strength than those with vertical wire rope units. It was also observed that the higher the initial prestressing force in the wire rope units, the higher the shear strength gained. The principal tensile stress in concrete decreases with the increase of the prestressing force in wire rope, as a result, the diagonal tensile cracking strength of strengthened beams was higher than that of the corresponding original beams. The validity of using ACI 318-05 and EC 2 shear provisions to predict the shear capacity of strengthened beams was examined. The shear capacity of strengthened beams having shear span-to-depth ratios below 2.5 is reasonably predicted using the ACI 318-05 formula. On the other hand, EC 2 overestimates the shear transfer capacity of wire rope units for beams having shear span-to-depth ratios above 2.5. c 2007 Elsevier Ltd. All rights reserved.
Keywords: Repair; Strengthening; Wire rope; Shear capacity
1. Introduction With a growing interest in restoration of concrete structures, several investigations [1–8] were conducted on shear strengthening of reinforced concrete beams by externally bonding steel plates or high strength non-metallic fibre laminates to concrete surfaces. Although this technique proved to be effective in enhancing shear strength of reinforced concrete beams, it has several shortcomings, such as debonding of external laminates from concrete surfaces due to interface shear stress concentration at the laminate end and the long term behavior of the system which may be affected by different coefficients of linear expansion of concrete and nonmetallic fibre laminates. Externally bonded laminates would also constitute an obstacle for inspection of strengthened
∗ Corresponding author. Tel.: +82 61 450 2456; fax: +82 61 450 6454.
E-mail address: [email protected] (K.H. Yang). c 2007 Elsevier Ltd. All rights reserved. 0141-0296/$ - see front matter doi:10.1016/j.engstruct.2006.12.013
regions in beams. In addition, fibres and adhesive would cause noxious fumes in fire. On the other hand, very few [9], if any, tests of predamaged reinforced concrete beams retrofitted with externally unbonded-type strengthening techniques were published. Teng et al. [9] carried out tests on deep beams strengthened with external steel clamping units and concluded that the externally unbonded-type shear strengthening method has a highly economical, environmental and structural efficiency. The present investigation reports the testing of reinforced concrete beams strengthened with externally unbonded wire rope units. Fifteen beams failed in shear were repaired and strengthened with wire rope units, and then retested to failure. The main variables investigated were shear span-to-depth ratio, and the prestressing force, orientation and spacing of wire rope units. In addition, shear capacity of strengthened beams is compared with that of the original beams and predictions by ACI 31805 [10] and EC 2 [11].
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2. Description of wire rope units Notation Ast Aw a av a/d bw d db C Rd Fi f f c0 fi f hi f vi f su f sw h j k k1 lp N sw T Tw Vc Vn Vw v ws wt α α1 β βd ρ ρw σ1 νe φ
area of longitudinal bottom reinforcement total area of four legs of a wire rope shear span clear shear span shear span-to-depth ratio section width effective section depth bolt diameter empirical coefficient in shear transfer capacity of concrete of EC 2 total initial tensile force in a wire rope unit flexural stress of concrete due to applied load cylinder compressive strength of concrete prestress of wire ropes initial horizontal stress normal to beam section due to prestress of wire rope initial vertical stress normal to beam longitudinal axis due to prestress of wire rope tensile strength of wire rope stress of wire rope after the occurrence of a diagonal tensile crack overall section depth ratio of the distance between top and bottom chords to effective section depth torque coefficient scale factor to allow size effect in EC 2 support width tensile force acting in bolt due to torque spacing of wire rope unit quantity of torque applied to bolt total resultant force in wire rope units after the occurrence of a diagonal tensile crack shear transfer capacity of concrete ultimate shear strength shear transfer capacity of wire rope units shear stress of concrete due to applied load concrete strut width in strut-and-tie model depth of bottom node in strut-and-tie model angle of a diagonal tensile crack to beam longitudinal axis angle of concrete strut with the beams longitudinal axis in deep beams in strut-and-tie model angle of wire rope arranged beam longitudinal axis coefficient to allow shear enhancement of deep beams in EC 2 longitudinal bottom reinforcement ratio wire rope unit ratio principal tensile stress in concrete struts effectiveness factor of concrete angle between web reinforcement and concrete strut in strut-and-tie model
Wire ropes, which play an important role in various offshore and onshore applications, have many advantages such as light weight, high-strength, and high flexibility. In the present investigation, the significance and shortcomings of using the wire rope technique as external shear reinforcement in concrete beams are explored. Fig. 1 shows the details of an externally unbonded-type wire rope unit for shear strengthening of reinforced concrete beams. A wire rope unit is comprised of an I-shaped steel plate, four legs of wire rope, four sets of eye-bolts and nuts, two angles, and two corner beads. The Ishaped steel plate of 20 mm thickness and 60 mm web width, having four holes for eye-bolts, is installed at the top surface of beams. U-typed wire ropes with spacing of 60 mm are coupled to the eye-bolts passing through the holes of the steel plate and prestressed by tightening of nuts, similar to the torque control method of high-strength bolts. Angles and corner beads having 3 mm thickness are positioned at beam corners to prevent bearing failure due to the high compression exerted by the wire ropes. The wire rope units are attached to concrete beams due to prestressing force of wire ropes obtained from tightening of nuts. In the case of flanged beams, a hole through the flange should be provided to install the wire rope units. When a reinforced concrete beam strengthened with wire rope units is loaded, they act as external stirrups to control diagonal tensile cracks and transfer shear force. 2.1. Torque–tensile force relationship In the developed wire rope units, the prestressing tensile effect is exerted on wire ropes by tensile forces in eye-bolts owing to tightening of nuts which can be controlled by the externally applied torque. If the friction coefficient is assumed to be constant, the relation between the externally applied torque T and tensile force N acting on a bolt can be written as follows [12]: T = kdb N
(1)
where db = bolt diameter, and k = a torque coefficient dependent on the friction coefficient and geometrical conditions of thread in bolts and nuts. To evaluate the torque coefficient of the proposed wire rope unit, forty specimens composed of eye-bolt, nut and wire rope with load cell were tested as shown in Fig. 2. The test results of the torque and tensile force relationship are also presented in Fig. 2. It indicates that the tensile force transferred to wire ropes linearly increased with the increase of torque as proposed by Eq. (1). From Fig. 2, a high correlation coefficient R 2 of 0.931 is achieved, therefore, the torque coefficient k in the developed wire rope unit can be reasonably assumed as 0.3. 3. Experimental investigation 3.1. Test specimen details Fifteen beams were tested to failure, repaired, strengthened, and then retested. Details of geometrical dimensions and wire
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Fig. 1. Details of developed wire rope units and strengthening procedure. (All dimensions are in mm.)
Fig. 2. Relation of N and T /db in a wire rope unit.
rope units arranged in test specimens are given in Table 1 and Fig. 3: Fig. 3(a) for original beams for the first test, Fig. 3(b) for vertically strengthened beams previously failed in shear, Fig. 3(c) for diagonally strengthened beams previously failed in shear. Shear span-to-depth ratios, a/d, were selected as 1.5, 2.5, and 3.25. In each shear span-to-depth ratio, two different orientations of wire rope units were examined, one of which was external vertical-type stirrups and the other was external 45◦ inclined-type stirrups. For beams having shear span-todepth ratio of 1.5, the spacing and total initial tensile force owing to prestressing were 150 mm and 46.4 kN, respectively. For beams having a shear span-to-depth ratio of 2.5, the effect of varying the total initial tensile force of the wire rope unit on the strengthened beam behavior was investigated as given in Table 1, whereas the spacing of the wire rope unit was kept constant at 150 mm. For beams having a shear span-to-depth ratio of 3.25, the spacing of wire rope units were 100 mm, 150 mm, and 200 mm, while the total initial tensile force of each
wire rope unit was 46.4 kN. In each shear span-to-depth ratio, a repaired beam without wire rope units was also tested to failure to assess the contribution of wire rope units to the beam shear capacity. For strengthening purposes, only three wire rope units, regardless of the shear span-to-depth ratio, were arranged in the region of diagonal tensile cracks of previously tested and failed beams. Gaps between steel plates and beams strengthened with inclined wire rope units were filled with cementitious mortar having compressive strength of 55 MPa. All test specimens had the same section size, distance between two-point concentrated top loads, and concrete design strength as follows: the width bw and overall depth h of beam section were 200 mm and 400 mm, respectively, the distance between two-point concentrated top loads was 360 mm, which was the same as the effective section depth d, and design concrete strength was 21 MPa. The concrete compressive strength of test specimens was designed to be low to simulate existing deteriorated concrete buildings. Three longitudinal reinforcing bars of 22 mm diameter, continuous over the full length of the beam and anchored outside the support by 90◦ hook according to ACI 318-05, were used as bottom reinforcement as shown in Fig. 3, which makes the longitudinal bottom reinforcement ratio, ρ = As /bw d = 0.016, where As = the longitudinal reinforcement area. The spans of test specimens were 1440 mm, 2160 mm, and 2700 mm for beams having shear span-to-depth ratios of 1.5, 2.5, and 3.25, respectively. It is also to be noted that all beams tested did not have any internal transverse reinforcement. Although concrete beams reinforced with internal transverse reinforcement would have more cracks at failure, such transverse reinforcement would have little effect on the shear behaviour of beams strengthened with the current technique as shear strength of unstrengthened beams is governed by a major diagonal crack
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(a) Original beams (for the first test).
(b) Vertically strengthened beams (for the second test).
(c) Diagonally strengthened beams (for the second test). Fig. 3. Specimen details and arrangement of wire rope units. (All dimensions are in mm.)
in their web together with yielding of internal transverse reinforcement. 3.2. Material properties The ingredients of ready-mixed concrete were ordinary Portland cement, irregular gravel of maximum size of 25 mm, and sand. Control specimens which were 100 mm diameter × 200 mm high cylinders were cast and cured simultaneously with the beams to determine the compressive strength of concrete. The results of concrete compressive strength of the cylinders are given in Table 1. Fig. 4 and Table 2 show the stress–strain relationships and mechanical properties of internal reinforcement, wire rope, steel plate, and eye-bolt used in the present study. The wire rope used consists of six strands laid helically over a smaller independent wire rope central core (IWRC). The wire rope does not exhibit a yield plateau as shown in Fig. 4. The effective elastic modulus of wire rope used in beam strengthening was 120 GPa, which was 60% of the elastic modulus of steel, as pointed out by Raoof and Kraincanic [13].
Fig. 4. Stress–strain relationships of steel and wire rope.
3.3. Test procedure All beams were tested under two-point concentrated top loads with loading rate of 5 kN/min using a 3000 kN capacity UTM. The beam surface was white washed to aid in the
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S.Y. Kim et al. / Engineering Structures 29 (2007) 2711–2722 Table 1 Details of test specimens Beam no.
f c0 (MPa)
1 2 3
24.5 24.5 22.5
4 5 6 7 8 9 10
24.7 24.7 24.5 24.1 22.5 22.5 20.6
11 12 13 14 15
24.7 24.5 22.5 24.8 20.6
a/d
1.5
2.5
3.25
a (mm)
540
900
1170
L (mm)
Details of wire rope unit Configuration sw (mm)
Fi (kN)
T (N m)
f i / f pu
ρw – 0.00064 0.0009
Only repair Vertical 45◦ Inclined
–
–
–
–
1440
150
46.4
35
0.53
–
–
2160
Only repair Vertical 45◦ Inclined Vertical 45◦ Inclined Vertical 45◦ Inclined Only repair Vertical 45◦ Inclined Vertical Vertical
–
2700
150
33.2
25
0.38
46.4
35
0.53
60
45
0.69
–
–
–
35
0.53
26 52
0.4 0.8
150 100 200
–
46.4
– 0.00064 0.0009 0.00064 0.0009 0.00064 0.0009 – 0.00064 0.0009 0.00096 0.00048
Note: f c0 = cylinder compressive strength, a/d = shear span-to-effective depth ratio, a = shear span, d = effective section depth, L = beam length between supports, sw = spacing of wire rope units, Fi = total initial tensile force of a wire rope unit, T = initial torque value applied in eye-bolt, f i = prestress applied in 4Aw1 (sin β+cos β) ), Aw1 = net area of single leg of wire rope, β = angle of wire wire rope, f pu = tensile strength of wire rope, ρw = ratio of wire rope unit (= bw sw rope arranged to the longitudinal beam axis, and bw = beam width. Table 2 Mechanical properties of reinforcement, steel plate, eye-bolt, and wire rope Type
f y (MPa)
εy
f su (MPa)
E s (GPa)
Reinforcement (22 mm) Steel plate Eye-bolt (10 mm) Wire rope (4.8 mm)
445 307 355 –
0.00244 0.00157 0.00187 –
620 448 465 2145
182 195 190 120
observation of crack development during testing. After each load increment, the load was kept constant while cracks were marked and photographed. At the same time, deflection was recorded by a 50 mm capacity linear variable differential transducer (LVDT) mounted at mid-span bottom face. Once beam failure occurred, the applied load was removed, all cracks and failure planes were repaired by injection of epoxy resin, and then the shear-span regions with diagonal tensile cracks were strengthened using three wire rope units. Retesting was then started under the same loading condition until the repaired or strengthened beam failed again. All test data were captured by a data logger and automatically stored. 4. Test results and discussions 4.1. Crack propagation and failure modes Typical crack propagation for original beams tested at different applied loads according to the variation of shear spanto-overall depth ratio is shown in Fig. 5. A symmetrical crack pattern was observed for both shear spans before failure. The first crack in all original beams always occurred vertically at a load of nearly 20%–30% of the ultimate load in the maximum moment region as given in Table 3. All original beams failed in shear. Beams having a/d = 1.5 failed along diagonal cracks joining the edges of load and support plates, which was very similar to the crack propagation of deep beams [14],
as depicted in Fig. 5(a). On the other hand, beams having a/d = 2.5 or a/d = 3.25 failed along diagonal cracks running downward from the loading point at nearly 30◦ –45◦ with the beam longitudinal axis as shown in Fig. 5(b) or (c). At failure, bond splitting cracks along longitudinal reinforcement were also observed in several beams tested having a/d = 3.25. The shear forces at which the first diagonal crack and failure occurred are given in Table 3. Fig. 6 shows the crack propagation for only repaired or repaired and strengthened beams tested for the second time. On each beam crack pattern, the failure plane of the original beam tested is also indicated using a ‘+’ mark line type. For beams repaired only, fewer cracks occurred compared with the original beams and the failure planes were very similar to those of the original beams as shown in Fig. 6(a), (d) and (k). While, for beams repaired and strengthened with wire rope units, many new flexural and diagonal tensile cracks appeared in the regions beyond the repaired crack regions, indicating a better crack distribution controlled by wire rope units. Failure planes of several strengthened beams were also different from those of the original beams as shown in Fig. 6(c), (e), (i), (j), (l), (n), and (o). For strengthened beams having a/d = 3.25, bond splitting cracks along the longitudinal reinforcement together with diagonal tensile cracks at failure appeared, which is similar to the failure mode of the original beams, indicating that the three wire rope units used could not fully cover the failure planes. 4.2. Mid-span deflection Mid-span deflections of different beams tested against the total applied load are shown in Fig. 7: Fig. 7(a) for beams having a/d = 1.5, Fig. 7(b) for beams having a/d = 2.5, and Fig. 7(c) for beams having a/d = 3.25. The deflections of original beams having the same shear span-to-depth ratio
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(a) a/ h = 1.5.
(b) a/ h = 2.5.
(c) a/ h = 3.25. Fig. 5. Typical crack patterns and failure of original beams. (Numbers indicate the total load in kN at which crack occurred.) Table 3 Details of test results and predictions Beam no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Original beams
After repair and strengthening
Experiments (kN) Vfl Vcr Vn
Experiments (kN) Vcr Vn Vw
63.3 64.1 62.6 28.4 33.3 39.2 33.3 34.3 34.4 37.2 25.8 26.5 28.9 26.0 23.1
100.5 102.9 99.9 89.2 81.1 80.3 85.7 80.8 76.9 70.9 70.8 75.9 70.7 75.1 67.6
163.0 152.5 149.5 90.4 83.3 82.3 87.9 81.0 76.9 72.0 71.1 76.8 71.8 76.7 70.5
87.5 137.0 107.0 79.0 96.0 91.5 95.0 99.0 85.2 106.0 64.2 82.0 70.0 90.3 66.5
135.5 234.3 259.0 80.0 118.5 129.7 125.5 131.0 133.1 138.2 64.1 90.0 93.5 100.1 82.8
– 98.8 123.5 – 30 42 45.5 51 53.1 58 – 26 29.5 36 18.8
Vw Vn
– 0.422 0.477 – 0.273 0.344 0.363 0.389 0.399 0.420 – 0.289 0.316 0.360 0.227
Predictions for Vn (kN) ACI EC 2
(Vcr ) S (Vcr ) F
First
Second
First
Second
149.0 149.0 136.8 65.1 65.1 64.9 64.4 62.5 62.5 60.2 63.3 63.1 60.7 63.4 58.4
149.0 192.7 198.6 65.1 108.8 126.7 108.1 124.3 106.2 121.9 63.3 106.8 153.3 128.9 91.1
100.3 100.3 97.5 75.5 75.5 75.3 74.8 73.2 73.2 71.0 75.5 75.3 73.2 75.6 71.0
100.3 181.3 212.0 75.5 199.9 251.3 155.8 187.6 135.4 159.0 75.5 156.2 244.9 256.2 101.1
0.871 1.331 1.071 0.886 1.184 1.139 1.109 1.225 1.108 1.495 0.907 1.080 0.990 1.202 0.984
(Vn ) S (Vn ) F
0.831 1.541 1.732 0.885 1.321 1.482 1.428 1.617 1.731 1.917 0.900 1.172 1.302 1.304 1.174
(Vn ) EC2 (Vn )Exp.
(Vn )ACI (Vn )Exp.
First
Second
First
Second
0.914 0.980 0.915 0.721 0.782 0.789 0.733 0.772 0.813 0.836 0.891 0.822 0.846 0.827 0.828
1.100 0.822 0.767 0.814 0.989 1.038 0.861 0.949 0.798 0.884 0.989 1.186 1.640 1.289 1.100
0.616 0.660 0.652 0.835 0.906 0.914 0.852 0.903 0.951 0.987 1.061 0.980 1.019 0.985 1.008
0.741 0.774 0.819 0.943 1.817 2.059 1.241 1.432 1.017 1.152 1.179 1.736 2.619 2.562 1.222
Note: V f l = shear force at first flexural crack, Vcr = shear force at first diagonal crack, Vn = ultimate shear strength, and Vw = shear transfer capacity of wire rope units. Subscripts F and S mean the first test results for original beams and the second test results for repaired or strengthened beams, respectively.
against the total applied load were very similar, therefore, the deflection results of beams 1, 4, and 11 in Fig. 7 are used as representative samples for original beams having a/d = 1.5, 2.5, and 3.25, respectively. The initial stiffness of repaired or strengthened beams until the occurrence of the first diagonal tensile crack of beams was nearly similar to that of the original beams. After the first diagonal tensile crack appeared, the deflection of strengthened beams having a/d = 2.5 or a/d = 3.25 sharply increased, but the load capacity of such beams also greatly increased compared with that of the corresponding original beams. Even the post-failure deformation of the beams strengthened with wire rope units was significantly different from that of the original or only repaired beams. Beams strengthened with wire rope units exhibited a slow release of energy at 60%–80% of the load capacity, whereas the original
and only repaired beams showed sudden, brittle disintegration after reaching the peak load capacity. 4.3. Ultimate shear strength Ultimate shear strength of original and strengthened beams is given in Table 3. Fig. 8 shows the ratio of ultimate shear strength of repaired or repaired and strengthened beams (Vn ) S to that of original beams (Vn ) F : Fig. 8(a) for different orientations of wire rope units, Fig. 8(b) for different initial tensile forces of wire rope units in beams having a/d = 2.5, and Fig. 8(c) for different spacings of wire rope units in beams having a/d = 3.25. The ultimate shear strength of beams only repaired by injection of epoxy resin had approximately 80% of that of the corresponding original beams, regardless of the
S.Y. Kim et al. / Engineering Structures 29 (2007) 2711–2722
(a) Beam 1.
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(b) Beam 2.
(c) Beam 3.
(d) Beam 4.
(e) Beam 5.
(f) Beam 6.
(g) Beam 7.
(h) Beam 8. Fig. 6. Crack patterns and failure of repaired or repaired and strengthened beams. (+++ indicates the failure plane of original beams.) (Numbers mean the total load in kN at which cracks occurred.)
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(i) Beam 9.
(j) Beam 10.
(k) Beam 11.
(l) Beam 12.
(m) Beam 13.
(n) Beam 14.
(o) Beam 15. Fig. 6. (continued)
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(a) Only repair and arrangement of wire rope unit.
(a) a/ h = 1.5.
(b) Initial tensile force in wire rope unit (a/ h = 2.5).
(b) a/ h = 2.5.
(c) Spacing of vertical wire rope unit (a/ h = 3.25). Fig. 8. Effect of different parameters on shear strength gained.
(c) a/ h = 3.25. Fig. 7. Mid-span deflection against total load.
shear span-to-depth ratio. While, the ultimate shear strength of beams strengthened with wire rope units increased relative to that of the corresponding original beam; the smaller the shear span-to-depth ratio, the higher the shear strength gained. Also, beams strengthened with inclined wire rope units exhibited higher shear strength than those strengthened with vertical wire rope units. The prestressing force in wire ropes also had a significant influence on the increase of shear strength of
strengthened beams; the larger the initial tensile force in wire rope units, the higher the increasing ratio of shear strength as shown in Fig. 8(b). For strengthened beams having a/d = 3.25, the spacing of wire rope unit had little influence on the enhancement of shear strength (see Fig. 8(c)) as the three wire rope units used failed to fully cover the failure planes as shown in Fig. 6(n)–(o). The shear strength of beam 14 strengthened with 100 mm spacing wire rope units was 1.3 times higher than that of the corresponding original beam as the diagonal failure plane occurred within the strengthened region as shown in Fig. 6(n). The ratio between the shear transfer contribution Vw of wire rope units and the beam shear capacity Vw is given in Table 3. The contribution Vw of wire rope units has been estimated as the difference between shear capacities of beams strengthened with wire rope units and the corresponding beam which was only repaired. The ratio Vw /Vn is higher for beams having smaller shear span-to-depth ratio, as the number of wire rope units was the same for all beams tested. 4.4. Effect of wire rope units on diagonal cracking loads Fig. 9 presents idealised stress distributions in concrete struts due to the prestressing force in wire ropes. Due to the prestressing force in wire ropes, the web of strengthened beams
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(a) Distribution of internal forces in concrete struts.
Fig. 10. Principal tensile stress of concrete against prestressing force of wire rope units.
(b) Distribution of biaxial compressive stresses due to prestress of wire ropes.
effect), respectively, for beams having vertical wire rope units. For different shear stresses v and f = 0, the variation of the principal tensile stress σ1 obtained from Eq. (2) against the initial tensile force of test specimens having wire rope units of 150 mm spacing is shown in Fig. 10. Fig. 10 shows that the principal tensile stress in concrete decreases with the increase of the prestressing force Fi in wire rope, as a result, the diagonal tensile cracking strength of beams strengthened with wire rope units was higher than that of the corresponding original beams as given in Table 3. 4.5. Code provisions for shear capacity
(c) Principal stresses in concrete struts. Fig. 9. Idealized stress distribution in concrete struts due to prestress of wire ropes.
is in a state of biaxial compressive stresses. The qualitative distribution of the biaxial compressive stresses obtained from a linear two-dimensional finite element (2-D FE) analysis is given in Fig. 9(b). Fig. 9(c) shows an element in the strengthened concrete beam web, subjected to vertical f vi and horizontal f hi stresses due to the prestress in wire ropes and flexural f and shear v stresses due to the external applied load. The ratio of the principal tensile stress σ1 to the shear stress v can be written as follows: s σ1 f vi + ( f + f hi ) f vi − ( f + f hi ) 2 = + + 1. (2) v 2v 2v As both f vi and f hi are compressive stresses in concrete resulting from the prestress in wire ropes, therefore, they can be β Fi cos β approximately written as λ1 Fbi wsin sw and λ2 bw h , respectively, where β = angle of wire rope with beam longitudinal axis, and Fi = total initial tensile force of a wire rope unit due to prestressing. At mid-height of beams tested, the average values of coefficients λ1 and λ2 obtained from a linear 2-D FE analysis are 0.75 and 0.85, respectively, for beams having inclined wire rope units, and 0.9 and 0.0 (neglecting Poission
4.5.1. ACI 318-05 The ultimate shear strength of slender beams based on extensive test results as proposed by ACI 318-05 can be written as follows: Vn = Vc + Vw
(3)
where Vc = shear capacity of concrete and Vw = shear transfer capacity of wire rope units replacing the shear capacity Vs of internal steel stirrups. As shear capacity of concrete in slender beams is commonly determined at the first diagonal crack, shear capacity Vc of concrete is p p Vn d Vc = 0.16 f c0 + 17ρ bw d ≤ 0.29 f c0 bw d (4) Mn where Mn = moment at critical section. ACI 318-05 recommends the use of the 45◦ truss analogy, therefore shear transfer capacity of wire rope units can be written as in the following: p Vw = Aw f sw d sin β(1 + cot β)/sw ≤ 0.66 f c0 bw d. (5) As the maximum stress of shear reinforcement is limited to 420 MPa in ACI 318-05, tensile stress of wire ropes in Eq. (5) can be assumed to be f sw = f su − f i ≤ 420 MPa. However, for beams having a shear span-to-depth ratio less than 2.0, the strut-and-tie model is recommended for shear design. From the strut-and-tie model shown in Fig. 11, the
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yield strength and spacing of shear reinforcement, respectively. Therefore, stress in wire ropes has to be limited as follows: f sw = f su − f i ≤
0.5νe f c0 bw sw · . sin β Aw
(9)
4.6. Comparison of shear strength of beams tested with code provisions
Fig. 11. Strut-and-tie model of deep beams according to ACI 318-05.
ultimate shear strength of such beams can be obtained from: Vn = νe f c0 bw ws sin α1
(6)
where ws = wt cos α1 + l p sin α1 = width of concrete strut, α1 = tan−1 ( jd/a) = angle of concrete strut with the beam longitudinal axis, wt = depth of bottom node, and l p = support width. Effectiveness factor of concrete νe is recommended as 0.6 for beams without both horizontal and vertical shear reinforcement. As the strut-and-tie model recommended by ACI 318-05 does not account for web reinforcement, in the present analysis, the contribution of wire rope units as given by Eq. (5) is also used for beams having shear span-to-overall depth ratio of 1.5. 4.5.2. EC 2 The shear capacity of beams specified in EC 2 is the same as Eq. (3), where Vc is given by: Vc = [C Rd k1 (100ρ f c0 )0.333 ]bw d ≥ 0.035k11.5 f c00.5 bw d for av /d > 2.0 Vc =
[βd C Rd k1 (100ρ f c0 )0.333 ]bw d
(7a) ≤
for av /d ≤ 2.0
0.5νe f c0 bw d (7b)
where C Rd = 0.18 = an empirical coefficient, k1 = 1 + (200/d)0.5 ≤ 2 = a scale factor to allow for the size effect, ρ = As /bw d ≤ 0.02 to allow for the effect of longitudinal reinforcement, βd = 2d/av ≤ 4 = coefficient to allow for shear enhancement in deep beams having av /d ≤ 2.0, av = clear shear span, and νe = 0.6(1 − f c0 /250) = effectiveness factor of concrete. The shear transfer capacity of shear reinforcement adopted by EC 2 assumes a constant strut angle, α = 45◦ , from the truss analogy having variable strut inclination, therefore, shear transfer capacity of wire rope units can be written as follows: Vw = Aw f sw jd sin β(1 + cot β)/sw ≥ 0.4bw d
(0.4 in MPa)
Comparisons between the predictions obtained from code provisions and experimental results of the shear strength Vn of beams strengthened with wire rope units are given in Table 3 and Fig. 12. The predictions of original beams are also given in Table 3. ACI 318-05 is conservative in predicting the shear strength of original beams without internal transverse reinforcement, while EC 2 overestimates the shear strength of original beams having a/d of 3.25. The measured shear strength for strengthened beams having a/d = 3.25 is lower than predictions obtained from both provisions as the three wire rope units used were not enough to cover the full shear spans of damaged beams. On the other hand, the shear strength of strengthened beams having a shear span-to-depth ratio below 2.5 is reasonably predicted using the ACI 318-05 formula. For beams having shear span-to-depth ratio above 2.5, predictions obtained from EC 2 are higher than those obtained from ACI 318-05 and experimental results although Eq. (8) for shear transfer capacity of wire rope units specified in EC 2 is very similar to Eq. (5) of ACI 318-05. In addition, the overestimation of shear capacity as predicted by EC 2 increases in beams having a smaller prestress in wire ropes, Beams 5, 6, 12, 13, and 14. This may be attributed to the fact that the limiting stress of wire ropes at failure specified by EC 2 given in Eq. (9) is much higher than that of ACI 318-05. Therefore, shear transfer capacity of wire rope units in strengthened beams would be properly evaluated using a truss analogy with the assumption that the developed stress in wire ropes at failure is below a certain value of 420 MPa as recommended by ACI 318-05.
(8)
where jd = 0.9d = distance between top and bottom chords. EC 2 also recommends that0 the shear reinforcement index Av f yh 0.5νe f c bw sv should be less than sin β , where Av , f yh , and sv = area,
5. Conclusions Fifteen reinforced concrete beams failed in shear were either repaired or repaired and externally strengthened using wire rope units, and then retested to failure. The following conclusions may be drawn: 1. The developed wire rope units are effective in controlling crack distribution of strengthened beams prefailed in shear. Many flexural and diagonal tensile cracks occurred outside the strengthened zones of the beams tested. 2. The initial stiffness of repaired or strengthened beams until the occurrence of the first diagonal crack at mid-height of web was nearly similar to that of original beams. However, beams strengthened with wire rope units exhibited a larger post-failure deformation than the corresponding original beams.
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Fig. 12. Comparison of test results and predictions by code provisions.
3. The ultimate shear strength of beams strengthened with wire rope units increased relative to that of the corresponding original beams. The strengthened beams with inclined wire rope units exhibited larger shear strength than those with vertical wire rope units. Also, the higher the initial presstress in the wire rope units, the higher the shear strength gained. 4. Prestressing force in wire rope units decreased the intensity of the principal tensile stress in concrete. As a result, higher diagonal cracking loads were observed in strengthened beams than in original beams. 5. Shear capacity of strengthened beams having shear spanto-depth ratio below 2.5 is reasonably predicted using the ACI 318-05 formula. On the other hand, the measured shear strength for beams having shear span-to-overall depth ratio of 3.25 is lower than the predictions obtained from ACI 31805 and EC 2 as the three wire rope units used failed to fully cover the failure planes. Acknowledgments This work was supported by the Regional Research Center Program (BIO-housing Research Institute), granted by the Korean Ministry of Education & Human Resources Development. References
[3]
[4]
[5]
[6]
[7]
[8]
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[11] [12] [13]
[1] Al-Sulaimani GJ, Sharif A, Basunbul IA, Baluch MH, Ghaleb BN. Shear repair of reinforced concrete by fiberglass plate bonding. ACI Structural Journal 1994;91(3):458–64. [2] Basunbul IA, Sharif AM, Al-Sulaimani GJ, Baluch MH. Repair of shear
[14]
cracked RC beams with bonded external steel plates. In: Proceedings of the ICSF 93, fourth international conference on structural failure and retrofitting. 1993. p. 629–34. Islam MR, Mansur MA, Maalej M. Shear strengthening of RC deep beams using externally bonded FRP system. Cement & Concrete Composites 2005;27:413–20. Malek M, Saadatmanesh H. Ultimate shear capacity of reinforced concrete beams strengthened with web-bonded fiber-reinforced plastic plates. ACI Structural Journal 1998;95(4):391–9. Paramasivam P, Ong KCG, Lim CTE. Repair of damaged RC beams using ferroccment laminates. In: Proceedings of ICSF 93, fourth international conference on structural failure and retrofitting. 1993. p. 613–20. Triantafillou TC. Shear strengthening of reinforced concrete beams using epoxy-bonded FRP composites. ACI Structural Journal 1998;95(2): 107–15. Pellegrino C, Modena C. FRP shear strengthening of RC beams with transverse steel reinforcement. Journal of Composites for Construction, ASCE 2001;6(2):104–11. Pellegrino C, Modena C. FRP shear strengthening of RC beams: Experimental study and analytical modelling. ACI Structural Journal 2006;103(5):720–8. Teng S, Kong FK, Poh SP, Guan LW, Tan KH. Performance of strengthened concrete deep beams predamaged in shear. ACI Structural Journal 1996;93(2):159–71. ACI Committee 318: Building code requirements for structural concrete (ACI 318-05) and commentary (ACI 318R-05). American Concrete Institute; 2005. The European Standard EN 1992-1-1:2004. Eurocode 2: Design of concrete structures. British Standards Institution; 2004. Bickford JH. An introduction to the design and behavior of bolt joints. Marcel Dekker INC.; 1990. Raoof M, Kraincanic I. Analysis of large diameter steel ropes. Journal of Engineering Mechanics, ASCE 1995;121(6):667–75. Yang KH, Eun HC, Chung HS, Lee ET. Shear characteristics of highstrength concrete deep beams without shear reinforcement. Engineering Structures 2003;25(8):1343–52.
Tests of reinforced concrete beams strengthened with wire rope units S.Y. Kim a , K.H. Yang b,∗ , H.Y. Byun c , A.F. Ashour d a Institute of BIO Housing, Chonnam National University, Gwangju, South Korea b Department of Architectural Engineering, Mokpo National University, Mokpo, Jeonnam, South Korea c Korea Engineering & Consultant, Inc., Hwasun, Jeonnam, South Korea d EDT1, School of Engineering, Design and Technology, University of Bradford, Bradford, BD7 1DP, UK
Received 20 September 2006; received in revised form 13 December 2006; accepted 17 December 2006 Available online 6 March 2007
Abstract This paper presents a simple unbonded-type shear strengthening procedure for reinforced concrete structures with wire rope units. Fifteen beams were tested to failure in shear, repaired, strengthened using the proposed wire rope units, and then retested. The main variables investigated were the shear span-to-depth ratio, and the prestressing force, orientation and spacing of wire rope units. The shear strength of beams strengthened with wire rope units increased relative to that of the corresponding original beams. Reinforced concrete beams strengthened with inclined wire rope units exhibited higher shear strength than those with vertical wire rope units. It was also observed that the higher the initial prestressing force in the wire rope units, the higher the shear strength gained. The principal tensile stress in concrete decreases with the increase of the prestressing force in wire rope, as a result, the diagonal tensile cracking strength of strengthened beams was higher than that of the corresponding original beams. The validity of using ACI 318-05 and EC 2 shear provisions to predict the shear capacity of strengthened beams was examined. The shear capacity of strengthened beams having shear span-to-depth ratios below 2.5 is reasonably predicted using the ACI 318-05 formula. On the other hand, EC 2 overestimates the shear transfer capacity of wire rope units for beams having shear span-to-depth ratios above 2.5. c 2007 Elsevier Ltd. All rights reserved.
Keywords: Repair; Strengthening; Wire rope; Shear capacity
1. Introduction With a growing interest in restoration of concrete structures, several investigations [1–8] were conducted on shear strengthening of reinforced concrete beams by externally bonding steel plates or high strength non-metallic fibre laminates to concrete surfaces. Although this technique proved to be effective in enhancing shear strength of reinforced concrete beams, it has several shortcomings, such as debonding of external laminates from concrete surfaces due to interface shear stress concentration at the laminate end and the long term behavior of the system which may be affected by different coefficients of linear expansion of concrete and nonmetallic fibre laminates. Externally bonded laminates would also constitute an obstacle for inspection of strengthened
∗ Corresponding author. Tel.: +82 61 450 2456; fax: +82 61 450 6454.
E-mail address: [email protected] (K.H. Yang). c 2007 Elsevier Ltd. All rights reserved. 0141-0296/$ - see front matter doi:10.1016/j.engstruct.2006.12.013
regions in beams. In addition, fibres and adhesive would cause noxious fumes in fire. On the other hand, very few [9], if any, tests of predamaged reinforced concrete beams retrofitted with externally unbonded-type strengthening techniques were published. Teng et al. [9] carried out tests on deep beams strengthened with external steel clamping units and concluded that the externally unbonded-type shear strengthening method has a highly economical, environmental and structural efficiency. The present investigation reports the testing of reinforced concrete beams strengthened with externally unbonded wire rope units. Fifteen beams failed in shear were repaired and strengthened with wire rope units, and then retested to failure. The main variables investigated were shear span-to-depth ratio, and the prestressing force, orientation and spacing of wire rope units. In addition, shear capacity of strengthened beams is compared with that of the original beams and predictions by ACI 31805 [10] and EC 2 [11].
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2. Description of wire rope units Notation Ast Aw a av a/d bw d db C Rd Fi f f c0 fi f hi f vi f su f sw h j k k1 lp N sw T Tw Vc Vn Vw v ws wt α α1 β βd ρ ρw σ1 νe φ
area of longitudinal bottom reinforcement total area of four legs of a wire rope shear span clear shear span shear span-to-depth ratio section width effective section depth bolt diameter empirical coefficient in shear transfer capacity of concrete of EC 2 total initial tensile force in a wire rope unit flexural stress of concrete due to applied load cylinder compressive strength of concrete prestress of wire ropes initial horizontal stress normal to beam section due to prestress of wire rope initial vertical stress normal to beam longitudinal axis due to prestress of wire rope tensile strength of wire rope stress of wire rope after the occurrence of a diagonal tensile crack overall section depth ratio of the distance between top and bottom chords to effective section depth torque coefficient scale factor to allow size effect in EC 2 support width tensile force acting in bolt due to torque spacing of wire rope unit quantity of torque applied to bolt total resultant force in wire rope units after the occurrence of a diagonal tensile crack shear transfer capacity of concrete ultimate shear strength shear transfer capacity of wire rope units shear stress of concrete due to applied load concrete strut width in strut-and-tie model depth of bottom node in strut-and-tie model angle of a diagonal tensile crack to beam longitudinal axis angle of concrete strut with the beams longitudinal axis in deep beams in strut-and-tie model angle of wire rope arranged beam longitudinal axis coefficient to allow shear enhancement of deep beams in EC 2 longitudinal bottom reinforcement ratio wire rope unit ratio principal tensile stress in concrete struts effectiveness factor of concrete angle between web reinforcement and concrete strut in strut-and-tie model
Wire ropes, which play an important role in various offshore and onshore applications, have many advantages such as light weight, high-strength, and high flexibility. In the present investigation, the significance and shortcomings of using the wire rope technique as external shear reinforcement in concrete beams are explored. Fig. 1 shows the details of an externally unbonded-type wire rope unit for shear strengthening of reinforced concrete beams. A wire rope unit is comprised of an I-shaped steel plate, four legs of wire rope, four sets of eye-bolts and nuts, two angles, and two corner beads. The Ishaped steel plate of 20 mm thickness and 60 mm web width, having four holes for eye-bolts, is installed at the top surface of beams. U-typed wire ropes with spacing of 60 mm are coupled to the eye-bolts passing through the holes of the steel plate and prestressed by tightening of nuts, similar to the torque control method of high-strength bolts. Angles and corner beads having 3 mm thickness are positioned at beam corners to prevent bearing failure due to the high compression exerted by the wire ropes. The wire rope units are attached to concrete beams due to prestressing force of wire ropes obtained from tightening of nuts. In the case of flanged beams, a hole through the flange should be provided to install the wire rope units. When a reinforced concrete beam strengthened with wire rope units is loaded, they act as external stirrups to control diagonal tensile cracks and transfer shear force. 2.1. Torque–tensile force relationship In the developed wire rope units, the prestressing tensile effect is exerted on wire ropes by tensile forces in eye-bolts owing to tightening of nuts which can be controlled by the externally applied torque. If the friction coefficient is assumed to be constant, the relation between the externally applied torque T and tensile force N acting on a bolt can be written as follows [12]: T = kdb N
(1)
where db = bolt diameter, and k = a torque coefficient dependent on the friction coefficient and geometrical conditions of thread in bolts and nuts. To evaluate the torque coefficient of the proposed wire rope unit, forty specimens composed of eye-bolt, nut and wire rope with load cell were tested as shown in Fig. 2. The test results of the torque and tensile force relationship are also presented in Fig. 2. It indicates that the tensile force transferred to wire ropes linearly increased with the increase of torque as proposed by Eq. (1). From Fig. 2, a high correlation coefficient R 2 of 0.931 is achieved, therefore, the torque coefficient k in the developed wire rope unit can be reasonably assumed as 0.3. 3. Experimental investigation 3.1. Test specimen details Fifteen beams were tested to failure, repaired, strengthened, and then retested. Details of geometrical dimensions and wire
S.Y. Kim et al. / Engineering Structures 29 (2007) 2711–2722
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Fig. 1. Details of developed wire rope units and strengthening procedure. (All dimensions are in mm.)
Fig. 2. Relation of N and T /db in a wire rope unit.
rope units arranged in test specimens are given in Table 1 and Fig. 3: Fig. 3(a) for original beams for the first test, Fig. 3(b) for vertically strengthened beams previously failed in shear, Fig. 3(c) for diagonally strengthened beams previously failed in shear. Shear span-to-depth ratios, a/d, were selected as 1.5, 2.5, and 3.25. In each shear span-to-depth ratio, two different orientations of wire rope units were examined, one of which was external vertical-type stirrups and the other was external 45◦ inclined-type stirrups. For beams having shear span-todepth ratio of 1.5, the spacing and total initial tensile force owing to prestressing were 150 mm and 46.4 kN, respectively. For beams having a shear span-to-depth ratio of 2.5, the effect of varying the total initial tensile force of the wire rope unit on the strengthened beam behavior was investigated as given in Table 1, whereas the spacing of the wire rope unit was kept constant at 150 mm. For beams having a shear span-to-depth ratio of 3.25, the spacing of wire rope units were 100 mm, 150 mm, and 200 mm, while the total initial tensile force of each
wire rope unit was 46.4 kN. In each shear span-to-depth ratio, a repaired beam without wire rope units was also tested to failure to assess the contribution of wire rope units to the beam shear capacity. For strengthening purposes, only three wire rope units, regardless of the shear span-to-depth ratio, were arranged in the region of diagonal tensile cracks of previously tested and failed beams. Gaps between steel plates and beams strengthened with inclined wire rope units were filled with cementitious mortar having compressive strength of 55 MPa. All test specimens had the same section size, distance between two-point concentrated top loads, and concrete design strength as follows: the width bw and overall depth h of beam section were 200 mm and 400 mm, respectively, the distance between two-point concentrated top loads was 360 mm, which was the same as the effective section depth d, and design concrete strength was 21 MPa. The concrete compressive strength of test specimens was designed to be low to simulate existing deteriorated concrete buildings. Three longitudinal reinforcing bars of 22 mm diameter, continuous over the full length of the beam and anchored outside the support by 90◦ hook according to ACI 318-05, were used as bottom reinforcement as shown in Fig. 3, which makes the longitudinal bottom reinforcement ratio, ρ = As /bw d = 0.016, where As = the longitudinal reinforcement area. The spans of test specimens were 1440 mm, 2160 mm, and 2700 mm for beams having shear span-to-depth ratios of 1.5, 2.5, and 3.25, respectively. It is also to be noted that all beams tested did not have any internal transverse reinforcement. Although concrete beams reinforced with internal transverse reinforcement would have more cracks at failure, such transverse reinforcement would have little effect on the shear behaviour of beams strengthened with the current technique as shear strength of unstrengthened beams is governed by a major diagonal crack
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(a) Original beams (for the first test).
(b) Vertically strengthened beams (for the second test).
(c) Diagonally strengthened beams (for the second test). Fig. 3. Specimen details and arrangement of wire rope units. (All dimensions are in mm.)
in their web together with yielding of internal transverse reinforcement. 3.2. Material properties The ingredients of ready-mixed concrete were ordinary Portland cement, irregular gravel of maximum size of 25 mm, and sand. Control specimens which were 100 mm diameter × 200 mm high cylinders were cast and cured simultaneously with the beams to determine the compressive strength of concrete. The results of concrete compressive strength of the cylinders are given in Table 1. Fig. 4 and Table 2 show the stress–strain relationships and mechanical properties of internal reinforcement, wire rope, steel plate, and eye-bolt used in the present study. The wire rope used consists of six strands laid helically over a smaller independent wire rope central core (IWRC). The wire rope does not exhibit a yield plateau as shown in Fig. 4. The effective elastic modulus of wire rope used in beam strengthening was 120 GPa, which was 60% of the elastic modulus of steel, as pointed out by Raoof and Kraincanic [13].
Fig. 4. Stress–strain relationships of steel and wire rope.
3.3. Test procedure All beams were tested under two-point concentrated top loads with loading rate of 5 kN/min using a 3000 kN capacity UTM. The beam surface was white washed to aid in the
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S.Y. Kim et al. / Engineering Structures 29 (2007) 2711–2722 Table 1 Details of test specimens Beam no.
f c0 (MPa)
1 2 3
24.5 24.5 22.5
4 5 6 7 8 9 10
24.7 24.7 24.5 24.1 22.5 22.5 20.6
11 12 13 14 15
24.7 24.5 22.5 24.8 20.6
a/d
1.5
2.5
3.25
a (mm)
540
900
1170
L (mm)
Details of wire rope unit Configuration sw (mm)
Fi (kN)
T (N m)
f i / f pu
ρw – 0.00064 0.0009
Only repair Vertical 45◦ Inclined
–
–
–
–
1440
150
46.4
35
0.53
–
–
2160
Only repair Vertical 45◦ Inclined Vertical 45◦ Inclined Vertical 45◦ Inclined Only repair Vertical 45◦ Inclined Vertical Vertical
–
2700
150
33.2
25
0.38
46.4
35
0.53
60
45
0.69
–
–
–
35
0.53
26 52
0.4 0.8
150 100 200
–
46.4
– 0.00064 0.0009 0.00064 0.0009 0.00064 0.0009 – 0.00064 0.0009 0.00096 0.00048
Note: f c0 = cylinder compressive strength, a/d = shear span-to-effective depth ratio, a = shear span, d = effective section depth, L = beam length between supports, sw = spacing of wire rope units, Fi = total initial tensile force of a wire rope unit, T = initial torque value applied in eye-bolt, f i = prestress applied in 4Aw1 (sin β+cos β) ), Aw1 = net area of single leg of wire rope, β = angle of wire wire rope, f pu = tensile strength of wire rope, ρw = ratio of wire rope unit (= bw sw rope arranged to the longitudinal beam axis, and bw = beam width. Table 2 Mechanical properties of reinforcement, steel plate, eye-bolt, and wire rope Type
f y (MPa)
εy
f su (MPa)
E s (GPa)
Reinforcement (22 mm) Steel plate Eye-bolt (10 mm) Wire rope (4.8 mm)
445 307 355 –
0.00244 0.00157 0.00187 –
620 448 465 2145
182 195 190 120
observation of crack development during testing. After each load increment, the load was kept constant while cracks were marked and photographed. At the same time, deflection was recorded by a 50 mm capacity linear variable differential transducer (LVDT) mounted at mid-span bottom face. Once beam failure occurred, the applied load was removed, all cracks and failure planes were repaired by injection of epoxy resin, and then the shear-span regions with diagonal tensile cracks were strengthened using three wire rope units. Retesting was then started under the same loading condition until the repaired or strengthened beam failed again. All test data were captured by a data logger and automatically stored. 4. Test results and discussions 4.1. Crack propagation and failure modes Typical crack propagation for original beams tested at different applied loads according to the variation of shear spanto-overall depth ratio is shown in Fig. 5. A symmetrical crack pattern was observed for both shear spans before failure. The first crack in all original beams always occurred vertically at a load of nearly 20%–30% of the ultimate load in the maximum moment region as given in Table 3. All original beams failed in shear. Beams having a/d = 1.5 failed along diagonal cracks joining the edges of load and support plates, which was very similar to the crack propagation of deep beams [14],
as depicted in Fig. 5(a). On the other hand, beams having a/d = 2.5 or a/d = 3.25 failed along diagonal cracks running downward from the loading point at nearly 30◦ –45◦ with the beam longitudinal axis as shown in Fig. 5(b) or (c). At failure, bond splitting cracks along longitudinal reinforcement were also observed in several beams tested having a/d = 3.25. The shear forces at which the first diagonal crack and failure occurred are given in Table 3. Fig. 6 shows the crack propagation for only repaired or repaired and strengthened beams tested for the second time. On each beam crack pattern, the failure plane of the original beam tested is also indicated using a ‘+’ mark line type. For beams repaired only, fewer cracks occurred compared with the original beams and the failure planes were very similar to those of the original beams as shown in Fig. 6(a), (d) and (k). While, for beams repaired and strengthened with wire rope units, many new flexural and diagonal tensile cracks appeared in the regions beyond the repaired crack regions, indicating a better crack distribution controlled by wire rope units. Failure planes of several strengthened beams were also different from those of the original beams as shown in Fig. 6(c), (e), (i), (j), (l), (n), and (o). For strengthened beams having a/d = 3.25, bond splitting cracks along the longitudinal reinforcement together with diagonal tensile cracks at failure appeared, which is similar to the failure mode of the original beams, indicating that the three wire rope units used could not fully cover the failure planes. 4.2. Mid-span deflection Mid-span deflections of different beams tested against the total applied load are shown in Fig. 7: Fig. 7(a) for beams having a/d = 1.5, Fig. 7(b) for beams having a/d = 2.5, and Fig. 7(c) for beams having a/d = 3.25. The deflections of original beams having the same shear span-to-depth ratio
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(a) a/ h = 1.5.
(b) a/ h = 2.5.
(c) a/ h = 3.25. Fig. 5. Typical crack patterns and failure of original beams. (Numbers indicate the total load in kN at which crack occurred.) Table 3 Details of test results and predictions Beam no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Original beams
After repair and strengthening
Experiments (kN) Vfl Vcr Vn
Experiments (kN) Vcr Vn Vw
63.3 64.1 62.6 28.4 33.3 39.2 33.3 34.3 34.4 37.2 25.8 26.5 28.9 26.0 23.1
100.5 102.9 99.9 89.2 81.1 80.3 85.7 80.8 76.9 70.9 70.8 75.9 70.7 75.1 67.6
163.0 152.5 149.5 90.4 83.3 82.3 87.9 81.0 76.9 72.0 71.1 76.8 71.8 76.7 70.5
87.5 137.0 107.0 79.0 96.0 91.5 95.0 99.0 85.2 106.0 64.2 82.0 70.0 90.3 66.5
135.5 234.3 259.0 80.0 118.5 129.7 125.5 131.0 133.1 138.2 64.1 90.0 93.5 100.1 82.8
– 98.8 123.5 – 30 42 45.5 51 53.1 58 – 26 29.5 36 18.8
Vw Vn
– 0.422 0.477 – 0.273 0.344 0.363 0.389 0.399 0.420 – 0.289 0.316 0.360 0.227
Predictions for Vn (kN) ACI EC 2
(Vcr ) S (Vcr ) F
First
Second
First
Second
149.0 149.0 136.8 65.1 65.1 64.9 64.4 62.5 62.5 60.2 63.3 63.1 60.7 63.4 58.4
149.0 192.7 198.6 65.1 108.8 126.7 108.1 124.3 106.2 121.9 63.3 106.8 153.3 128.9 91.1
100.3 100.3 97.5 75.5 75.5 75.3 74.8 73.2 73.2 71.0 75.5 75.3 73.2 75.6 71.0
100.3 181.3 212.0 75.5 199.9 251.3 155.8 187.6 135.4 159.0 75.5 156.2 244.9 256.2 101.1
0.871 1.331 1.071 0.886 1.184 1.139 1.109 1.225 1.108 1.495 0.907 1.080 0.990 1.202 0.984
(Vn ) S (Vn ) F
0.831 1.541 1.732 0.885 1.321 1.482 1.428 1.617 1.731 1.917 0.900 1.172 1.302 1.304 1.174
(Vn ) EC2 (Vn )Exp.
(Vn )ACI (Vn )Exp.
First
Second
First
Second
0.914 0.980 0.915 0.721 0.782 0.789 0.733 0.772 0.813 0.836 0.891 0.822 0.846 0.827 0.828
1.100 0.822 0.767 0.814 0.989 1.038 0.861 0.949 0.798 0.884 0.989 1.186 1.640 1.289 1.100
0.616 0.660 0.652 0.835 0.906 0.914 0.852 0.903 0.951 0.987 1.061 0.980 1.019 0.985 1.008
0.741 0.774 0.819 0.943 1.817 2.059 1.241 1.432 1.017 1.152 1.179 1.736 2.619 2.562 1.222
Note: V f l = shear force at first flexural crack, Vcr = shear force at first diagonal crack, Vn = ultimate shear strength, and Vw = shear transfer capacity of wire rope units. Subscripts F and S mean the first test results for original beams and the second test results for repaired or strengthened beams, respectively.
against the total applied load were very similar, therefore, the deflection results of beams 1, 4, and 11 in Fig. 7 are used as representative samples for original beams having a/d = 1.5, 2.5, and 3.25, respectively. The initial stiffness of repaired or strengthened beams until the occurrence of the first diagonal tensile crack of beams was nearly similar to that of the original beams. After the first diagonal tensile crack appeared, the deflection of strengthened beams having a/d = 2.5 or a/d = 3.25 sharply increased, but the load capacity of such beams also greatly increased compared with that of the corresponding original beams. Even the post-failure deformation of the beams strengthened with wire rope units was significantly different from that of the original or only repaired beams. Beams strengthened with wire rope units exhibited a slow release of energy at 60%–80% of the load capacity, whereas the original
and only repaired beams showed sudden, brittle disintegration after reaching the peak load capacity. 4.3. Ultimate shear strength Ultimate shear strength of original and strengthened beams is given in Table 3. Fig. 8 shows the ratio of ultimate shear strength of repaired or repaired and strengthened beams (Vn ) S to that of original beams (Vn ) F : Fig. 8(a) for different orientations of wire rope units, Fig. 8(b) for different initial tensile forces of wire rope units in beams having a/d = 2.5, and Fig. 8(c) for different spacings of wire rope units in beams having a/d = 3.25. The ultimate shear strength of beams only repaired by injection of epoxy resin had approximately 80% of that of the corresponding original beams, regardless of the
S.Y. Kim et al. / Engineering Structures 29 (2007) 2711–2722
(a) Beam 1.
2717
(b) Beam 2.
(c) Beam 3.
(d) Beam 4.
(e) Beam 5.
(f) Beam 6.
(g) Beam 7.
(h) Beam 8. Fig. 6. Crack patterns and failure of repaired or repaired and strengthened beams. (+++ indicates the failure plane of original beams.) (Numbers mean the total load in kN at which cracks occurred.)
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S.Y. Kim et al. / Engineering Structures 29 (2007) 2711–2722
(i) Beam 9.
(j) Beam 10.
(k) Beam 11.
(l) Beam 12.
(m) Beam 13.
(n) Beam 14.
(o) Beam 15. Fig. 6. (continued)
S.Y. Kim et al. / Engineering Structures 29 (2007) 2711–2722
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(a) Only repair and arrangement of wire rope unit.
(a) a/ h = 1.5.
(b) Initial tensile force in wire rope unit (a/ h = 2.5).
(b) a/ h = 2.5.
(c) Spacing of vertical wire rope unit (a/ h = 3.25). Fig. 8. Effect of different parameters on shear strength gained.
(c) a/ h = 3.25. Fig. 7. Mid-span deflection against total load.
shear span-to-depth ratio. While, the ultimate shear strength of beams strengthened with wire rope units increased relative to that of the corresponding original beam; the smaller the shear span-to-depth ratio, the higher the shear strength gained. Also, beams strengthened with inclined wire rope units exhibited higher shear strength than those strengthened with vertical wire rope units. The prestressing force in wire ropes also had a significant influence on the increase of shear strength of
strengthened beams; the larger the initial tensile force in wire rope units, the higher the increasing ratio of shear strength as shown in Fig. 8(b). For strengthened beams having a/d = 3.25, the spacing of wire rope unit had little influence on the enhancement of shear strength (see Fig. 8(c)) as the three wire rope units used failed to fully cover the failure planes as shown in Fig. 6(n)–(o). The shear strength of beam 14 strengthened with 100 mm spacing wire rope units was 1.3 times higher than that of the corresponding original beam as the diagonal failure plane occurred within the strengthened region as shown in Fig. 6(n). The ratio between the shear transfer contribution Vw of wire rope units and the beam shear capacity Vw is given in Table 3. The contribution Vw of wire rope units has been estimated as the difference between shear capacities of beams strengthened with wire rope units and the corresponding beam which was only repaired. The ratio Vw /Vn is higher for beams having smaller shear span-to-depth ratio, as the number of wire rope units was the same for all beams tested. 4.4. Effect of wire rope units on diagonal cracking loads Fig. 9 presents idealised stress distributions in concrete struts due to the prestressing force in wire ropes. Due to the prestressing force in wire ropes, the web of strengthened beams
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(a) Distribution of internal forces in concrete struts.
Fig. 10. Principal tensile stress of concrete against prestressing force of wire rope units.
(b) Distribution of biaxial compressive stresses due to prestress of wire ropes.
effect), respectively, for beams having vertical wire rope units. For different shear stresses v and f = 0, the variation of the principal tensile stress σ1 obtained from Eq. (2) against the initial tensile force of test specimens having wire rope units of 150 mm spacing is shown in Fig. 10. Fig. 10 shows that the principal tensile stress in concrete decreases with the increase of the prestressing force Fi in wire rope, as a result, the diagonal tensile cracking strength of beams strengthened with wire rope units was higher than that of the corresponding original beams as given in Table 3. 4.5. Code provisions for shear capacity
(c) Principal stresses in concrete struts. Fig. 9. Idealized stress distribution in concrete struts due to prestress of wire ropes.
is in a state of biaxial compressive stresses. The qualitative distribution of the biaxial compressive stresses obtained from a linear two-dimensional finite element (2-D FE) analysis is given in Fig. 9(b). Fig. 9(c) shows an element in the strengthened concrete beam web, subjected to vertical f vi and horizontal f hi stresses due to the prestress in wire ropes and flexural f and shear v stresses due to the external applied load. The ratio of the principal tensile stress σ1 to the shear stress v can be written as follows: s σ1 f vi + ( f + f hi ) f vi − ( f + f hi ) 2 = + + 1. (2) v 2v 2v As both f vi and f hi are compressive stresses in concrete resulting from the prestress in wire ropes, therefore, they can be β Fi cos β approximately written as λ1 Fbi wsin sw and λ2 bw h , respectively, where β = angle of wire rope with beam longitudinal axis, and Fi = total initial tensile force of a wire rope unit due to prestressing. At mid-height of beams tested, the average values of coefficients λ1 and λ2 obtained from a linear 2-D FE analysis are 0.75 and 0.85, respectively, for beams having inclined wire rope units, and 0.9 and 0.0 (neglecting Poission
4.5.1. ACI 318-05 The ultimate shear strength of slender beams based on extensive test results as proposed by ACI 318-05 can be written as follows: Vn = Vc + Vw
(3)
where Vc = shear capacity of concrete and Vw = shear transfer capacity of wire rope units replacing the shear capacity Vs of internal steel stirrups. As shear capacity of concrete in slender beams is commonly determined at the first diagonal crack, shear capacity Vc of concrete is p p Vn d Vc = 0.16 f c0 + 17ρ bw d ≤ 0.29 f c0 bw d (4) Mn where Mn = moment at critical section. ACI 318-05 recommends the use of the 45◦ truss analogy, therefore shear transfer capacity of wire rope units can be written as in the following: p Vw = Aw f sw d sin β(1 + cot β)/sw ≤ 0.66 f c0 bw d. (5) As the maximum stress of shear reinforcement is limited to 420 MPa in ACI 318-05, tensile stress of wire ropes in Eq. (5) can be assumed to be f sw = f su − f i ≤ 420 MPa. However, for beams having a shear span-to-depth ratio less than 2.0, the strut-and-tie model is recommended for shear design. From the strut-and-tie model shown in Fig. 11, the
S.Y. Kim et al. / Engineering Structures 29 (2007) 2711–2722
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yield strength and spacing of shear reinforcement, respectively. Therefore, stress in wire ropes has to be limited as follows: f sw = f su − f i ≤
0.5νe f c0 bw sw · . sin β Aw
(9)
4.6. Comparison of shear strength of beams tested with code provisions
Fig. 11. Strut-and-tie model of deep beams according to ACI 318-05.
ultimate shear strength of such beams can be obtained from: Vn = νe f c0 bw ws sin α1
(6)
where ws = wt cos α1 + l p sin α1 = width of concrete strut, α1 = tan−1 ( jd/a) = angle of concrete strut with the beam longitudinal axis, wt = depth of bottom node, and l p = support width. Effectiveness factor of concrete νe is recommended as 0.6 for beams without both horizontal and vertical shear reinforcement. As the strut-and-tie model recommended by ACI 318-05 does not account for web reinforcement, in the present analysis, the contribution of wire rope units as given by Eq. (5) is also used for beams having shear span-to-overall depth ratio of 1.5. 4.5.2. EC 2 The shear capacity of beams specified in EC 2 is the same as Eq. (3), where Vc is given by: Vc = [C Rd k1 (100ρ f c0 )0.333 ]bw d ≥ 0.035k11.5 f c00.5 bw d for av /d > 2.0 Vc =
[βd C Rd k1 (100ρ f c0 )0.333 ]bw d
(7a) ≤
for av /d ≤ 2.0
0.5νe f c0 bw d (7b)
where C Rd = 0.18 = an empirical coefficient, k1 = 1 + (200/d)0.5 ≤ 2 = a scale factor to allow for the size effect, ρ = As /bw d ≤ 0.02 to allow for the effect of longitudinal reinforcement, βd = 2d/av ≤ 4 = coefficient to allow for shear enhancement in deep beams having av /d ≤ 2.0, av = clear shear span, and νe = 0.6(1 − f c0 /250) = effectiveness factor of concrete. The shear transfer capacity of shear reinforcement adopted by EC 2 assumes a constant strut angle, α = 45◦ , from the truss analogy having variable strut inclination, therefore, shear transfer capacity of wire rope units can be written as follows: Vw = Aw f sw jd sin β(1 + cot β)/sw ≥ 0.4bw d
(0.4 in MPa)
Comparisons between the predictions obtained from code provisions and experimental results of the shear strength Vn of beams strengthened with wire rope units are given in Table 3 and Fig. 12. The predictions of original beams are also given in Table 3. ACI 318-05 is conservative in predicting the shear strength of original beams without internal transverse reinforcement, while EC 2 overestimates the shear strength of original beams having a/d of 3.25. The measured shear strength for strengthened beams having a/d = 3.25 is lower than predictions obtained from both provisions as the three wire rope units used were not enough to cover the full shear spans of damaged beams. On the other hand, the shear strength of strengthened beams having a shear span-to-depth ratio below 2.5 is reasonably predicted using the ACI 318-05 formula. For beams having shear span-to-depth ratio above 2.5, predictions obtained from EC 2 are higher than those obtained from ACI 318-05 and experimental results although Eq. (8) for shear transfer capacity of wire rope units specified in EC 2 is very similar to Eq. (5) of ACI 318-05. In addition, the overestimation of shear capacity as predicted by EC 2 increases in beams having a smaller prestress in wire ropes, Beams 5, 6, 12, 13, and 14. This may be attributed to the fact that the limiting stress of wire ropes at failure specified by EC 2 given in Eq. (9) is much higher than that of ACI 318-05. Therefore, shear transfer capacity of wire rope units in strengthened beams would be properly evaluated using a truss analogy with the assumption that the developed stress in wire ropes at failure is below a certain value of 420 MPa as recommended by ACI 318-05.
(8)
where jd = 0.9d = distance between top and bottom chords. EC 2 also recommends that0 the shear reinforcement index Av f yh 0.5νe f c bw sv should be less than sin β , where Av , f yh , and sv = area,
5. Conclusions Fifteen reinforced concrete beams failed in shear were either repaired or repaired and externally strengthened using wire rope units, and then retested to failure. The following conclusions may be drawn: 1. The developed wire rope units are effective in controlling crack distribution of strengthened beams prefailed in shear. Many flexural and diagonal tensile cracks occurred outside the strengthened zones of the beams tested. 2. The initial stiffness of repaired or strengthened beams until the occurrence of the first diagonal crack at mid-height of web was nearly similar to that of original beams. However, beams strengthened with wire rope units exhibited a larger post-failure deformation than the corresponding original beams.
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Fig. 12. Comparison of test results and predictions by code provisions.
3. The ultimate shear strength of beams strengthened with wire rope units increased relative to that of the corresponding original beams. The strengthened beams with inclined wire rope units exhibited larger shear strength than those with vertical wire rope units. Also, the higher the initial presstress in the wire rope units, the higher the shear strength gained. 4. Prestressing force in wire rope units decreased the intensity of the principal tensile stress in concrete. As a result, higher diagonal cracking loads were observed in strengthened beams than in original beams. 5. Shear capacity of strengthened beams having shear spanto-depth ratio below 2.5 is reasonably predicted using the ACI 318-05 formula. On the other hand, the measured shear strength for beams having shear span-to-overall depth ratio of 3.25 is lower than the predictions obtained from ACI 31805 and EC 2 as the three wire rope units used failed to fully cover the failure planes. Acknowledgments This work was supported by the Regional Research Center Program (BIO-housing Research Institute), granted by the Korean Ministry of Education & Human Resources Development. References
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