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Punching shear behavior of reinforced concrete slabs using steel fibers in the mix
HBRC Journal (2016) xxx, xxx–xxx
Housing and Building National Research Center
HBRC Journal http://ees.elsevier.com/hbrcj
Punching shear behavior of reinforced concrete slabs using steel fibers in the mix Ahmed M. Abdel-Rahman, Nasr Z. Hassan *, Adel M. Soliman Civil Eng. Dept., Helwan University, Cairo, Egypt Received 7 September 2016; revised 19 October 2016; accepted 6 November 2016
KEYWORDS Flat slab; Steel fiber; Punching shear; Failure load
Abstract One of the major problems of flat slab is the punching shear failure of slab-column connection. This form of failure must be avoided. Fourteen slab-column connections are tested to failure and categorized in two phases. The first ‘‘Phase I” consisted of testing ten interior square slabs axially loaded. The second ‘‘Phase II” consisted of testing four specimens under eccentric loading to study the influence of moment transfer at the slab-column connection on the punching shear failure of the slabs. The main parameters evaluated were, fiber volume ratio which was 0.5%, 1.0% and 1.5% and, punching area as dimensions of the square portion of the slab having steel fibers at the column vicinity of lengths d + 200 mm, 2d + 200 mm and 3d + 200 mm. All slabs have same dimensions of 1700 mm 1700 mm with thickness 150 mm and reinforcement ratio of 1.2%. All tested specimens were loaded incrementally up to failure. However using steel fiber increased both the failure load and energy absorbing capacity. Summarily, it was found that slabs with a 1.5% steel fiber ratio led to high failure load capacity. Results showed that using steel fiber only in a portion of slab that is equal to slab thickness from column face was sufficient to give the optimum enhancement in both failure load and ductility behavior. Three-dimensional finite element model was created to using ANSYS R14.5 ANSYS (2012) program to simulate the behavior of the tested specimens. Crack pattern, mode of failure and energy absorption were analyzed here in this study. Ó 2016 Housing and Building National Research Center. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Introduction * Corresponding author. E-mail address: [email protected] (N.Z. Hassan). Peer review under responsibility of Housing and Building National Research Center.
Production and hosting by Elsevier
From a structural aspect, the main reason for adding fibers is to improve the fracture characteristics and structural behavior through the fibers ability to bridge cracks. Fiber bridging over the cracks leads to increased shear, punching and moment resistance, reduced crack spacing and crack widths, increased flexural stiffness and increased ductility in compression. Steel fiber reinforcement concrete (SFRC) [1] is considered as a method of strengthening structural elements such as flat
http://dx.doi.org/10.1016/j.hbrcj.2016.11.001 1687-4048 Ó 2016 Housing and Building National Research Center. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
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A.M. Abdel-Rahman et al.
slabs [2,3], and it was used to enhance flexural strength and punching shear strength of the concrete slabs. This current research program was conducted to study enhancing the behavior of punching shear of reinforced concrete flat slabs by adding steel fiber in the mix. An experimental study was conducted for fourteen reinforced concrete slabs. Two specimens were casted without steel fiber as control specimens, one for axially centric loaded specimens and the other for eccentric loaded to study the effect of applying moment. The other twelve specimens considered the variation of steel fiber volume fraction which was 0.5%, 1.0% and 1.5% and the square area of fiber from column edge with length d, 2d and 3d, while there are three specimens of eccentric loaded of steel fiber volume fraction 0.5%, 1.0% and 1.5% only at a distance d from column face. This research includes studying the crack patterns, failure modes, loads deflection relationship, steel strains, the stiffness degradation, ductility ratio, energy absorption, and stiffness degradation. Experimental program The experimental study was carried out on fourteen full scale slab-column connections were tested to failure with
Fig. 1
dimensions 1700 mm 1700 mm and thickness 150 mm, and the reinforcement ratio was constant for all slabs of 1.2%. Fig. 1 indicates the dimensions and reinforcement details of one slab. These slabs were divided into five groups A, B, C, D and E. The first group A has the control specimens without steel fiber and consists of two slabs, one loaded axially and the other has eccentric load. The second group B consists of three specimens of different steel fiber volume fractions 0.5%, 1.0% and 1.5% respectively but with constant length of square area from column face having steel fiber equal to d. The other groups C and D were the same as group B, but with different lengths of square area from column face having steel fiber equal to 2d and 3d respectively. The last group E was the same as group B, but they were tested under eccentric load to create applying moment. Table 1 summarizes the specimen details of the experimental program. This study includes also the effect of each variable on crack pattern, stiffness, energy absorption, and ductility ratio of the tested slabs. From these parameters the enhancement of the behavior of punching shear of reinforced concrete slabs by adding steel fiber in the mix around the column can be determined considering the following: 1. Effect of steel fiber volume fraction.
Details of the tested specimen (A1).
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
Punching shear behavior of reinforced concrete slabs Table 1
3
Test program and specimen details.
Group
Symbol
Slab dimensions L L t mm mm mm
Fiber volume fraction%
Area of fiber from column edge
Test load
(A) Control
A1 A2
1700 1700 150 1700 1700 150
0% 0%
0 0
Axial load Applied moment
(B)
B1 B2 B3
1700 1700 150 1700 1700 150 1700 1700 150
0.5% 1.0% 1.5%
d*d d*d d*d
Axial load Axial load Axial load
(C)
C1 C2 C3
1700 1700 150 1700 1700 150 1700 1700 150
0.5% 1.0% 1.5%
2d * 2d 2d * 2d 2d * 2d
Axial load Axial load Axial load
(D)
D1 D2 D3
1700 1700 150 1700 1700 150 1700 1700 150
0.5% 1.0% 1.5%
3d * 3d 3d * 3d 3d * 3d
Axial load Axial load Axial load
(E)
E1 E2 E3
1700 1700 150 1700 1700 150 1700 1700 150
0.5% 1.0% 1.5%
d*d d*d d*d
Applied moment Applied moment Applied moment
Material characteristics The concrete mix used in the tested slabs consisted of Portland cement, sand, gravel, and water with ratios of 1:2.13:2.96:0.54 by weight respectively. All used materials match with ECP 203 limits [4]. The main longitudinal reinforcement has yield stress of 400 MPa for 16 mm diameter bars and 500 MPa for 10 mm diameter bars. The average characteristic concrete strength of tested cubes was 30 MPa. Steel fibers of 500 mm length, 0.52 mm width and 0.72 mm thickness each used to be added to the concrete mix with a variable volume fraction ratio Fig. 2. The yield stress of the steel fiber is 400 MPa [2]. Fig. 2
Steel fiber.
Test setup 2. Effect of increasing the square area around the column having steel fiber in the mix. 3. Effect of axially and eccentrically loaded specimens taking the effect of moment into consideration.
The tests were carried out in the reinforced concrete laboratory of the Faculty of Engineering, El-Mataria, Helwan University. A very rigid steel frame consisting of horizontal and vertical
(2) Hydraulic jack (5) Load cell (4) Point load
(4) Plates (8) Dial Gauges
(3) Column 200X200 (6) Specimen (7) Horizontal I-Beams
(1) Frame
Fig. 3a
Test setup and loading system of groups B, C and D.
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A.M. Abdel-Rahman et al. to the axis of the column centrically (groups B, C and D) or eccentrically (group E) using rigid steel plate Fig. 3a and b. Measurements
Fig. 3b
To record vertical deflection of slab specimens, four dial gauges were used to record vertical deflection of the slabs at various locations, the gauges were installed on the top surface of slab, and two gauges were attached exactly at the column face, one from each side to measure the central deflection of the slab. The other two gauges were installed at the midpoint between the column face and the edge of the slab Fig. 3a. An electric resistance gauge (10 mm length, 120 ohms resistance with gauge factor of 2.10) was mounted and glued to the main reinforcement. The locations of the strain gauges are shown in Fig. 4. The applied load was measured incrementally during loading till failure.
Test setup and loading system of group E.
Crack patterns For all slabs first crack was initiated at early stage of loading and then propagated as the applied load increased. At early stage of loading, micro cracks propagated parallel to the bottom reinforcement mesh. It was noted that these cracks had no influence on the final failure mode. With the increase in the applied load, these cracks became wider and propagated in several directions (normally diagonal directions). In the meantime, more cracks occurred and propagated in the similar manner as the earlier cracks did. Figs. 5, 6 and 8 indicate the view of crack pattern from top and bottom of specimens A1, B2 and E1 respectively. Main reinforcement ratio has been chosen to ensure that the ultimate flexure failure load is bigger than punching failure load value. Test results Fig. 4
Mode of failure
Electrical strain gauges location.
I-sections was used as a base to support a slab specimen. The load was applied vertically using a hydraulic jack with maximum capacity 1000 kN centric or eccentric of the column axis. A system of rigid steel I beams was used to transverse the applied single concentrated load coming from load cell directly
Almost the main mode of failure of all specimens was punching shear failure that occurred suddenly in a brittle manner in the column vicinity [6–8]. For the control specimen A1 Fig. 5, the failure occurred at a load level of 275 kN and for the specimen B2 Fig. 6 (specimen with steel fiber ratio of 1.0%), the failure occurred at a load level of 320 kN. However the failure
A1
A1 i) Bottom View Fig. 5
ii) Top View Crack pattern for specimen A1.
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
Punching shear behavior of reinforced concrete slabs
5
B2
B2 i) Bottom View Fig. 6
Fig. 7
ii) Top View Crack pattern for specimen B2.
Crack pattern for specimen A2.
mechanism of the specimen B2 was more ductile than that of the specimens A1, yet it is still brittle failure. The relatively ductile behavior of B3 over that of A1 resulted from the contribution of the steel fiber in increasing the punching shear cone area. For example in the case of specimen A1, the radius of the punching cone was measured to be about 1.1d from the column face. This value was noted at the bottom surface of the slab which is almost the typical value of punching shear failure cone of typical concrete flat slabs. The crack patterns and failure surface of the specimen A1 were compatible to the ACI
318-14, where the punching cone starts at the column face with a cone angle of 45°. The radius of the punching cone in the case of the Specimen B3 was found to be about 1.7d from the column face with an increase of 30% compared to that of the Specimen A1. For specimen E1, (the specimen with 0.5% steel fiber ratio), the first crack observed at a load of 100 kN, with increasing the applied load, more radial and tangential shear cracks [5] was noted on the bottom of the slab (tension side). Closer to the failure load, tangential cracks were dominated by a major punching shear crack forming the punching cone. The failure occurred suddenly around the slab-column connection at a load level of 225 kN. The radius of punching cone was noted to be about 1.25d from the column face, similar to the control slab A2. The cracks concentrated more at the left side of the slab where the moment was applied. The crack patterns of specimens A2 and E1 are shown in Figs. 7 and 8 respectively. Load deflection relationship Referring to Tables 2 and 3, it can be noticed that the measured deflection of all slabs with steel fiber in the mix is smaller than that of the control specimens slabs A1 and A2. It shows that the maximum deflection was in the center of the specimen and as the distance increases from the column center the deflec-
E1
E1 i) Bottom View Fig. 8
ii) Top View Crack pattern for specimen E1.
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A.M. Abdel-Rahman et al. Test results of axially loaded specimens.
Table 2 Group
Symbol
Cracking stage
Failure stage
Pcr (kN)
Dcr (mm)
PU (kN)
DU (mm)
Ductility index (ld)
Absorbed energy (kN mm)
Group A
A1
125
6.45
275
16.6
12.00
4430
Group B
B1 B2 B3
150 150 150
6.50 5.15 4.51
300 320 400
15.1 15.98 19.03
8.50 8.24 10.50
7145 8446.5 12079.75
Group C
C1 C2 C3
150 150 150
7.92 6.85 5.60
335 350 375
17.55 17.17 16.57
13.00 10.90 10.25
10708 8985.6 8307.5
Group D
D1 D2 D3
150 150 150
6.65 5.09 3.69
345 369 385
13.57 11.83 11.39
9.50 8.30 7.50
5780 7328.5 7640
Test results of eccentrically loaded specimens.
Table 3
Symbol
Cracking stage Pcr (kN)
Mcr (kN m)
Dcr (mm)
PU (kN)
MU (kN m)
Du (mm)
Group A
A2
96.7
19.34
3.82
201.7
40.34
Group E
E1 E2 E3
100 100 115.9
20 20 23
3.46 3.02 2.57
225 238 250
45 47.6 50
400 350 300 250 200 150 100 50 0
Failure stage
Ductility index (ld)
Absorbed energy (kN mm)
9.53
4.90
1760
10.08 9.98 10.05
5.30 5.65 5.73
2256.5 2628.2 3228
400 A1 B1 B2 B3
350
A1 D1 D2 D3
300
Load (KN)
Load (KN)
Group
250 200 150 100
0
10
20
30
40
50
50
0
Central Deflection (mm)
0
400
Load (KN)
C2
250
C3
200
40
50
Load-central deflection for specimens of group D.
A2
250
C1
300
30
300
A1
350
Load (KN)
20
Central Deflection (mm) Fig. 11
150 100
E1
200
E2
150
E3
100 50
50 0
0 0
10
20
30
40
0
50
Load-central deflection for specimens of group C.
5
10
15
20
Central Deflection (mm)
Central Deflection (mm)
Fig. 10
10
Load-central deflection for specimens of group B.
Fig. 9
Fig. 12
Load-central deflection for specimens of group E.
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
Punching shear behavior of reinforced concrete slabs
Fig. 13
Fig. 14
7
Solid65 element for concrete model.
LINK180 Geometry ANSYS R14.5 [10].
tion is much decreased with almost symmetrical shape from both sides of the column toward small values at support. This means that using steel fiber in the mix enhances the stiffness and ductility of all slabs. The amount of stiffness-regain depends on the location of steel fiber in the slab. Figs. 9–12 indicate the load–central deflection curve for groups B, C, D and E respectively relative to its corresponding control specimen A1 or A2 Ductility index and absorbed energy Also the ductility index and absorbed energy [9] calculated for each slab specimen relative to control slab are listed in Tables 2 and 3 for all specimens. As a result of the brittle nature of the failure mode of the slabs, the main reinforcement did not reach their yield point. The energy absorption based on displacement was calculated as the area under the load-deflection curve. Similar conclusion was made earlier regarding the relationship between the steel fiber ratio and ductility behavior of the slabs in terms of energy absorption. It was noted that the higher the steel fiber ratio, the higher the energy absorption value and consequently the better ductility behavior of the slabs. Finite elements and numerical analysis The finite element program, ANSYS R14.5 [10], program was used in this study to simulate the behavior of the fourteen slabs
tested previously. The finite element model describes the used reinforced concrete element, modeling of concrete in tension, and multi axial compression state of stresses. Also, the cracking model behavior of concrete is introduced. An eight-node solid element, solid65, was used to model the concrete as solid element Fig. 13, which has eight nodes with three degrees of freedom at each node, translations in x, y, and z directions. A three dimensional element link 180 was used to model the steel reinforcement, the element has two nodes, and each node has three translations degrees of freedom, in x, y, and z directions as shown in Fig. 14. Steel fibers are a randomly distributed matrix mixed with concrete caused significant changes in concrete properties. Based on the previous statement, fibrous concrete can be represented as a new material with new elastic modulus (Es), tensile strength (ft), and compressive strength (fc). The relation between material properties for the concrete without fibers and that provided with fibers was used in modeling fibrous concrete in ANSYS program. In addition to these properties ANSYS program has a parameter described the crack surface bt with open and closed state. These factors play an important role for modeling fiber reinforced concrete. Fig. 15 represents stress-stain curve of (SFRC), and Fig. 16 shows the influence of fiber content on tensile strength. Figs. 17–22 indicate details of the numerical models represented in ANSYS program as concrete mesh and steel mesh for all groups A, B, C and E.
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A.M. Abdel-Rahman et al.
Fig. 18 Fig. 15
Stress strain curve in compression of SFRC [11].
Fig. 16
Influence of fiber content on tensile strength [11].
Concrete mesh for groups B, C and D.
Fig. 19
Fig. 17
Concrete mesh for A1.
Fig. 20
Concrete mesh for A2.
Concrete mesh for Group E.
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
Punching shear behavior of reinforced concrete slabs
9 The numerical results are presented in terms of the load carrying capacity, modes of failure and crack pattern. Test experimental results presented are compared with those calculated from the finite element program and represented in Table 4. Conclusions Phase I: axially loaded slabs
Fig. 21
Steel reinforcement mesh for groups B, C and D.
Fig. 22
Table 4
Steel reinforcement mesh for group E.
1. All tested specimens of this phase have been failed in a typical punching shear mode of failure. It was noted that the less the steel fiber ratio the more brittle the failure was. The failure was very brittle in nature and sudden. Once the failure occurred, the slab did not carry any further load. The higher the steel fiber ratio was the more ductile behavior was noted. Yet the failure was still due to punching shearing stresses. 2. The crack patterns for all these specimens were identical. The significant discrepancy among them was noted closer to their failure load in terms of ductility ratio and dimensions of the punching failure cone. Increasing the steel fiber ratio significantly improved the slab ductility and increased the projected area of the punching failure cone. 3. The results of specimens of Phase I of the research work showed that the punching cone angle of the slabs with steel fibers less than or equal to 0.5% was 45 degree. This value decreased with the increase in the steel fiber ratio to 1.0% or 1.5%. For un-fibered specimens or those with low steel fiber ratio, the punching failure cone starts at the column face as predicted in most of the available codes and standard guidelines. With the increase in the steel fiber ratio the failure plane switched away from the column face toward the weak planes in the slabs. Punching outside the fibered-concrete zone was observed in slabs B1, C1 and D1. Precisely, the failure was developed by localization of the strains in a critical shear plane closer to the edge of the zone with steel fiber. As the result of increasing the zone with steel fiber, punching cone was always observed inside the fibered-zone.
Comparison experimental and finite element predicted results.
Group
Symbol
Experimental
Numerical
Num./Exp.
PU (kN)
DU (mm)
PU (kN)
DU (mm)
Load
Deflection
Group A
A1 A2
275 201.7
16.6 9.53
290 160
13.24 4.48
1.054 0.793
0.798 0.470
Group B
B1 B2 B3
300 320 400
15.1 15.98 19.03
320 350 370
9.65 10.70 11.17
1.066 1.094 0.925
0.639 0.670 0.587
Group C
C1 C2 C3
335 350 375
17.55 17.17 16.57
350 360 390
15.51 16.36 14.12
1.045 1.029 1.040
0.884 0.953 0.852
Group D
D1 D2 D3
345 369 385
13.57 11.83 11.39
360 380 400
14.17 13.89 10.73
1.200 1.152 1.066
1.044 1.174 0.942
Group E
E1 E2 E3
225 238 250
10.08 9.98 10.05
180 190 200
4.05 4.28 3.78
0.800 0.798 0.800
0.402 0.429 0.376
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
10 4. It was found that load-deflection curves had almost the same profile for all specimens in Groups A, B, C and D. The curve initially had a steep behavior until cracking load. Once the first crack initiated, the load-deflection relationship started to be more curved until reaching the ultimate load of the slab. 5. In general, it has been found that the axial strains of the flexural reinforcement were inversely proportional to the distance from slab center. Also, the reinforcement passing the failure cone boundaries had the greatest value of strain. Moreover, it was noticed that the tension reinforcement did not reach the yield point before the punching failure. The maximum strain recorded was 1200le (yield strain is about 2000le). 6. It was obvious that increasing the steel fiber ratio increased both the initial and tangent slopes of the load-deformation curve. For example increasing the steel fiber ratio from 0% (Specimen A1) to 1.5% (Specimen B3) increased the initial stiffness of the slab by 70% (23 kN/mm for the Specimen A1 and 33.3 kN/mm for the Specimen B3).
Phase II: eccentric loaded slabs 1. The purpose of testing these slabs under aforesaid state of loading was to determine the interaction between shear and moment capacities of the tested slabs and to understand the influence of the steel fiber ratio on such behavior. 2. It was found that the higher the steel fiber ratio was the higher the ultimate load carrying capacity of the specimens. Increasing the steel fiber by 1.5% enhanced the ultimate capacity of the specimens by 24%. The steel fiber ratio had similar effect on the ultimate load carrying capacity of the slabs in Phase I and Phase II. The ultimate load was almost linear proportional with the steel fiber ratio in both load cases. 3. The main mode of failure of all of the specimens was punching shear failure that occurred suddenly in a brittle manner around the column. In general it was noted that increasing the steel fiber did not affect the general behavior of the slab neither the failure mode. However it significantly enhanced the ultimate capacity of the slab. 4. In general, it has been concluded that the axial strains of the flexural reinforcement were inversely proportional to the distance from slab center. Also, the reinforcement passing the failure cone boundaries had the greatest value of strain. Moreover, it was noticed that the tension reinforcement reached the yield point for the three tested specimens with value about 6000le and this occurred only at the strain gauges located exactly at the column face. Yet all other strain gauges did not record any yielding strain. This indicated that small portion of the steel reinforcement reached the yield point.
A.M. Abdel-Rahman et al. The comparisons between the 3D finite element numerical predictions and experimental results for all the specimens showed that there was a very good agreement between the 3-D predicted load capacities and the experimental results for all the test specimens. The average numerical-to experimental load ratio is 0.98 with a standard deviation of 0.14. This indicates an excellent agreement. For all the test specimens, the finite element analysis accurately predicts the mode of failure observed in the experiments. The finite element models are also able to capture exact crack pattern observed experimentally for all tested specimens. Conflict of interest None declared. References [1] F. Altun et al, Effects of steel fiber addition on mechanical properties of concrete and RC beams, Construct. Build. Mater. 21 (2006) 654–661. [2] The European Standard EN 14889-1:2006 (CEN, 2006) – Fibers for concrete – Part 1: Steel Fibers – Definitions, Specifications and Conformity. [3] R.N. Swamy, H.M. Bahia, The effectiveness of steel fibers as shear reinforcement, Concr. Int. 7 (3) (1985) 35–40. [4] ECP-203-2012, Egyptian Code of Practice for Design and Construction of Reinforced Concrete Structures 2012. [5] A. Muttoni, M. Fernandez, The critical shear crack theory as a mechanical model for punching shear design and its application to code provisions MC2010, in: FIB Bulletin 57: Shear and Punching Shear in RC and FRC Elements, Lausanne (Switzerland), 2010. pp. 31–60. [6] K.K. Choi, N.M. Reda Taha, H.G. Park, A.K. Maji, Punching shear strength of interior concrete slab column connections reinforced with steel fibers, Cem. Concr. Compos. 29 (2007) 409–420. [7] Nguyen-Minh, M. Rovnak, T. Tran-Quoc, Nguyen-Kim, Punching shear resistance of steel fiber reinforced concrete flat slabs, in: Proceedings of the Twelfth East Asia-Pacific Conference on Structural Engineering and Construction, 2011, EASEC12, pp. 1830–1837. [8] S.D.B. Alexander, S.H. Simmonds, Punching shear tests of concrete slab-column joints containing fiber reinforcement, ACI Struct. J. 89 (4) (1992) 425–432. [9] ACI Committee 318, Building Code Requirements for Structural Concrete and Commentary (ACI 318M–05), American Concrete Institute, Farmington Hills, MI, 2005, p. 430. [10] ANSYS, ANSYS Help. Release 14.5 Copyright, 2012. [11] C.D. Johnston, Steel fiber reinforced mortar and concrete. A review of mechanical properties. In fiber reinforced concrete ACI – SP 44 – Detroit, 1974.
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Housing and Building National Research Center
HBRC Journal http://ees.elsevier.com/hbrcj
Punching shear behavior of reinforced concrete slabs using steel fibers in the mix Ahmed M. Abdel-Rahman, Nasr Z. Hassan *, Adel M. Soliman Civil Eng. Dept., Helwan University, Cairo, Egypt Received 7 September 2016; revised 19 October 2016; accepted 6 November 2016
KEYWORDS Flat slab; Steel fiber; Punching shear; Failure load
Abstract One of the major problems of flat slab is the punching shear failure of slab-column connection. This form of failure must be avoided. Fourteen slab-column connections are tested to failure and categorized in two phases. The first ‘‘Phase I” consisted of testing ten interior square slabs axially loaded. The second ‘‘Phase II” consisted of testing four specimens under eccentric loading to study the influence of moment transfer at the slab-column connection on the punching shear failure of the slabs. The main parameters evaluated were, fiber volume ratio which was 0.5%, 1.0% and 1.5% and, punching area as dimensions of the square portion of the slab having steel fibers at the column vicinity of lengths d + 200 mm, 2d + 200 mm and 3d + 200 mm. All slabs have same dimensions of 1700 mm 1700 mm with thickness 150 mm and reinforcement ratio of 1.2%. All tested specimens were loaded incrementally up to failure. However using steel fiber increased both the failure load and energy absorbing capacity. Summarily, it was found that slabs with a 1.5% steel fiber ratio led to high failure load capacity. Results showed that using steel fiber only in a portion of slab that is equal to slab thickness from column face was sufficient to give the optimum enhancement in both failure load and ductility behavior. Three-dimensional finite element model was created to using ANSYS R14.5 ANSYS (2012) program to simulate the behavior of the tested specimens. Crack pattern, mode of failure and energy absorption were analyzed here in this study. Ó 2016 Housing and Building National Research Center. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Introduction * Corresponding author. E-mail address: [email protected] (N.Z. Hassan). Peer review under responsibility of Housing and Building National Research Center.
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From a structural aspect, the main reason for adding fibers is to improve the fracture characteristics and structural behavior through the fibers ability to bridge cracks. Fiber bridging over the cracks leads to increased shear, punching and moment resistance, reduced crack spacing and crack widths, increased flexural stiffness and increased ductility in compression. Steel fiber reinforcement concrete (SFRC) [1] is considered as a method of strengthening structural elements such as flat
http://dx.doi.org/10.1016/j.hbrcj.2016.11.001 1687-4048 Ó 2016 Housing and Building National Research Center. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
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A.M. Abdel-Rahman et al.
slabs [2,3], and it was used to enhance flexural strength and punching shear strength of the concrete slabs. This current research program was conducted to study enhancing the behavior of punching shear of reinforced concrete flat slabs by adding steel fiber in the mix. An experimental study was conducted for fourteen reinforced concrete slabs. Two specimens were casted without steel fiber as control specimens, one for axially centric loaded specimens and the other for eccentric loaded to study the effect of applying moment. The other twelve specimens considered the variation of steel fiber volume fraction which was 0.5%, 1.0% and 1.5% and the square area of fiber from column edge with length d, 2d and 3d, while there are three specimens of eccentric loaded of steel fiber volume fraction 0.5%, 1.0% and 1.5% only at a distance d from column face. This research includes studying the crack patterns, failure modes, loads deflection relationship, steel strains, the stiffness degradation, ductility ratio, energy absorption, and stiffness degradation. Experimental program The experimental study was carried out on fourteen full scale slab-column connections were tested to failure with
Fig. 1
dimensions 1700 mm 1700 mm and thickness 150 mm, and the reinforcement ratio was constant for all slabs of 1.2%. Fig. 1 indicates the dimensions and reinforcement details of one slab. These slabs were divided into five groups A, B, C, D and E. The first group A has the control specimens without steel fiber and consists of two slabs, one loaded axially and the other has eccentric load. The second group B consists of three specimens of different steel fiber volume fractions 0.5%, 1.0% and 1.5% respectively but with constant length of square area from column face having steel fiber equal to d. The other groups C and D were the same as group B, but with different lengths of square area from column face having steel fiber equal to 2d and 3d respectively. The last group E was the same as group B, but they were tested under eccentric load to create applying moment. Table 1 summarizes the specimen details of the experimental program. This study includes also the effect of each variable on crack pattern, stiffness, energy absorption, and ductility ratio of the tested slabs. From these parameters the enhancement of the behavior of punching shear of reinforced concrete slabs by adding steel fiber in the mix around the column can be determined considering the following: 1. Effect of steel fiber volume fraction.
Details of the tested specimen (A1).
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
Punching shear behavior of reinforced concrete slabs Table 1
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Test program and specimen details.
Group
Symbol
Slab dimensions L L t mm mm mm
Fiber volume fraction%
Area of fiber from column edge
Test load
(A) Control
A1 A2
1700 1700 150 1700 1700 150
0% 0%
0 0
Axial load Applied moment
(B)
B1 B2 B3
1700 1700 150 1700 1700 150 1700 1700 150
0.5% 1.0% 1.5%
d*d d*d d*d
Axial load Axial load Axial load
(C)
C1 C2 C3
1700 1700 150 1700 1700 150 1700 1700 150
0.5% 1.0% 1.5%
2d * 2d 2d * 2d 2d * 2d
Axial load Axial load Axial load
(D)
D1 D2 D3
1700 1700 150 1700 1700 150 1700 1700 150
0.5% 1.0% 1.5%
3d * 3d 3d * 3d 3d * 3d
Axial load Axial load Axial load
(E)
E1 E2 E3
1700 1700 150 1700 1700 150 1700 1700 150
0.5% 1.0% 1.5%
d*d d*d d*d
Applied moment Applied moment Applied moment
Material characteristics The concrete mix used in the tested slabs consisted of Portland cement, sand, gravel, and water with ratios of 1:2.13:2.96:0.54 by weight respectively. All used materials match with ECP 203 limits [4]. The main longitudinal reinforcement has yield stress of 400 MPa for 16 mm diameter bars and 500 MPa for 10 mm diameter bars. The average characteristic concrete strength of tested cubes was 30 MPa. Steel fibers of 500 mm length, 0.52 mm width and 0.72 mm thickness each used to be added to the concrete mix with a variable volume fraction ratio Fig. 2. The yield stress of the steel fiber is 400 MPa [2]. Fig. 2
Steel fiber.
Test setup 2. Effect of increasing the square area around the column having steel fiber in the mix. 3. Effect of axially and eccentrically loaded specimens taking the effect of moment into consideration.
The tests were carried out in the reinforced concrete laboratory of the Faculty of Engineering, El-Mataria, Helwan University. A very rigid steel frame consisting of horizontal and vertical
(2) Hydraulic jack (5) Load cell (4) Point load
(4) Plates (8) Dial Gauges
(3) Column 200X200 (6) Specimen (7) Horizontal I-Beams
(1) Frame
Fig. 3a
Test setup and loading system of groups B, C and D.
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A.M. Abdel-Rahman et al. to the axis of the column centrically (groups B, C and D) or eccentrically (group E) using rigid steel plate Fig. 3a and b. Measurements
Fig. 3b
To record vertical deflection of slab specimens, four dial gauges were used to record vertical deflection of the slabs at various locations, the gauges were installed on the top surface of slab, and two gauges were attached exactly at the column face, one from each side to measure the central deflection of the slab. The other two gauges were installed at the midpoint between the column face and the edge of the slab Fig. 3a. An electric resistance gauge (10 mm length, 120 ohms resistance with gauge factor of 2.10) was mounted and glued to the main reinforcement. The locations of the strain gauges are shown in Fig. 4. The applied load was measured incrementally during loading till failure.
Test setup and loading system of group E.
Crack patterns For all slabs first crack was initiated at early stage of loading and then propagated as the applied load increased. At early stage of loading, micro cracks propagated parallel to the bottom reinforcement mesh. It was noted that these cracks had no influence on the final failure mode. With the increase in the applied load, these cracks became wider and propagated in several directions (normally diagonal directions). In the meantime, more cracks occurred and propagated in the similar manner as the earlier cracks did. Figs. 5, 6 and 8 indicate the view of crack pattern from top and bottom of specimens A1, B2 and E1 respectively. Main reinforcement ratio has been chosen to ensure that the ultimate flexure failure load is bigger than punching failure load value. Test results Fig. 4
Mode of failure
Electrical strain gauges location.
I-sections was used as a base to support a slab specimen. The load was applied vertically using a hydraulic jack with maximum capacity 1000 kN centric or eccentric of the column axis. A system of rigid steel I beams was used to transverse the applied single concentrated load coming from load cell directly
Almost the main mode of failure of all specimens was punching shear failure that occurred suddenly in a brittle manner in the column vicinity [6–8]. For the control specimen A1 Fig. 5, the failure occurred at a load level of 275 kN and for the specimen B2 Fig. 6 (specimen with steel fiber ratio of 1.0%), the failure occurred at a load level of 320 kN. However the failure
A1
A1 i) Bottom View Fig. 5
ii) Top View Crack pattern for specimen A1.
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
Punching shear behavior of reinforced concrete slabs
5
B2
B2 i) Bottom View Fig. 6
Fig. 7
ii) Top View Crack pattern for specimen B2.
Crack pattern for specimen A2.
mechanism of the specimen B2 was more ductile than that of the specimens A1, yet it is still brittle failure. The relatively ductile behavior of B3 over that of A1 resulted from the contribution of the steel fiber in increasing the punching shear cone area. For example in the case of specimen A1, the radius of the punching cone was measured to be about 1.1d from the column face. This value was noted at the bottom surface of the slab which is almost the typical value of punching shear failure cone of typical concrete flat slabs. The crack patterns and failure surface of the specimen A1 were compatible to the ACI
318-14, where the punching cone starts at the column face with a cone angle of 45°. The radius of the punching cone in the case of the Specimen B3 was found to be about 1.7d from the column face with an increase of 30% compared to that of the Specimen A1. For specimen E1, (the specimen with 0.5% steel fiber ratio), the first crack observed at a load of 100 kN, with increasing the applied load, more radial and tangential shear cracks [5] was noted on the bottom of the slab (tension side). Closer to the failure load, tangential cracks were dominated by a major punching shear crack forming the punching cone. The failure occurred suddenly around the slab-column connection at a load level of 225 kN. The radius of punching cone was noted to be about 1.25d from the column face, similar to the control slab A2. The cracks concentrated more at the left side of the slab where the moment was applied. The crack patterns of specimens A2 and E1 are shown in Figs. 7 and 8 respectively. Load deflection relationship Referring to Tables 2 and 3, it can be noticed that the measured deflection of all slabs with steel fiber in the mix is smaller than that of the control specimens slabs A1 and A2. It shows that the maximum deflection was in the center of the specimen and as the distance increases from the column center the deflec-
E1
E1 i) Bottom View Fig. 8
ii) Top View Crack pattern for specimen E1.
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
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A.M. Abdel-Rahman et al. Test results of axially loaded specimens.
Table 2 Group
Symbol
Cracking stage
Failure stage
Pcr (kN)
Dcr (mm)
PU (kN)
DU (mm)
Ductility index (ld)
Absorbed energy (kN mm)
Group A
A1
125
6.45
275
16.6
12.00
4430
Group B
B1 B2 B3
150 150 150
6.50 5.15 4.51
300 320 400
15.1 15.98 19.03
8.50 8.24 10.50
7145 8446.5 12079.75
Group C
C1 C2 C3
150 150 150
7.92 6.85 5.60
335 350 375
17.55 17.17 16.57
13.00 10.90 10.25
10708 8985.6 8307.5
Group D
D1 D2 D3
150 150 150
6.65 5.09 3.69
345 369 385
13.57 11.83 11.39
9.50 8.30 7.50
5780 7328.5 7640
Test results of eccentrically loaded specimens.
Table 3
Symbol
Cracking stage Pcr (kN)
Mcr (kN m)
Dcr (mm)
PU (kN)
MU (kN m)
Du (mm)
Group A
A2
96.7
19.34
3.82
201.7
40.34
Group E
E1 E2 E3
100 100 115.9
20 20 23
3.46 3.02 2.57
225 238 250
45 47.6 50
400 350 300 250 200 150 100 50 0
Failure stage
Ductility index (ld)
Absorbed energy (kN mm)
9.53
4.90
1760
10.08 9.98 10.05
5.30 5.65 5.73
2256.5 2628.2 3228
400 A1 B1 B2 B3
350
A1 D1 D2 D3
300
Load (KN)
Load (KN)
Group
250 200 150 100
0
10
20
30
40
50
50
0
Central Deflection (mm)
0
400
Load (KN)
C2
250
C3
200
40
50
Load-central deflection for specimens of group D.
A2
250
C1
300
30
300
A1
350
Load (KN)
20
Central Deflection (mm) Fig. 11
150 100
E1
200
E2
150
E3
100 50
50 0
0 0
10
20
30
40
0
50
Load-central deflection for specimens of group C.
5
10
15
20
Central Deflection (mm)
Central Deflection (mm)
Fig. 10
10
Load-central deflection for specimens of group B.
Fig. 9
Fig. 12
Load-central deflection for specimens of group E.
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Punching shear behavior of reinforced concrete slabs
Fig. 13
Fig. 14
7
Solid65 element for concrete model.
LINK180 Geometry ANSYS R14.5 [10].
tion is much decreased with almost symmetrical shape from both sides of the column toward small values at support. This means that using steel fiber in the mix enhances the stiffness and ductility of all slabs. The amount of stiffness-regain depends on the location of steel fiber in the slab. Figs. 9–12 indicate the load–central deflection curve for groups B, C, D and E respectively relative to its corresponding control specimen A1 or A2 Ductility index and absorbed energy Also the ductility index and absorbed energy [9] calculated for each slab specimen relative to control slab are listed in Tables 2 and 3 for all specimens. As a result of the brittle nature of the failure mode of the slabs, the main reinforcement did not reach their yield point. The energy absorption based on displacement was calculated as the area under the load-deflection curve. Similar conclusion was made earlier regarding the relationship between the steel fiber ratio and ductility behavior of the slabs in terms of energy absorption. It was noted that the higher the steel fiber ratio, the higher the energy absorption value and consequently the better ductility behavior of the slabs. Finite elements and numerical analysis The finite element program, ANSYS R14.5 [10], program was used in this study to simulate the behavior of the fourteen slabs
tested previously. The finite element model describes the used reinforced concrete element, modeling of concrete in tension, and multi axial compression state of stresses. Also, the cracking model behavior of concrete is introduced. An eight-node solid element, solid65, was used to model the concrete as solid element Fig. 13, which has eight nodes with three degrees of freedom at each node, translations in x, y, and z directions. A three dimensional element link 180 was used to model the steel reinforcement, the element has two nodes, and each node has three translations degrees of freedom, in x, y, and z directions as shown in Fig. 14. Steel fibers are a randomly distributed matrix mixed with concrete caused significant changes in concrete properties. Based on the previous statement, fibrous concrete can be represented as a new material with new elastic modulus (Es), tensile strength (ft), and compressive strength (fc). The relation between material properties for the concrete without fibers and that provided with fibers was used in modeling fibrous concrete in ANSYS program. In addition to these properties ANSYS program has a parameter described the crack surface bt with open and closed state. These factors play an important role for modeling fiber reinforced concrete. Fig. 15 represents stress-stain curve of (SFRC), and Fig. 16 shows the influence of fiber content on tensile strength. Figs. 17–22 indicate details of the numerical models represented in ANSYS program as concrete mesh and steel mesh for all groups A, B, C and E.
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A.M. Abdel-Rahman et al.
Fig. 18 Fig. 15
Stress strain curve in compression of SFRC [11].
Fig. 16
Influence of fiber content on tensile strength [11].
Concrete mesh for groups B, C and D.
Fig. 19
Fig. 17
Concrete mesh for A1.
Fig. 20
Concrete mesh for A2.
Concrete mesh for Group E.
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
Punching shear behavior of reinforced concrete slabs
9 The numerical results are presented in terms of the load carrying capacity, modes of failure and crack pattern. Test experimental results presented are compared with those calculated from the finite element program and represented in Table 4. Conclusions Phase I: axially loaded slabs
Fig. 21
Steel reinforcement mesh for groups B, C and D.
Fig. 22
Table 4
Steel reinforcement mesh for group E.
1. All tested specimens of this phase have been failed in a typical punching shear mode of failure. It was noted that the less the steel fiber ratio the more brittle the failure was. The failure was very brittle in nature and sudden. Once the failure occurred, the slab did not carry any further load. The higher the steel fiber ratio was the more ductile behavior was noted. Yet the failure was still due to punching shearing stresses. 2. The crack patterns for all these specimens were identical. The significant discrepancy among them was noted closer to their failure load in terms of ductility ratio and dimensions of the punching failure cone. Increasing the steel fiber ratio significantly improved the slab ductility and increased the projected area of the punching failure cone. 3. The results of specimens of Phase I of the research work showed that the punching cone angle of the slabs with steel fibers less than or equal to 0.5% was 45 degree. This value decreased with the increase in the steel fiber ratio to 1.0% or 1.5%. For un-fibered specimens or those with low steel fiber ratio, the punching failure cone starts at the column face as predicted in most of the available codes and standard guidelines. With the increase in the steel fiber ratio the failure plane switched away from the column face toward the weak planes in the slabs. Punching outside the fibered-concrete zone was observed in slabs B1, C1 and D1. Precisely, the failure was developed by localization of the strains in a critical shear plane closer to the edge of the zone with steel fiber. As the result of increasing the zone with steel fiber, punching cone was always observed inside the fibered-zone.
Comparison experimental and finite element predicted results.
Group
Symbol
Experimental
Numerical
Num./Exp.
PU (kN)
DU (mm)
PU (kN)
DU (mm)
Load
Deflection
Group A
A1 A2
275 201.7
16.6 9.53
290 160
13.24 4.48
1.054 0.793
0.798 0.470
Group B
B1 B2 B3
300 320 400
15.1 15.98 19.03
320 350 370
9.65 10.70 11.17
1.066 1.094 0.925
0.639 0.670 0.587
Group C
C1 C2 C3
335 350 375
17.55 17.17 16.57
350 360 390
15.51 16.36 14.12
1.045 1.029 1.040
0.884 0.953 0.852
Group D
D1 D2 D3
345 369 385
13.57 11.83 11.39
360 380 400
14.17 13.89 10.73
1.200 1.152 1.066
1.044 1.174 0.942
Group E
E1 E2 E3
225 238 250
10.08 9.98 10.05
180 190 200
4.05 4.28 3.78
0.800 0.798 0.800
0.402 0.429 0.376
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001
10 4. It was found that load-deflection curves had almost the same profile for all specimens in Groups A, B, C and D. The curve initially had a steep behavior until cracking load. Once the first crack initiated, the load-deflection relationship started to be more curved until reaching the ultimate load of the slab. 5. In general, it has been found that the axial strains of the flexural reinforcement were inversely proportional to the distance from slab center. Also, the reinforcement passing the failure cone boundaries had the greatest value of strain. Moreover, it was noticed that the tension reinforcement did not reach the yield point before the punching failure. The maximum strain recorded was 1200le (yield strain is about 2000le). 6. It was obvious that increasing the steel fiber ratio increased both the initial and tangent slopes of the load-deformation curve. For example increasing the steel fiber ratio from 0% (Specimen A1) to 1.5% (Specimen B3) increased the initial stiffness of the slab by 70% (23 kN/mm for the Specimen A1 and 33.3 kN/mm for the Specimen B3).
Phase II: eccentric loaded slabs 1. The purpose of testing these slabs under aforesaid state of loading was to determine the interaction between shear and moment capacities of the tested slabs and to understand the influence of the steel fiber ratio on such behavior. 2. It was found that the higher the steel fiber ratio was the higher the ultimate load carrying capacity of the specimens. Increasing the steel fiber by 1.5% enhanced the ultimate capacity of the specimens by 24%. The steel fiber ratio had similar effect on the ultimate load carrying capacity of the slabs in Phase I and Phase II. The ultimate load was almost linear proportional with the steel fiber ratio in both load cases. 3. The main mode of failure of all of the specimens was punching shear failure that occurred suddenly in a brittle manner around the column. In general it was noted that increasing the steel fiber did not affect the general behavior of the slab neither the failure mode. However it significantly enhanced the ultimate capacity of the slab. 4. In general, it has been concluded that the axial strains of the flexural reinforcement were inversely proportional to the distance from slab center. Also, the reinforcement passing the failure cone boundaries had the greatest value of strain. Moreover, it was noticed that the tension reinforcement reached the yield point for the three tested specimens with value about 6000le and this occurred only at the strain gauges located exactly at the column face. Yet all other strain gauges did not record any yielding strain. This indicated that small portion of the steel reinforcement reached the yield point.
A.M. Abdel-Rahman et al. The comparisons between the 3D finite element numerical predictions and experimental results for all the specimens showed that there was a very good agreement between the 3-D predicted load capacities and the experimental results for all the test specimens. The average numerical-to experimental load ratio is 0.98 with a standard deviation of 0.14. This indicates an excellent agreement. For all the test specimens, the finite element analysis accurately predicts the mode of failure observed in the experiments. The finite element models are also able to capture exact crack pattern observed experimentally for all tested specimens. Conflict of interest None declared. References [1] F. Altun et al, Effects of steel fiber addition on mechanical properties of concrete and RC beams, Construct. Build. Mater. 21 (2006) 654–661. [2] The European Standard EN 14889-1:2006 (CEN, 2006) – Fibers for concrete – Part 1: Steel Fibers – Definitions, Specifications and Conformity. [3] R.N. Swamy, H.M. Bahia, The effectiveness of steel fibers as shear reinforcement, Concr. Int. 7 (3) (1985) 35–40. [4] ECP-203-2012, Egyptian Code of Practice for Design and Construction of Reinforced Concrete Structures 2012. [5] A. Muttoni, M. Fernandez, The critical shear crack theory as a mechanical model for punching shear design and its application to code provisions MC2010, in: FIB Bulletin 57: Shear and Punching Shear in RC and FRC Elements, Lausanne (Switzerland), 2010. pp. 31–60. [6] K.K. Choi, N.M. Reda Taha, H.G. Park, A.K. Maji, Punching shear strength of interior concrete slab column connections reinforced with steel fibers, Cem. Concr. Compos. 29 (2007) 409–420. [7] Nguyen-Minh, M. Rovnak, T. Tran-Quoc, Nguyen-Kim, Punching shear resistance of steel fiber reinforced concrete flat slabs, in: Proceedings of the Twelfth East Asia-Pacific Conference on Structural Engineering and Construction, 2011, EASEC12, pp. 1830–1837. [8] S.D.B. Alexander, S.H. Simmonds, Punching shear tests of concrete slab-column joints containing fiber reinforcement, ACI Struct. J. 89 (4) (1992) 425–432. [9] ACI Committee 318, Building Code Requirements for Structural Concrete and Commentary (ACI 318M–05), American Concrete Institute, Farmington Hills, MI, 2005, p. 430. [10] ANSYS, ANSYS Help. Release 14.5 Copyright, 2012. [11] C.D. Johnston, Steel fiber reinforced mortar and concrete. A review of mechanical properties. In fiber reinforced concrete ACI – SP 44 – Detroit, 1974.
Please cite this article in press as: A.M. Abdel-Rahman et al., Punching shear behavior of reinforced concrete slabs using steel fibers in the mix, HBRC Journal (2016), http://dx.doi.org/10.1016/j.hbrcj.2016.11.001