This paper examines the structural response of reinforced concrete flat slabs, provided with fully-embedded shear-heads, through detailed three-dimensional nonlinear numerical simulations and parametric assessments using concrete damage plasticity models. Validations of the adopted nonlinear finite element procedures are carried out against experimental results from three test series. After gaining confidence in the ability of the numerical models to predict closely the full inelastic response and failure modes, numerical investigations are carried out in order to examine the influence of key material and geometric parameters. The results of these numerical assessments enable the identification of three modes of failure as a function of the interaction between the shear-head and surrounding concrete. Based on the findings, coupled with results from previous studies, analytical models are proposed for predicting the rotational response as well as the ultimate strength of such slab systems. Practical recommendations are also provided for the design of shear-heads in RC slabs, including the embedment length and section size. The analytical expressions proposed in this paper, based on a wide-ranging parametric assessment, are shown to offer a more reliable design approach in comparison with existing methods for all types of shear-heads, and are suitable for direct practical application.
. [J]. Frontiers of Structural and Civil Engineering, 2020, 14(2): 331-356.
Dan V. BOMPA, Ahmed Y. ELGHAZOULI. Nonlinear numerical simulation of punching shear behavior of reinforced concrete flat slabs with shear-heads. Front. Struct. Civ. Eng., 2020, 14(2): 331-356.
cruciform shear-head made of I sections or back-to-back welded channels
CTP:
cruciform shear-head with two-way two pair of channels running at the column
supportd:
bending effective depth
d0:
shear effective depth
dg0, dg:
aggregate size
dvfb:
centroid of bottom flange
Ec:
elastic concrete modulus
Es, Ev:
steel elastic modulus
fc:
concrete strength
fct:
tensile strength of concrete
fys:
reinforcement yield strength
fyv:
shear-head yield strength
h:
flat slab thickness
hv:
shear-head depth
ky:
factor for failure criterion
Kc:
factor for the shape of the deviatoric plane
L:
specimen size/span
lm:
mesh size
lv:
shear-head embedded length
Mv,i:
moment carried by one shear-head
Mv,i,R:
moment capacity of one shear-head
mi:
moment action per unit width
mRk:
plastic moment of hybrid sectors
mRc:
plastic moment of concrete sectors
nv:
number of shear-heads
rc
= 2bc/p and bc = (bc1 + bc2)/2 (for rectangular columns)
re:
exterior slab radius
rs:
slab radius (loading radius)
tf:
shear-head flange thickness
tw:
shear-head web thickness
V:
load
Ve:
volume of the mesh element
Vflex:
is the flexural strength
Vi:
is the shear action
Vtest:
test ultimate strength
Vnum:
numerical ultimate strength
Vu:
ultimate punching shear strength
Wv,pl:
shear-head plastic section modulus
d:
displacement response
e:
strain
ec1:
crushing strain
h:
shear-head distribution factor
к:
force distribution factor
ly:
rotation coefficient
lm:
flexibility factor
m:
steel-concrete friction coefficient
rl:
flexural reinforcement ratio
s:
stress
sc,max:
strut crushing strength
q:
punching shear crack angle
j:
dilation angle
y:
rotation
ε:
potential eccentricity
1
S Lips, M Fernández Ruiz, A Muttoni. Experimental investigation on punching strength and deformation capacity of shear-reinforced slabs. ACI Structural Journal, 2012, 109: 889–900
2
H G Park, Y N Kim, J G Song, S M Kang. Lattice shear reinforcement for enhancement of slab-column connections. Journal of Structural Engineering, 2012, 138(3): 425–437 https://doi.org/10.1061/(ASCE)ST.1943-541X.0000484
3
A V Gosav, Z I Kiss, T Oneţ, D V Bompa. Failure assessment of flat slab-to-column members. Magazine of Concrete Research, 2016, 68(17): 887–901 https://doi.org/10.1680/jmacr.15.00405
4
S. Bryl Flat slabs with shear-heads. Schweizerische Bauzeitung, 1969, 87(10): 181–183 (in German)
5
R Gomes, P Regan. Punching strength of slabs reinforced for shear with offcuts of rolled steel I-section beams. Magazine of Concrete Research, 1999, 51(2): 121–129 https://doi.org/10.1680/macr.1999.51.2.121
6
W G Corley, N M Hawkins. Shear-head reinforcement for slabs. ACI Journal Proceedings, 1968, 65(10): 811–824 https://doi.org/10.14359/7514
7
N W Hawkins, W G Corley. Moment transfer to columns in slabs with shear-head reinforcement. Special Publication, 1974, 42: 847–880
8
R K Al-Hamd, M Gillie, L S Cunningham, H Warren, A S Albostami. Novel shear-head reinforcement for slab-column connections subject to eccentric load and fire. Archives of Civil and Mechanical Engineering, 2019, 19(2): 503–524 https://doi.org/10.1016/j.acme.2018.12.011
9
B Ngekpe, S Abbey, A Olubanwo. Structural performance of a modified shear-head assembly for edge steel column embedded in reinforced concrete slab. Engineering Solid Mechanics, 2019, 7(1): 59–70 https://doi.org/10.5267/j.esm.2018.11.001
10
S G Gilbert, C Glass. Punching failure of reinforced concrete flat slabs at edge columns. Structural Engineer. Part B, 1987, 65: 16–28
11
A Kenel, T. Keller External Steel Shear Heads for Retroactive Enhancement of Punching Shear Strength in Existing Flat Slabs. Technical Report. F. J. Aschwanden AG, CH-3250. 2013
12
D V Bompa, A Y Elghazouli. Structural performance of RC flat slabs connected to steel columns with shear-heads. Engineering Structures, 2016, 117: 161–183 https://doi.org/10.1016/j.engstruct.2016.03.022
13
J Kahn. US Patent, 926,497. 1909
14
R M Hardison. US Patent, 1,550,317. 1925
15
W H Wheeler. Thin flat-slab floors prove rigid under test. Engineering News Record, 1936, 116(2): 49–50
16
T Godycki, J Kozicki. Eccentrically loaded interior slab-column connections with shear-head reinforcement. Materials and Structures, 1984, 17(2): 145–148 https://doi.org/10.1007/BF02473666
17
M M Majeed, A N. Abbas Punching shear strength characteristics of flat plate panels reinforced with shear-head collars: Experimental investigation. Civil Engineering Journal, 2019, 5(3): 528–539
18
K M Huber, S Bryl. Discussion of “Shear reinforcement for concrete slabs” by Walter H. Dilger and Amin Ghali (December, 1981). Journal of Structural Engineering, 1984, 110(1): 169–171 https://doi.org/10.1061/(ASCE)0733-9445(1984)110:1(169)
19
T Frangi, D Tonis, A Muttoni. Assessment of column supports made of steel. Schweizer Ingenieur und Architekt, 1997, 1997: 12–14 (in German)
20
P S Chana, F K Birjandi. Design Guidance on Structural Steel Shear-Heads in Concrete (Shear-Head Development Tests). Concrete Research and Innovation Centre, Imperial College, London. Report No. CRIC95/001/F. 1996
21
W Piel, G Hanswille. Composite shear-head systems for improved punching shear resistance of flat slabs. Construction in Steel and Concrete, 2006, V: 226–235 https://doi.org/10.1061/40826(186)22
22
A Y Elghazouli, B A Izzuddin. Realistic modeling of composite and reinforced concrete floor slabs under extreme loading. II: Verification and application. Journal of Structural Engineering, 2004, 130(12): 1985–1996 https://doi.org/10.1061/(ASCE)0733-9445(2004)130:12(1985)
23
J M Castro, A Y Elghazouli, B A Izzuddin. Modelling of the panel zone in steel and composite moment frames. Engineering Structures, 2005, 27(1): 129–144 https://doi.org/10.1016/j.engstruct.2004.09.008
24
J M Castro, A Y Elghazouli, B A Izzuddin. Assessment of effective slab widths in composite beams. Journal of Constructional Steel Research, 2007, 63(10): 1317–1327 https://doi.org/10.1016/j.jcsr.2006.11.018
25
J Lemaitre. Evaluation of dissipation and damage in metals submitted to dynamic loading. In: Proceedings of International Conference of Mechanical Behavior of Materials 1 (ICM 1). Kyoto: The Society of Material Science, 1971, 1–20
26
Z P Bažant, B H Oh. Crack band theory for fracture of concrete. Matériaux et Constructions, 1983, 16(3): 155–177 https://doi.org/10.1007/BF02486267
J Ozbolt. Size effect and ductility of concrete and reinforced concrete structures. Dissertation for Habilitation. Stuttgart: Universität Stuttgart, 1995
29
T Rabczuk, J Akkermann, J Eibl. A numerical model for reinforced concrete structures. International Journal of Solids and Structures, 2005, 42(5–6): 1327–1354 https://doi.org/10.1016/j.ijsolstr.2004.07.019
30
T N Bittencourt, P A Wawrzynek, A R Ingraffea, J L Sousa. Quasi-automatic simulation of crack propagation for 2D LEFM problems. Engineering Fracture Mechanics, 1996, 55(2): 321–334 https://doi.org/10.1016/0013-7944(95)00247-2
31
S Loehnert, T Belytschko. A multiscale projection method for macro/microcrack simulations. International Journal for Numerical Methods in Engineering, 2007, 71(12): 1466–1482 https://doi.org/10.1002/nme.2001
32
J Oliyer. Continuum modelling of strong discontinuities in solid mechanics using damage models. Computational Mechanics, 1995, 17(1–2): 49–61 https://doi.org/10.1007/BF00356478
33
P Areias, T Rabczuk. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122 https://doi.org/10.1002/nme.4477
34
P Areias, T Rabczuk, P P Camanho. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63 https://doi.org/10.1016/j.tafmec.2014.06.006
J Oliver. A consistent characteristic length for smeared cracking models. International Journal for Numerical Methods in Engineering, 1989, 28(2): 461–474 https://doi.org/10.1002/nme.1620280214
37
R Fan, J Fish. The RS-method for material failure simulations. International Journal for Numerical Methods in Engineering, 2008, 73(11): 1607–1623 https://doi.org/10.1002/nme.2134
38
D V Swenson, A R Ingraffea. Modeling mixed-mode dynamic crack propagation using finite elements: Theory and applications. Computational Mechanics, 1988, 3(6): 381–397 https://doi.org/10.1007/BF00301139
39
G T Camacho, M Ortiz. Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures, 1996, 33(20–22): 2899–2938 https://doi.org/10.1016/0020-7683(95)00255-3
40
G Lilliu, J G M. van Mier Simulation of 3D crack propagation with the lattice model. In: Proceedings of the International Congress on Advanced Materials, Processes and Applications (Materials Week). Frankfurt: Bauverlag BV GambH, 2000
41
J Oliver. On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations. International Journal of Solids and Structures, 2000, 37(48–50): 7207–7229 https://doi.org/10.1016/S0020-7683(00)00196-7
42
J H Song, P M A Areias, T Belytschko. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering, 2006, 67(6): 868–893 https://doi.org/10.1002/nme.1652
43
T Rabczuk, T Belytschko. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343 https://doi.org/10.1002/nme.1151
44
T Rabczuk, G Zi. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760 https://doi.org/10.1007/s00466-006-0067-4
45
T Rabczuk, G Zi, S Bordas, H Nguyen-Xuan. A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758 https://doi.org/10.1016/j.engfracmech.2008.06.019
46
T Rabczuk, T Belytschko. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49 https://doi.org/10.1007/s10704-005-3075-z
47
T Rabczuk, T Belytschko. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799 https://doi.org/10.1016/j.cma.2006.06.020
48
T Rabczuk, G Zi, S Bordas, H Nguyen-Xuan. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455 https://doi.org/10.1016/j.cma.2010.03.031
49
T Rabczuk, S Bordas, G Zi. On three-dimensional modelling of crack growth using partition of unity methods. Computers and Structures, 2010, 88(23–24): 1391–1411
50
P Areias, M A Msekh, T Rabczuk. Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143 https://doi.org/10.1016/j.engfracmech.2015.10.042
51
P Areias, T Rabczuk. Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elements in Analysis and Design, 2017, 132: 27–41 https://doi.org/10.1016/j.finel.2017.05.001
52
P Areias, T Rabczuk, M A Msekh. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 322–350 https://doi.org/10.1016/j.cma.2016.01.020
53
P Areias, J Reinoso, P P Camanho, J César de Sá, T Rabczuk. Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation. Engineering Fracture Mechanics, 2018, 189: 339–360 https://doi.org/10.1016/j.engfracmech.2017.11.017
54
L Kachanov. Rupture time under creep conditions. Izvestiia Akademii Nauk SSSR. Seriia Khimicheskaia, 1958, 8: 26–31
55
U Cicekli, G Z Voyiadjis, R K Abu Al-Rub. A plasticity and anisotropic damage model for plain concrete. International Journal of Plasticity, 2007, 23(10–11): 1874–1900 https://doi.org/10.1016/j.ijplas.2007.03.006
56
P Grassl, M Jirásek. Damage-plastic model for concrete failure. International Journal of Solids and Structures, 2006, 43(22–23): 7166–7196 https://doi.org/10.1016/j.ijsolstr.2006.06.032
B Xu, D V Bompa, A Y Elghazouli, A M Ruiz-Teran, P J Stafford. Behaviour of rubberised concrete members in asymmetric shear tests. Construction & Building Materials, 2018, 159: 361–375 https://doi.org/10.1016/j.conbuildmat.2017.10.091
R V Gorga, L F Sanchez, B Martín-Pérez. FE approach to perform the condition assessment of a concrete overpass damaged by ASR after 50 years in service. Engineering Structures, 2018, 177: 133–146 https://doi.org/10.1016/j.engstruct.2018.09.043
61
B Belletti, A Muttoni, S Ravasini, F Vecchi. Parametric analysis on punching shear resistance of reinforced concrete continuous slabs. Magazine of Concrete Research, 2018, 12: 1–32 https://doi.org/10.1680/jmacr.18.00123
62
A Marí, A Cladera, E Oller, J M Bairán. A punching shear mechanical model for reinforced concrete flat slabs with and without shear reinforcement. Engineering Structures, 2018, 166: 413–426 https://doi.org/10.1016/j.engstruct.2018.03.079
63
A Wosatko, J Pamin, M A Polak. Application of damage-plasticity models in finite element analysis of punching shear. Computers & Structures, 2015, 151: 73–85 https://doi.org/10.1016/j.compstruc.2015.01.008
64
M I Moharram, D V Bompa, A Y. Elghazouli Performance and design of shear-keys in hybid RC beam and steel column systems. Ce/Papers, 2017, 1(2–3): 2031–2040
65
D V Bompa, A Y. Elghazouli Force transfer mechanisms between steel columns and reinforced concrete beams by means of shear keys. In: Proceedings of EUROSTEEL 2014: The 7th European Conference on Steel and Composite Structures. Napoli: ECCS, 2014, 10–12
66
H Behnam, J S Kuang, B Samali. Parametric finite element analysis of RC wide beam-column connections. Computers & Structures, 2018, 205: 28–44 https://doi.org/10.1016/j.compstruc.2018.04.004
67
J D Nzabonimpa, W K Hong, J Kim. Nonlinear finite element model for the novel mechanical beam-column joints of precast concrete-based frames. Computers & Structures, 2017, 189: 31–48 https://doi.org/10.1016/j.compstruc.2017.04.016
68
M A Eder, R L Vollum, A Y Elghazouli, T Abdel-Fattah. Modelling and experimental assessment of punching shear in flat slabs with shear-heads. Engineering Structures, 2010, 32(12): 3911–3924 https://doi.org/10.1016/j.engstruct.2010.09.004
69
D V Bompa, A Y Elghazouli. Numerical modelling and parametric assessment of hybrid flat slabs with steel shear heads. Engineering Structures, 2017, 142: 67–83 https://doi.org/10.1016/j.engstruct.2017.03.070
70
D V Bompa, A Y Elghazouli. Ultimate behaviour and design of hybrid flat slabs with steel shear heads. Ce/Papers, 2017, 1(2–3): 2310–2319
71
B Burley, T. Boothby Medical Office Building Malvern, PA. Final Report. Penn State University, Technical Report. 2005
72
M N Gnädinger. Punching shear strength of flat slabs with shear-heads. Thesis for the Master’s Degree. Lucerne: Hochschule Luzern, 2011
73
K De Sutter. Numerical investigation of the punching shear behaviour of flat plates with column head strengthening. Thesis for the Master’s Degree. Munchen: Technische Universitat Munchen, 2015
74
J Hugenschmidt, A Fischer, L Schiavi. Investigation of punching reinforcement in flat slabs. Beton- und Stahlbetonbau, 2014, 109(4): 257–264 (In German) https://doi.org/10.1002/best.201300086
75
A Zhang, X Ma, H Fang, J Mu, T Liu. Seismic behaviour of connections between prefabricated RC flat slabs and square steel tube columns. Engineering Structures, 2018, 173: 800–812 https://doi.org/10.1016/j.engstruct.2018.07.040
76
J W Kim, C H Lee, T H K Kang. Shear-head reinforcement for concrete slab to concrete-filled tube column connections. ACI Structural Journal, 2014, 111(3): 629–638 https://doi.org/10.14359/51686623
CEN (European Committee for Standardization). EN 1992-1-1. Eurocode 2: Design of Concrete Structures—Part 1-1: General Rules and Rules for Buildings. Brussels: CEN, 2004
79
The International Federation for Structural Concrete: FIB. FIB Bulletin No. 66-Model Code 2010—Final draft, Vol 2. Lausanne: The International Federation for Structural Concrete: FIB, 2012
80
ACI (American Concrete Institute). ACI 318M-14 Building Code Requirements for Structural Concrete and Commentary. Farmington Hills, MI: ACI, 2014
81
S Guandalini, O L Burdet, A Muttoni. Punching tests of slabs with low reinforcement ratios. ACI Structural Journal, 2009, 106: 87–95 https://doi.org/10.14359/56287
M I Moharram, D V Bompa, A Y Elghazouli. Experimental and numerical assessment of mixed RC beam and steel column systems. Journal of Constructional Steel Research, 2017, 131: 51–67 https://doi.org/10.1016/j.jcsr.2016.12.019
84
D A Hordijk. Local approach to fatigue of concrete. Dissertation for the Doctoral Degree. Delft: Delft University of Technology, 1991
85
D V Bompa, T Onet. Punching shear strength of RC flat slabs at interior connections to columns. Magazine of Concrete Research, 2016, 68(1): 24–42 https://doi.org/10.1680/macr.14.00402
86
A S Genikomsou, M A Polak. Finite element analysis of punching shear of concrete slabs using damaged plasticity model in ABAQUS. Engineering Structures, 2015, 98: 38–48 https://doi.org/10.1016/j.engstruct.2015.04.016
87
D V Bompa, T Onet. Identification of concrete damaged plasticity constitutive parameters. In: The National Technical Scientific Conference—Modern Technologies for the 3rd Millenium. Oradea: University of Oradea, 2010