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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (2) : 331-356     https://doi.org/10.1007/s11709-019-0596-5
RESEARCH ARTICLE
Nonlinear numerical simulation of punching shear behavior of reinforced concrete flat slabs with shear-heads
Dan V. BOMPA(), Ahmed Y. ELGHAZOULI
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK
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Abstract

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.

Keywords non-linear numerical modelling      concrete damage plasticity      RC flat slabs      shear-heads      punching shear     
Corresponding Authors: Dan V. BOMPA   
Online First Date: 16 March 2020    Issue Date: 08 May 2020
 Cite this article:   
Dan V. BOMPA,Ahmed Y. ELGHAZOULI. Nonlinear numerical simulation of punching shear behavior of reinforced concrete flat slabs with shear-heads[J]. Front. Struct. Civ. Eng., 2020, 14(2): 331-356.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-019-0596-5
http://journal.hep.com.cn/fsce/EN/Y2020/V14/I2/331
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Ahmed Y. ELGHAZOULI
Fig.1  Schematic of failure surfaces for specimens with and without cruciform shear-heads [6]: (a) AN-1, (b) AC-1, (c) AH-1; (d) crack distribution for closed box shear-heads [19]; (e) crack patterns for hybrid RC flat slabs with cruciform shear-heads [12].
Fig.2  Schematic representation of (a) full scale specimens PG1, PG2b, PG5, PG10, PG11; (b) half scale specimens PG6, PG7, PG8, PG9; (c) double scale specimen PG3 from Guandalini [81]; (d) FSSH series; (e) SH series from Chana and Birjandi [20]; (f) A and B series (Corley and Hawkins [6]); cruciform shear-heads made of (g) welded back-to-back channel or I section (CRH); (h) two pairs of channels at the support region (CTP) shear-heads; (i) closed-box shear-heads (CBX).
Fig.3  Numerical models: (a) typical axisymmetric 3D representation; (b) side view and mesh; (c) uniaxial concrete model; (d) steel model; (e) basic friction model; (f) decay law.
Fig.4  Identification of constitutive and numerical parameters for PG1 [81]: (a) mesh size; (b) tension stiffening reponse; (c) dilation angle φ.
Fig.5  Numerical validation: Guandalini et al. test series [47]. (a) PG2b; (b) PG4; (c) PG5; (d) PG10; (e) PG3; (f) PG1; (g) PG6; (h) PG 11 (continuous curves: V-d from numerical simulations, while dashed black curves depict V-d from tests).
specimen shear-head section shear-head type shear-head length lv (mm) column size bc (mm) slab radius rs (mm) slab thickness h (mm) effective depth d (mm) shear depth d0 (mm) reinforcement ratio rl (%) rebar yield strength fys (MPa) concrete strength fc (MPa) test strength Vtest (kN) prediction
Vnum (kN)
Vtest/
Vnum
PG3 N/A 520 2850 500 456 456 0.33 520 32 2153 2218 0.97
PG1 N/A 260 1500 250 210 210 1.50 573 28 1023 991 1.03
PG11 N/A 260 1500 250 210 210 0.75 570 32 763 775 0.98
PG2b N/A 260 1500 250 210 210 0.25 552 41 440 458 0.96
PG4 N/A 260 1500 250 210 210 0.25 541 32 408 448 0.91
PG5 N/A 260 1500 255 210 210 0.33 555 29 550 528 1.04
PG10 N/A 260 1500 255 210 210 0.33 577 29 540 533 1.01
PG6 N/A 130 752 125 96 96 1.50 526 35 238 230 1.04
PG7 N/A 130 752 125 100 100 0.75 550 35 241 220 1.09
PG8 N/A 130 752 140 117 117 0.33 525 35 140 149 0.94
PG9 N/A 130 752 140 117 117 0.25 525 35 115 125 0.92
AN-1 N/A 254 914 146 111 111 1.50 403 19 334 314 1.06
AC-1 2 × C 3” 7.1 CTP 330 254 914 146 111 82 1.50 404 18 544 530 1.03
AC-2 2 × C 3” 7.1 CTP 483 254 914 146 111 82 1.50 413 18 479 465 1.03
AC-3 2 × C 3” 4.1 CTP 406 254 914 146 111 84 1.50 407 21 458 432 1.06
AH-1 I 3” × 7.5 CRH 381 254 914 146 111 85 1.30 438 23 426 408 1.04
AH-2 I 3” × 5.7 CRH 381 254 914 146 111 85 1.30 436 22 443 425 1.04
AH-3 I 3” × 5.7 CRH 178 254 914 146 111 85 1.30 440 22 406 414 0.98
BN-1 N/A 203 914 146 111 111 2.20 444 20 266 273 0.97
BC-1 2 × C 3” 7.1 CTP 254 203 914 146 111 82 0.80 420 20 319 342 0.93
BH-1 I 3” × 7.5 CRH 432 203 914 146 111 85 1.00 437 20 394 337 1.17
BH-2 I 3” × 5.7 CRH 127 203 914 146 111 85 1.00 423 18 301 276 1.09
BH-3 I 3” × 5.7 CRH 356 203 914 146 111 85 1.00 439 22 402 355 1.13
SH1 N/A 140 563 120 100 100 0.80 500 37 256 226 1.13
SH2 C 76 × 38 × 7 CTP 300 140 563 120 100 71 0.80 500 35 405 388 1.04
SH3 C 76 × 38 × 7 CRH 275 140 563 120 100 71 0.80 500 36 420 421 1.00
SH5 C 76 × 38 × 7 CBX 200 140 563 120 100 71 0.80 500 34 437 406 1.08
SH16 C 76 × 38 × 7 CTP 300 140 563 120 100 71 0.80 500 31 376 411 0.92
SH7 N/A 140 563 120 98 98 1.50 500 36 312 339 0.92
SH8 C 76 × 38 × 7 CTP 300 140 563 120 98 69 1.50 500 32 542 505 1.07
SH9 C 76 × 38 × 7 CRH 275 140 563 120 98 69 1.50 500 35 592 516 1.15
SH11 C 76 × 38 × 7 CBX 200 140 563 120 98 69 1.50 500 31 580 564 1.03
FSSH1 N/A 300 1200 250 205 205 1.00 500 34 976 1008 0.97
FSSH2 C127 × 64 × 15 CRH 615 300 1200 250 205 134 1.00 500 31 1484 1515 0.98
FSSH3 C127 × 64 × 15 CTP 615 300 1200 250 205 134 1.00 500 33 1745 1533 1.14
FSSH4 C102 × 51 × 10 CBX 410 300 1200 250 205 123 1.00 500 34 1611 1611 1.00
Tab.1  Comparison between ultimate strengths obtained from tests and numerical simulations
Fig.6  Numerical validations: Chana and Birjandi test series [20]. (a) SH1; (b) SH2; (c) SH3; (d) SH5; (e) SH7; (f) SH8; (g) SH0; (h) SH11; (i) FSSH1; (j) FSSH2; (k) FSSH3; (l) FSSH4 (continuous black curves represent the V-d from numerical simulations, while dashed black curves depict V-d from tests).
Fig.7  Tension damage patterns for slabs with and without shear-heads, and stresses in shear-heads for Specimens: (a) SH2; (b) SH3; (c) SH5; (d) SH1.
Fig.8  Numerical validations for Corley and Hawkins test series [6]: (a) AN-1; (b) AC-1; (c) AC-2; (d) AC-3; (e) AH-1; (f) AH-2; (g) AH-3; (h) BN-1; (i) BC-1; (j) BH-1; (k) BH-2; (l) BH-3 (continuous black curves represent the V-d from numerical simulations, while dashed black curves depict V-d from tests).
Fig.9  Influence of the embedment length on the tension damage and compression fields.
Fig.10  Influence of the embedment length and reinforcement ratio on the slab capacity and rotation: (a) CTP, d = 170 mm, hv = 100 mm, lv/hv = 1.0, fc = 30 MPa; (b) CTP, d = 170 mm, hv = 100 mm, lv/hv = 3.0, fc = 30 MPa; (c) CTP, d = 170 mm, hv = 100 mm, lv/hv = 5.0, fc = 30 MPa; (d) CRH, d = 170 mm, hv = 100 mm, lv/hv = 1.0, fc = 30 MPa; (e) CRH, d = 170 mm, hv = 100 mm, lv/hv = 3.0, fc = 30 MPa; (f) CRH, d = 170 mm, hv = 100 mm, lv/hv = 5.0, fc = 30 MPa; (g) CBX, d = 170 mm, hv = 100 mm, lv/hv = 1.0, fc = 30 MPa; (h) CBX, d = 170 mm, hv = 100 mm, lv/hv = 2.0, fc = 30 MPa; (i) CBX, d = 170 mm, hv = 100 mm, lv/hv = 5.0, fc = 30 MPa.
Fig.11  Influence of the slab radius on the slab capacity and rotations: (a) CTP, d = 270 mm, hv = 150 mm, rl = 0.7%, fc = 30 MPa; (b) CTP, d = 370 mm, hv = 200 mm, rl = 0.5%, fc = 30 MPa; (c) CRH, d = 290 mm, hv = 160 mm, rl = 0.7%, fc = 30 MPa; (d) CRH, d = 370 mm, hv = 200 mm, rl = 0.5%, fc = 30 MPa; (e) CBX, d = 270 mm, hv = 150 mm, rl = 0.9%, fc = 30 MPa; (f) CBX, d = 370 mm, hv = 200 mm, rl = 0.7%, fc = 30 MPa.
Fig.12  Influence of the slab depth on the slab capacity and rotation: (a) CTP, d = 270 mm, lv/hv = 3.0, hv = 150 mm, fc = 30 MPa; (b) CTP, d = 370 mm, lv/hv = 3.0, hv = 200 mm, fc = 30 MPa; (c) CRH, d = 290 mm, lv/hv = 3.0, hv = 160 mm, fc = 30 MPa; (d) CRH, d = 370 mm, lv/hv = 3.0, hv = 200 mm, fc = 30 MPa; (e) CBX, d = 270 mm, lv/hv = 3.0, hv = 150 mm, fc = 30 MPa; (f) CBX, d = 370 mm, lv/hv = 3.0, hv = 200 mm, fc = 30 MPa.
Fig.13  Relationship between (a) capacity ratio and lv/d, (b) rotation ratio and lv/d; for concrete strength of 30 and 50 MPa.
Fig.14  (a) Strut transfer scheme for slabs with shear-heads; control perimeter for: (b) slabs with cruciform H/I shear-heads (CRH), (c) cruciform with two parallel channels (CTP), (d) closed box shear-heads (CBX).
Fig.15  Strength predictions for existing models: (a) ACI318, (b) Eurocode 2, (c) Model Code 2010; proposed models: (d) bilinear, (e) modified Model Code 2010.
Fig.16  Comparative assessment: (a) required control perimeter and shear-head length; (b) moment response.
Fig.17  Assumed force distribution for shear-heads as a function of embedment length: (a) lv/hv = 5.0, lv/rs = 0.36; (b) lv/hv = 3.00, lv/rs = 0.29; (c) lv/hv = 2.00, lv/rs = 0.14; (d) lv/hv = 1.00; lv/rs = 0.07.
Avv: shear-head shear active area
a: distance between parallel steel profiles
b0: control perimeter
bc: column size
bv: shear-head width
cc, ck: location of neutral axis
CBX: closed box shear-head
CRH: 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
  
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