Lajes lisas de concreto armado com aberturas em diferentes distâncias do pilar

Lourenço, Diego da Silva; Liberati, Elyson Andrew Pozo; Marques, Marília Gonçalves; Almeida, Luiz Carlos de; Trautwein, Leandro Mouta

Diego da Silva Lourenço

State University of Campinas - UNICAMP, School of Civil Engineering, Architecture and Urban Design, Campinas, São Paulo, Brazil

http://orcid.org/0000-0001-6703-1336

Elyson Andrew Pozo Liberati

State University of Maringá - UEM, Civil Engineering Department, Maringá, Paraná, Brazil

http://orcid.org/0000-0002-7905-1593

Marília Gonçalves Marques

Federal University of Viçosa - UFV, Rio Paranaiba, Brazil, Brazil

http://orcid.org/0000-0003-0234-5224

Luiz Carlos de Almeida

State University of Campinas - UNICAMP, School of Civil Engineering, Architecture and Urban Design, Campinas, São Paulo, Brazil

http://orcid.org/0000-0001-8431-8929

Leandro Mouta Trautwein

State University of Campinas - UNICAMP, School of Civil Engineering, Architecture and Urban Design, Campinas, São Paulo, Brazil

http://orcid.org/0000-0002-4631-9290

Corresponding author: Elyson Andrew Pozo Liberati. E-mail: eapliberati@uem.br

Conflict of interest: Nothing to declare.

Author contributions: LIBERATI and MARQUES: conceptualization, writing, data curation, formal analysis, methodology, writing, data curation; ALMEIDA and TRAUTEWIN: funding acquisition, supervision.

Editors: Maurício de Pina Ferreira, José Luiz Antunes de Oliveira e Sousa, Guilherme Aris Parsekian.

Slab	Openings [mm]	s [mm]	Column [mm]	ρ [%]	d [mm]	f_c [MPa]	f_t [MPa]	E_c [GPa]
LR	-	-	150 x 150	1.58	90	39.8	3.4	32.0
LF1	150 x 150	0	150 x 150	1.23	92	46.0	3.8	37.5
LF2	150 x 150	90	150 x 150	1.26	91	46.3	3.8	37.8
LF3	150 x 150	180	150 x 150	1.23	92	45.9	3.8	37.4
LF4	150 x 150	270	150 x 150	1.49	93	41.2	3.6	31.3

Local	Slab	Bar size [mm]	f_y [MPa]	ε_y [mm/m]	f_u [MPa]	ε_u [mm/m]	E_s [GPa]
Top reinforcement	LR	12.5	576	3.2	735	15.4	180
	LF4		576	3.2	735	15.4	180
	LF1		563	2.85	728	15.5	198
	LF2
	LF3
Bottom reinforcement	All slabs	6.3	569	3.1	724	9.9	184

Slab	f_c [MPa]	d [mm]	V_u^{^a} [kN]	V_u^{^a}/V_flex^{^b}	V_u,norm^{^c} [kN]	Energy Dissipation Capacity [kNmm]	Failure Mode
LR	39.8	90	247	0.51	-	1,945.78	Punching
LF1	46.0	92	221	0.64	206	1,505.88	Punching
LF2	46.3	91	250	0.64	232	1,761.34	Punching
LF3	45.9	92	231	0.59	215	2,105.93	Punching
LF4	41.2	93	273	0.57	268	2,126.35	Punching

Authors	Slab	Openings [mm]	s [mm]	d [mm]	f_c [MPa]	b_0,ACI [mm]	V_u [kN]	V_u/(b₀d√f_c) [√MPa]
Test results	LR	-	-	90	39.8	960	247	0.453
	LF1	1x(150 x 150)	0	92	46.0	726	221	0.488
	LF2	1x(150 x 150)	90	91	46.3	855	250	0.472
	LF3	1x(150 x 150)	180	92	45.9	898	231	0.413
	LF4	1x(150 x 150)	270	93	41.2	920	273	0.497
Teng et al. [¹⁰10 S. Teng, H. K. Cheong, K. L. Kuang, and J. Z. Geng, "Punching shear strength of slabs with openings and supported on rectangular columns," ACI Struct. J., vol. 101, no. 5, pp. 678–687, 2004.]	OC11	-	-	105	36.0	1,224	423	0.548
	OC11H30	1x(400 x 200)	0	108	33.9	924	349	0.601
	OC11V20	1x(200 x 400)	0	105	38.6	765	207	0.415
	OC13H50	1x(400 x 200)	0	110	36.3	1,803	443	0.371
	OC13V40	1x(200 x 400)	0	109	43.0	1,485	340	0.320
Borges et al. [¹¹11 L. L. J. Borges, G. S. Melo, and R. B. Gomes, "Punching shear of reinforced concrete flat plates with openings," ACI Struct. J., vol. 110, no. 4, pp. 1-10, 2013.]	1	-	-	100	20.8	1200	193	0.352
	2	1x(300 x 300)	0	100	20.6	800	99	0.273
	4	1x(500 x 500)	0	100	19.6	720	77	0.241
	6	1x(300 x 300)	300	100	20.0	1200	135	0.251
	8	1x(500 x 500)	300	100	20.1	1200	116	0.215
Balomenos et al. [¹⁴14 G. P. Balomenos, A. S. Genikomsou, and M. A. Polak, "Investigation of the effect of openings of interior reinforced concrete flat slabs," Struct. Concr., vol. 19, pp. 1–10, 2018., http://dx.doi.org/10.1002/suco.201700201. http://dx.doi.org/10.1002/suco.201700201... ]	SB1-0	2x(70 x 70)	0	90	44.0	1,114	182	0.274
	SB-0	2x(150 x 150)	0	90	44.0	660	145	0.368
	SB1-1	2x(70 x 70)	90	90	44.0	1,180	198	0.281
	SB-1	2x(150 x 150)	90	90	44.0	1,020	180	0.296
	SB1-2	2x(70 x 70)	180	90	44.0	1,229	213	0.290
	SB-2	2x(150 x 150)	180	90	44.0	1,126	197	0.293
	SB1-3	2x(70 x 70)	270	90	44.0	1,253	218	0.291
	SB-3	2x(150 x 150)	270	90	44.0	1,177	212	0.302

Slab	Eurocode 2 [¹1 European Committee for Standardization, EN 1992-1-1: Design of Concrete Structures, Part 1-1: General Rules and Rules for Buildings. Brussels, Belgium: CEN, 2010.] [mm]	NBR 6118 [²2 Brazilian Association of Technical Standards, NBR 6118: Design of Concrete Structures – Procedures. Rio de Janeiro, Brazil, 2014.] [mm]	ACI 318 [³3 American Concrete Institute, ACI 318R-19: Building Code Requirements for Structural Concrete and Commentary. Farmington Hills, MI, USA: American Concrete Institute, 2019.] [mm]	fib Model Code [⁴4 Federation Internationale Du Béton, Model Code for Concrete Structures. Germany: Ernst & Sohn, 2010.] [mm]
LR	1,731	1,731	960	883
LF1	1,318	1,318	726	667
LF2	1,514	1,514	855	776
LF3	1,606	1,606	898	819
LF4	1,658	1,658	920	840

Slab	V_u [kN]	V_EC [kN]	V_u/V_EC	V_NBR [kN]	V_u/V_NBR	V_ACI [kN]	V_u/V_ACI	V_MC [kN]	V_u/V_MC
LR	247	223	1.11	278	0.89	180	1.37	207	1.19
LF1	221	168	1.32	207	1.07	150	1.47	165	1.34
LF2	250	192	1.30	239	1.05	175	1.43	190	1.32
LF3	231	204	1.13	253	0.91	185	1.25	202	1.14
LF4	273	219	1.25	270	1.01	181	1.51	206	1.33
*Average*			1.22		0.99		1.41		1.26
CV (%)			7.9		8.1		7.2		7.0

V_{ACI} = min \{\begin{matrix} 0 .33 \cdot λ_{s} \cdot \sqrt{f_{c}} \cdot b_{0} \cdot d \\ 0 .17 \cdot (1 + \frac{2}{β}) \cdot λ_{s} \cdot \sqrt{f_{c}} \cdot b_{0} \cdot d \\ 0 .08 \cdot (2 + \frac{α_{s} d}{b_{0}}) \cdot λ_{s} \cdot \sqrt{f_{c}} \cdot b_{0} \cdot d \end{matrix}

[1] Corresponding author: Elyson Andrew Pozo Liberati. E-mail: eapliberati@uem.br

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Lajes lisas de concreto armado com aberturas em diferentes distâncias do pilar

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