Assessment of design codes for the in-service behaviour of steel-concrete composite slabs

Oliveira, Lucas Antônio Morais; Borghi, Tainá Mascarenhas; Rodrigues, Yury Ouriques; El Debs, Ana Lucia Homce de Cresce

doi:10.1590/S1983-41952021000500001

Lucas Antônio Morais Oliveira

Universidade de São Paulo – USP, Escola de Engenharia de São Carlos, Departamento de Engenharia de Estruturas, São Carlos, SP, Brasil

http://orcid.org/0000-0003-0248-4814

Tainá Mascarenhas Borghi

Universidade de São Paulo – USP, Escola de Engenharia de São Carlos, Departamento de Engenharia de Estruturas, São Carlos, SP, Brasil

http://orcid.org/0000-0002-7139-8541

Yury Ouriques Rodrigues

Universidade de São Paulo – USP, Escola de Engenharia de São Carlos, Departamento de Engenharia de Estruturas, São Carlos, SP, Brasil

http://orcid.org/0000-0002-9752-3160

Ana Lucia Homce de Cresce El Debs

Universidade de São Paulo – USP, Escola de Engenharia de São Carlos, Departamento de Engenharia de Estruturas, São Carlos, SP, Brasil

http://orcid.org/0000-0001-6359-7674

Corresponding author: Lucas Antônio Morais Oliveira. E-mail: lucasantonio12@usp.br

Conflict of interest: Nothing to declare.

Author contributions: LAMO: conceptualization, data curation, formal analysis, investigation, methodology, validation, writing-original draft; TMB: conceptualization, formal analysis, visualization, writing-review & editing; YOR: data curation, investigation, validation, writing-review & editing; ALHCE: conceptualization, resources, supervision, visualization, writing-review & editing.

Editors: Samir Maghous, Guilherme Aris Parsekian.

Profile Steel Decking	Thickness $(t_{s d})$	Cross Section Area $(A_{s d})$	Centroid Height $(h_{s d})$	Second moment of area $(I_{s d})$
MD55	0.76 mm	975 mm²/m	27.5 mm	565,550 $m m^{4} / m$

Input data	Unit	Concrete (_C) Uncracked section	Concrete (_C) Cracked section	Steel Decking (_Sd)	Steel mesh (_S)
Cross-section area (A)	$m m^{2} / m$	97,454.4	29.933	975	102
First area moment (B)	$m m^{3} / m$	7,163,690.7	3,293,668	26,812.5	9695.6
Second moment of area (I)	$m m^{4} / m$	635,595,091	364,648,226	1,302,894	921,189
Elastic modulus (E)	$N / m m^{2}$	30,000	30.000	204,000	191,000
Uncracked section:	$R_{A,0, u n c r} = 3,139 \times 10^{6} N; R_{B,0} = 2,219 \times 10^{8} Nmm; R_{I,0} = 1,948 \times 10^{10} Nmm ²$
Cracked section:	$R_{A,0, c r} = 1,113 \times 10^{6} N; R_{B,0, c r} = 1,058 \times 10^{8} Nmm; R_{I,0, c r} = 1,135 \times 10^{10} Nmm ²$

$E_{ef, cs} = 12,687 M P a;$	$A_{c, uncr} = 97,454.4 {mm}^{2};$	$R_{A, cs, uncr} = 1453.5 \times 10^{6} N;$
$ε_{r, cs, \infty} = - 110 \cdot 10^{- 6} mm / mm;$	$B_{c, uncr} = - 7,163,691 {mm}^{3};$	$R_{B, cs, uncr} = - 980.9 \times 10^{8} Nmm;$
$\begin{matrix} κ_{r, cs, \infty} \end{matrix} = - 4.38 m m^{- 1};$	$I_{c, uncr, r} = 635.6 \times 10^{6} {mm}^{4};$	$R_{0, cs, uncr} = 2725.4 \cdot 10^{18} N^{2} {mm}^{2} .$

Measured	Instantaneous deflection (Inst.)			Long-term deflection (L.T.)			Total deflection (Inst.+L.T.)	Ratio (Inst.)/(LT)
Measured	Self- weight (1)	Imposed Load (2)	Total	8-28 days	29-134 days	Total	Total deflection (Inst.+L.T.)	Ratio (Inst.)/(LT)
Experimental	0.35	0.65	1.00	1.65	1.82	3.47	4.47	3.47
Predicted	0.67	0.63	1.30	0.97	2.30	3.27	4.57	2.52
Ratio Exp./Pred)	0.52	1.03	0.77	1.76	0.79	1.06	0.98	-

Author(s)	Slab ID	Profiled Steel Decking	Span (mm)	Slab Thickness (mm)	Self-weight (kPa)	Imposed Load (kPa)	Duration test (days)
Al-deen et al. [¹⁰10 S. Al-Deen, G. Ranzi, and B. Uy, "Non-uniform shrinkage in simply-supported composite steel concrete slabs," Steel Compos. Struct., vol. 18, no. 2, pp. 375–394, 2015., http://dx.doi.org/10.12989/scs.2015.18.2.375. http://dx.doi.org/10.12989/scs.2015.18.2... ]	CS1	Condeck HP55^a [²⁴24 Stramit Condeck HP, Composite Slab System, Product Technical Manual, Queensland, Australia: Stramit Condeck HP, 2012.]	3000	180	4.40	None	239
	CS2		3000	180	4.40	None	239
Gholamhoseini [⁸8 A. Gholamhoseini, "Long-term deformation of composite concrete slabs," Concr. Aust., vol. 38, no. 4, pp. 25–32, 2014a., http://dx.doi.org/10.1080/13287982.2016.1238531. http://dx.doi.org/10.1080/13287982.2016.... ] [⁹9 A. Gholamhoseini, "Time-dependent deflection of composite concrete slabs," ACI Struct. J., vol. 111, no. 4, pp. 765–776, 2014b., http://dx.doi.org/10.14359/51686629. http://dx.doi.org/10.14359/51686629... ]	1LT-70-0	Filders KF70^b [²⁵25 Fielders Australia Kingflor, Composite Steel Formwork System Design Manual, Marleston, Australia: Fielders Australia Kingflor, 2008.]	3100	150	3.00	None	247
	2LT-70-3					3.40
	3LT-70-3					3.40
	4LT-70-6					6.00
	5LT-70-6					6.00	197
	6LT-40-0	Filders KF40^c [²⁵25 Fielders Australia Kingflor, Composite Steel Formwork System Design Manual, Marleston, Australia: Fielders Australia Kingflor, 2008.]	3100	150	3.20	None	244
	7LT-40-3					3.40	251
	8LT-40-3					3.40
	9LT-40-6					6.40
	10LT-40-6					6.40

Composite Slab	Steel decking	Concrete
▪ CS1 [¹⁰10 S. Al-Deen, G. Ranzi, and B. Uy, "Non-uniform shrinkage in simply-supported composite steel concrete slabs," Steel Compos. Struct., vol. 18, no. 2, pp. 375–394, 2015., http://dx.doi.org/10.12989/scs.2015.18.2.375. http://dx.doi.org/10.12989/scs.2015.18.2... ]	Profile: Clip-pan Condeck HP55	Normal concrete
	Steel thickness: 0.75 mm	Compressive strength: $f_{c 28} = 27.30 M P a$
	Centroid height (bottom face): 15.3 mm	Elastic modulus: $E_{c} = 26.40 G P a$
▪ CS2 [¹⁰10 S. Al-Deen, G. Ranzi, and B. Uy, "Non-uniform shrinkage in simply-supported composite steel concrete slabs," Steel Compos. Struct., vol. 18, no. 2, pp. 375–394, 2015., http://dx.doi.org/10.12989/scs.2015.18.2.375. http://dx.doi.org/10.12989/scs.2015.18.2... ]	Steel area: 1,211 $m m^{2} / m$	Flexural tensile strength: $f_{c t, f} = 3.13 M P a$
	Second moment: $I_{s} =$ 488,000 $m m^{4} / m$
	Elastic modulus: $E_{s} = 200 G P a$
▪ LT-70 [⁸8 A. Gholamhoseini, "Long-term deformation of composite concrete slabs," Concr. Aust., vol. 38, no. 4, pp. 25–32, 2014a., http://dx.doi.org/10.1080/13287982.2016.1238531. http://dx.doi.org/10.1080/13287982.2016.... ] [⁹9 A. Gholamhoseini, "Time-dependent deflection of composite concrete slabs," ACI Struct. J., vol. 111, no. 4, pp. 765–776, 2014b., http://dx.doi.org/10.14359/51686629. http://dx.doi.org/10.14359/51686629... ]	Profile: Trapezoidal KF70	Normal concrete
	Steel thickness: 0.75 mm	Compressive strength: $f_{c 28} = 28.00 M P a$
	Centroid height (bottom face): 27.7 mm	Elastic modulus: $E_{c} = 30.725 G P a$
	Steel area: 1.100 $m m^{2} / m$	Flexural tensile strength: $f_{c t, f} = 3.50 M P a$
	Second moment: $I_{s} =$ 584,000 $m m^{4} / m$	Flexural tensile strength: $f_{c t, f} = 3.50 M P a$
	Elastic modulus: $E_{s} = 212 G P a$
▪ LT-40 [⁸8 A. Gholamhoseini, "Long-term deformation of composite concrete slabs," Concr. Aust., vol. 38, no. 4, pp. 25–32, 2014a., http://dx.doi.org/10.1080/13287982.2016.1238531. http://dx.doi.org/10.1080/13287982.2016.... ] [⁹9 A. Gholamhoseini, "Time-dependent deflection of composite concrete slabs," ACI Struct. J., vol. 111, no. 4, pp. 765–776, 2014b., http://dx.doi.org/10.14359/51686629. http://dx.doi.org/10.14359/51686629... ]	Profile: Trapezoidal KF40	Normal concrete
	Steel thickness: 0.75 mm	Compressive strength: $f_{c 28} = 35.50 M P a$
	Centroid height (bottom face): 14.0 mm	Elastic modulus: $E_{c} = 28.20 G P a$
	Steel area: 1.040 $m m^{2} / m$	Flexural tensile strength: $f_{c t, f} = 3.80 M P a$
	Second moment: $I_{s} =$ 269,000 $m m^{4} / m$
	Elastic modulus: $E_{s} = 193 G P a$

Slabs ID	Imposed Load / Self- weight	Deflections at the end of test (t)			Final predicted deflection
Slabs ID	Imposed Load / Self- weight	Tests Results (mm)⁽¹⁾	AS/NZS 2327 (mm)⁽²⁾	Ratio* ^{(1) / (2)}	AS/NZS 2327 ( $t_{\infty}$ ) (mm)⁽³⁾	BS5950 $(2 / 3 E_{c m})$ (mm)⁽⁴⁾	$(E_{c m} / 3)$ (mm)⁽⁵⁾	EC4 $(E_{c m} / 2)$ (mm) ⁽⁶⁾	Ratio** ^{(3) / (6)}
CS1	None	3.02	2.96	(1.02)	5.17	0.67	1.05	0.81	(6.38)
CS2		2.85	2.68	(1.06)	4.48	0.65	0.99	0.78	(5.74)
1LT-70-0		4.04	4.60	(0.88)	6.11	1.01	1.56	1.22	(5.01)
6LT-40-0		4.99	5.33	(0.94)	7.24	1.04	1.58	1.24	(5.84)
2LT-70-3	1.13	6.70	5.87	(1.14)	7.40	2.15	3.33	2.60	(2.85)
3LT-70-3	1.13	5.86	5.87	(1.00)	7.40	2.15	3.33	2.60	(2.85)
7LT-40-3	1.06	7.30	6.55	(1.11)	8.75	2.14	3.27	2.56	(3.42)
8LT-40-3	1.06	6.57	6.55	(1.00)	8.75	2.14	3.27	2.56	(3.42)
4LT-70-6	2.00	6.76	7.41	(0.91)	10.86	3.03	4.69	3.65	(2.98)
5LT-70-6		6.58	7.08	(0.93)	10.86	3.03	4.69	3.65	(2.98)
9LT-40-6		6.94	7.63	(0.91)	10.06	3.11	4.75	3.73	(2.70)
10LT-40-6		8.26	7.63	(1.08)	10.06	3.11	4.75	3.73	(2.70)
Presented	0.94	4.40	4.57	(0.98)	7.93	2.54	3.86	3.07	(2.58)
			Average = 0.99 *		Average = 5.74 / C.O.V = 9.8% (No imposed load) **
			C.O.V = 9.6% *		Average = 2.90 / C.O.V = 11.1% (With imposed load) **

R_{A,0} = \sum_{i = 1}^{m_{c}} A_{c (i)} \cdot E_{c (i),0} + \sum_{i = 1}^{m_{s}} A_{s (i)} \cdot E_{s (i)} + A_{s d} \cdot E_{s d} = R_{A, c} + R_{A, s} + R_{A, s d}

R_{B,0} = \sum_{i = 1}^{m_{c}} B_{c (i)} \cdot E_{c (i),0} + \sum_{i = 1}^{m_{s}} y_{s (i)} \cdot A_{s (i)} \cdot E_{s (i)} + B_{s d} \cdot E_{s d} = R_{B, c} + R_{B, s} + R_{B, s d}

R_{I,0} = \sum_{i = 1}^{m_{c}} I_{c (i)} \cdot E_{c (i),0} + \sum_{i = 1}^{m_{s}} y_{s (i)}^{2} \cdot A_{s (i)} \cdot E_{s (i)} + I_{s d} \cdot E_{s d} = R_{I, c} + R_{I, s} + R_{I, s d}

σ_{cs} = \frac{E_{ef, cs}}{R_{I, cs} \cdot R_{A, cs} - R_{B, cs}^{2}} \cdot [(R_{I, cs} - y \cdot R_{B, cs}) \cdot f_{cs 1} + (R_{B, cs} - y \cdot R_{A, cs}) \cdot f_{cs 2}] - E_{ef, cs} \cdot (ε_{r, cs} - y \cdot κ_{cs})

[\begin{matrix} f_{cs 1} \\ f_{cs 2} \end{matrix}] = E_{ef, cs} \cdot [\begin{matrix} A_{c} \cdot ε_{r, cs} - B_{c} \cdot κ_{r, cs} \\ - B_{c} \cdot ε_{r, cs} + I_{c} \cdot κ_{r, cs} \end{matrix}]

κ_{cs, uncr} = [\begin{matrix} \frac{R_{B, cs, uncr}}{R_{0, cs, uncr}} & \frac{R_{A, cs, uncr}}{R_{0, cs, uncr}} \end{matrix}] \cdot E_{ef, cs} \cdot [\begin{matrix} A_{c, uncr} \cdot ε_{r, cs} - B_{c, uncr} \cdot κ_{r, cs} \\ - B_{c, uncr} \cdot ε_{r, cs} + I_{c, uncr} \cdot κ_{r, cs} \end{matrix}]

κ_{cs, cr} = [\begin{matrix} \frac{R_{B, cs, cr}}{R_{0, cs, cr}} & \frac{R_{A, cs, cr}}{R_{0, cs, cr}} \end{matrix}] \cdot E_{ef, cs} \cdot [\begin{matrix} A_{c, cr} \cdot ε_{r, cs} - B_{c, cr} \cdot κ_{r, cs} \\ - B_{c, cr} \cdot ε_{r, cs} + I_{c, cr} \cdot κ_{r, cs} \end{matrix}]

I_{uncr} = \frac{b \cdot h_{c}^{3}}{12 \cdot n} + \frac{b \cdot h_{c}}{n} \cdot {(y_{u} - \frac{h_{c}}{2})}^{2} + \frac{b_{m} \cdot h_{Sd}^{3}}{12 \cdot n} + \frac{b_{m} \cdot h_{p}}{n} \cdot {(h_{t o t a l} - y_{u} - \frac{h_{Sd}}{2})}^{2} + A_{Sd} \cdot {(y_{S d} - x_{u})}^{2} + I_{Sd} = 10,337,783 m m^{4} / m . (on steel modulus)

y_{uncr} = \frac{b \cdot \frac{h_{c}^{2}}{2} + b_{m} \cdot h_{Sd} \cdot (h - \frac{h_{S d}}{2}) + n \cdot A_{S d} \cdot y_{S d}}{b \cdot h_{c} + b_{m} \cdot h_{Sd} + n \cdot A_{Sd}} = 57.67 m m .

[1] Corresponding author: Lucas Antônio Morais Oliveira. E-mail: lucasantonio12@usp.br

Brasil

Brasil

Assessment of design codes for the in-service behaviour of steel-concrete composite slabs

Avaliação dos códigos de projeto para o comportamento em serviço de lajes mistas de aço-concreto

Abstract