Metodologia para avaliação estrutural de pontes existentes de concreto armado

Andrade, Matheus Sant’Anna; Cardoso, Marco Antônio Nakata; Oliveira, Diôgo Silva de; Gardioli, Letícia Negris; Santos, Carol Ferreira Rezende; Ribeiro, José Carlos Lopes; Carvalho, José Maria Franco de; Lenz Junior, Kléos Magalhães César

doi:10.1590/S1983-41952025000400008

person Matheus Sant’Anna Andrade

writing – review & editing · writing – original draft · methodology · investigation · formal analysis · conceptualization

schoolUniversidade Federal de Viçosa – UFV, Departamento de Engenharia Civil, Viçosa, MG, Brasil

0000-0001-8680-4859

person Marco Antônio Nakata Cardoso

methodology · investigation · formal analysis · conceptualization

schoolUniversidade Federal de Viçosa – UFV, Departamento de Engenharia Civil, Viçosa, MG, Brasil

0009-0000-0514-1273

person Diôgo Silva de Oliveira

writing – review & editing · supervision · methodology · conceptualization

schoolUniversidade Federal de Viçosa – UFV, Departamento de Engenharia Civil, Viçosa, MG, Brasil

0000-0002-4771-8971

person Letícia Negris Gardioli

writing – review & editing · conceptualization

schoolUniversidade Federal de Viçosa – UFV, Departamento de Engenharia Civil, Viçosa, MG, Brasil

0009-0004-7784-6087

person Carol Ferreira Rezende Santos

writing – review & editing · conceptualization

schoolUniversidade Federal de Viçosa – UFV, Departamento de Engenharia Civil, Viçosa, MG, Brasil

0000-0001-5573-5651

person José Carlos Lopes Ribeiro

writing – review & editing · funding

schoolUniversidade Federal de Viçosa – UFV, Departamento de Engenharia Civil, Viçosa, MG, Brasil

0000-0003-4069-7001

person José Maria Franco de Carvalho

writing – review & editing · funding

schoolUniversidade Federal de Viçosa – UFV, Departamento de Engenharia Civil, Viçosa, MG, Brasil

0000-0001-5785-3213

person Kléos Magalhães César Lenz Junior

writing – review & editing · funding

schoolUniversidade Federal de Viçosa – UFV, Departamento de Engenharia Civil, Viçosa, MG, Brasil

0000-0003-4779-4226

Corresponding author: Matheus Sant’Anna Andrade. E-mail:
matheus.andrade@ufv.br

Conflict of interest:

Nothing to declare.

Editors:

Túlio Bittencourt, Daniel Cardoso.

Period	Live Load composition	Details
1940-1960		The live load model was comprised of multiple vehicles side-by-side. One roller (2.5 x 6.0 m) up to 24 ton. plus n trucks (up to 12 ton. each), alongside a uniformly distributed load (up to 5 kN/m²). The number of trucks, n, was calculated by the number of traffic lanes minus one.
1960-1984		One 36-ton. truck with 3 axles, alongside a 5 kN/m² uniformly distributed load on the front and rear of the vehicle, plus a 3 kN/m² on the sides
After 1984		One 45-ton. truck with 3 axles, alongside a 5 kN/m² uniformly distributed load.

Rating	DNIT [⁴¹]		ABNT [⁴²]
Rating	Condition	Description	ABNT [⁴²]
5	Excellent	No damages	Excellent
4	Good	No major damages	Good
3	Fair	Potentially problematic Bridge	Fair
2	Poor	Major problems detected	Poor
1	Critical	Critical condition	Critical
0			Emergencies

Load type	Normal Ultimate Combination		Special Combination
Load type	NBR 8681	NBR 7187	Special Combination
Permanent	1.35	1.20	1.25
Live load	1.50	1.35	1.30

Bridge	Deck Section	Information
Teixeiras Stream Bridge		Location: Teixeiras – MG; Year: 1980; Design Vehicle Class: 36 ton; Length: 32 m; Span Length: 6/20/6 m; Width: 10 m; Two girders cast in place.
Coimbra I Viaduct		Location: Coimbra – MG; Year: 1985; Design Vehicle Class: 36 ton; Length: 100 m; Span Length: 6/22/22/22/22/6 m; Width: 9.6 m; Two girders cast in place.
Pirapetinga River Bridge		Location: Piranga – MG; Year: 2013; Design Vehicle Class: 45 ton; Length: 49 m; Span Length: 16.33/16.33/16.33 m; Width: 9.0 m; Two girders cast in place.

Method	Teixeiras Stream Bridge	Coimbra I Viaduct	Pirapetinga River Bridge
Condition State
DNIT [⁴¹]	3	4	4
ABNT [⁵⁶]	3	4	4
FHWA [⁴⁹]	5	5	5
COST 345 [¹²]	2-3	2-3	2
Capacity reduction factor
Slovenian	0.84	0.87	0.87
Lithuanian	0.82	0.90	0.90
American	0.85	0.95	0.95

Section	Teixeiras Stream Bridge	Coimbra I Viaduct	Pirapetinga River Bridge
Bent	9.6	9.6	10.9
Mid-widening	10.9	10.6	12.1
Current	13.8	13.5	15.5
f_ck,design	15	15	25

Core Id.	Teixeiras Stream Bridge		Coimbra I Viaduct		Pirapetinga River Bridge
Core Id.	fc (MPa)	Carbonation depth (cm)	fc (MPa)	Carbonation depth (cm)	fc (MPa)	Carbonation depth (cm)
1	11.05	5.0	46.13	3.0	38.13	2.5
2	14.71	5.0	36.45	2.0	33.77	2.0
3	11.89	4.0	40.80	2.0	38.13	2.0
4	16.81	2.0	35.35	2.5	38.26	3.0
5	17.08	2.5	44.11	2.0	32.46	2.0
6	14.82	3.0	37.87	2.5	38.04	2.0
7	-	-	31.13	2.5	-	-
Mean	14.39	3.6	38.83	2.4	36.37	2.3
Maximum	-	5.0	-	3.0	-	3.0
CV (%)	17.3		13.4		7.1

Standard	Teixeiras	Coimbra	Pirapetinga
Reinforced concrete design	NB 1-1978 [²¹]	NB 1-1978 [²¹]	NBR 6118-2007 [⁵⁸]
Bridge design	NB 2-1961 [³⁴]	NB 2-1961 [³⁴]	NBR 7187-2003 [⁵⁹]
Live load	NB 6-1960 [³⁷]	NB 6-1960 [³⁷]	NBR 7188-1984 [³⁸]

Period	Load effect	Formulation	Eq.
1980’s	Bending moment	$A_{s} = \frac{M_{R d}}{f_{s} ∙ (d - 0.5 ∙ y)}$	(5)
1980’s	Shear	$ω_{t} = 1.15 ∙ τ_{w d} - τ_{c} = \frac{1.15}{f_{s}} ∙ \frac{V_{d}}{b_{w} ∙ d} - ψ_{1} ∙ \sqrt{f_{c k}}$	(6)
2010’s	Bending moment	$A_{s} = \frac{M_{R d}}{f_{s} ∙ (d - 0.5 ∙ y)}$	(7)
	Shear	$V_{c} = 0.6 ∙ f_{c t d} ∙ b_{w} ∙ d$	(8)
	Shear	$V_{s w} = (\frac{A_{s w}}{s}) ∙ 0.9 ∙ d ∙ f_{y w d} ∙ (sen α + \cos α)$	(9)

Bridge	Permanent load effects			Live load effects¹
Bridge	BMS²	BS²	S²	BMS²	BS²	S²
Teixeiras	2202.4	1574.3	752.2	2354.7	1819.1	515.9
Coimbra I	1949.3	3314.7	894.7	1836.8	2158.6	578.5
Pirapetinga	1438.9	1806.0	673.1	1632.9	1263.5	581.2

Reinforcement type	Teixeiras	Coimbra	Pirapetinga
Bending at midspan (cm²)	110.8	98.3	88.4
Bending over the supports (cm²)	100.4	152.1	86.2
Shear strength (cm²/m)	25.6	25.6	16.1

Bridge	Teixeiras Stream		Coimbra I Viaduct		Pirapetinga River
Approach	I	II	I	II	I	II
Bending at midspan (kN.m)	7478,2	7500,2	6709,4	6906,2	5096,2	5130,7
Bending over the supports (kN.m)	5662,5	5740,7	7844,7	9792,4	4879,5	5096,3
Shear (kN)	2258,4	2286,3	2402,0	3157,9	1824,3	2168,9

Type	Vehicle	Load1	Length2	Axles	First axle¹	Other Axles3	Ref.
Standard	C36	36	6.0	3	12	2x12	ABNT NBR 7188 [³⁸]
Standard	TB45	45	6.0	3	15	2x15	ABNT NBR 7188 [³⁵]
Certified	RT 74/20	74	19.8	9	6	8x8.5	El Debs et al. [⁶⁶]
	RT 74/25	74	25.0	9	6	8x8.5
	BT 74/25	74	24.9	9	6	8x8.5
	B 49/14	48.5	13.5	6	6	5x8.5
	3S3	48.5	16.25	6	6	5x8.5	Cardoso [⁶¹]
	3I3	53	16.1	6	6	2x8.5 + 3x10
	3S3+4	58.5	16.25	7	6	5x8.5 +1 x 10
Indivisible	PBT-200	199.8	54.45	20	6	2x10.5 + 7x11.43+ 10x9.28	Cardoso [⁶¹]

Bridge	Permanent			Live load1
Bridge	BMS²	BS²	S²	BMS²	BS2	S²
Teixeiras	2307.0	1475.3	639.9	1848.9	1602.0	382.2
Coimbra I	1827.6	3606.6	791.0	2369.1	2238.2	628.4
Pirapetinga	1308.0	1827.4	553.4	942.5	958.9	240.7

Vehicle	Coimbra Viaduct I					Teixeiras Stream Bridge					Pirapetinga River Bridge
	Approach I			Avg	II	Approach I			Avg	II	Approach I			Avg	II
	A1	B2	C3	Avg	II	A¹	B²	C³	Avg	II	A¹	B²	C³	Avg	II
C36	0.97	0.90	1.21	1.08	1.36	1.02	0.98	1.04	1.02	1.33	-	-	-	-	-
TB45	0.64	0.88	0.80	0.71	0.90	0.76	0.73	0.77	0.75	0.99	1.20	1.30	1.43	1.31	1.57
RT74/20	0.62	0.94	0.78	0.70	0.88	0.82	0.78	1.01	0.81	1.09	0.85	0.92	1.01	0.93	1.11
RT74/25	0.66	0.91	0.83	0.75	0.94	0.96	0.92	1.18	0.95	1.29	0.92	0.99	1.09	1.00	1.20
BT74/25	0.64	0.97	0.81	0.72	0.91	0.97	0.93	1.07	0.97	1.31	0.91	0.98	1.08	0.99	1.19
B 49/14	0.69	0.99	0.86	0.77	0.97	0.86	0.83	1.07	0.86	1.16	0.95	1.04	1.14	1.04	1.25
3S3	0.70	1.04	0.88	0.79	0.99	0.97	0.93	1.20	0.96	1.30	1.06	1.15	1.26	1.16	1.39
3I3	0.74	0.93	0.93	0.83	1.04	1.04	0.99	1.16	1.03	1.40	1.01	1.09	1.20	1.10	1.32
3S3+4	0.66	0.88	0.82	0.74	0.93	0.87	0.84	1.04	0.87	1.17	0.93	1.01	1.11	1.02	1.22
PBT200	0.62	0.69	0.78	0.70	0.88	0.97	0.93	1.20	0.96	1.30	0.98	1.06	1.17	1.07	1.29

R_{d} = A_{s} ∙ \frac{f_{y}}{γ_{S}} ∙ (d - \frac{0.5 ∙ (f_{y} / γ_{s}) ∙ A_{s}}{0.85 ∙ (f_{c} / γ_{c}) ∙ b})

[1] Note: $A_{s}$ is the reinforcement area; $M_{R d}$ is the resistance of the cross-section, which is assumed equal to the load effects ( $M_{S d})$ ; $f_{s}$ is the reinforcing steel yield strength; $d$ is the girder effective height; $y$ is the height of the rectangular tension distribution diagram on the compressed portion of the cross-section; $ω_{t}$ is the reinforcement/area ratio; $ψ_{1}$ is a factor to account for the concrete capacity to absorb the shear stresses; $f_{c t d}$ is the tensile concrete strength; $b_{w}$ is the girder width; $A_{s w} / s$ is the stirrup area per length; $f_{y w d}$ is the reinforcing steel yield strength; and $á$ is the inclination of the stirrups.

Metodologia para avaliação estrutural de pontes existentes de concreto armado

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