Prediction of the ultimate capacity of reinforced concrete elements using nonlinear analysis methodologies

Palomo, Ingrid Rocio Irreño; Martínez, Juan de Jesus; Benedetty, Carlos Alberto; Almeida, Luiz Carlos de; Trautwein, Leandro Mouta; Krahl, Pablo Augusto

doi:10.1590/S1983-41952024000200010

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 17 (2) • 2024 • https://doi.org/10.1590/S1983-41952024000200010 linkcopy

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10.1590/S1983-41952024000200011

Prediction of the ultimate capacity of reinforced concrete elements using nonlinear analysis methodologies

Predição da capacidade última de elementos em concreto armado usando metodologias de análises não linear

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This work aims to investigate the ultimate capacity of reinforced concrete elements in terms of cracking and stiffness loss. Nonlinear finite element analysis (NLFEA) was performed in the ATENA software and compared with a proposed numerical simulation of nonlinear static analysis (NLSA), where material cracking is evaluated based on the loss of tangent stiffness of the elements. The analysis was applied to a low-rise reinforced concrete frame with constant axial loads in the columns, and monotonic lateral load applied at the top beam level. Both methodologies showed good agreement regarding the capacity curve and crack patterns, and the numerical simulation NLSA allowed the identification of the sequence of elements' stiffness loss. The results indicated a substantial similarity between the numerical simulation NLFEA and NLSA and the experimental test, indicating a high potential in predicting the nonlinear behavior of reinforced concrete.

Keywords:
reinforced concrete; frames; nonlinear analysis; cracking

Parameter	Concrete	Long. Steel	Transv. Steel	Reference
Elastic Modulus - $E$	23674 MPa	192500 MPa	200000 MPa	[²⁷]
Hardening modulus - $E_{s h}$	/	3100 MPa	3100 MPa	[²⁷]
Fracture energy - $G_{f}$	90 N/m	/	/	[³⁵]
Shear factor - $S_{f}$	50	/	/	adopted
Compression strength - $f_{c}$	30 MPa	/	/	[²⁷]
Tensile strength - $f_{t}$	1.81 MPa	/	/	[²⁷]
Strength at onset of nonlinear behavior - $f_{c o}$	3.6 MPa	/	/	[³]
Plastic strain at compressive strength - ${ε_{c}^{p}}_{}^{}$	0.00185	/	/	[³⁴]
Reduction factor of the compressive strength	0.8	/	/	[³]
Yield strength - $f_{y}$	/	418 MPa	596 MPa	[²⁷]
Ultimate strength - $f_{u}$	/	454 MPa	640 MPa	[²⁷]
Yield strain - $ε_{s}$	/	0.00217	0.00298	[²⁷]
Strain hardening - $ε_{s h}$	/	0.0095	0.0095	[²⁷]
Ultimate strain - $ε_{u}$	/	0.0669	0.0695	[²⁷]

Model	Mesh size	Ultimate load [kN]	Error [%]
Experimental test		332	---
Coarse mesh	100 mm	345.1	3.8
Medium mesh	80 mm	340.9	2.6
Fine mesh	50 mm	332.8	0.24

Element	Numerical result -NLFEA	Numerical result -NLSA	Experimental result
Flexural cracks in the beam B1	59.4 kN (Figure 17a)	61.6 kN – elements 1 and 14, stiffness: 41% (Figure 17b)	52.5 kN
Flexural cracks at the base of the columns	152.8 kN (Figure 18a)	145 kN – element 1, column C1, stiffness: 43%	145 kN
Flexural cracks at the base of the columns	152.8 kN (Figure 18a)	145 kN – element 1, column C2, stiffness: 50% (Figure 18b)	145 kN

Element	Numerical result -NLFEA	Numerical result -NLSA	Experimental result
Yielding in the longitudinal reinforcement of beam B1	281.5 kN (Figure 19a)	302.4 kN – element 1, stiffness: 0.75%	264 kN (top)
Yielding in the longitudinal reinforcement of beam B1	281.5 kN (Figure 19a)	302.4 kN – element 14, stiffness: 0.85% (Figure 19b)	287 kN (bottom)
Yielding in the longitudinal reinforcement of column	326.1 kN (Figure 20a)	320 kN – element 1, column C1, stiffness: 0.81%	323 kN
Yielding in the longitudinal reinforcement of column	326.1 kN (Figure 20a)	335.2 kN – element 1, column C2, stiffness: 2.7% (Figure 20b)	323 kN
Yielding in the longitudinal reinforcement of beam B2	326.1 kN (Figure 20a)	340.8 kN – element 1, stiffness: 1.0%	329 kN
Yielding in the longitudinal reinforcement of beam B2	326.1 kN (Figure 20a)	340.8 kN – element 14, stiffness: 0.75% (Figure 21)	329 kN

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