Figure 1
Relationship between torsion moment, bending moment and shear force.
Figure 2
Subroutine for Problem 1.
Figure 3
Generalized truss model with parallel chords [1010 J. S. Giongo, Concreto Armado: Dimensionamento de Elementos Estruturais Fletidos Solicitados por Força Cortante, 1st ed. São Carlos, Brasil: EESC - Departamento de Engenharia de Estruturas, 2011.].
Figure 4
Concrete contribution to the ties [1010 J. S. Giongo, Concreto Armado: Dimensionamento de Elementos Estruturais Fletidos Solicitados por Força Cortante, 1st ed. São Carlos, Brasil: EESC - Departamento de Engenharia de Estruturas, 2011.].
Figure 5
Thin-walled tube analogy and generalized space truss [1212 J. K. Wight, Reinforced Concrete - Mechanics and Design, 7th ed., Hoboken, NJ, USA: Pearson, 2016.].
Figure 6
Section of the vertical wall detailing the stirrups force [1212 J. K. Wight, Reinforced Concrete - Mechanics and Design, 7th ed., Hoboken, NJ, USA: Pearson, 2016.].
Figure 7
Section of a vertical wall of the truss detailing the chords and struts forces [1212 J. K. Wight, Reinforced Concrete - Mechanics and Design, 7th ed., Hoboken, NJ, USA: Pearson, 2016.].
Figure 8
Failure domains for flexure [99 Associação Brasileira de Normas Técnicas, Projeto de Estruturas de Concreto - Procedimento, NBR 6118, 2014.].
Figure 9
RC concrete cross section under flexure [1212 J. K. Wight, Reinforced Concrete - Mechanics and Design, 7th ed., Hoboken, NJ, USA: Pearson, 2016.].
Figure 10
Shear and torsion stresses on a hollow and solid section [1212 J. K. Wight, Reinforced Concrete - Mechanics and Design, 7th ed., Hoboken, NJ, USA: Pearson, 2016.].
Figure 11
MCFT equilibrium, compatibility and constitutive relationships [
1616 E. C. Bentz, F. J. Vecchio, and M. P. Collins, "Simplified modified compression field theory for calculating shear strength of reinforced concrete elements," ACI Struct. J., vol. 103, no. 4, pp. 614–624, 2006, http://dx.doi.org/10.14359/16438.
http://dx.doi.org/10.14359/16438...
].
Figure 12
Acting and resisting forces and strains on a section [
1616 E. C. Bentz, F. J. Vecchio, and M. P. Collins, "Simplified modified compression field theory for calculating shear strength of reinforced concrete elements," ACI Struct. J., vol. 103, no. 4, pp. 614–624, 2006, http://dx.doi.org/10.14359/16438.
http://dx.doi.org/10.14359/16438...
].
Figure 13
Inclination of the compression field as a function of longitudinal deformation [
1717 E. C. Bentz and M. P. Collins, "Development of the 2004 Canadian Standards Association (CSA) A23.3 shear provisions for reinforced concrete," Can. J. Civ. Eng., vol. 33, no. 5, pp. 521–534, May 2006, http://dx.doi.org/10.1139/L06-005.
http://dx.doi.org/10.1139/L06-005...
].
Figure 14
Subroutine for Problem 2.
Figure 15
Subroutine for Problem 3.
Figure 16
Test setup for combined action on beams S1 to S7 (dimensions in mm) [
2020 H. E. I. Badawy, A. E. McMullen, and I. J. Jordaan, "Experimental investigation of the collapse of reinforced concrete curved beams," Mag. Concr. Res., vol. 29, no. 99, pp. 59–69, 1977, http://dx.doi.org/10.1680/macr.1977.29.99.59.
http://dx.doi.org/10.1680/macr.1977.29.9...
].
Figure 17
S1 to S7 beams cross section (dimensions in cm and bars diameter in mm).
Figure 18
Test setup for combined action on beams M5 a M7 [
2121 A. E. McMullen and J. Warwaruk, The Torsional Strength of Rectangular Reinforced Concrete Beams Subjected to Combined Loading. Edmonton, Canada: The Univ. Alberta, Dep. Civ. Eng.; 1967. Accessed: Oct. 4, 2021. [Online]. Available: https://era.library.ualberta.ca/items/5086dede-150c-43e1-8a0a-8a0a27d5605f/download/04ed74f7-789e-486d-ba8d-aa3b0ddc554b.
https://era.library.ualberta.ca/items/50...
].
Figure 19
M5 to M7 beams cross section (dimensions in cm and bars diameter in mm).
Figure 20
Interaction surface according to NBR and AASHTO for beams S1-S7.
Figure 21
Adapted from Rahal’s AASHTO surface for beams S1-S4 [
1919 K. N. Rahal, "Evaluation of AASHTO-LRFD general procedure for torsion and combined loading," ACI Struct. J., vol. 103, no. 5, pp. 683–692, 2006., http://dx.doi.org/10.14359/16920.
http://dx.doi.org/10.14359/16920...
].M5 to M7 beams.
Figure 22
Interaction surface according to NBR and AASHTO for beams M5 e M6.
Figure 23
Interaction surface according to NBR and AASHTO for beams M7.
Figure 3
Generalized truss model with parallel chords [1010 J. S. Giongo, Concreto Armado: Dimensionamento de Elementos Estruturais Fletidos Solicitados por Força Cortante, 1st ed. São Carlos, Brasil: EESC - Departamento de Engenharia de Estruturas, 2011.].
Figure 4
Concrete contribution to the ties [1010 J. S. Giongo, Concreto Armado: Dimensionamento de Elementos Estruturais Fletidos Solicitados por Força Cortante, 1st ed. São Carlos, Brasil: EESC - Departamento de Engenharia de Estruturas, 2011.].
Figure 5
Thin-walled tube analogy and generalized space truss [1212 J. K. Wight, Reinforced Concrete - Mechanics and Design, 7th ed., Hoboken, NJ, USA: Pearson, 2016.].
Figure 6
Section of the vertical wall detailing the stirrups force [1212 J. K. Wight, Reinforced Concrete - Mechanics and Design, 7th ed., Hoboken, NJ, USA: Pearson, 2016.].
Figure 7
Section of a vertical wall of the truss detailing the chords and struts forces [1212 J. K. Wight, Reinforced Concrete - Mechanics and Design, 7th ed., Hoboken, NJ, USA: Pearson, 2016.].
Figure 8
Failure domains for flexure [99 Associação Brasileira de Normas Técnicas, Projeto de Estruturas de Concreto - Procedimento, NBR 6118, 2014.].
Figure 9
RC concrete cross section under flexure [1212 J. K. Wight, Reinforced Concrete - Mechanics and Design, 7th ed., Hoboken, NJ, USA: Pearson, 2016.].
Figure 10
Shear and torsion stresses on a hollow and solid section [1212 J. K. Wight, Reinforced Concrete - Mechanics and Design, 7th ed., Hoboken, NJ, USA: Pearson, 2016.].
Figure 11
MCFT equilibrium, compatibility and constitutive relationships [
1616 E. C. Bentz, F. J. Vecchio, and M. P. Collins, "Simplified modified compression field theory for calculating shear strength of reinforced concrete elements," ACI Struct. J., vol. 103, no. 4, pp. 614–624, 2006, http://dx.doi.org/10.14359/16438.
http://dx.doi.org/10.14359/16438...
].
Figure 12
Acting and resisting forces and strains on a section [
1616 E. C. Bentz, F. J. Vecchio, and M. P. Collins, "Simplified modified compression field theory for calculating shear strength of reinforced concrete elements," ACI Struct. J., vol. 103, no. 4, pp. 614–624, 2006, http://dx.doi.org/10.14359/16438.
http://dx.doi.org/10.14359/16438...
].
Figure 13
Inclination of the compression field as a function of longitudinal deformation [
1717 E. C. Bentz and M. P. Collins, "Development of the 2004 Canadian Standards Association (CSA) A23.3 shear provisions for reinforced concrete," Can. J. Civ. Eng., vol. 33, no. 5, pp. 521–534, May 2006, http://dx.doi.org/10.1139/L06-005.
http://dx.doi.org/10.1139/L06-005...
].
Figure 14
Subroutine for Problem 2.
Figure 15
Subroutine for Problem 3.
Figure 16
Test setup for combined action on beams S1 to S7 (dimensions in mm) [
2020 H. E. I. Badawy, A. E. McMullen, and I. J. Jordaan, "Experimental investigation of the collapse of reinforced concrete curved beams," Mag. Concr. Res., vol. 29, no. 99, pp. 59–69, 1977, http://dx.doi.org/10.1680/macr.1977.29.99.59.
http://dx.doi.org/10.1680/macr.1977.29.9...
].
Figure 17
S1 to S7 beams cross section (dimensions in cm and bars diameter in mm).
Figure 18
Test setup for combined action on beams M5 a M7 [
2121 A. E. McMullen and J. Warwaruk, The Torsional Strength of Rectangular Reinforced Concrete Beams Subjected to Combined Loading. Edmonton, Canada: The Univ. Alberta, Dep. Civ. Eng.; 1967. Accessed: Oct. 4, 2021. [Online]. Available: https://era.library.ualberta.ca/items/5086dede-150c-43e1-8a0a-8a0a27d5605f/download/04ed74f7-789e-486d-ba8d-aa3b0ddc554b.
https://era.library.ualberta.ca/items/50...
].
Figure 19
M5 to M7 beams cross section (dimensions in cm and bars diameter in mm).
Figure 20
Interaction surface according to NBR and AASHTO for beams S1-S7.
Figure 21
Adapted from Rahal’s AASHTO surface for beams S1-S4 [
1919 K. N. Rahal, "Evaluation of AASHTO-LRFD general procedure for torsion and combined loading," ACI Struct. J., vol. 103, no. 5, pp. 683–692, 2006., http://dx.doi.org/10.14359/16920.
http://dx.doi.org/10.14359/16920...
].M5 to M7 beams.
Figure 22
Interaction surface according to NBR and AASHTO for beams M5 e M6.
Figure 23
Interaction surface according to NBR and AASHTO for beams M7.
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