3D Fiber-Based Frame Element with Multiaxial Stress Interaction for RC Structures

Alexander Kagermanov,Paola Ceresa

doi:10.1155/2018/8596970

Alexander Kagermanov, Paola Ceresa

Open Access

https://doi.org/10.1155/2018/8596970

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Abstract

A three-dimensional fiber-based frame element accounting for multiaxial stress conditions in reinforced concrete structures is presented. The element formulation relies on the classical Timoshenko beam theory combined with sectional fiber discretization and a triaxial constitutive model for reinforced concrete consisting of an orthotropic, smeared crack material model based on the fixed crack assumption. Torsional effects are included through the Saint-Venant theory of torsion, which accounts for out-of-plane displacements perpendicular to the cross section due to warping effects. The formulation was implemented into a force-based beam-column element and verified against monotonic and cyclic tests of reinforced concrete columns in biaxial bending, beams in combined flexure-torsion, and flexure-torsion-shear.

Highlights

A three-dimensional fiber-based frame element accounting for multiaxial stress conditions in reinforced concrete structures is presented. e element formulation relies on the classical Timoshenko beam theory combined with sectional fiber discretization and a triaxial constitutive model for reinforced concrete consisting of an orthotropic, smeared crack material model based on the fixed crack assumption
Gregori et al [16] used a similar element to that used by Mazars et al but with a parabolic shear strain profile and Coulomb theory for torsion. e constitutive model was based on the MCFT. e cross section was subdivided into three regions based on the dominant stress conditions: 1D, 2D, and 3D, where the corresponding constitutive models were applied
In the Timoshenko beam theory (TBT), cross sections are not constrained to remain orthogonal to the beam axis, as in the Euler–Bernoulli beam theory, due to shear distortions of an infinitesimal beam element. e kinematics of any point of the beam is completely described by three independent displacements and rotations of the beam axis as follows (Figure 2): d 􏼐uovowoθxθyθz􏼑

Summary

Frame Element Formulation

In the Timoshenko beam theory (TBT), cross sections are not constrained to remain orthogonal to the beam axis, as in the Euler–Bernoulli beam theory, due to shear distortions of an infinitesimal beam element. e kinematics of any point of the beam is completely described by three independent displacements and rotations of the beam axis as follows (Figure 2):. Axial and shear strains at a given section fiber are given as zu εx zx εo − χzy + χyz, zv zu zω cxy zx + zy coy − αz + zy α,. E section forces consistent with the section strains are obtained from integration of the axial and shear stress distributions over the cross section as follows:. Incremental section forces and strains are related by the tangent stiffness matrix of the section as follows: Ks zS zε z ze BTσ σdA. E D matrix is obtained from condensation of the (6 × 6) material stiffness matrix assuming that the total stresses σy, σz, and τyz are zero in the beam element as follows: σy σc,y + ρsyσs,y 0, σz σc,z + ρszσs,z 0,.

Constitutive Model

Verification Examples

Conclusions