Second-order torsion effects in concrete buildings

ABSTRACT: The internal forces due to torsion in global analysis of buildings, and its second-order effects, usually are not properly considered in structural design or even in design code’s prescriptions. Although the γZ coefficient, which is used to the evaluation of global second-order effects, has a wide, useful and consolidated application, it is true that specific torsional aspects are not well considered by it. This paper discusses the little-known γθ coefficient, an analogous proposition to the γZ coefficient, but focused specifically on the consideration of torsional effects. After the discussion on the concepts and the design methodology, several buildings are evaluated and their displacements and the coefficients γZ and γθ are calculated. Comparing these parameters, and also the results obtained by the P–Δ method, it is demonstrated the importance and the reliability of the γθ coefficient.

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Relação entre os coeficientes α e γz para edifícios altos de concreto armado e alvenaria estrutural

Revista Principia - Divulgação Científica e Tecnológica do IFPB ◽

10.18265/1517-0306a2020v1n51p158-165 ◽

2020 ◽

Vol 1 (51) ◽

pp. 158

Author(s):

João Paulo Reis Menezes ◽

Camila De Sousa Vieira ◽

David Leonardo Nascimento de Figueiredo Amorim

Keyword(s):

Reinforced Concrete ◽

Structural Design ◽

Second Order ◽

Analytical Relation ◽

Order Effects ◽

Masonry Buildings ◽

Reinforced Concrete Buildings ◽

Concrete Buildings ◽

Design Values ◽

Second Order Effects

<p class="Normal1">The inherent relation between the instability parameters α and γz is studied in this paper. Such parameters are simplified criteria widely used in structural design in Brazil to evaluate the necessity to consider the global second order effects. Thus, an analytical relation between the parameters α and γz is proposed through a simple example. For this, design values of α and γz of thirty reinforced concrete buildings and twenty-two masonry buildings were used. The obtained results prove the accuracy of the proposed formulation for both types of construction</p>

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Statistical analysis of second order effects variation with the stories height of reinforced concrete buildings

Revista IBRACON de Estruturas e Materiais ◽

10.1590/s1983-41952017000200005 ◽

2017 ◽

Vol 10 (2) ◽

pp. 333-357

Author(s):

D.M. OLIVEIRA ◽

N.A. SILVA ◽

C.C. RIBEIRO ◽

S.E.C. RIBEIRO

Keyword(s):

Reinforced Concrete ◽

Statistical Analysis ◽

Second Order ◽

Order Effects ◽

Reinforced Concrete Buildings ◽

First Order ◽

Concrete Buildings ◽

Ideal Situation ◽

Second Order Effects ◽

The Ideal

Abstract In this paper the simplified method to evaluate final efforts using γ z coefficient is studied considering the variation of the second order effects with the height of the buildings. With this purpose, several reinforced concrete buildings of medium height are analyzed in first and second order using ANSYS software. Initially, it was checked that the (z coefficient should be used as magnifier of first order moments to evaluate final second order moments. Therefore, the study is developed considering the relation (final second order moments/ first order moments), calculated for each story of the structures. This moments relation is called magnifier of first order moments, "γ", and, in the ideal situation, it must coincide with the γ z value. However, it is observed that the reason γ /γ z varies with the height of the buildings. Furthermore, using an statistical analysis, it was checked that γ /γ z relation is generally lower than 1.05 and varies significantly in accordance with the considered building and with the presence or not of symmetry in the structure.

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A Simple Approach for the Design of Ductile Earthquake-Resisting Frame Structures Counting for P-Delta Effect

Buildings ◽

10.3390/buildings9100216 ◽

2019 ◽

Vol 9 (10) ◽

pp. 216

Author(s):

Shehu ◽

Angjeliu ◽

Bilgin

Keyword(s):

Order Effect ◽

Simple Approach ◽

Second Order ◽

Frame Structures ◽

Order Effects ◽

Lateral Loads ◽

Stability Coefficient ◽

Internal Forces ◽

Second Order Effects ◽

The Stability

In the last decades, the possibility to use the inelastic capacities of structures have driven the seismic design philosophy to conceive structures with ductile elements, able to obtain large deformations without compromising structural safety. In particular, the utilization of high-strength elements combined with the purpose of reducing inertial masses of the construction has highlighted the second-order effect as a result of the “lightweight” structure’s flexibility. Computational aspects of inclusion of the second-order effects in the structural analysis remain an open issue and the most common method in the current design practices uses the stability coefficient θ. The stability coefficient estimates the ratio between the second-order effect and lateral loads’ effects. This coefficient is used then to amplify the lateral loads’ effects in order to consider the second-order effects, within a certain range proposed by codes of practices. In the present paper, we propose a simple approach, as an alternative to the stability coefficient method, in order to take into consideration P-Delta effects for earthquake-resisting ductile frame structures in the design process. The expected plastic deformations, which can be assessed by the behavior factor and the elastic deformations of the structure, are expected to magnify the P-Delta effects compared to those estimated from an elastic approach. The real internal forces are approximated by modifying the stiffness matrix of the structure in such a way as to provide a compatible amplification effect. This concept is herein implemented with a three-step procedure and illustrated with well-documented case studies from the current literature. The obtained results show that the method, although simple, provides a good approximation compared to more refined and computationally expensive methods. The proposed method seems promising for facilitating the design computations and increasing the accuracy of the internal forces considering the second-order effects and the amplification from the inelastic deformations.

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