Closed-form expressions for lateral deflection of low-rise rigidly framed concrete structures

Magued Iskander, Farah Masood, Saumil Parikh, Andrew J. Dimond, Walid Aboumoussa

Research output: Contribution to journalArticle

Abstract

Approximate closed-form rational expressions for calculating the lateral deflection of low-rise rigidly framed concrete structures subject to different lateral force distributions were developed. The expressions were derived by treating the structure as an equivalent cantilever beam, neglecting flexure deformation, and determining the shear deflection. The computed elastic deformations neglect concrete cracking. A parametric finite element (FEM) analysis, of 42 000 different rigid frame configurations, was performed to calibrate the closed-form expressions, using multivariate nonlinear regression analysis. Three numerical examples are presented to illustrate application of the expressions as well as their accuracy and validity. A Weibull statistical analysis was performed for each equation and determined that the expressions had better than 80% probability to yield deflections that are within 25% of the values computed using FEM. Furthermore, there is a 97% certainty that each equation will yield a deflection that is within 50% of that computed using FEM. The errors are random and are not dependant on the building or cell aspect ratio, number of stories or bays, inertia of beams or columns. The proposed closed-form expressions serve as a useful tool for preliminary design and for verifying numerical solutions using hand computations.

Original languageEnglish (US)
Pages (from-to)20-33
Number of pages14
JournalCanadian Journal of Civil Engineering
Volume39
Issue number1
DOIs
StatePublished - Jan 2012

Fingerprint

concrete structure
Concrete construction
deflection
Forms (concrete)
Random errors
Cantilever beams
Elastic deformation
Regression analysis
Aspect ratio
Statistical methods
Concretes
Finite element method
flexure
inertia
regression analysis
statistical analysis

Keywords

  • Analytical
  • Approximate
  • Building
  • Drift
  • Earth retaining
  • Estimate
  • Rigid frame
  • Shear deformation
  • Structural analysis

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Environmental Science(all)

Cite this

Closed-form expressions for lateral deflection of low-rise rigidly framed concrete structures. / Iskander, Magued; Masood, Farah; Parikh, Saumil; Dimond, Andrew J.; Aboumoussa, Walid.

In: Canadian Journal of Civil Engineering, Vol. 39, No. 1, 01.2012, p. 20-33.

Research output: Contribution to journalArticle

Iskander, Magued ; Masood, Farah ; Parikh, Saumil ; Dimond, Andrew J. ; Aboumoussa, Walid. / Closed-form expressions for lateral deflection of low-rise rigidly framed concrete structures. In: Canadian Journal of Civil Engineering. 2012 ; Vol. 39, No. 1. pp. 20-33.
@article{52d823ab0a5e4f5bbabc1f8eb2da66ce,
title = "Closed-form expressions for lateral deflection of low-rise rigidly framed concrete structures",
abstract = "Approximate closed-form rational expressions for calculating the lateral deflection of low-rise rigidly framed concrete structures subject to different lateral force distributions were developed. The expressions were derived by treating the structure as an equivalent cantilever beam, neglecting flexure deformation, and determining the shear deflection. The computed elastic deformations neglect concrete cracking. A parametric finite element (FEM) analysis, of 42 000 different rigid frame configurations, was performed to calibrate the closed-form expressions, using multivariate nonlinear regression analysis. Three numerical examples are presented to illustrate application of the expressions as well as their accuracy and validity. A Weibull statistical analysis was performed for each equation and determined that the expressions had better than 80{\%} probability to yield deflections that are within 25{\%} of the values computed using FEM. Furthermore, there is a 97{\%} certainty that each equation will yield a deflection that is within 50{\%} of that computed using FEM. The errors are random and are not dependant on the building or cell aspect ratio, number of stories or bays, inertia of beams or columns. The proposed closed-form expressions serve as a useful tool for preliminary design and for verifying numerical solutions using hand computations.",
keywords = "Analytical, Approximate, Building, Drift, Earth retaining, Estimate, Rigid frame, Shear deformation, Structural analysis",
author = "Magued Iskander and Farah Masood and Saumil Parikh and Dimond, {Andrew J.} and Walid Aboumoussa",
year = "2012",
month = "1",
doi = "10.1139/L11-104",
language = "English (US)",
volume = "39",
pages = "20--33",
journal = "Canadian Journal of Civil Engineering",
issn = "0315-1468",
publisher = "National Research Council of Canada",
number = "1",

}

TY - JOUR

T1 - Closed-form expressions for lateral deflection of low-rise rigidly framed concrete structures

AU - Iskander, Magued

AU - Masood, Farah

AU - Parikh, Saumil

AU - Dimond, Andrew J.

AU - Aboumoussa, Walid

PY - 2012/1

Y1 - 2012/1

N2 - Approximate closed-form rational expressions for calculating the lateral deflection of low-rise rigidly framed concrete structures subject to different lateral force distributions were developed. The expressions were derived by treating the structure as an equivalent cantilever beam, neglecting flexure deformation, and determining the shear deflection. The computed elastic deformations neglect concrete cracking. A parametric finite element (FEM) analysis, of 42 000 different rigid frame configurations, was performed to calibrate the closed-form expressions, using multivariate nonlinear regression analysis. Three numerical examples are presented to illustrate application of the expressions as well as their accuracy and validity. A Weibull statistical analysis was performed for each equation and determined that the expressions had better than 80% probability to yield deflections that are within 25% of the values computed using FEM. Furthermore, there is a 97% certainty that each equation will yield a deflection that is within 50% of that computed using FEM. The errors are random and are not dependant on the building or cell aspect ratio, number of stories or bays, inertia of beams or columns. The proposed closed-form expressions serve as a useful tool for preliminary design and for verifying numerical solutions using hand computations.

AB - Approximate closed-form rational expressions for calculating the lateral deflection of low-rise rigidly framed concrete structures subject to different lateral force distributions were developed. The expressions were derived by treating the structure as an equivalent cantilever beam, neglecting flexure deformation, and determining the shear deflection. The computed elastic deformations neglect concrete cracking. A parametric finite element (FEM) analysis, of 42 000 different rigid frame configurations, was performed to calibrate the closed-form expressions, using multivariate nonlinear regression analysis. Three numerical examples are presented to illustrate application of the expressions as well as their accuracy and validity. A Weibull statistical analysis was performed for each equation and determined that the expressions had better than 80% probability to yield deflections that are within 25% of the values computed using FEM. Furthermore, there is a 97% certainty that each equation will yield a deflection that is within 50% of that computed using FEM. The errors are random and are not dependant on the building or cell aspect ratio, number of stories or bays, inertia of beams or columns. The proposed closed-form expressions serve as a useful tool for preliminary design and for verifying numerical solutions using hand computations.

KW - Analytical

KW - Approximate

KW - Building

KW - Drift

KW - Earth retaining

KW - Estimate

KW - Rigid frame

KW - Shear deformation

KW - Structural analysis

UR - http://www.scopus.com/inward/record.url?scp=84855590688&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855590688&partnerID=8YFLogxK

U2 - 10.1139/L11-104

DO - 10.1139/L11-104

M3 - Article

AN - SCOPUS:84855590688

VL - 39

SP - 20

EP - 33

JO - Canadian Journal of Civil Engineering

JF - Canadian Journal of Civil Engineering

SN - 0315-1468

IS - 1

ER -