Strength and Stiffness of Reinforced Concrete Columns under 2012-11-08¢  The strength and stiffness

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  • 1. Report No. 2. Government Acce .. ion No.

    FHWATX-77-7-2F

    4. Ti t'e and Subtit'e

    STRENGTH AND STIFFNESS OF REINFORCED CONCRETE COLUMNS UNDER BIAXIAL BENDING

    7. Author/5)

    V. Mavichak and R. W. Furlong

    9. Performing Organizotion Name and Addre ..

    Center for Highway Research The University of Texas at Austin Austin, Texas 78712

    ~~------------------------------------------------------~ 12. Sponsoring Agency Nome ond Addre ..

    Texas State Department of Highways and Public Transportation; Transportation Planning Division

    P. O. Box 5051 Austin, Texas 78763 1 S. Supplementory Note.

    TECHNICAL REPORT STANDARD TITLE PAGE

    3. Recipient's Cotolog No.

    S. Report Dote

    November 1976 6. Performing Orgonizotion Code

    B. Performing Orgoni zotion Report No.

    Research Report 7-2F

    10. Work Unit No.

    11. Controct or Gront No.

    Research Study 3-5-73-7 13. Type of Report QIIId Period Coyered

    Final

    14. Sponsoring Agency Code

    Work done in cooperation with the U. S. Department of Transportation, Federal Highway Administration. Research Study Title: ''Design Parameters for Columns in Brid2e Bents"

    16. Abstract

    The strength and stiffness behavior of reinforced concrete columns subjected to biaxial bending and compression was investigated. In order to provide data points on biaxial interaction surfaces, nine rectangular cross section columns and fifteen partial circular cross section columns were loaded to failure as moments were increased while thrust was maintained at a constant value. Test data included longitudinal strain profiles as well as transverse displacement measurements at all levels of load. Test measurements were compared with a discrete element analytical model that was modified to provide results that were in favorable agreement with measured response. Test results from other investigators were included in the data against which analytical results were checked. The reciprocal thrust equation was selected as the simplest analytical expression that provided approximations of strength that were consistent with test results. The influence of slenderness effects in skew bending was examined. The moment magnifier method was used for approximate analysis of slenderness. Member stiffness relationships recommended by the ACI Building Code were studied in addition to alternate approximations of EI. The ACI procedures were found to five safe results at low thrust levels only if ACI Eq (10-7) was used. Moment magnification used separately for each principal axis of bending appeared to give rational reflections of biaxial behavior. The discrete element analytical model was also used to produce more analytical data for com- parison with the approximate methods of analysis. Simple approximations of EI were not found to be consistent with test data when thrust levels varied and when slenderness ratios were large. 17. Key Word.

    columns, reinforced concrete, strength, stiffness, biaxial bending, compression

    18. Oi .trlbution Statelllen'

    No restrictions. This document is available to the public through the National Technical Information Service, Springfield, Virginia 22161.

    19. Security Ciani I. (ol thl. report)

    Unclassified

    20. Security CIani I. Col thi. page) 21. No. of Page. 22. Prj ce

    Unclassified 242

    Form DOT F 1700.7 (8-581

  • STRENGTH AND STIFFNESS OF REINFORCED CONCRETE COLUMNS UNDER BIAXIAL BENDING

    by

    V. Mavichak and R. W. Furlong

    Research Report 7-2F

    Project 3-5-73-7 Design Parameters for Columns in Bridge Bents

    Conducted for

    Texas State Department of Highways and Public Transportation

    In Cooperation with the U. S. Department of Transportation

    Federal Highway Administration

    by

    CENTER FOR HIGHWAY RESEARCH THE UNIVERSITY OF TEXAS AT AUSTIN

    November 1976

  • The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.

    There was no invention or discovery conceived or first actually reduced to practice in the course of or under this contract, including any art, method, process, machine, manufacture, design or composition of matter, or any new and useful improvement thereof, or any variety of plant which is or may be patentable under the patent laws of the United States of America or any foreign country.

    ii

  • A B S T R ACT

    The strength and stiffness behavior of reinforced concrete

    columns subjected to biaxial bending and compression was investigated.

    In order to provide data points on biaxial interaction surfaces, nine

    rectangular cross section columns and fifteen partial circular cross

    section columns were loaded to failure as moments were increased while

    thrust was maintained at a constant value. Test data included longi-

    tudinal strain profiles as well as transverse displacement measure-

    ments at all levels of load. Test measurements were compared with a

    discrete element analytical model that was modified to provide results

    that were in favorable agreement with measured response. Test results

    from other investigators were included in the data against which

    analytical results were checked.

    The reciprocal thrust equation:

    = 1 P x

    + 1 P

    y

    1 P

    o

    was selected as the simplest analytical expression that provided

    approximations of strength that were consistent with test results.

    The influence of slenderness effects in skew bending was examined.

    The moment magnifier method was used for approximate analysis of slen-

    derness. Member stiffness relationships recommended by the ACI Building

    Code (ACI 318-71) were studied in addition to alternate approximations

    of EI. The ACI procedures were found to give safe results at low

    thrust levels only if ACI Eq. (10-7) was used. Moment magnification

    used separately for each principal axis of bending appeared to give

    rational reflections of biaxial behavior. The discrete element

    analytical model was also used to produce more analytical data for

    comparison with the approximate methods of analysis. Simple

    iii

  • iv

    approximations of EI were not found to be consistent with test data

    when thrust levels varied and when slenderness ratios were large.

    A deflection limit method for computing member strength was

    introduced. The method involved assigning to the nominal eccentricity

    an additional eccentricity that is a function of the slenderness ratio.

    An empirical equation and a procedure for computing member strength

    were proposed on the basis of agreement with experimental data.

    KEY WORDS: columns, reinforced concrete, strength, stiffness,

    biaxial bending, compression

  • SUM MAR Y

    All reinforced concrete columns must be proportioned to resist

    compression thrust that is assumed to act at some degree of eccentric-

    ity away from the longitudinal centroid of the column. This report

    contains an analytic and laboratory investigation of concrete columns

    that are required to resist thrust that is eccentric about both

    principal axes of member cross sections. Heretofore, the design of

    columns to resist biaxially eccentric thrust has been dependent upon

    largely unverified analytic combinations of design procedures for

    uniaxial thrust.

    The investigation incorporates results from other laboratories

    where columns with square cross sections were tested. Since the

    shape of columns in bridge structures frequently is rectangular or

    partially circular (rectangular with circular ends), nine rectangular

    specimens and fifteen partially circular specimens were tested as a

    part of this investigation.

    The investigation revealed that cross section strength and

    cross section ductility are significantly undervalued analytically

    if the customary Whitney constant stress block model is used to repre-

    sent the limit strength of concrete on nonrectangular compression

    zones. The investigation indicated that biaxially eccentric thrust

    capacity p. can be analyzed more accurately in terms of uniaxial 1

    thrust capacities P and P , and a squash load strength P in the x y 0

    following equation of reciprocals

    I p.

    1

    = I P

    x +

    v

    I P Y

    I P o

    (A)

  • vi

    The effects of slenderness can be incorporated through moment

    magnificatian factors applied separately to each uniaxial thrust

    capacity P and P • x y The skew bending tendency to twist the column

    was found to be negligible. Values of flexural stiffness of cross

    sections under thrusts less than O.4P should reflect the effects of o

    cracking and reinforcement percentage.

    Simplified general formulas for flexural stiffness must

    reflect lower bound resistance to deflection, and consequently they

    become useless for moment magnifier application