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Materials and Structures

, Volume 41, Issue 2, pp 269–286 | Cite as

Comparison between solid and hollow reinforced concrete beams

  • Ali Said Alnuaimi
  • Khalifa S. Al-Jabri
  • Abdelwahid Hago
Original Article

Abstract

Comparison between test results of seven hollow and seven solid reinforced concrete beams is presented. All of the fourteen beams were designed as hollow sections to resist combined load of bending, torsion and shear. Every pair (one hollow and one solid) was designed for the same load combinations and received similar reinforcement. The beams were 300 × 300 mm cross-section and 3,800 mm length. The internal hollow core for the hollow beams was 200 × 200 mm creating a peripheral wall thickness of 50 mm. The main variables studied were the ratio of bending to torsion which was varied between 0.19 and 2.62 and the ratio in the web of shear stress due to torsion to shear stress due to shear force which was varied between 0.59 and 6.84. It was found that the concrete core participates in the beams’ behaviour and strength and cannot be ignored when combined load of bending, shear and torsion are present. Its participation depends partly on the ratio of the torsion to bending moment and the ratio of shear stress due to torsion to the shear stress due to shear force. All solid beams cracked and failed at higher loads than their counterpart hollow beams. The smaller the ratio of torsion to bending the larger the differences in failure loads between the hollow and solid beams. The longitudinal steel yielded while the transverse steel experienced lower strain values.

Keywords

Reinforced concrete Bending Shear Torsion Direct design Combined load 

Notations

ε/εy

Ratio of applied strain at each increment to yield strain

(ε/εy)Lng

Maximum strain ratio measured in the longitudinal steel

(ε/εy)Strp

Maximum strain ratio measured in the stirrups

Dif. F.L

Percentage of the difference in failure load between the solid and hollow beams

fc

Concrete cylinder compressive strength

fcu

Concrete cube compressive strength

ft

Concrete cylinder tensile split test

fy

Yield stress of the longitudinal steel

fyv

Yield stress of the transverse steel

L.F

Load factor (percentage of applied load to design load) = (T i/T M i/M d)/2 at any load increment i

Le/Ld

Failure load ratio = (T e/T M e/M d)/2 for the last (failure) load increment

LFCR

Load factor when first crack was noticed

Md, Td, Vd

Design bending moment, torsion and shear force respectively

Me, Te, Ve

Experimentally measured bending moment, torsion and shear force at failure respectively

Ti, Mi, Vi

Experimentally measured torsion, bending moment and shear force at load increment i

θo

Average angle of inclination of cracks near failure load

Δ

Maximum vertical displacement at mid-span

σy

Applied normal stress in the y direction

τshr

Applied shear stress due to shear force

τtor

Applied shear stress due to torsion

τxy+

Net applied shear stress due to torsion and shear where stresses are added, (=τshr + τtor)

τxy

Net applied shear stress due to torsion and shear where stresses are subtracted, (=τshr−τtor)

Nx

Applied in-plane force per unit length in the x direction on a element with thickness t, (=σxser t)

Ny

Applied in-plane force per unit length in the y direction on a element with thickness t, (=σy t)

Nxy

Applied in-plane shear force per unit length on a element with thickness t, (=τ xy t)

Nxs

Steel resisting force in x direction

Nys

Steel resisting force in y direction

σ1

Concrete principle stress in direction 1

σ2

Concrete principle stress in direction 2

N1

Concrete resisting force in the principle direction 1, (=σ 1 t)

N2

Concrete resisting force in the principle direction 2, (=σ 2 t)

Ao

Area of concrete enclosed by the centre line of the shear flow

Ac

Concrete gross cross-sectional area

I

Moment of inertia of the cross-section

References

  1. 1.
    Hsu TTC (1968) Torsion of structural concrete-behaviour of reinforced concrete rectangular members. SP-18, American Concrete Institute, Detroit, Michigan, pp 261–306Google Scholar
  2. 2.
    Mitchell, D, Collins MP (1974) Behaviour of structural concrete beams in pure torsion, publication No. 74–06. Department of Civil Engineering, University of Toronto, Toronto, Ontario, CanadaGoogle Scholar
  3. 3.
    Ojha Surendra K (1974) Deformation of reinforced concrete rectangular beams under combined torsion, bending and shea. ACI J 71–26:383–391Google Scholar
  4. 4.
    Thurlimann B (1979) Torsional strength of reinforced and prestressed concrete beams-CEB approach. Institut fur Baustatik und konstruktion, ETH. Zurich, (92):117–143Google Scholar
  5. 5.
    Collins MP, Mitchell D (1991) Pre-stressed concrete structures. Prentice Hall Inc., Englewood Cliffs, NJGoogle Scholar
  6. 6.
    Rahal KN, Collins MP (1995) Analysis of sections subjected to combined shear and torsion—a theoretical model. ACI Struct J 92(4):459–469Google Scholar
  7. 7.
    Rahal KN (2000) Torsional strength of reinforced concrete beams. Canadian J Civil Eng 27:445–453CrossRefGoogle Scholar
  8. 8.
    MacGregor JG, Ghoneim MG (1995) Design for torsion. ACI Struct J S92–S20:211–218Google Scholar
  9. 9.
    Fouad E, Ghoneim M, Issa M, Shaheen H (2000) Combined shear and torsion In normal and high-strength concrete beams (1): Experimental Study. J Eng Appl Sci 47(6):1059–1078Google Scholar
  10. 10.
    Bhatt P, Ebireri JO (1989) Direct design of beams for combined bending and torsion, Stavebnicky Casopis, Building Journal (Bratislava), v 37, n 4 Apr., pp 249–263, in English, ISSN: 0039-078X, Coden: STVCA2Google Scholar
  11. 11.
    Nielsen TB (1985) Optimization of reinforcement in shells, folded plates, walls and slabs. ACI J 82–26:304–309Google Scholar
  12. 12.
    Nielsen MP (1978) Some examples of lower-bound design of reinforcement in plane stress problems. IABSE colloquium, Copenhagen, Session V. Plasticity in Reinforced Concrete, Final report 29:317–324 AugGoogle Scholar
  13. 13.
    Nielsen MP (1974) Optimum design of reinforced concrete shells and slabs. Structural research laboratory, Technical University of Denmark, Report NR.R44, pp 190–200Google Scholar
  14. 14.
    Alnuaimi AS, Bhatt P (2004) Direct design of hollow reinforced concrete beams, part I: design procedure. Struct Concrete J 5(4):139–146CrossRefGoogle Scholar
  15. 15.
    Alnuaimi AS, Bhatt P (2004) Direct design of hollow reinforced concrete beams, part II: experimental investigation. Struct Concrete J 5(4):147–160Google Scholar

Copyright information

© RILEM has copyright 2007

Authors and Affiliations

  • Ali Said Alnuaimi
    • 1
  • Khalifa S. Al-Jabri
    • 1
  • Abdelwahid Hago
    • 1
  1. 1.Department of Civil and Architectural, Engineering College of engineeringSultan Qaboos UniversityMuscatSultanate of Oman

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