# Comparison between solid and hollow reinforced concrete beams

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## 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/ε
_{y} Ratio of applied strain at each increment to yield strain

- (ε/ε
_{y})Lng Maximum strain ratio measured in the longitudinal steel

- (ε/ε
_{y})Strp Maximum strain ratio measured in the stirrups

- Dif. F.L
Percentage of the difference in failure load between the solid and hollow beams

*f*′_{c}Concrete cylinder compressive strength

*f*_{cu}Concrete cube compressive strength

*f*′_{t}Concrete cylinder tensile split test

*f*_{y}Yield stress of the longitudinal steel

*f*_{yv}Yield stress of the transverse steel

- L.F
Load factor (percentage of applied load to design load) = (

*T*_{i}/*T*_{d }+*M*_{i}/*M*_{d})/2 at any load increment*i**L*_{e}/*L*_{d}Failure load ratio = (

*T*_{e}/*T*_{d }+*M*_{e}/*M*_{d})/2 for the last (failure) load increment- LFCR
Load factor when first crack was noticed

*M*_{d},*T*_{d},*V*_{d}Design bending moment, torsion and shear force respectively

*M*_{e},*T*_{e},*V*_{e }Experimentally measured bending moment, torsion and shear force at failure respectively

*T*_{i},*M*_{i, }*V*_{i }Experimentally measured torsion, bending moment and shear force at load increment

*i**θ*^{o}Average angle of inclination of cracks near failure load

- Δ
Maximum vertical displacement at mid-span

- σ
_{y} Applied normal stress in the y direction

- τ
_{shr} Applied shear stress due to shear force

- τ
_{tor} Applied shear stress due to torsion

- τ
_{xy}+ Net applied shear stress due to torsion and shear where stresses are added, (=τ

_{shr }+ τ_{tor})*τ*_{xy}−Net applied shear stress due to torsion and shear where stresses are subtracted, (=τ

_{shr}−τ_{tor})*N*_{x}Applied in-plane force per unit length in the

*x*direction on a element with thickness*t*, (=σ_{xser}*t*)*N*_{y}Applied in-plane force per unit length in the

*y*direction on a element with thickness*t*, (=σ_{y}*t*)*N*_{xy}Applied in-plane shear force per unit length on a element with thickness

*t*, (=*τ*_{xy}*t*)*N*_{x}^{s}Steel resisting force in

*x*direction*N*_{y}^{s}Steel resisting force in

*y*direction- σ
_{1} Concrete principle stress in direction 1

- σ
_{2} Concrete principle stress in direction 2

*N*_{1}Concrete resisting force in the principle direction 1, (=

*σ*_{1}*t*)*N*_{2}Concrete resisting force in the principle direction 2, (=

*σ*_{2}*t*)*A*_{o}Area of concrete enclosed by the centre line of the shear flow

*A*_{c}Concrete gross cross-sectional area

*I*Moment of inertia of the cross-section

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