# Effect of under-reinforcement on the flexural strength of corroded beams

## Authors

- First Online:

- Received:
- Accepted:

DOI: 10.1617/s11527-007-9241-1

- Cite this article as:
- O’Flaherty, F.J., Mangat, P.S., Lambert, P. et al. Mater Struct (2008) 41: 311. doi:10.1617/s11527-007-9241-1

- 9 Citations
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## Abstract

Reinforced concrete beams are normally designed as under-reinforced to provide ductile behaviour i.e. the tensile moment of resistance, *M*_{t(0)} is less than the moment of resistance of the compressive zone, *M*_{c}. The degree of under-reinforcement (*M*_{t(0)}/*M*_{c} ratio) can depend upon the preferences of the designer in complying with design and construction constraints, codes and availability of steel reinforcement diameters and length. *M*_{t(0)}/*M*_{c} is further influenced during service life by corrosion which decreases *M*_{t(0)}. The paper investigates the influence of *M*_{t(0)}/*M*_{c} on the residual flexural strength of corroded beams and determines detailing parameters (e.g. size and percentage of steel reinforcement, cover) on *M*_{t(0)}/*M*_{c}. Corroded reinforced concrete beams (100 mm × 150 mm deep) with varying *M*_{t(0)}/*M*_{c} ratios were tested in flexure. The results of the investigation were combined with the results of similar work by other researchers and show that beams with lower *M*_{t(0)}/*M*_{c} ratios suffer lower flexural strength loss when subjected to tensile reinforcement corrosion. Cover to the main steel does not directly influence *M*_{t(0)}/*M*_{c} and, thus, the residual flexural strength of corroded beams is not normally affected by increased cover. A simplified expression for estimating the residual strength of corroded beams is also given.

### Keywords

Under-reinforcedCorrosionFlexuralDurabilityStructural### Notation

*A*Atomic weight of iron

*A*_{S}Area of tensile reinforcement

- \({A_S^{\prime}}\)
Area of compressive reinforcement (hanger bars)

*a*Rebar surface area before corrosion

- α
Slope of

*M*_{t(corr)}/*M*_{c}against percent of corrosion*b*Breadth of beam section

- β
Intercept (or

*M*_{t(0)}/*M*_{c}ratio)*C*Cover to main steel reinforcement

*d*Effective depth to main steel

*d*′Effective depth to compressive steel

- δ
Material loss due to corrosion

- \({\Updelta \omega}\)
Weight loss due to corrosion

*F*Faraday’s constant

*F*_{cc}Force in the concrete in compression

*F*_{sc}Force in the steel in compression

*f*_{cu}Compressive strength of concrete

- \({f_y^{\prime}}\)
Yield strength of compressive steel

- γ
Density of steel

- γ
_{c} Partial safety factor for the strength of concrete

- γ
_{s} Partial safety factor for the strength of steel reinforcement

*h*Height of beam section

*I*Electrical current

*i*Corrosion current density

*M*_{c}Maximum moment of resistance of the concrete in the compression zone

*M*_{t(0)}Moment of resistance of the control beam in the tensile zone

*M*_{t(corr)}Moment of resistance of the corroded beam in the tensile zone

- Ø
Diameter of the main steel reinforcement

- Ø′
Diameter of the compressive steel reinforcement

*R*Material loss per year due to corrosion

*s*Depth of idealised compressive stress block

*T*High yield steel reinforcement

*T*′Time in years

*t*Time in seconds

*x*Depth to neutral axis

*Z*Valence of iron

*z*Lever arm