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Theoretical Model for Ultimate Moment Capacity of RC Beams Strengthened by Unbonded Reinforcement

  • Research Article - Civil Engineering
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Abstract

The paper presents a theoretical model for ultimate moment capacity of simply supported reinforced concrete beams by way of retrofitting external unbonded ordinary reinforcement. The advantage of this strengthening technique developed by the author in late 1990s lies in its simplicity and speed in installation along with no special and/or additional skills required for installation. The paper provides the general description of the behaviour along with effect of various parameters supported by a theoretical model to calculate the ultimate moment capacity of the retrofitted beams. The theoretical model has been validated through 22 tested specimens having varying parameters, and has been shown to be capable of predicting the ultimate moment capacities of retrofitted beams with sufficient accuracy.

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Abbreviations

A sb :

Area of bonded conventional reinforcement

A sub :

Area of external unbonded conventional reinforcement

A sc :

Area of compression reinforcement

a v :

Shear span

b :

Width of the beam

calc-f sb :

Calculated stress in bonded reinforcement

calc-f sub :

Calculated stress in external unbonded reinforcement

calc-M ult :

Calculated ultimate moment capacity of beam

d :

Effective depth of bonded reinforcement

d′:

Distance of centre of compression reinforcement from extreme compression fibre

d ub :

Effective depth of external unbonded reinforcement

E s :

Modulus of elasticity of conventional steel

E c :

Modulus of elasticity of concrete

EUBRF:

External unbonded ordinary reinforcement

f cu :

Cube strength of concrete

f c :

Maximum compressive stress in concrete

f yb :

Yield strength of conventional bonded tensile reinforcement

f yc :

Yield strength of conventional bonded compression reinforcement

f yub :

Yield strength of conventional external unbonded reinforcement

f st :

Initial tightening stress in external unbonded reinforcement

f sb :

Stress in bonded reinforcement

f sub :

Stress in external unbonded reinforcement

h :

Overall depth of section

L :

Total length of beam (in present study referred to as span of beam)

M u :

Ultimate moment capacity of the beam

meas-f sb :

Measured stress in bonded reinforcement

meas-f sub :

Measured stress in unbonded reinforcement

meas-M ult :

Measured ultimate moment capacity of beam

Q b :

Bonded reinforcement quotient

Q c :

Compression reinforcement quotient

Q ub :

External unbonded reinforcement quotient

Q t :

Unbonded reinforcement quotient associated with initial tightening stress

x :

Neutral surface depth (British Practice and as used in the present model)

x b :

Neutral surface depth for a balanced section

z :

Internal lever arm of tension force

β :

Plastic length factor associated with beams with external unbonded reinforcement

γ m :

Partial safety factors for materials

δc :

Concrete extension at the level of external unbonded reinforcement over the plastic length ‘βx’

\({\varepsilon_{\rm c}}\) :

Limiting strain at which concrete crushes (taken as 0.0035 in present study)

\({\varepsilon_{\rm cb}}\) :

Strain in concrete at the level of bonded reinforcement

\({\varepsilon_{\rm cub}}\) :

Strain in concrete at the level of external unbonded reinforcement

\({\varepsilon_{\rm t}}\) :

Surface strain at level of bonded bars

\({\varepsilon_{\rm sub}}\) :

Strain in external unbonded reinforcement

\({\varepsilon_{\rm sb}}\) :

Strain in bonded reinforcement

ρ b :

Reinforcement ratio for bonded bars

ρ ub :

Reinforcement ratio for unbonded bars

ρ c :

Reinforcement ratio for compression bars

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Rafeeqi, S.F.A. Theoretical Model for Ultimate Moment Capacity of RC Beams Strengthened by Unbonded Reinforcement. Arab J Sci Eng 37, 1849–1870 (2012). https://doi.org/10.1007/s13369-012-0294-2

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