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Probabilistic analysis of the cracking of RC beams

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Abstract

Three beams of rectangular cross-section and having same cross-sectional dimensions were tested in two-point bending, over an effective span of 4.2 m. All three beams contained steel only in the tension zone and the tension steel was distributed in three different ways. A deterministic analysis of strains, crack spacings and crack widths for all three beams is carried out and the results are compared with the respective experimental values. A probabilistic analysis of strains, crack spacings and crack widths is performed for all the three beams at different stages of loading.

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Abbreviations

A ct :

Effective concrete area intension

A st :

Area of tension reinforcement

A st1 :

Area of tension reinforcement in top row (i.e. atd 1)

A st2 :

Area of tension reinforcement in bottom row (i.e. atd 2)

a c :

Average spacing of cracks

a m :

Average spacing of cracks when they have just formed (i.e. atM=M cr for a flexural specimen)

b :

Width of section

D :

Total depth of the section

d :

Effective depth

d1,d2:

Depths to the two rows of reinforcing steel from extreme-compression fibre

E s :

Modulus of elasticity of steel

E c :

Modulus of elasticity of concrete (initial tangent modulus)

f bu :

Ultimate bond strength

f ct :

Tensile strength of concrete

f c :

Compression strength of concrete cylinder

f r :

Modulus of rupture of concrete

f y :

Yield strength of reinforcement

h 1 :

Depth to the level at which strain is required

I :

Moment of inertia of cross-section

I g :

Moment of inertia of uncracked crosssection

I cr :

Moment of inertia of cracked transformed section

k b :

Factor giving average bond stress (k b=2/3 in this investigation)

k t :

Factor giving average tensile stress (k t=2/3 in this investigation)

l :

Effective span of beam

l 1 :

Distance of section XX from an already formed crack

M :

External moment

M cr :

Cracking moment

M u :

Ultimate moment

R :

Rate of loading (35 psi sec−1)

W as :

Average crack width at the level of steel

W ms :

Maximum crack width at the level of steel

x :

Neutral axis depth of a cracked section

γ:

A constant (=0.33 in this study)

ɛs :

Strain in reinforcement

σbs :

Maximum bond stress

σsr :

Steel stress at first cracking

σtx :

Maximum tensile stress in the effective concrete at section XX

ϕ:

Diameter of bar

μ:

Mean

σ:

Standard deviation

COV:

Coefficient of variation

Ωccyl :

Compression cylinder strength coefficient of variation

P :

Effective reinforcement ratioA st/A ct

References

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Science, 12, Bangalore, India

    Prakash Desayi & K. Balaji Rao

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  1. Prakash Desayi
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  2. K. Balaji Rao
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Desayi, P., Rao, K.B. Probabilistic analysis of the cracking of RC beams. Materials and Structures 20, 408–417 (1987). https://doi.org/10.1007/BF02472491

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  • DOI: https://doi.org/10.1007/BF02472491

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