Safety Against Limit States

Safety Against Limit States

Variation in Material Strength

A) Variability of material strength due to the variation in the quality of ingredients and basic factors during the manufacture of concrete. This variation is allowed by fixing characteristic strength.
Experiments have revealed that the probability distribution of concrete is approx. follow Gaussian distribution curve if the number of samples is infinite (very large).

  • More is the area (fig 2) under the Gaussian distribution curve less is the quality control achieved in preparing the concrete and less is the area under the curve more is the quality control achieved.

B) Variability on account of faults and difficulties during construction, the state of stress on account of loading, the speed, duration, and repetition of loading, and the environmental conditions. The strength of concrete in a structure may be reduced on account of inadequate compaction and curing. The assumptions made in the statistical analysis (characteristic strength) are invalid for such variations the statistical principles cannot be applied. These variations are covered by a partial safety for material strength. The design strength of material fd is given by IS456 clause 36.3.

 f_{d}=\frac{f}{\gamma_{m}}

where
f = characteristic strength of material; fck for concrete and fy for steel
γm partial safety factor for concrete = 1.5 but for steel the partial safety factor is 1.15

  • The partial safety factor for concrete is more than steel because concrete is a brittle material and any
  • weakness may lead to sudden failure while steel is a ductile material that gives sufficient warning before failure. Steel is produced in more control environment than concrete hence strength of steel approximately correspond to their actual strength in a structure.
Safety Against Limit States

Also, Read————————– Limit State Method 0f Design | Reinforced Cement Concrete |

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