Characteristic Strength Of Limit States

Characteristic Strength Of Limit States IS 456

As per IS456 clause 36.1 Strength of cube size 150 x 150 x 150 mm after 28 days , below which not more than 5% of the test result are expected to fall. It is represented by M25 which means 25 N/mm2
or 25 MPa.

 Mean Strength ( F_{m} ) F_{m}= \frac{Sum\: of \: strength\: of \:all\: the \:samples}{Number \:of \:samples}

  F_{m}= \frac{\Sigma f}{m}
m = total number of samples

Standard deviation  (\sigma) -A quantity expressing by how much the members of a group differ from the mean value for the group. its unit is N/mm2. As per IS 456 clause 9.2.4.1 minimum samples required to determine standard deviation is 30.

 \sigma = \sqrt{\frac{\Sigma (f-f_m)^{2}}{m}} when m is less than 30

 \sigma = \sqrt{\frac{\Sigma (f-f_m)^{2}}{m-1}} m is more or equal than 30

When sufficient test result is not available the values of standard deviation is taken as follows

Table 8 of IS 456

Grade of concreteStandard deviation
M10, M153.5 N/mm2
M20,M254N/mm2
M30 to M505N/mm2
Characteristic Strength Of Limit States

The equation of curve is   y=\frac{e^{-(f-f_m)/\sigma^2}}{\sigma}

If we take compressive strength equal to mean strength (fck=fm) than the definition of characteristic strength will be , Strength of cube size 150 x 150 x 150 mm after 28 days , below which not more than 50% of the test result are expected to fall

IS code 456 clause 9.2.2 Characteristic Strength  f_{ck}= f_{m}- 1.65\sigma

The coefficient of variation is the ratio expressed as = \frac{\sigma \ast 100}{fm} 100%

Sampling of Mix

3 specimen make one sample. As per IS 456 Clause 15.4 The individual variation of specimen should not be more than +/- 15% of the average. If variation is more than +/- 15% sample are invalid.
The number of samples depends upon the quantity of concrete in the work (cubic meter).

As per IS 456 clause 15.2.2

Quantity of concreteNo. of Samples
1-5 m31
6-15m32
16-30m33
31-50m34
51m3 and above4 plus additional samples for each additional 50m

Acceptance Criteria:-

Compressive Strength as per IS 456 clause 16.1 (Amendment Aug2007)

Table 11 IS 456

Specified Grade Mean of the Group of 4 non overlapping Consecutive test result in N/mm2 Individual test result N/mm2
M15 and above=f_{ck} \:+.825\sigma
=f_{ck} \:+3
whichever is greater
 =f_{ck} \:-3

Flexural Strength as per IS456 clause 16.2
When both the following conditions are met the concrete complies with the specified flexure strength.
a) The mean strength determined from any group of four consecutive test results exceeds the specified characteristic strength by at least 0.3N/mm2.
b) The strength determined from any test result is not less than the specified characteristic strength minus 0.3N/mm2.

Variation in Load

A) The variability of loads applied on a structure is, throughout its design life, covered by fixing up a characteristic load that takes into account the statistical variation of the load.

 f_k = f_m \:+\:1.65 \sigma

fk= characteristic load
fm = the mean load
  \sigma = Standard deviation

Characteristic Strength Of Limit States

IS456 clause 36.2 Characteristic load is defined to be that value of the load which has a 95% probability of not exceeding during the life of the structure.

B) The variation of load on a member may be due to an error in design assumption. There may be additional uncertainties such as possible unfavorable deviation of load beyond the characteristic value. Adverse load effects occur due to design and constructional discrepancies. Examples are; possible neglect of temperature, shrinkage, and creep stresses, dimensional error in span, incorrect positioning of reinforcement, etc. all these variations are covered by a partial safety factor for loads. The design load Fd for a given type of loading and the limit state is given by IS456 clause 36.3.2

 f_d = f_k * γ  d

Where γf is a partial safety factor according to the type of loading and the limit state being considered.

Type of LoadCode No
Dead LoadIS:1911
Live and Wind LoadIS: 875
Seismic LoadS: 1893

Note: while considering earthquake loading, EL should be substituted for WL.

  • Partial safety factor for serviceability is taken as 1 because we need to estimate the actual deflection and crack widths not the safe (conservative) values.
  • The reduce load factor of 1.2 recognizes the reduced probability of all the three imposed loads reaching their characteristic or peak values simultaneously.
  • For design purpose, the maximum load is taken from the above load combinations.
Characteristic Strength Of Limit States

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

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