 # Stress-Strain Curve for Concrete

stress-strain curve of concrete. It can be seen that the peak of stress (maximum compressive stress) for different grades of concrete is different but the strain value for all the grades is 0.002 i.e 0.2%. The value of stress at 0.002 strain is called compressive strength of concrete

• Lower strength concrete has greater deformability i.e lower the strength of concrete more is the ductility.
• The point where the curve ends is called crushing strain.
• It can be seen from the above curve that the strain at the crushing point is more in a lower grade of cement in comparison to a higher grade of concrete (ϵ3 > ϵ2 > ϵ1)

As per the American code, for experimental determination of the stress-strain curve for a concrete, cylindrical specimen of 150mm diameter and 300mm height be used. If the ratio of height to diameter (h/d=2) is maintained then all the cylinder specimens will give the same strength but if the h/d ratio is reduced then for the same concrete the strength obtain will be more and vice versa

• Cylinders are used because we have to obtain uniaxial stress condition, which is not possible in cube as in cube the edges will give lateral strain and hence the strength obtain from cube will be more than strength obtain from cylinder.
• But IS 456 suggest to use the cube of size 150mm and made necessary modification which is as follows:

f‘c = 0.8 fck —— (1)

where
f‘c = compressive strength obtained from 150mm by 300mm cylinder
fck = compressive strength obtained from 150mm cube.

• The cylinder strength is 80% of strength obtain from cube or cube strength is 125% of cylindercial strength
• Same as cylinder, if we use cube of small dimension than strength obtain will be more and if we use cube of larger dimension than strength obtain will be less. ( strength obtain from 200mm cube will be less than strength obtain from 100mm cube.

### Stress-Strain Curve in Field

f‘c = compressive strength of cylinder of size 150 x 300mm
γm = partial safety factor concrete =1.5

As per international recommendation, the figure is taken as a stress-strain curve infield, in this curve, an additional factor of safety of 0.85 is introduced because of variation of experiment in the field and in the laboratory. Also, the stress after the peak is assumed to be linear and constant up to 0.0035 strain.

The maximum stress value as per Indian Standard,
maximum stress 0.85*f‘c/ γm (substituting value of f‘c from eq 1)
= = if γm = 1.5 then
Maximum stress value will be equal to 0.45 fck

Hence, the variation of strain from 0 to 0.002 with respect to stress varies linearly up to a stress value of or 0.45fck and then stress becomes constant up to crushing stress of 0.0035.

For the parabolic portion 0≤ ϵc≤ 0.002 For the horizontal portion 0.002≤ ϵc≤ 0.0035
fc = 0.45fck