Appendix F.Temperature Correction When Used On Concrete

In a free field, where no loads are acting, the thermal concrete strains are given by the following equation:

µε_thermal = (T₁ – T₀) x CF₂

Equation 14: Thermal Concrete Strains

CF₂ represents the coefficient of expansion of concrete. Unless this figure is known, assume a nominal value of 10.4 microstrains/°C.

If the actual strain of the concrete member is required, (i.e., the change of unit length that would be measured by a dial gauge attached to the surface,) you can arrive at this using this equation:

µε_actual = (R₁ – R₀)B + (T₁ – T₀) x CF₁

Equation 15: Actual Strain

Where CF₁ represents the coefficient of expansion of steel = 12.2 microstrains/°C, and (R₁ – R₀)B is the apparent strain recorded by the readout box.

To calculate the strain in the concrete due to load changes only:

µε_load = µε_actual – µε_thermal = (R₁ – R₀)B + (T₁ – T₀) x (CF₁ – CF₂)

Equation 16: Strain Due to Load Changes Only

Note the following example, where B = 0.91

R₀ = 3000 microstrain, T₀ = 20 °C

R₁ = 2900 microstrain, T₁ = 30 °C

µε_apparent = (2900 – 3000) x 0.91 =  –91_{(compressive)}

µε_actual = (2900 – 3000) x 0.91 =  + (30 – 20) x 12.2 = 31_(tensile)

µε_thermal = (30 – 20) x 10.4 = 104_(tensile) 

µε_load = (2900 – 3000) x 0.91 + (30 – 20) x (12.2 – 10.4) = –73_{(compressive)}

Note: Because assumptions have been made regarding the thermal coefficients for the concrete, these equations should only be used as a general guide.

Explanation: The apparent compressive strain, indicated by the readout box after application of the batch factor, B, is (R₁ – R₀) x B = –91 microstrain. If the strain in the concrete had not changed, the steel vibrating wire would have expanded and gone slack by the equivalent of (30 – 20) x 12.2 = –12.2 microstrain, therefore the concrete must have actually expanded by +31 microstrain to account for the observed apparent strain. The concrete should have expanded by (30 – 20) x 10.4 = +104 microstrain on account of the temperature increase, the fact that it didn't reach this value must mean that there has been a superimposed buildup of compressive strain equal to 104 – 31 = –73 microstrains. This, multiplied by Young's Modulus, will give the actual stress in the concrete caused by the imposed load change.