Appendix G.Measurement and Correction of Temperature Effects
If the ends of the structural member are free to expand or contract without restraint, strain changes can take place without any change in stress. On the other hand, if the ends of the structural member are restrained by some semi-rigid medium, then any increase in temperature of the structural member will result in a buildup of compressive load-related strain in the member, even though the actual strain would be tensile.
The reason for this is because the member is restrained from expansion but the vibrating wire is not. An increase in temperature will produce expansion in the vibrating wire, which in turn will cause a reduction in wire tension. This results in a decrease in the vibrational frequency. The magnitude of this temperature-induced, compressive strain increase would be measured accurately by the strain gauge, and can be determined using Equation 5.
These temperature-induced stresses can be separated from any external, load-induced stresses by reading both the strain and temperature of the gauge at frequent intervals. These readings should take place during a period when the external loading from construction activity remains unchanging. When these strain changes are plotted against the corresponding temperature changes, the resulting graph will show a straight-line relationship, the slope of which yields a factor KT microstrain/degree. This factor can be used to calculate the temperature-induced stress, as shown by the following equation:
σ temperature induced = KT (T1–T0)E
equation 10: Temperature-Induced Stress
This can be subtracted, if desired, from the combined load related stress change using the following equation:
σ combined temp and load related = [(R1–R0)B + (T1–T0) (C1–C2)]E
equation 11: Combined Temperature and Load-Related Stress
To give that part of the stress change due to construction activity loads only, use the following equation:
σ external load = [(R1–R0)B + (T1–T0) (C1–C2) – KT (T1–T0)]E
equation 12: External Load Stress
Note that the correction factor (KT) may change with time and with construction activity as the rigidity of the restraint may change. In such a case, it would be advisable to calculate a new temperature correction factor by repeating the above procedure.
If, for whatever reason, the actual strain of the concrete member is required (e.g., the change of unit length that would be measured by a dial gauge attached to the surface), this is given by the equation:
μεactual =(R1–R0)B + (T1–T0)C1
Where C1 represents the coefficient of expansion of steel = 12.2 microstrain/°C.
This equation may seem less than intuitive and therefore requires some explanation. As an example, assume first that the strain gauge is inside a concrete slab that is perfectly restrained at its ends. If the temperature rises by one °C, then the vibrating wire undergoes an expansion of 12.2 microstrains and (R1-R0)B would be -12.2 microstrains, therefore the result of Equation 5 in Section 6.5 would be zero actual strain in the concrete slab.
On the other hand, if the concrete slab is free of all restraint, and experiences a temperature change of 1 °C, then the concrete would expand 10 microstrains, while the vibrating wire would expand 12.2 microstrains. The value of (R1-R0)B would then be -2.2 microstrains (the vibrating wire would slacken slightly), and Equation 5 would yield a value of 10 microstrains.