Question: We're supplying the concrete for bridge piers on a state DOT project. The specifications set a maximum allowable concrete temperature difference between the center of the piers and their exterior faces. The state requires use of the Schmidt formula to show the calculated temperature difference. What is the Schmidt formula, why is it used, and where can I learn how to make the calculations?
Answer: During mass pours, such as for bridge piers, design engineers want to eliminate any potential for cracks that are detrimental to concrete performance. Concrete has a low thermal conductivity, meaning that the heat generated by the hydration process escapes slowly from the structure's center. When specifying concrete in thick structures, engineers try to minimize the temperature difference between interior sections and formed or finished surfaces. They can calculate a temperature difference that won't result in thermal stresses high enough to cause cracking.ACI 207.1R-87, "Mass Concrete," section 5.4.3, describes Schmidt's method for determining actual temperature gradients. It's simple enough to be performed with a desk calculator, although more complex calculations may require a spreadsheet or other software program. The section in ACI 207.1R gives an example problem that shows how the method works.If you don't feel comfortable making such calculations, there are consultants who will make them for you or help train your field technicians to perform them. One such consultant is Kenneth Roush, P.E., E&L Support Services, Clearwater, Fla., 727-726-1846.When state DOT officials examine the calculation results, they generally require the contractor to take measures that reduce differences between internal and external temperature so the calculated difference does not exceed a value of around 35 degrees F. Usually, the contractor can reduce the difference by using insulating blankets that retain the heat of hydration near the surface, stabilizing core and surface temperatures after peak internal temperatures have been reached.