Unlike most other commonly used engineering materials, concrete experiences a characteristic marked increase in “creep” when it is heated for the first time under load. To investigate this phenomenon, a study of the thermal strain behavior of concrete was conducted (Magazine of Concrete Research, Dec. 1985). Concrete specimens were prepared and a constant load applied to each. The test specimens were then heated to a specified temperature at a rate of 1°C per minute, with the specimens randomly assigned to one of five temperature settings (100°, 200°, 300°, 400°, and 500°C). For each specimen, the difference between the free (unloaded) thermal strain and load-induced thermal strain, called the total thermal strain, was calculated. The sample size, mean, and standard deviation of the total thermal strain values for each temperature setting are given in the table on p. 758. Thermal strain is recorded in units × 10⁶.

a. Find the totals for each temperature and the total for all 78 strain measurements. Then compute CM and SST.

b. Since we do not know the value of Σ_i=1ⁿ y_i², calculate SSE using the pooled method:

c. Find SS(Total).

d. Construct an analysis of variance table for the data.

e. Is there sufficient evidence to indicate that heating temperature affects the mean total thermal strain of concrete? Test using α = .01.

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Number of Standard Temperature specimens Mean Deviation 100 16 52 55 200 16 112 108 300 16 143 127 400 16 186 136 500 14 257 178