Case 1. For t, = 3.0 in., E, = 100.0 ksi, 10.0 < E < 85.0 ksi,
1 1 2
10.0 < E < 200.0 ksi, and with E3 between 6.0 and 35.0 ksi,
4
-K
E = K (D D ) 2 Eqn. 4.11
3 1 4 10
-0.3562 9 -0.7185
K = 22.74(E ) + 3.503 x 10 (E )(E ) Eqn. 4.12
1 2 4 2
0.1528
-0 10183(E )
K = [3.4455 + 0.00841(E )](E ) 2 Eqn. 4.13
2 2 4
The accuracy of the E3 prediction equation presented above appeared
good within the stipulated range of variables listed above. However, it
was not simplified enough to allow the development of a more comprehen-
sive equation to include varying E1 and t values. Multiple linear
regression analyses (39) were performed using various combinations of
variables and transformations in an attempt to develop a relatively
simple E3 prediction equation for t, values of 3.0, 4.5, and 6.0 in.
The best results from these analyses produced a complex equation
containing 13 variables.
Case 2. For 3.0 < t < 6.0 in., 100.0 < E < 1000.0 ksi,
1 1
10.0 < E < 85.0 ksi, and 0.35 < E < 200.0 ksi,
2 4