ON THE EFFECTS OF CIRCULAR BOLT PATTERNS ON THE ...

2
A value of R 1
implies that S is zero and the regression prediction equation passes through all the
2
data points. A value of R 0.
90 means that 90 % of the sum of squares of the deviations of the
observed (or directly determined)
obtained.
'
x i values about their
96
'
x 0 can be explained by the prediction equation
In the parametric study conducted, all the cases considered had the independent parameters inputted
into the finite element computer program, ABAQUS, and the output was the response of the dependent
variables. The coefficient of multiple determination value
2
R was the unique criterion used to measure
the accuracy of the prediction equations to characterize the hysteresis behavior of the connection.
5.6.3 Equations Of Hysteresis Behavior
The nonlinear regression analysis was used to derive a set of equations to model the hysteresis
behavior of the connections with circular bolt pattern configuration. To increase the accuracy of the
regression analysis and reduce the error in the prediction of the dependent variables, the numeric models
are divided into two sub-categories as below,
Category-1: Models with an end-plate thickness greater than the bolt diameter, t /b 1,
Categoty-2: Models with an end-plate thickness smaller than the bolt diameter, t /b 1.
The categories of each connection are indicated in Tables 5-5 and 5-6 for models with circular and
square bolt pattern, respectively.
The empirical equation for four parameters My, E, Et, and θf was developed by conducting the non-
linear regression analyses. This is accomplished by multiplication of the undetermined powers for all the
geometric parameters. It simply implies that the changes in these geometric parameters are independent
to each other thus, they are independent variables. The aforementioned empirical equations for the My, E,
Et, and θf of the connections with circular bolt pattern are presented in Equations 5-13 through 5-20. Also
the empirical equations for these dependent parameters for the connections with square bolt pattern
configuration are presented in Equations 5.21 through 5.28.
5-6-3-1 The prediction equations for Category-1 connections with circular bolt pattern, / 1: