FIGURE 31.27 Typical crane columns.

boundary conditions was developed by Lui and Sun (1995). On the basis of the story stiffness concept and accounting for both member and frame instability effects in the formulation, Lui and Sun (1995) proposed the following procedure (see Figure 31.28):

1. Apply the fictitious lateral loads a P (a is an arbitrary factor, 0.001 maybe used) in such a direction as to create a deflected geometry for the frame that closely approximates its actual buckled configuration.

2. Perform a first-order elastic analysis on the frame subjected to the fictitious lateral loads (Figure 31.28b). Calculate Aj/EH, where Aj is the average lateral deflection at the intermediate load points (i.e., points B and F) of columns and EH is the sum of all fictitious lateral loads that act at and above the intermediate load points.

3. Calculate z using the results obtained from a first-order elastic analysis for lower shafts (i.e., segments AB and FG), according to Equation 31.89.

4. Calculate the K-factor for the lower shafts using Equation 31.88.

5. Calculate the K-factor for upper shafts using the following formula:

where Pis the applied load and subscripts U and L represent the upper and lower shafts, respectively.

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