Calculation of equivalent length for compressive instability
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As shown in the figure: In the standard definition of 151 and Example 3.1 in the examples, why is c from Figure 7-2 chosen instead of e for calculating the equivalent length for compressive instability? What is the essential difference between c, d, and e? 2. Should b in the formula be (250+177)/√2? ?
The last piece should be a full support plate
In other words, is the full-size tail support plate equivalent to the tube sheet?
1. In the calculation of the equivalent length for compressive instability, c in Figure 7-2 is chosen instead of e because c represents the length of the compression zone, while e represents the length of the torsion zone. In instability calculations, the length of the compressed region is a key parameter determining the instability behavior of the structure; therefore, c is chosen as the equivalent length for compressive instability. The essential difference is that the compression zone refers to the area where compressive stress is generated due to longitudinal bending when the member is under compression, whereas the torsion zone refers to the area where torsional force acts on the member in the longitudinal direction when it is under compression. Their formation mechanisms and stress patterns are different, so they need to be considered separately when calculating the instability length. 2. Regarding the calculation of b in the formula, according to the formula, b should be 250/√2, rather than (250+177)/√2. This is because b represents the distance from the center of the member to its compressed edge; when the member is under compression, this distance is the length measured vertically downward through the center of the member’s cross-section to the compressed edge. Based on the geometric relationship, it equals the radius of the rod multiplied by √2, rather than plus some other length. .