Structures Homework - Column Slenderness Calculation

What is the criteria for determining whether a column is slender or not based on the slenderness ratio?

The criteria for determining if a column is slender is based on the slenderness ratio. If the slenderness ratio is greater than 5, the column is considered slender. If the slenderness ratio is less than 5, the column is not considered slender.

Understanding Column Slenderness Ratio

Slenderness Ratio Calculation: The slenderness ratio of a column is calculated by dividing the column's length by its least radius of gyration. The least radius of gyration depends on the shape of the column.

Round Column:

For a round column, the slenderness ratio is calculated by dividing the length of the column by half of its diameter. This formula is used to determine the slenderness ratio for Column 1 to Column 4 in the homework.

Square Column:

For a square column, the slenderness ratio is calculated by dividing the length of the column by the product of its side length and the square root of 2. This formula is applied to Column 5 to Column 8 in the homework.

Rectangle Column:

For a rectangular column, the slenderness ratio is calculated by dividing the length of the column by the minimum value between its width and depth divided by the square root of 2. This formula is utilized for Column 9 and Column 10 in the homework.

Analysis of Slenderness Ratios:

Based on the given data, the slenderness ratios for the columns are calculated as follows:
  • Column 1: 100
  • Column 2: 10.3
  • Column 3: 10
  • Column 4: 100
  • Column 5: 100
  • Column 6: 10.7
  • Column 7: 10
  • Column 8: 100
  • Column 9: 10.1
  • Column 10: 100

Conclusion:

Based on the slenderness ratio criteria, columns with a ratio greater than 5 are considered slender, while columns with a ratio less than 5 are not slender. Therefore, Columns 1, 2, 3, 4, 6, 7, 8, and 10 are slender, and Columns 5 and 9 are not slender.
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