Allowable Stress in a Long Column

A column is a structural element that is used to support compressive loads. Long columns are those whose length is greater than three times their least lateral dimension. The allowable stress in a long column is the maximum stress that the column can withstand without failure.

Factors Affecting Allowable Stress in a Long Column

Several factors affect the allowable stress in a long column. These include:

1. Slenderness Ratio

The slenderness ratio is the ratio of the length of the column to its least lateral dimension. The slenderness ratio affects the allowable stress in a long column. As the slenderness ratio increases, the allowable stress decreases. This is because a long column is more likely to buckle than a short column.

2. Length of the Column

The length of the column also affects the allowable stress. As the length of the column increases, the allowable stress decreases. This is because a longer column is more likely to buckle than a shorter column.

3. Radius of Gyration

The radius of gyration is a measure of the distribution of mass in a column. It is the square root of the ratio of the moment of inertia of the column to its cross-sectional area. Increasing the radius of gyration increases the allowable stress in a long column. This is because a column with a larger radius of gyration is less likely to buckle than a column with a smaller radius of gyration.

4. Eccentricity

Eccentricity refers to the distance between the centroid of the column and the line of action of the compressive load. Increasing eccentricity decreases the allowable stress in a long column. This is because eccentric loading creates bending stresses in the column, which can cause it to buckle.

Conclusion

In conclusion, the allowable stress in a long column can be increased by increasing the length of the column. This is because a longer column is less likely to buckle than a shorter column. However, increasing the length of the column may not always be practical. Other factors that affect the allowable stress in a long column include the slenderness ratio, radius of gyration, and eccentricity.

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