27.2.2. Eccentric Columns

Sources of bending, Fig. 27.4

1. Unsymmetric moments ML = MR
2. Uncertainty of loads (must assume a minimum eccentricity)
3. Unsymmetrical reinforcement

Eccentric columns are those that experience bending due to loads applied away from their central axis. The sources of this bending include:

1. Unsymmetric Moments: When the moments (ML and MR) about the column's axis are not equal, it creates a twisting effect.
2. Uncertainty of Loads: When the loads can vary, engineers need to account for this by assuming a minimum distance (eccentricity) from the center to ensure safety.
3. Unsymmetrical Reinforcement: If the reinforcement within the column is not balanced around its axis, this can further enhance the bending effects.

Imagine a seesaw where the weight is off-center. If one side has more weight than the other, the seesaw will tip and bend. Similarly, when loads on an eccentric column are not evenly distributed, it can lead to bending.

Types of Failure, Fig. 27.5

1. Large eccentricity of load failure by yielding of steel
2. Small eccentricity of load failure by crushing of concrete
3. Balanced condition

Eccentric columns can fail in different ways depending on how the load is applied:

1. Large Eccentricity: If the load is significantly off-center, the steel within the column may yield or bend before the concrete fails.
2. Small Eccentricity: If the load is only slightly eccentric, the concrete can crush under the pressure before the steel yields.
3. Balanced Condition: There exists a specific eccentricity where both the steel yields and the concrete crushes at the same time, leading to a balanced failure.

Think of a pencil with a heavy weight on one end. If you push down hard on the end, the pencil can bend. If the weight is lighter, the pencil may just break at the pressure point instead of bending first. This highlights how the position of the load affects the type of failure.

Assumptions A = A ;(cid:26) = As = A0 s = f = f There is one specific eccentricity e = M such that failure will be triggered by simultaneous

1. Steel yielding
2. Concrete crushing

In a balanced condition, there is a critical point known as 'eccentricity' where both the concrete and steel reach their failure points at the same time. This happens under specific conditions, where:

• The areas (A) and forces are balanced.
• Both materials, steel and concrete, are pushed to their limits together, leading to simultaneous failure.

Imagine two runners at a finish line. If both runners are exactly evenly matched and reach the finish line at the same time, they represent a balanced condition. In columns, this means steel and concrete reach their breaking point together under specific loading conditions.

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