In the Euler’s buckling formula we assume that the load P acts through the centroid of the cross-section. However in reality this might not always be the case: the load P might be applied at an offset, or the slender member might not be completely straight.
To account for this, we assume that the load P is applied at a certain distance e (e for eccentricity) away from the centroid. This then would obviously change the way we calculate our buckling load, which is what the secant formula is for.
We use the secant formula to calculate the maximum deflection ν_{max} and maximum stress σ_{max} due to an eccentric load:
In the Euler’s buckling formula we assume that the load P acts through the centroid of the cross-section. However in reality this might not always be the case: the load P might be applied at an offset, or the slender member might not be completely straight.
To account for this, we assume that the load P is applied at a certain distance e (e for eccentricity) away from the centroid. This then would obviously change the way we calculate our buckling load, which is what the secant formula is for.
We use the secant formula to calculate the maximum deflection ν_{max} and maximum stress σ_{max} due to an eccentric load:
While the formula is complex, questions from this subtopic are usually very straight-forward. You only need to note that the expression within the secant term (sec [...]) is in radians. (Btw sec θ = 1/cos θ)
Let’s look at an example now.
While the formula is complex, questions from this subtopic are usually very straight-forward. You only need to note that the expression within the secant term (sec [...]) is in radians. (Btw sec θ = 1/cos θ)
Let’s look at an example now.