Mechanical Engineering - Strength of Materials - Discussion

Moment of inertia is tendency of a body to resist angular acceleration. Buckling means A body leading towards a failure mode. Maximum moment of inertia resits this buckling because it is its tendency. So minimum moment of inertia only leads to buckling.

Buckling and bending are similar in that they both involve bending moments. In bending these moments are substantially independent of the resulting deflections, whereas in buckling the moments and deflections are mutually inter-dependent. So moments, deflections and stresses are not proportional to loads.

Buckling:

Sudden failure of column in lateral direction is called Buckling. It occurs when the Euler's critical load (n*pi^2*E*I)/L^2 is less than allowable compression load.

Moment of inertia.
Tendency to resist angular acceleration.

So from above two definition it is clear that when moment of inertia is low , then the column is more vulnerable to buckling as it couldn't resist much of lateral movement. Answer D. clear ;)

Moment of inertia refers to the resistance offered to the rotation along the axis. Consider the whole body rotating and there is aportion which has minimum moment of inertia. So it cannot resist the rotational motion and hence starts to buckle.

Area Moment of Inertia or we can say second moment of area is defined as the resistance to bending. So more the area moment of inertia, less will be the bending. Hence in the direction of bending the beam has minimum area moment of inertia.

The equation relating the buckling load and the moment of inertia is.

P=pi^2*EI/l.

So when I decreases the the load required for buckling also decreases thus gets deformed at a very low load.

Here l is the effective load.

@All.

Consider a rectangular cross-section. Length along x and width along y(Length> Width). Draw you will see it will bend in the Y direction. Since it is thin that way. And moment of inertia in max in that direction.

Moment of inertia generally means the inertia due to movement.

If the moment of inertia is less the force required to change its state of rest will be less.

So the direction with less moment of inertia is easy to buckle.

According to Euler's formula, Critical load that can be applied for bucking to occur is (n*pi^2*E*I)/L^2.

The Critical load is proportional to Moment of inertia. So buckling occurs easily on low Moment of inertia side.

Bending: Load applied perpendicular to the length of the bar, causing it to curve.

Buckling: Compressive load applied along the length of the bar, causing it to bend sideways when the load is critical.

A column will tend to buckle in xx, yy, is minimum MOI because the moment of inertia is the same about in xx and yy directions. When MOI is different in x-axis and y-axis then the MOI MAXIMUM.