Bending (Topic: 12020)

A force acting perpendicular to the longitudinal axis of a member will subject the member to bend.

The bending will give stresses over the cross section of the member. The highest stress occurring in the fibres most distant from the neutral axis. At one side of the neutral axis the stress will be in tension on the other in compression.

The stress is defined as:

Where: M is the bending moment in the section where the stress is to be calculated.

I is the moment of inertia.

y is the max. distance from the outermost fibre to the centroid.

A bending member will deflect. The basic equation for the maximum deflection can be written as:

Where: C is a constant to be found in tables and dependent on:

- Type of load

- Where the load is acting

- Conditions of the supports

Q is the total load on the member

L is the span of the member

E is the Young's modulus of elasticity

I is the moment of inertia of the cross section

When a moment, M, is the load, the equation for the maximum deflection can be written as:

A bending member can also be unstable and buckle if the compressive flange of the member is free to buckle.

References: [18]