Importance of beam deflections; pure bending examples

Importance of computing deflection

A beam may be strong enough in bending and shear yet still fail to serve its purpose if it deflects too much. Deflection is computed because:

1. Serviceability: codes limit deflection (for example span/250 for total, span/350 for loads after finishes) so floors do not feel springy or unsafe.
2. Protection of finishes: large deflection cracks plaster, partitions, tiles and glazing.
3. Appearance: sagging beams and slabs look unsafe and spoil the structure.
4. Machine alignment: shafts and machine beds need small deflection for gears, bearings and rails to work properly.
5. Drainage and ponding: sagging roofs collect water and increase the load.
6. Statically indeterminate beams: deflection (compatibility) conditions are needed to find the extra reactions.
7. Vibration control: stiffness affects natural frequency and comfort.

Two examples of pure bending

1. A simply supported beam with two equal loads placed symmetrically at equal distances from the supports: the portion between the loads has constant bending moment and zero shear force.
2. A simply supported beam with equal overhangs carrying equal point loads at both free ends (for example, a railway wagon axle, loaded at its ends outside the wheels): between the supports the bending moment is constant and the shear force is zero. A bar bent into an arc by equal and opposite couples at its ends is also in pure bending.