Page 55 - Engineering Plastics Handbook

Products and Design 29

on the linear elastic region and must be compensated with safety fac-
tors, especially for long-term applications and elevated temperatures [5].
Beam equations are based on the following conditions:

1. Perpendicular loads are applied to straight beams with symmetric
uniform cross sections.
2. Deflection is due to bending.
3. Neutral axis for the beam is a central horizontal axis where both
tensile and compressive strain (and stress) are considered to be zero.

Types of beams
■ Simple supported beam, load at center of beam. Beam is supported at
both ends. To calculate the maximum deflection for a beam supported
at both ends and center-loaded, use
3
∆ max = CL F
4 bd 3
where ∆ max = maximum deflection, cm (in)
C = compliance factor, cm (in)
L = length of beam between two supports, cm (in)
F = applied load at center of beam, N (lb)
b = beam width, cm (in)
d = beam thickness, cm (in)
■ Simple supported beam, load off-center
■ Simple supported beam, two equal loads symmetrically located between
center and the two supported ends
■ Simple supported beam, load spread uniformly along beam length
■ Beam fixed at both ends, load at center of beam
■ Beam fixed at both ends, load spread uniformly along beam length
■ Beam fixed at both ends, load at any point along beam
■ Beam fixed at both ends, uniform load per unit length
■ Cantilever beam, load at free end
■ Cantilever beam, load spread uniformly along beam length
■ Cantilever beam fixed at one end, free at other end

Deflection in beam bending
Deflection of bending beam equations is used for designing panels, doors,
floors, columns, other building and architectural products, rails, shafts,
and platforms [19].