Page 56 - Engineering Plastics Handbook

30 Introduction

Deflection in beam bending is determined by the second moment of
inertia I and section modulus, by using the geometry of the cross sec-
tion, illustrated with (1) polygons—square, rectangle, hollow rectangle,
triangle, pentagon, hexagon, and octagon––and (2) beams of I, U, and
T shapes––circular and hollow circular. Section modulus is a function
of the cross-sectional area of a beam, independent of the type of mate-
rial used. It can be expressed as

I = M
d

3 3
where I = section modulus, cm (in )
M = moment of inertia of a cross section about a neutral axis,
4 4
cm (in )
d = distance from neutral axis to outermost fibers, cm (in)

Types of Circular and Rectangular Flat Plates
Flat plate equations are based on the following conditions:

1. Perpendicular loads are applied to flat plates with uniform cross
sections.
2. Deflection is less than one-half the plate wall thickness.
3. Resin is homogeneous and isotropic.
■ Circular flat plate, simply supported around circumference, load
applied at the center of the plate. To calculate the maximum deflec-
tion for a circular flat plate simply supported around the circumfer-
ence when a load is applied at the center of the plate, use

( + ν
2
1
∆ = 33 )( − ν ) Fr
max 3
4π(1 + ν)E d
where ∆ max = maximum deflection, cm (in)
ν= Poisson’s ratio
E = flexural modulus, MPa (psi)
F = applied load at center of circular plate, N (lb)
r = radius, cm (in)
d = beam thickness, cm (in)
■ Circular plate, simply supported around circumference, load uni-
formly distributed
■ Circular plate, fixed around circumference, load uniformly distributed