NOTATION

A		Area, or a constant
B		Constant
C		Constant
E		Modulus of elasticity
e		Eccentricity
F		Force
G		Modulus of rigidity
I		Second moment of area (Table A.1)
K		Shape constant (Table 36.1), or second polar moment of area
M		Bending moment
P		Reduced load
Q		Fictitious force
R		Force reaction
r		Ring radius
		Centroidal ring radius
T		Torsional moment
U		Strain energy
V		Shear force
W		Resultant of a distributed load
w		Unit distributed load
X		Constant

Methods of computing the stresses in curved beams for a variety of cross sections are included in this chapter. Rings and ring segments loaded normal to the plane of the ring are analyzed for a variety of loads and span angles, and formulas are given for bending moment, torsional moment, and deflection.

38.1 BENDING IN THE PLANE OF CURVATURE

The distribution of stress in a curved member subjected to a bending moment in the plane of curvature is hyperbolic ([38.1], [38.2]) and is given by the equation

(38.1)

where r = radius to centroidal axis

y = distance from neutral axis

e = shift in neutral axis due to curvature (as noted in Table 38.1)

Table 38.1: