Table 17 Formulas for tangential and radial forces, moment and stress in circular rings subject to bending in the plane of the curve
Case 1
Diametrically opposed forces
Solid rectangular section
Enter dimensions of cross section:
Height of rectangular section:
Radius of curvature measured to centroid of section:
Width of rectangular section:
Half-height:
Shape constant for rectangle:
Enter properties and loading of ring:
Modulus of elasticity:
Poisson's ratio:
Load:
Conditions:
If R/d
If R/d < 8, then the beam can generally be considered thick.
Moment of inertia of section about centroidal axis:
Moment of inertia of section about principal axis:
Area:
Constants:
Modulus of rigidity:
Distance from centroidal axis to neutral axis measured toward center of curvature:
Hoop-stress deformation factor:
Transverse radial shear deformation factor:
Hoop-stress corrections:
Change in vertical diameter (an increase is positive) for pipe or tube:
Change in vertical diameter (an increase is positive) for Thin ring of unit length:
?????????????????????
?????????????????????????