Appendix F
Strength of Chain Tensioned
over a Curved Surface
The chafing chain at the end of a tow line or SPM hawser normally is guided through a chock:
at the edge of t.he taD-ker deck. This chock restrains t.he chain from excessive lateral movement
and provides a curved surface for the chain to bear against. The diameter of this curved surface
must be large eoough to prevent overstressing of the chain when it is subjected to high towing or
mooring loads. The problem of defining a crit.eria for the minimum diameter of chock surfaces was
addressed by both analysis and e~periment in thjs slUdy.
F.1 THREE CASES OF CHAIN ON A CURVeD SURFACE
Analysis of the stresses in a chain tensioned over a curved surface is more complex than first
appears. Three cases of chains tensioned over curved surfaces are i.IIustrated in Figure F I. Case I
is that of an ungrooved surface, such as a chock. Tbe chain links He at angles to the surface,
alternatively lying to one side and then lhe mhcr, with all links bearing against the surface. This is
the case of primary inlerest in rhis study.The second and third cases apply to grooved surfaces, such as anchor chain wincUasses and chain
sheaves. On grooved surfaces, every second chain link projects into a groove in the surface and
has its transverse axis perpendicular or upright to the surface. I nlervening links lie with their
transverse axis parallel 01 Oat on the surface. In case the groove is so sbaUow that the upright link
rests on the bottom of the groove and the nat link is lifted tree of tbe surface. In this c~se bending
stresses are exerted on the upright links onJy. In case 3 the groove is so deep that the upright links
do not touch bottom. and the nat links bear against tbe curved surface. Only the nat links are
subjected to bending stresses in this case.Grooved surfaces are discussed to distingwsh them from the ungrooved case and to aHow discussion
of other analyses and recommendations. An intermediate case can exist in which both rhe flat and
upright Links touch the surface. ID the c.1se of chain lying over a very small ungrooved surface with
only one or several links in contact, alternating links may lie flat and upright to the surface as in
the second and third cases.F.2 DEFINITION OF ANGLES AND OTHER TERMS
Dimension and angles of chain Links tying on a curved surface are shown in Figure Fl. Tbe chai.n
diameter, d, is the nominal diameter of the bar from which the common stud link is formed.
For common stud links the overall link length L is 6 times d and Ihe link. with B is 3.6 lime. rI.The ruameter of tJle curved surface over which the chain is bent will be defined as D. This must
nOt be confused with the diameter of the opening in the bow chock. For case 2. the shallow-grooved
surface with contact at the bottom of the groove. D is analyzed as the ruameter to the bottom of
Ihc. groove.The ratio of beDding surface diameter to chain diameter Did will be used as a criteria for surface
diameter. This diameter ratio should oot be confused with the ratio of tbe surface raruus to chain
diameter which is sometimes referred to in recommendations made by others.