Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 195

Fig. 3.14 Forces on the tape
piece running on the sheave

S

F

M o

Q

ˑ o

S

First, in Fig. 3.14 , that part of the tape will be examined which runs on the
sheave. The curvature of the tape increases from the point where the force S is
effective to the point where the tape meets the sheave. At this point, the radius of
tape curvature is the same as the radius of the sheave. As a simplification, it is
supposed that the pressure is constant and does not deform either the tape or the
sheave which means the tape and the sheave are to be considered as being rigid in
the crosswise direction. The force F at the boundary angle # 0 is

F ¼ S cos # 0 :

ð 3 : 14 Þ

Without taking its direction into account, this tensile force F is constant over
the contact bow, and a little less than the outer force S. A contact forceQ exists
between the tape and the sheave

Q ¼ S sin # 0 : ð 3 : 15 Þ

According to the assumed simplification, the tape and sheave are rigid in a
crosswise direction and the effects of the contact force Q are only to be found in a
line parallel to the sheave axis.

Boundary Angle # 0

In order to calculate the bending curvature of the tape, the method will be used
which Isaachsen ( 1907 ) already applied for calculating ropes in aerial rope ways.
In Fig. 3.13 , the bending moment M referred to the point x is,

M ¼ S y : ð 3 : 16 Þ