Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 198

Fig. 3.15 Tape element from
the contact bow

F F

dQ

R o

d ˑ

Fig. 3.16 Force plan of the
tape element forces

F

d ˑ

dQ

F

dQ ¼ 2 F sin d #
2

and for small angles with sin # = # it is

dQ ¼ F d #: ð 3 : 25 Þ

On the side it is

dQ ¼ q D 0
2

d #: ð 3 : 26 Þ

Derived from ( 3.25 ) and ( 3.26 ), the global line pressure is then S & F and
D 0 & D

q 0 ¼ 2 S
D

: ð 3 : 27 Þ

Equation ( 3.27 ) shows in a slightly simplified derivation that the line pressure is
constant over the contact bow except for the two contact points which are loaded
by the single force Q.

Example 3.2 Tape stretched over sheave, Fig. 3.17

Data:
Steel tape width

b = 30 mm

Thickness d = 2mm

Sheave diameter D 0 = 800 mm

Tensile force S = 10 kN

Results:
Contact force Q = 500 N ( 3.15 )
Boundary angle # 0 = 2.86 ( 3.24 )
Tape tensile force F = 9,988 N ( 3.14 )
Line pressure

q =25N/mm( 3.27 )

Lever arm y 0 = 1.0 mm ( 3.23 )