(1) Force analysis under vertical force F
0
F
0 has a transverse bending effect on the edge teeth, producing a bending normal
stress r MF 0 , and bending shear stress s F 0 on section I À I
0 . r MF 0 can be found as
follows:
M F 0 ¼ F
0 R cos a þ h
ð
Þ
ð11:54Þ
It produces the maximum bending normal stress in J À J
0 plane.
r M F 0 ¼
M F 0
W Z
¼
F
0 R cos a þ h
ð
Þ
W Z
¼
4F
0 R cos a þ h
ð
Þ
pR 3
ð11:55Þ
where W y ¼
pd
3
32 and d is the diameter of section J À J
0 , and d ¼ 2R.
Because M F 0 is perpendicular to the bending moment produced by the axial load
P and reaches the maximum value in the same section, its maximum stress point is
at the other two points of J À J
0 section, the two points of U and V shown in
Fig. 11.32, and U is under compression and V is under tension.
s F 0 can be found as follows:
The maximum shear stress produced by bending occurs at the centroid point B of
I À I
0 section, but the direction is perpendicular to the shear force produced by the
axial force P:
s F 0 ¼
4F
0
3A
¼
4F
0
3p R sin a
ð
Þ
2
¼
4F
3p R sin a
ð
Þ
2
ð11:56Þ
Fig. 11.31 Schematic
diagram for force analysis of
side teeth acted by F
248
11 Pneumatic Down-the-Hole Hammer