n05_static
page 1 of 6
L = 0.75 in
r = 0.05 in
D = 0.75 in
d = 0.5 in
9T #41
roller chain
sprocket
SAE 1045 cold-rolled
steel
1 HP at 400 rpm
P=T
 33000 ft .lbf
T = P /  = 1 HP
 HP. min

 min  rev  12 in 



 = 157.6 in.lbf
 400 rev  2 rad  ft 
rSPR
F
#41 ANSI chain, pitch p = 0.5 inch, maximum working load = 314 lbf, McMaster-Carr
pitch circumference = 2  rSPR ≈ (9T) p
rSPR ≈ (9T) p / 2  = 0.7162 in
rSPR
 = 360° / number of teeth = 40°
p = 0.5 in
sin /2 = (p/2) / rSPR
EXACT rSPR = (p/2) / (sin /2) = 0.731 in
T = F rSPR
F = T / rSPR = 220 lbf
bending moment M = F L = 165 in.lbf
torsion moment T = 157.6 in.lbf
I =  d4 / 64 = 3.068 x 10-3 in4
c = d / 2 = 0.25 in
J =  d4 / 32 = 6.136 x 10-3 in4
p

n05_static
165 in .lbf 0.25 in 
NOM = M c / I =
NOM = T c / J =
3.068x10
3
in 4

157.6 in .lbf 0.25 in 
6.136x10
3
in 4

page 2 of 6
= 13.45 ksi
= 6.421 ksi

maximum shear failure criterion (OLD)
x = 13.45 ksi
 x / 2
MAX =
y = 0
0.5 S y
 MAX
xy = 6.421 ksi

2

2
xy
1045 cold-rolled steel
N=
= 4.14
= 9.30 ksi
Sy = 77 ksi
y -xy
Table A-9 Norton
Eq 5.10 and 5.11 Norton
von Mises failure criterion
x = 13.45 ksi
’ =
y = 0
xy = 6.421 ksi
 2x   2y   x  y  3 2xy = 17.45 ksi
1045 cold-rolled steel
N=
Sy
'
= 4.41
Sy = 77 ksi
Eq 5.7d Norton
Table A-9 Norton
Eq 5.8a Norton
iterative solution for new diameter
NOM = M c / I =
x xy
M d2 64 32 M

 d4
 d3
NOM = T c / J =
try NEW d = 0.625 in
3
 0 .5 
NEW ’ = OLD ’ 
 = 0.512 OLD ’
 0.625 
T d2 32 16 T

 d4
 d3
n05_static
page 3 of 6
static stress concentration factors
shaft bending
D/d = 1.5
A = 0.93836
b = -0.25759
Figure C-2 Norton
Kt = A(r/d)b = 1.698
r/d = 0.1
 = Kt NOM = 22.84 ksi
shaft torsion
D/d = 1.5
interpolated
A = 0.8526
b = -0.2334
Figure C-3 Norton
Kt = A(r/d)b = 1.459
r/d = 0.1
 = Kt NOM = 9.368 ksi

maximum shear failure criterion (OLD)
x = 22.84 ksi
 x / 2
MAX =
y = 0
0.5 S y
 MAX
xy = 9.368 ksi

2

2
xy
1045 cold-rolled steel
N=
= 2.61
= 14.77 ksi
Sy = 77 ksi
y -xy
Table A-9 Norton
Eq 5.10 and 5.11 Norton
von Mises failure criterion
x = 22.84 ksi
’ =
y = 0
xy = 9.368 ksi
 2x   2y   x  y  3 2xy = 28.02 ksi
1045 cold-rolled steel
N=
Sy
'
= 2.75
x xy
Sy = 77 ksi
Eq 5.7d Norton
Table A-9 Norton
Eq 5.8a Norton
key length
assume 1020 hot-rolled
Sy = 30 ksi
Table A-9 Norton
n05_static
d = 0.5 inch DIA shaft
w = 0.125 inch square key
page 4 of 6
Table 10-2 Norton
assume LKEY = 0.625 inch < L overhang
T = 157.6 in.lbf
rSHAFT = 0.25 inch
ASHEAR = w L = 0.078125 in2
' =
3  = 13.98 ksi
NYIELD = SY / ' = 2.15
FKEY = T / rSHAFT = 630.4 lbf
 = FKEY / ASHEAR = 8069.1 psi
n05_static
page 5 of 6
fatigue stress concentration (notch sensitivity) factors
full reversed bending
NOM = 13.45 ksi
1045 cold-rolled steel
Sut = 91 ksi
Neuber
a = 0.0692
1
q=
1
a
in
= 0.7637
Kt = 1.698
Table A-9 Norton
interpolated
Table 6-6 Norton
Eq 6.13 Norton
r
Kf = 1 + q ( Kt – 1 ) = 1.533
Eq 6.11b Norton
 = Kf NOM = 20.62 ksi
alt’ =  = 20.62 ksi
NOM = 6.421 ksi
constant torsion
Kt = 1.459
no fatigue stress concentration (notch sensitivity) factor
mean’ =
3 2xy = 16.23 ksi
 = Kt NOM = 9.368 ksi
Eq 5.7d Norton
modified endurance limit
1045 cold-rolled steel
Sut = 91 ksi
Se’ = 0.5 Sut = 45.5 ksi
CLOAD = 1.0
Eq 6.5a Norton
bending
Eq 6.7a Norton
CSIZE = 0.869 d -0.097 = 0.9294
CSURF = 0.76
machined
CSURF = A(Sut)b = 0.817
Table A-9 Norton
circular section
Eq 6.7b Norton
Figure 6-26 Norton
A = 2.7
b = -0.265
machined
Eq 6.7e and Table 6-3 Norton
use CSURF = 0.76
CTEMP = 1.0
CRELI = 0.814
normal environmental temperature range
R = 99%
Table 6-4 Norton
Eq 6.7f Norton
n05_static
page 6 of 6
Se = CLOAD CSIZE CSURF CTEMP CRELI Se’ = (1) (0.9294) (0.76) (1) (0.814) 45.5 ksi = 26.16 ksi
fatigue factor of safety
 400 rev  60 min


 min  hr
 24 hr 
 = 576,000 rev/day

 day 
use infinite life
N>106
alt’ = 20.62 ksi
mean’ = 16.23 ksi
Nalt = SN / alt’ = 1.269
SN = Se = 26.16 ksi
Sut = 91 ksi
Nmean = Sut / mean’ = 5.607
NGOODMAN = Nalt Nmean / (Nalt + Nmean) = 1.03
1045 cold-rolled steel
Sy = 77 ksi
NFIRST = Sy / (alt’ + mean’) = 2.09
Table A-9 Norton