Shafting

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1
Shear Stress
$S_s=\frac{T_c}{J}
2
Section Modulus Solid Shaft
$Z=\frac{π}{32}(D³)
3
Section Modulus Hollow Shaft
$Z=\frac{π}{32D_o}(D⁴-d⁴)
4
Polar Moment of Inertia Solid Shaft
$J=\frac{\pi}{32}D^4
5
Polar Moment of Inertia Hollow Shaft
$J=\frac{\pi}{32}(D_o^4-D_i^4)
6
Shear Stress Solid Shaft
$S_s=\frac{16T}{\pi D^3}
7
Max Shear Stress (outside)
$S_s=\frac{16TD_o}{\pi (D_o^4-D_i^4)}
8
Min Shear Stress (inside)
$S_s=\frac{16TD_i}{\pi (D_o^4-D_i^4)}
9
Polar Section Modulus
$Z_p=\frac{π}{16}D^3
10
Power
$P=2πTN
11
Power SI
$P=\frac{NT}{9.549x10^6}
12
Power English
$P=\frac{NT}{63025}
13
Main Power Transmitting shaft (4000psi)
$P=\frac{ND^3}{80}
14
Lineshaft carrying pulleys (6000 psi)
$P=\frac{ND^3}{53.5}
15
Short shafts, small, countershafts (8500 psi)
$P=\frac{ND^3}{38}
16
Torsional Deflection
$\theta=\frac{TL}{JG}$

TaLong ni Janno Gibbs
17
Torsional Deflection given G
$\theta=\frac{2S_sL}{GD}$

$S_s=\frac{G \theta D}{2L} $

GOD2Long
18
Modulus of Rigidity
$G=12x10^6 psi
19
Shear Stress (Bolts) Couplings
$S_s=\frac{8T}{πd^2D_bn}
20
Compressive Stress (Flange) Couplings
$S_c=\frac{2T}{dtD_bn}
21
Maximum Shear Stress Shaft
$Ss=\frac{16}{πD^3}\sqrt{M^2+T^2}
22
Maximum Normal Stress Shaft
$S_T=\frac{16}{πD^3}\left(M+\sqrt{M^2+T^2}\right)
23
Equivalent Bending Moment
$M_e=\frac{1}{2}\left(M+\sqrt{M^2+T^2}\right)
24
Equivalent Twisting Moment
$T_e=\sqrt{M^2+T^2}
25
Length No Bending Action except own weight
$L=8.95\sqrt[3]{D^2}
26
Length Subject in bending action
$L=5.2\sqrt[3]{D^2}
27
Allowable Twist = 0.08°/ft
Diameter 2 formulas
$D=0.29\sqrt[4]{T}$

$D=4.6\sqrt[4]{\frac{P}{N}}
28
Shear Stress Keys
$S_s=\frac{F}{WL}=\frac{2T}{WLD}$
$S_s=\frac{2T}{AD}
29
Compressive Stress Keys
$S_c=\frac{4T}{tLD}
30
Torque and Force
$T=F\left(\frac{D}{2}\right)$

$F=\frac{2T}{D}
31
Recommended Width of Keys
$W=\frac{1}{4}D
32
Stress Formula Using Torque with Diameter na Extra
$S=\frac{2T}{AD}
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