Equation sheet
Uniaxial Stress and Strain
Stresses on Inclined Sections
Elongation with Continuously Varying Loads
L
L
N ( x)dx
EA( x)
0
 =  d = 
0
Strain Energy with Non-Prismatic Bars
L
Ductility
L1 − Lo
(100)
Lo
A − A1
% Reduction = o
(100)
Ao
[ N ( x)]2 dx
U non − prismatic = 
2 EA( x)
0
% Elongation =
Poisson’s Ratio
 =−
lateral strain
'
=−
axial strain

EA 2 max
W (h +  max ) =
2L
Stress-Concentration Fator ‘K’
Shear Modulus
G=
Impact Loading
E
2(1 +  )
Allowable Stress
Required Area =
Load To Be Transmitted
Allowable Stress
Ramberg-Osgood Stress-Strain Law
Coiled Springs
Stiffness:
Flexibility:
Thermal Effects
 T =  (T )
Bolts and Turnbuckles
 = np ,  = 2np
The Torsion Formula
Equations Sheet
Angle of Twist for a Varying Cross Section
and a Varying Toque
L
Distributed Load Relationships
dV
 q
dx
L
T ( x)dx
GI p ( x)
0
   d  
0
dM
V
dx
Curvature of a Beam
Transmission of Power by Circular Shafts
 nT
P     fT 
60
Nonuniform Torsion

1


d
dx
x  
Normal Stresses in Beams
x  
Ey

  E y
Section Moduli
Torsion of Noncircular Prismatic Shafts
J ellipse 
 a 3b3
a b
2
2
J triangle 
ht 4
15 3
Derivation of Shear Formula
J rectangle  k2bt 3
Thin-Walled Tubes
T
f 
2 Am
4 Am 2
J  Lm
ds
0 t

T
2tAm
Properties of Plane Areas
y

  y
Equations Sheet
Beams with Axial Loads
Centroids of Plane Areas