Mechanics of Engineering Formula

Trigonometry Law of Cosines :

Law of Sines :

  =   +  − 2cos 2cos r

in 

=

in in =  

Elastic Constants and Hooke’s Law

  =  [ − ( +  )] + Δ  1   = [ −  +  ] +Δ   1   = [ − ( +  )] + Δ   = 21 1 +    =   = − Safety Factor

 =

  

Centroid Triangle

Quarter Circle

Rectangle

 Area

 Area

 Area

Second Moment of Area y x

h

 I  x  

 I  y   b

1

bh 3

y

12

hb

3

x D

 I  x 

 D

  

4

64



12

Nomenclature as according to lecture notes

 R

  

4

 I  x  

bh 3 36

4

 I  y 

hb 3 36

Parallel-Axis Theorem

  =  + ′′    =  + ′′  Polar Second Moment of Area Solid shaft R

 J  

 R



0

Hollow shaft

2  r  dr   3

1 2

     =  =    Shear Stress Equation in Beams

  ̅   =  

Torsion Relationship

     =  =     Axially Loaded Bodies In series :

  = ∑ 

In parallel :

 = ∑  

R4

  

Bending Equation

=

Ro Ri

 J  

 Ro



 Ri

2  r  dr   3

1

 R

  

2

4

o

 Ri4 