CIVIL ENGINEERING FORMULAS

FIGURE 2.1 (Continued)

D

dm

ds

dm

a

b

s

do

D Outer fiber

Shaft section

Shaft torque formulas and location of

maximum shear stress in the shaft

Shaft section

Shaft angle-of-twist section formulas

Angle-of-twistθ =

D,do,di,dm,ds,s,a,b = shaft sectional dimensions, in (mm)

N = modulus of rigidity, psi (MPa)

L = length of shaft, in (mm)

T = torque, in.lb (N.m)

θ = twist, radians

Location of

max shear

Torque formulas

T =

Outer fiber

Ends of minor axis

Middle of sides

Midpoint of major sides

32 TL

π D^4 N

πD^3 f

16

πdmdm^2 f

16

f

π

16

0.208S^3 f

A^2 B^2 f

3 A+ 1.8B

32 TL

π (d 04 – d 14 )N

di

7.11TL

s^4 N

3.33 (a^2 +b^2 )TL

a^3 b^3 N

16 (dm^2 +ds^2 )TL

πdm^3 ds^3 N

(do^4 – di^4 )

do

S

A

B

di

ds

do

20