CIVIL ENGINEERING FORMULAS

TABLE 2.7 Polar Moment of Intertia and Maximum Torsional Shear

BEAM FORMULAS 77

Strain Energy in Torsion

For a member subjected to torsion

(2.40)

U (2.41)

JG 2

2 L

U

T^2 L

2 JG

2 r

2 r 2 R

a

a

b

a

Polar moment of

inertiaJ

Maximum shear*

vmax

at periphery

2 T

πr^3

at midpoint

of each side

at midpoint

of longer sides

– 0.21 1 –

R=^2 T

208 a^3

T(3a – 1.8b)

a^2 b^2

π(R^4 – r^4 )

at outer

periphery

2 TR

π(R^4 – r^4 )

b^4

12 a^4

at midpoint

of each side

20 T

a^3

1

2

πr^4

1

2

0.0214a^4

1

3

b

a

0.141a^4

ab^3

*Ttwisting moment, or torque.