According to Seely and Smith, the Torsional Constant is not the Polar Moment of Inertia unless the Section

is circular. The Torsion Constant for a tube with varying thickness is (Table 14, Page 276):

C th tb, b, h, ( )2 th⋅ tb⋅ b th−( )

2⋅ h tb−( )

2⋅

b th−( ) th⋅ h tb−( ) tb⋅+:=

h

b

th

tb

Check: A tube with constant thickness:

h 16 in⋅:= b 8 in⋅:=

th .375 in⋅:= tb .375 in⋅:=

C th tb, b, h, ( ) 458 in4

= AISC lists J as 436 in4

Given: A tube with varying thickness:

h 58.5 in⋅:= b 24 in⋅:=

th 1.00 in⋅:= tb 2.25 in⋅:= C th tb, b, h, ( ) 50361 in4

=

Let L 10ft:=

Shear Modulus of Elasticity: G 12000ksi:=

Constant Twisting Moment: T 100kip ft⋅:=

The angle of twist for a cantilever: : ϕT L⋅

C th tb, b, h, ( ) G⋅:= ϕ 0.000238 rad=

ϕ 0.013653 deg=

Tube Torsion Constant.xmcdz-1 __________________________________________________