SME
Statics · Problem type
Polar moment of a shaft or tube
Use this for “Find J for a tube 60 mm outside and 40 mm inside.”
Diagram
J = 1,021,000 mm⁴, about the center
This is an example. Type your own values to start a new problem.
J (mm⁴)
=
π
×
(
(
dₒ (mm)
)
4
−
(
dᵢ (mm)
)
4
)
32
Formulas
J
=
π
×
dₒ
4
−
dᵢ
4
32
1.021 ×
10
6
=
π
×
60
4
−
40
4
32
Assumptions
•
J is about the shaft’s center, the axis it twists about.
•
A tube is a solid round less its bore; a solid shaft has dᵢ = 0.
Step-by-step
WE KNOW
dₒ = 60 mm, dᵢ = 40 mm
FIND
polar moment of area (J)
Step 1 · Find polar moment of area (J)
Use J = π × (dₒ⁴ − dᵢ⁴) ÷ 32
A
solid
round’s
πd⁴
32,
less
the
bore’s.
J
=
π
×
60
4
−
40
4
32
J
=
π
×
12,960,000 − 2,560,000
32
J
=
π
×
10,400,000
32
J
=
10,400,000π
32
J
=
1.021 ×
10
6
mm⁴
Check
Put the numbers back in. Both sides should match.
1.021 ×
10
6
=
π
×
60
4
−
40
4
32
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.