Idler / support axle bending
Bending stress, deflection and end slope of a solid or hollow support axle, for an applied moment and (separately) an end force.
Second moment of area, I_x7.85 10⁻⁹ m⁴
Section modulus, W_x = I_x/(D/2)0.79 10⁻⁶ m³
Bending stress (moment case), σ = M/W_x127.32 10⁶ Pa
Deflection (moment case), δ(L)30.32 10⁻³ m
End slope (moment case), φ(L)3.47 deg
Bending stress (force case), σ = F·L/W_x127.32 10⁶ Pa
Deflection (force case), δ(L)20.21 10⁻³ m
End slope (force case), φ(L)1.74 deg
Method & references
- Bending of a solid or hollow support (idler) axle under an applied moment or end force.
The computation is a literal port of the original client-side JavaScript from /calculators/t14_8c.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.