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Machine Design
Constraints
The direction of the moment follows the rule of cross product
Stress Tensor
- σx
- τxy
- τxz
- τyx
- σy
- τyz
- τzx
- τzy
- σz
Bending
σx = My / J
J = ∫ y2 dA
Circular section: J = π d4 / 64 → σx = 32 M / π d3
Rectangular section: J = 1 / 12 bd3 → σx = 6 M / bd2
Shear
τmax = VQ / BJ = 3 V / 2 A
Circular section: τmax = 4 V / 3 A
Torque
τmax = Mt · r / Jp
Circular section: Jp = πd4 / 32 → τmax = 16 Mt / π d3
Notch Effect
Theoretical kt = τmax / σnom
σmax = F (axial) / Anet , σnom = My / J (bending)
kt = τmax / σnom
Effect of ku on the safety factor η (static assessment): the constitutive law of the material should be taken into account.
Experimental stress concentration factor:** Ks = Foum (unit load without notch) / Feim (unit load with notch)