These formulas are used to solve either a shaft (with one or more sections) or a beam (with one constant section) with multiple supports and loads.
The shaft/beam axis is aligned with the Z axis. If the impact of the material density is included in the calculation, the gravity vector is aligned with the Y axis.
Shear forces:
Bending moments:
Deflection angle:
where:
|
E |
modulus of elasticity in tension |
|
|
J |
moment of inertia |
|
|
G |
modulus of rigidity |
|
| β |
shear displacement ratio |
Deflection:
Bending stress:
Shear stress:
Torsion stress:
Tension stress:
Reduced stress:
where:
| σ B | bending stress | |
| σ T |
tension stress |
|
| τ | torsion stress | |
| τ S | shear stress | |
| α | α = 3 for HMH | |
| α = 4 for Tresca-Guest |
Sample Calculation
Modulus of elasticity E = 210 000 MPa
Modulus of rigidity G = 81 000 MPa
Shear displacement ratio β = 1.118
Mode of reduced stress: HMH
Do not include the material density.
Support Forces:
Maximal shear stress:
Maximal torsion stress:
Maximal moment:
Maximal bending stress:
Maximal reduced stress:
Angle of twist:
