VALICALC / MECHANICAL ENGINEERING SUITE / DS19

Shaft Loads, Fatigue & Deflection Design Sheet

Choose a simply supported or cantilever shaft and define signed point forces. A shared Euler–Bernoulli beam solver uses actual segment diameters. Static strength, supplied fatigue history, stiffness and the ideal bare-shaft natural frequency remain distinct checks.

Verified mathematical models with explicit assumptions. Component capacity and applicability are shown as separate checks.

Labeled example inputs • SI calculations • Project revision 0 • No account or cloud upload

01 / ENGINEERING INPUTS

Define the operating point

Section modelBoundary conditions

Uniform shaft length

Selected uniform outside diameter

Uniform shaft bore

Support A position

Support B position

Young modulus (example; replace with applicable data)

MPa

Shear modulus (example; replace with applicable data)

MPa

Constant internal torque magnitude

N·m

Constant axial force magnitude

Applicable yield strength (0 = unknown)

MPa

Required nominal yield factor

Allowed resultant deflection (0 = unknown)

Allowed total twist (0 = unknown)

deg

Section for supplied fatigue history (1-based)

Alternating bending moment amplitude

N·m

Mean bending moment magnitude

N·m

Alternating torsion amplitude

N·m

Mean torsion magnitude

N·m

Supplied fatigue bending factor Kf

Supplied fatigue torsion factor Kfs

Supplied elastic bending factor Kt

Supplied elastic torsion factor Kts

Corrected endurance strength (0 = unknown)

MPa

Ultimate strength (0 = unknown)

MPa

Required modified Goodman factor

Density for ideal bare-shaft frequency

kg/m³

Operating RPM for comparison only

rpm

Point loads

Point load 1

Point load position

Signed Y force

Signed Z force

02 / CALCULATE → SELECT → RECALCULATE

Calculation & checks

Maximum resultant bending moment

150 N·m

Maximum nominal von Mises stress

65.34268 MPa

Sampled maximum resultant deflection

0.53894 mm

Sampled maximum resultant slope

0.15439 deg

Total constant-torque twist

0.54038 deg

Fatigue equivalent alternating stress

56.58842 MPa

Fatigue equivalent mean stress

32.67134 MPa

Conservative supplied-history peak stress

65.34268 MPa

Ideal bare-shaft first bending frequency

10,155.57947 rpm

Operating / ideal frequency ratio

0.1477

Original schematic; not a manufacturing drawing. Supports A / B · Signed point forces · Segmented shaft. Actual dimensions and model checks are listed in the calculation record.

Intermediate values and comparisons - SI units
Section	Outside d (m)	Bore d (m)	Peak M (N·m)	Normal σ (Pa)	Torsion τ (Pa)	Nominal VM (Pa)
1	0.03	0	150	56,588,424.210452	18,862,808.070151	65,342,683.901842

Support reactions (force N / moment N·m) - SI units
Plane	Reaction	x (m)	Value
Y	Support force	0	500
Y	Support force	0.6	500
Z	Support force	0	0
Z	Support force	0.6	0

Beam sample stations / signs follow entered axes - SI units
x (m)	Y deflection (m)	Y moment (N·m)	Y shear (N)
0	0	-1.241e-13	500
0.0375	-0.000101	18.75	500
0.075	-0.000198	37.5	500
0.1125	-0.000289	56.25	500
0.15	-0.000371	75	500
0.1875	-0.000439	93.75	500
0.225	-0.000493	112.5	500
0.2625	-0.000527	131.25	500
0.3	-0.000539	150	500
0.3	-0.000539	150	-500
0.3375	-0.000527	131.25	-500
0.375	-0.000493	112.5	-500
0.4125	-0.000439	93.75	-500
0.45	-0.000371	75	-500
0.4875	-0.000289	56.25	-500
0.525	-0.000198	37.5	-500
0.5625	-0.000101	18.75	-500
0.6	0	-1.159e-13	-500

Criterion-specific verification

UNKNOWN · Entered nominal static yield criterion
Nominal smooth-section bending + axial + torsion. Local static stress concentrations are excluded. No positive applicable limit was supplied.
UNKNOWN · Entered elastic deflection criterion
128 subdivisions per force-free beam element sample resultant deflection. This is not a gear alignment approval. No positive applicable limit was supplied.
UNKNOWN · Entered total twist criterion
Constant internal torque in all entered segments. No positive applicable limit was supplied.
UNKNOWN · Supplied-history modified Goodman criterion
Only the selected section and independently supplied moments/endurance/factors are checked. No overall shaft fatigue approval.
UNKNOWN · Supplied-history elastic peak criterion
Conservative amplitude + mean envelope at the selected section. No positive applicable limit was supplied.
UNKNOWN · All-section notch / endurance qualification
Shoulders, keyways, surface effects and fatigue history require applicable source inputs. Static force rows are not an alternating load spectrum.
BLOCKED · Real rotor critical speed / operating margin
Displayed eigenfrequency assumes a uniform bare beam, no attached mass, gyroscopic effect or support compliance. It is not a safe operating speed.

Method and calculation trace

Two-plane Hermite Euler–Bernoulli elements: nodes at supports, point forces and every section boundary; diagonal scaling and equilibrium residual checks precede output.

I = π(do⁴−di⁴)/64; J = 2I. Nominal extreme fiber includes |Faxial|/A and resultant bending; torque is constant along the shaft.

Modified Goodman: equivalent alternating / corrected endurance + equivalent mean / ultimate ≤ 1 / entered required factor. No material endurance correction is fabricated.

Selecting any actual segment diameter changes EI, deflection, section stress and torsional stiffness. A continuous nominal diameter result is not a stock-size recommendation.

Assumptions & scope

Small-deflection linear Euler–Bernoulli beam with isotropic sections, point forces and ideal supports. Constant axial force/torque act over the whole shaft. No shear deformation, distributed/self-weight loads, bearing compliance or gyroscopic effects.

Nominal static stress excludes shoulder/keyway concentration. Goodman uses the independently entered critical-section mean/alternating moments and supplied corrected endurance/notch data; it does not infer a fatigue history from static forces.

Ideal first bending frequency applies only to a uniform bare shaft supported at both ends, without attached masses. It is not a rotor critical-speed approval. Stepped/attached-mass dynamics remain blocked.

Worked example

A 600 mm span, 30 mm solid shaft, 210 GPa modulus and a central 1000 N force has 500 N reactions and 150 N·m peak bending. The analytic center deflection is FL³/(48EI). Changing either segment diameter reruns stiffness and section stress from unrounded SI inputs.

Calculation methods and sources

A = π(do²−di²)/4; I = π(do⁴−di⁴)/64; J = 2I; σ = |N|/A + Mc/I; τ = Tc/J

Circular isotropic smooth sections; nominal extreme-fiber stress and von Mises, constant axial force/torque. No local notch approval.

TU Delft linear structural mechanics; independent cross-section integration. Volume 1 does not supply Chapter 10 shaft methods.

Ke = EI/L³ [[12,6L,−12,6L], [6L,4L²,−6L,2L²], [−12,−6L,12,−6L], [6L,2L²,−6L,4L²]]

Two bending planes; Hermite elements at point loads/supports/section boundaries. Actual section EI is assembled, scaled, solved and residual-checked. Deflection maxima are sampled at 128 subdivisions per element.

TU Delft Euler–Bernoulli beam elements, equations 4.29–4.43; independent analytic beam cases.

1/nGoodman = σa,eq/Se + σm,eq/Sut

Supplied critical-section mean/alternating moments, corrected endurance and bending/torsion factors; equivalent stresses use distortion energy. Does not infer a fatigue spectrum or empirical endurance corrections.

W.H. Dornfeld, Fairfield University, fluctuating fatigue course notes; independent algebraic stress-equivalence checks.

ω1 = π²/L² √(EI/(ρA)); n1 = 60ω1/(2π)

Exact first mode of the uniform simply supported bare Euler–Bernoulli beam: substitute sin(πx/L) into EI y'''' + ρA y¨ = 0. No attached components, elastic bearings or real-rotor approval.

Independent beam eigenfunction derivation; TU Delft beam assumptions. Real rotor model remains blocked.

Textbook references identify the method context. Historical numerical catalog, material and service-factor tables have not been copied or treated as current product ratings.

Related calculators and references

Existing component-selection Jobs → · All mechanical worksheets →

Common questions

Does this approve a real component?

No. The worksheet separates mathematical results from criterion-specific checks. Actual motor, belt, gear, shaft, bearing and joint capacity need applicable current source data and engineering review.

What changes after choosing a physical size?

The worksheet recalculates the outputs and geometry from the entered actual dimensions or discrete tooth/link count. Dependent checks are reevaluated; previously saved results are not restored as approvals.