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Lesson 36 of 78 · Beams, Deflection & Failure

Failure, Fatigue & the Structural Design Review

Machines rarely fail as a uniform coupon under one perfect pull. They loosen, wear, buckle, crack at a shoulder, slip at a joint, overload during a jam, corrode, overheat, or drift out of alignment. MIT’s materials curriculum distinguishes elastic response, plastic flow, creep, fracture, and fatigue because each has different evidence and countermeasures 1.

Screen the limit states

  • Yield: permanent deformation under peak combined stress.
  • Buckling: instability of a slender compression member, often before material yield.
  • Fatigue: crack initiation and growth under fluctuating stress.
  • Fracture: unstable crack growth when toughness is insufficient for stress and flaw size.
  • Creep: time-dependent deformation at relevant temperature and stress.
  • Wear and fretting: surface loss or damage from contact and small oscillatory motion.
  • Joint failure: slip, separation, embedment, bolt fatigue, weld cracking, or thread stripping.
  • Functional failure: excessive deflection, vibration, backlash, or alignment loss.

Fatigue as an alternating-load problem

For a stress cycle with maximum \(\sigma_{max}\) and minimum \(\sigma_{min}\), define

\[ \sigma_a=\frac{\sigma_{max}-\sigma_{min}}{2}, \qquad \sigma_m=\frac{\sigma_{max}+\sigma_{min}}{2}. \]

Both alternating and mean stress matter. Surface finish, size, environment, notches, residual stress, and reliability change fatigue performance. A motor mount seeing 20 to 80 MPa has \(\sigma_a=30\) MPa and \(\sigma_m=50\) MPa. Calling it “an 80 MPa load” loses the cycle information.

Fault loads deserve their own cases

Normal operation may not govern. Include hard stop, e-stop deceleration, dropped payload, jammed conveyor, seized bearing, pressure spike, off-center part, maintenance leverage, and transport. Define whether each is expected repeatedly, rare but survivable, or allowed to cause controlled sacrificial damage.

A compact structural review package

  1. Annotated assembly and load path.
  2. Load-case table with sources and combinations.
  3. FBDs and reaction calculations.
  4. Internal-force, stress, deflection, and stability checks.
  5. Connection and fatigue screens.
  6. Assumptions and uncertainty register.
  7. Verification plan: inspection, proof load, strain measurement, deflection test, or teardown.

Safe verification

Use barriers, remote loading, controlled energy, and competent supervision for structural tests. Do not place a person on or near an unproven load-bearing mechanism. Increase load in bounded steps, inspect between steps, define stop criteria in advance, and treat unexpected noise, slip, or permanent set as data—not a dare to continue.

Course project

Complete the review package for a small machine frame or robot pedestal. Your conclusion must name the governing limit state, margin, and verification evidence still missing. Engineering confidence is calibrated: “calculation suggests” and “test demonstrates” are different claims.

Source trail

References

  1. 1
    Mechanical Behavior of Materials. MIT OpenCourseWare. verifiedUndergraduate treatment of elastic and plastic deformation, creep, fracture, and the processing-structure-property relationship. Cited at: mechanical response.
Further reading
  • Mechanics of Materials. MIT OpenCourseWare. verifiedOpen modules on stress, strain, trusses, torsion, bending, deflection, yielding, fracture, fatigue, and material properties.
  • Elements of Mechanical Design. MIT OpenCourseWare. verifiedModeling, design, integration, fabrication, and characterization of bearings, springs, gears, cams, mechanisms, shafts, drives, and connections.

Check your understanding

  1. Why can a part fail below its monotonic yield strength?
  2. Which review question is most useful?