ken youssefi mechanical & aerospace engr., sjsu discontinuity in cross section stepped shafts...

Ken Youssefi Mechanical & Aerospace Engr., SJSU

Discontinuity in Cross Section

Stepped shafts

Discontinuity

Discontinuity


Water filter fatigue failure


Bracket with screw holes

High stress



Infrared analysis reveals the points of greatest stress on a Renault part’s surface caused by weld points and helps estimate fatigue limits for those critical areas (bottom).



Bolt failure at the junction of the thread and solid section. Location of higher stresses.

Discontinuity


Concept of Stress Concentration

Theoretical stress concentration factor, Kt

Maximum stress at the discontinuity

Nominal stress, max stress with no discontinuity

Kt is used for normal stresses and Kts for shear stresses.


Concept of Stress Concentration

Consider an elliptical hole in an infinitely large plate loaded in uniform tension. Using the theory of elasticity the theoretical stress concentration factor is given by the equation below.

Elliptical hole

2b

2a

• For a circular hole Kt = 3

• The equation can be applied to a longitudinal crack where b << a


Stress Concentration FactorStress concentration factor is found using experimental methods.

• Photoelasticity – a plane polarized light is passed thru a photelastic material (all transparent plastics) resulting in a

colorful fringe pattern indicating the intensity of the stress.


Photoelasticity Apparatus

Stress Distribution using Photoelasticity Method



Stress Concentration Factor

• Brittle Coating – a specially prepared lacquers are usually applied by spraying on the actual part. After air drying, the part is subjected to stress. A pattern of small cracks appear on the surface. Data could be used to locate strain gauges for precise measurement of the stress. The method is sensitive to temperature and humidity.


Stress Concentration Factor• Electrical strain gauges

The method is the most popular and widely accepted for strain measurements and stress analysis. The strain gauge consists of a grid of strain-sensitive metal foil bonded to a plastic backing material. When the gauge is subjected to a mechanical deformation, its electrical resistance changes proportionally. The change in voltage is converted to strain and the stress is calculated from the strain.

R = ρL / A

Resistivity Wire length

Cross sectionResistance


Wheatstone Bridge Circuit Schematic

3-Element strain gauge Rosettes 0°/45°/90°

Strain gauges are placed a t the location of maximum stress



Stress Concentration Factor• Finite Element method

The CAD model is subdivided into many small pieces of simple shapes called elements.

FEA program writes the equations governing the behavior of each element taking into consideration its connectivity to other elements.

These equations relate the unknowns, for example displacements in stress analysis, to known material properties, restraints and loads.

The program assembles the equations into a large set of simultaneous algebraic equations (thousands or even millions).

These equations are then solved by the program to obtain the stress distribution for the entire model.


Stress Concentration FactorRound shafts in axial Tension



Round section with a fillet

Bending

Torsion



Flat plate in Tension with a hole

Flat plate in Bending with a hole

ken youssefi mechanical & aerospace engr., sjsu discontinuity in cross section stepped shafts...

Documents

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discontinuity nominal

max stress

shafts discontinuity

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points of greatest stress

screw holes high stress

cross section bracket