3 - VARIABLE STRESS ANALYSIS ME 418
TOPIC NO. 3
VARIABLE STRESS ANALYSIS
This topic includes the following: SINUSOIDAL STRESS VARIATIONS
3.1 Variable Stress analysis with stress
a. alternating c. repeated
concentration
b. reversed d. fluctuating
3.2 Variable Stress analysis without stress
concentration
3.3 Definite life design
3.4 Indefinite life design
VARIABLE STRESSES. Many machines and
structural members are subjected to loads
that are not static but vary in magnitude. ( From Paul H. Black and O. Eugene Adams,
This type of loading induces cyclic or fatigue Jr., “Machine Design” 3rd edition, McGraw-
stresses in the members. With the increase in Hill Kogakusha, Ltd.,1968)
mechanization, design to resist fatigue
failure has become of increasing importance
in many areas of engineering. For example,
many factories employ heavy machinery
operating at high speeds, new means of rapid
transportation are being developed with
corresponding sources of vibration and cyclic
stresses, and improvements in design
efficiency require component parts to where
operate at higher static and dynamic-stress
levels. Smax + Smin
Sm = (mean or average stress)
2
Smax - Smin
Sa = (alternating stress)
2
MACHINE DESIGN 1 Page 27
, 3 - VARIABLE STRESS ANALYSIS ME 418
For Varying Shear (Torsional Stress)
involving yield strength
1 Sms Sas
= +
N Sys Sns
where
Sns = shearing endurance strength
Sys = yield strength in shear
Sms = mean stress
Soderberg Equation
Sas = alternating or variable stress in
(for Ductile Materials)
shear
1 Sm Sa
= + ESTIMATIONS OF ENDURANCE STRENGTHS. .
N Sy Sn ( From Virgil Moring Faires, “Design of
Machine Elements”, 4th edition, Macmillan
Company,1962)
Goodman Equation
(for Brittle Materials) For wrought steel in its more
commonly met commercial forms, it is often
1 Sm Sa assumed that the average endurance limit
= + for an average Su is
N Su Sn
Sn’ ≈ 0.5 Su
Sn’ ≈ (250)(BHN) psi
where
N = factor of safety which should be limited to a maximum
Smax = maximum induced stress Brinell of about 400.
Smin = minimum induced stress
Sm = mean or average stress For reversed axial loading
Sa = alternating stress
Sy = material’s yield point Sn max = (0.8)(Sn from standard specimen,
Su = material’s ultimate point rotating beam)
Sn = endurance strength
MACHINE DESIGN 1 Page 28
TOPIC NO. 3
VARIABLE STRESS ANALYSIS
This topic includes the following: SINUSOIDAL STRESS VARIATIONS
3.1 Variable Stress analysis with stress
a. alternating c. repeated
concentration
b. reversed d. fluctuating
3.2 Variable Stress analysis without stress
concentration
3.3 Definite life design
3.4 Indefinite life design
VARIABLE STRESSES. Many machines and
structural members are subjected to loads
that are not static but vary in magnitude. ( From Paul H. Black and O. Eugene Adams,
This type of loading induces cyclic or fatigue Jr., “Machine Design” 3rd edition, McGraw-
stresses in the members. With the increase in Hill Kogakusha, Ltd.,1968)
mechanization, design to resist fatigue
failure has become of increasing importance
in many areas of engineering. For example,
many factories employ heavy machinery
operating at high speeds, new means of rapid
transportation are being developed with
corresponding sources of vibration and cyclic
stresses, and improvements in design
efficiency require component parts to where
operate at higher static and dynamic-stress
levels. Smax + Smin
Sm = (mean or average stress)
2
Smax - Smin
Sa = (alternating stress)
2
MACHINE DESIGN 1 Page 27
, 3 - VARIABLE STRESS ANALYSIS ME 418
For Varying Shear (Torsional Stress)
involving yield strength
1 Sms Sas
= +
N Sys Sns
where
Sns = shearing endurance strength
Sys = yield strength in shear
Sms = mean stress
Soderberg Equation
Sas = alternating or variable stress in
(for Ductile Materials)
shear
1 Sm Sa
= + ESTIMATIONS OF ENDURANCE STRENGTHS. .
N Sy Sn ( From Virgil Moring Faires, “Design of
Machine Elements”, 4th edition, Macmillan
Company,1962)
Goodman Equation
(for Brittle Materials) For wrought steel in its more
commonly met commercial forms, it is often
1 Sm Sa assumed that the average endurance limit
= + for an average Su is
N Su Sn
Sn’ ≈ 0.5 Su
Sn’ ≈ (250)(BHN) psi
where
N = factor of safety which should be limited to a maximum
Smax = maximum induced stress Brinell of about 400.
Smin = minimum induced stress
Sm = mean or average stress For reversed axial loading
Sa = alternating stress
Sy = material’s yield point Sn max = (0.8)(Sn from standard specimen,
Su = material’s ultimate point rotating beam)
Sn = endurance strength
MACHINE DESIGN 1 Page 28
