Machine Design

1.What is the difference between static stress and fluctuating stress in machine design?

Parameter	Static Stress	Fluctuating Stress
Definition	Stress that remains constant with time.	Stress that varies with time (changes in magnitude and sign).
Load Type	Steady, unchanging load.	Repeated, alternating, or cyclic load.
Failure Type	Produces immediate or static failure.	Causes fatigue failure over time.
Design Basis	Yield strength (Sy).	Endurance limit (Se), fatigue theories.
Examples	Columns under constant load, beams with static weight.	Rotating shafts, connecting rods, springs.

2.Types of Dynamic / Fluctuating Stresses ?

Type of Stress	Definition	Stress Range	Example
Fluctuating Stress	Stress varies between two unequal values.	σmin to σmax (both ≠ in magnitude)	Shaft with variable torque
Completely Reversed Stress	Stress changes from equal tension to equal compression.	+σ to –σ	Rotating beam test
Alternating Stress	Stress varies symmetrically between +σ and –σ; used in fatigue.	+σa to –σa	Fatigue analysis of rods
Repeated Stress	Stress varies between zero and a maximum value.	0 to +σ	Springs in machines
Variable Stress	Stress changes continuously with time due to varying load.	Irregular	Machine components under dynamic load

3.S–N Curve (Wöhler Curve) ?

• The S–N curve shows the relationship between stress amplitude (S) and number of cycles to failure (N) during fatigue loading.
• As stress decreases, the number of cycles to failure increases.
• Used for predicting fatigue life of components.

Types of S–N Curves

Type of S–N Curve	Definition	Materials	Key Feature
Finite Life Curve	Shows failure at high stresses within limited cycles.	Most materials	Steep drop in life as stress increases.
Endurance Limit Curve	Curve becomes horizontal after a point; below this stress, failure won’t occur.	Ferrous materials (steel)	Has endurance limit (Se).
No Endurance Limit Curve	No horizontal region; failure occurs at any stress if cycles are high enough.	Non-ferrous materials (Al, Cu)	Only fatigue strength at specific cycles.
Low Cycle Fatigue Curve	Represents high stress + low cycles (<10⁴).	Heavy load components	Plastic deformation dominates.
High Cycle Fatigue Curve	Represents low stress + high cycles (>10⁴–10⁶).	Steel, Aluminum	Elastic deformation dominates.

4.Fatigue Failure Theories ?

Theory / Criterion	Description	Used For	Nature
Soderberg Line	Very safe; uses yield strength with endurance limit.	Ductile materials, conservative design.	Linear & most conservative.
Goodman Line	Uses ultimate strength with endurance limit.	General fatigue design.	Linear; less conservative than Soderberg.
Gerber Curve	Uses a parabolic curve between endurance limit and ultimate strength.	Ductile materials under fluctuating loads.	Nonlinear; more accurate, less conservative.
ASME Elliptic Theory	Combines shear, yield, and endurance limits in elliptical form.	Shafts & machine members.	Moderate conservatism, realistic.
Modified Goodman	Similar to Goodman but includes factor of safety.	General purpose, safer than Goodman.	Linear with safety factor.
Goodman–Soderberg Comparison	Not a theory, but used to compare how conservative each is.	Design selection.	Soderberg < Goodman < Gerber (conservative → less conservative).