Statics and Load Paths
On a simply supported beam, these are the two upward forces found at the supports.
What are reaction forces?
Increasing the shaft diameter from d to 1.2d while keeping the torque constant causes this to decrease noticeably. (Hint: What do you calculate with torque?)
What is torsional shear stress?
Unlike a basic strength calculation, Castigliano’s theorem answers questions about this.
What is displacement or rotation?
Instead of choosing the Tresca criterion simply because it is the default, this is what should determine the appropriate failure model.
What are the material behavior and loading conditions?
Repeated loading means that this type of failure must now be considered in addition to static strength.
What is fatigue?
By increasing this geometric condition, you can decrease the bending moment of a beam.
What is length?
These shaft features commonly govern because they act as stress risers.
What are shoulders, fillets, and diameter changes?
If a design passes strength but fails a deflection limit, it is controlled by this.
What is stiffness?
For a smooth ductile metal part, this failure theory usually matches yielding better than Tresca.
What is von Mises?
A student who plugs peak stress directly into Goodman is probably confusing it with these two quantities.
What are mean stress and alternating stress?
Skipping this in a mechanics problem often causes mistakes with assumptions and force directions. (Should always be the first step)
What is a free-body diagram?
If two shafts carry the same bending moment and one has diameter d while the other has 2d, the smaller shaft has about this many times more bending stress.
sigmabending = (32M)/(pi*d3)
What is eight?
In the elastic region, this material property matters more for deflection than yield strength.
What is elastic modulus?
This theory is usually a poor choice for ductile steel because it is more appropriate for brittle materials.
What is Maximum Normal Stress?
If Gerber passes but Goodman fails, it suggests the design is sensitive to this.
What is the chosen fatigue model or desired conservatism?
When the boundary conditions are incorrect, these 2 things can be wrong.
What are the reactions and internal load path?
The global maximum stress in an FEA plot may not govern if it occurs at one of these mesh-sensitive locations.
What is a singularity or support artifact?
A design may survive without yielding but still fail because this quantity is too large.
What is deflection?
These two theories are commonly used for brittle materials because they account for different tensile and compressive strengths.
What are Coulomb-Mohr and Modified Mohr?
These factors reduce the ideal endurance limit to a more realistic design endurance limit.
What are Marin factors?
When a point load moves closer to one support, this shifts toward the nearer support.
What is the reaction distribution?
This shaft feature is more dangerous in fatigue because it creates a local stress concentration.
What is a keyway?
Simple Castigliano problems in this course assume this type of behavior.
What is linear elastic behavior?
If a design fails under Tresca but barely passes under von Mises, the design should be described this way.
What is marginal or sensitive to the chosen failure model?
Even if an endurance-limit screen fails, this equation may still show that finite life is acceptable.
What is Basquin’s equation?