Shigleys 10th Edition Example 5-1 Static Failure: Tresca MSS vs Von Mises DE Safety Factor Pt 2 of 2

Описание: In this video, we continue solving Shigley’s Mechanical Engineering Design (10th Edition), Example 5-1, examining additional stress states using the two major static failure criteria for ductile materials:
• Tresca (Maximum Shear Stress Theory)
• von Mises (Distortion Energy Theory)

This is Part 2 of the walkthrough of Example 5-1. In the previous video we solved parts (a) and (b). Here we examine the remaining stress states (c), (d), and (e) and see how the failure theories behave in different regions of the principal stress plane. We:
• Identify the principal stresses
• Plot the stress state on the failure diagrams
• Determine the Tresca (MSS) factor of safety against yielding
• Calculate the von Mises stress
• Determine the von Mises (DE) factor of safety against yielding

5-1c — Opposite-Sign Principal Stresses
In part (c) the principal stresses fall in the negative/positive quadrant of the principal stress plane. This means the material experiences one tensile stress and one compressive stress simultaneously. This case is important because combined tension and compression often produces larger shear stresses, making yielding more likely.

5-1d — Compression Quadrant
In part (d) both principal stresses lie in the negative/negative quadrant, meaning the material is under combined compressive stresses. We again apply both failure criteria and compare the predicted factor of safety. This highlights how the theories behave when stresses are entirely compressive.

5-1e — Hydrostatic Stress State
Part (e) produces a hydrostatic stress condition, where the stresses are the same in all three orthogonal directions: σ₁ = σ₂ = σ₃
This means the material experiences uniform tensile stress in every direction. An important result follows:
• Hydrostatic stress produces no shear stress
• No distortion energy develops in the material
Because yielding in ductile metals is driven by shear deformation, both Tresca and von Mises predict no yielding under pure hydrostatic stress.

🧠 Key Engineering Insight
Ductile materials yield because of distortion (shear deformation), not because of uniform pressure.

That is why:
• Hydrostatic pressure alone does not cause yielding
• Failure theories focus on shear stress or distortion energy
• The principal stress quadrant strongly affects the factor of safety

Understanding how stresses move around the principal stress plane is fundamental to machine design.

📚 Textbook Reference: Mechanical Engineering Design, 10th Edition Budynas & Nisbett (Shigley’s)

🔥 Hashtags
#MechanicalEngineering
#FailureTheory
#Tresca
#VonMises
#HydrostaticStress
#MachineDesign
#MechanicsOfMaterials
#EngineeringStudents
#Shigley
#StrengthOfMaterials
#The_Mechanical_Pencil