Stress Transformation Explained | Principal Stresses & Maximum Shear Derivation

Understand stress transformation from first principles through a clear animated derivation using force equilibrium. This lesson begins with the three-dimensional stress tensor and plane-stress condition. It then derives the normal and shear stresses acting on an inclined plane step by step. Topics covered: Stress at a point and the Cauchy stress tensor Complementary shear stresses Plane stress versus plane strain Stress sign conventions Rotated axes and inclined-plane geometry Triangular-wedge equilibrium Normal-stress transformation equation Shear-stress transformation equation Stress on the perpendicular face Stress invariants and verification checks Principal planes and principal stresses Maximum in-plane shear stress The 45-degree relationship between principal and maximum-shear planes Absolute maximum shear using all three principal stresses #StressTransformation #PrincipalStress #PrincipalStresses #MaximumShearStress #PlaneStress #StressTensor #StrengthOfMaterials #MechanicsOfMaterials #SolidMechanics #EngineeringMechanics #StructuralEngineering #MechanicalEngineering #CivilEngineering #EngineeringEducation #MohrsCircle