Week+1 POwerpoint

Course Overview

• Course Code: AME 3353 Design – Mechanical Components

• Instructor: Dr. Yijie Jiang

• Institution: School of Aerospace and Mechanical Engineering, University of Oklahoma

Stress in Three Dimensions

• Types of Loadings:

  • Normal Force (N): Perpendicular to cross-section.

  • Shear Force (V): Parallel to cross-section, calculable in 2D.

  • Bending Moment (M): Moment bending around an axis in the cross-section, calculable in 2D.

  • Torsional Moment (T): Moment bending around an axis perpendicular to the cross-section.

Normal Stress

• Calculation: Can be evaluated in all axes (x, y, z).

• Units: Force/Area (e.g., Pa, psi).

• Types:

  • Tensile Stress: Stretching along an axis.

  • Compressive Stress: Compressing along an axis.

Shear Stress

• Calculation: Applicable in all axes (x, y, z).

• Units: Force/Area (e.g., Pa, psi).

• Notation: First subscript indicates surface, second indicates direction.

Average Normal Stress

• For an axially loaded bar, assuming material is homogeneous and isotropic.

• Formula: ( \sigma_{avg} = \frac{P}{A} )

Average Shear Stress

• Simple Shear: Caused by direct load.

• Formula: ( \tau_{avg} = \frac{V}{A} )

Strain

• Types:

  • Normal Strain: Calculated along primary axes (dimensionless).

  • Shear Strain: Calculated in primary planes (typically degrees or radians).

• Normal Strain Formula: ( \epsilon_{avg} = \frac{\Delta L}{L_0} )

Stress-Strain Diagram

• Relationship between stress (y-axis) and strain (x-axis).

• Uses nominal stress and strain data.

• Key points include elastic limit and yield stress.

Regions of a Stress-Strain Curve

• Elastic Region: Returns to original shape when unloaded.

• Yielding Region: Permanent deformation begins after yield stress.

• Strain Hardening Region: Additional load increases strain until ultimate stress.

• Necking Region: Localized area decreases in cross-section until fracture.

Torsion and Torque

• Twisting moment about a member's longitudinal axis.

• Formula for maximum shear stress in circular cross-sections: ( \tau_{max} = \frac{T\cdot c}{J} )

Sign Convention for Torque

• Right-hand rule: positive if moment is outward.

Angle of Twist

• Related to torque, cross-sectional area, and shear modulus.

• Formula: ( \phi = \frac{T\cdot L}{J\cdot G} )

Statically Indeterminate Members

• Analyzing using statics and compatibility conditions for reactions.

Shear and Moment Diagrams

• Positive internal shear causes clockwise rotation.

• Procedure for creating diagrams includes determining reactions, drawing shear/moment diagrams.

Example Problems

• Determining normal strain in wires under torque and elongation in an aluminum rod under load.