MJ

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.