ME101-Lecture05-KD_2025

Rigid Body Equilibrium

  • A rigid body remains in equilibrium if:

    • Sum of all external forces acting on it is zero.

    • Sum of moments of external forces about any point is zero.

Free Body Diagram (F.B.D.)

  • Represents all external forces on the body:

    • External forces include:

      • Applied loads

      • Support reactions

  • Must show magnitudes and lines of action; does not include internal forces.

    • Example: A man standing on a floor.

Free Body Diagram Example

  • Factors in play for an example involving a 544H DEERE:

    • Body weight

    • Tractor weight

    • Axes of force actions (y and x)

    • Boom weight and response forces

    • Load dynamics from bucket to other components (rear wheel reactions).

Space Diagram vs Free-Body Diagram

  • Space Diagram:

    • Sketch showing all physical conditions of the problem.

  • Free-Body Diagram:

    • Sketch focused only on forces acting on the selected particle.

Types of Connection and Reactions

  • Reactions depend on the type of connection:

    1. Tension force if acting along the direction of a cable or link.

    2. Force along the link axis if weightless.

    3. Perpendicular force at contact surface (e.g., roller).

    4. Pin connected with force acting perpendicularly in slots.

    • Various types of supports can lead to one or more unknowns depending on structural interaction.

Categories of Equilibrium in Two Dimensions

  • Rigid Body Force System:

    • Important configurations include:

      1. Collinear: Forces acting along a line.

      2. Concurrent: Forces meet at a point.

      3. Parallel: Forces acting parallel; sum of forces in both directions equals zero.

      4. General: Not constrained to any specific dominance in orientation (combined analysis needed).

Categories of Equilibrium in Three Dimensions

  • Similar categories as in two dimensions but accounting for:

    1. Concurrent forces at a point in 3D.

    2. Concurrent forces along a line.

    3. Parallel forces in three dimensions.

    4. General equilibrium with equations applicable in all three dimensions.

Equilibrium of a Rigid Body in Two Dimensions

  • Conditions of equilibrium defined where:

    • All forces sum to zero in both x and y directions.

    • Moments about any point in the structure must also be zero.

  • Statically indeterminate structures arise when there are more unknowns than equations.

Rigid Body Equilibrium Examples

  • A typical analysis involving forces acting on a joist is provided:

    1. Create and analyze Free Body Diagram (F.B.D.) with identified forces (reaction at A, weight).

    2. Direction of the reaction identified and solved using a force triangle to establish magnitude.

    3. Tension in the rope can be calculated along with loads from joist dynamics.

Structural Analysis Overview

  • Engineering Structure:

    • Connects multiple members to effectively transfer loads safely.

    • Includes trusses, frames, machines, beams, and cables.

Structural Analysis: Plane Truss

  • A framework built from members at connections:

    • Each joint may be welded, riveted, bolted, or pinned.

    • Analysis leverages basic principles of truss design (triangle shapes typically used for stability).

Basic Assumptions in Truss Analysis

  • Two-force member assumptions focus on:

    • Minimal weight effects relative to supported loads

    • External forces applied at pin connections for simplified analysis.

  • Special considerations for roller/rocker connections to allow for necessary deformations.

Truss Analysis: Method of Joints

  • Analyze forces at each joint where:

    1. Conditions of equilibrium are satisfied for forces.

    2. Draw F.B.D. and establish external reactions.

    3. Identify internal forces based on equilibrium principles at each joint.

Final Steps in Analysis and Check

  • Negative forces in analysis may indicate incorrect initial assumptions.

  • Zero Force Member checks ensure all members are validated under load conditions.