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# Department of Mechanical Engineering

### MCEN 2023 - Statics and Structures

1. Statics of Particles

• Represent a directed distance and a force as a vector in either two- or three-dimensions in Cartesian coordinates.
• Add forces and resolve forces into rectangular components.
• Explain the idea of force equilibrium and Newton’s first law of motion, and determine when a system of forces is in equilibrium.
• Isolate an appropriate particle in a physical system and develop a free-body diagram for the system of forces acting on the particle.
• Do the above for both forces in a plane (2-D) or in space (3-D).

2. Equivalent Force Systems: Rigid Bodies

• Explain the ideas of a rigid body and its connection to a particle, the moment of a force about a point, the moment of a force about an axis, a couple, and external and internal forces.
• Compute the moment of a force about a point using formal 3-D vector multiplication (cross product), and identify the simplification that results in two-dimensions.
• Compute the moment of a force about an axis using formal vector multiplication in three-dimensions (dot product and mixed triple product), and identify the simplification that results in two-dimensions.
• Compute the rectangular components of a moment.
• Compute the moment of a couple, identify equivalent couples, and add couples.
• Resolve a given force (and system of forces) into an equivalent force-couple system.

3. Equilibrium of Rigid Bodies in Two- and Three-Dimensions

• Identify when a force system acting on a rigid body is in equilibrium and express this in both vector and component form.
• Identify equivalent force/moment systems.
• Isolate an appropriate free body of a physical system and develop a free-body diagram for the system of forces and moments acting on the body. Apply this to such elements as pulleys, hinges, beams, cables, bearings, etc.
• Classify the types of reaction supports and connections for two- and three-dimensional structures (pinned, built-in, etc.).
• Write and solve the equilibrium equations for rigid body in two- and three-dimensions.
• Classify two- and three-dimensional rigid body systems as either statically determinant or indeterminate.
• Identify bodies acted upon by only two or three forces and identify their properties.

4. Analysis of Truss and Frame Structures

• Define truss, frame, and machine structures and describe the various load, joint, and boundary conditions that are possible.
• Draw free body diagrams of two-dimensional truss members and joints.
• Compute the forces in two-dimensional truss members using the methods of joints and sections.
• Identify multi-force members in frame structures and draw free body diagrams of two-dimensional frame members and joints.
• Compute the forces in two-dimensional frame members by dismantling the structure and analyzing each member of the structure as a two-force or a multi-force member.
• Identify the input and output forces of a machine and analyze it using the same procedure as for a frame.
• Identify short cuts that can be taken in the analysis of truss and frame structures.

5. Distributed Force Systems

• Define the terms: center of gravity, centroid, and first moment of an area or line.
• Compute the center of gravity of a two-dimensional body, the centroid of an area and a line, and the first moments of an area about an axis.
• Take advantage of symmetry in these computations.
• Compute the center of gravity of composite bodies.
• Compute concentrated loads that are equivalent to a specified distributed load.

6. Friction

• Define static and kinetic friction, friction force, the coefficients of static and kinetic friction, and the angles of static and kinetic friction.
• Draw free body diagrams of each part in a frictional system.
• Analyze problems of friction for cases when motion is and is not impending.

7. ITLL Experiments (carried out throughout the semester)

• Perform experiments in the ITLL to confirm theoretical work. Applications are to two- and three-dimensional force, moment, and truss analysis.
• Become familiar with load cells, Wheatstone bridge circuits for strain measurement, and other measurement equipment.
• Perform experiments in the context of design and optimization.

Catalog Description

Statics of Particles; Equivalent Force Systems: Rigid Bodies; Equilibrium of Rigid Bodies in Two- and Three-Dimensions; Analysis of Truss and Frame Structures; Distributed Force Systems; Friction. Lectures and homework assignments involve computer work and hands-on laboratory work in the ITLL, documented by written reports.

Prerequisites: APPM 1360.