Portland Community College | Portland, Oregon

This course is required for all students in the Civil and Mechanical Engineering Technology program, and is a prerequisite for many other CMET courses. Students must take this course while also taking CMET 111 Engineering Technology Orientation. Full-time students will generally take this course in their first term of the program.

The student will be able to:

1. Analyze forces on rigid bodies in equilibrium.
2. Communicate analysis and results clearly: orally, in writing, and through diagrams and calculations.
3. Work in small groups with individuals of diverse cultural backgrounds.
4. Apply knowledge gained in this course in subsequent engineering courses such as Strength of Materials, Dynamics, Fluid Mechanics, and many others.

Individual, small group, and full class discussion; homework problems; examinations; and small group problem-solving sessions may be used to assess outcomes.
Lecture, homework, and in-class group activities will be coordinated.
Specific evaluation procedures will be defined during the first week of class. In general, grading will depend on weekly tests, homework, class participation, and a comprehensive final exam.

1. Analysis of an engineering problem begins with a simplified model of the actual situation.
2. A large complex problem consists of many inter-related smaller problems which must be solved in a logical order.
3. Solution of an engineering problem in not useful unless communicated clearly and completely.
4. A complete and correct free-body diagram is necessary for analysis of any equilibrium problem.
5. There is often more than one correct approach to the solution of an engineering problem. Sharing ideas with others will often lead to the most efficient or clearest solution.

CONTENT:
1. Vector operations in two dimensions, using semi-graphical methods (parallelogram law and triangle rule).
            a. Find resultant of two vectors.
            b. Resolve a vector into two components along any two axes.
            c. Solve other problems involving a resultant vector and two components.
2. Vector operations in two dimensions, using two perpendicular components.
            a. Resolve a vector into two components along two perpendicular axes.
            b. Find resultant of two or more vectors.
3. Equilibrium of a particle in two dimensions:
            a. Develop an understanding of Newton’s first law of motion.
            b. Construct free-body diagram of a particle in equlibrium.
            c. Recognize statically determinate and indeterminate particles.
            d. Solve for unknown forces by using an equilibrium force triangle.
            e. Write and solve equilibrium equations using summations of forces.
4. Moment of a force about a point in two dimensions:
            a. Calculate the moment of a force about a point.
            b. Use Varignon’s theorem to calculate a moment.
            c. Use the principle of transmissibility of forces.
            d. Calculate the moment of a couple.
            e. Replace a system of forces by an equivalent force and couple moment at a given point.
5. Equilibrium of a rigid body in two dimensions:
            a. Construct the free-body diagram of a rigid body in equilibrium.
            b. Recognize statically determinate and indeterminate rigid bodies.
            c. Write and solve equilibrium equations using summation of moments about a point, and summation of forces.
6. Internal forces: find internal force and bending moment in a member of a structure.
7. Analysis of structures in two dimensions:
            a. Trusses: use the method of joints and the method of sections to solve for the internal forces in members of a truss. Identify                             zero-force members of a truss.
            b. Frames and machines: solve for the forces exerted on one member of a frame or machine by another member.
8. Centroids and centers of gravity
            a. Calculate the centroid of a composite area.
            b. Calculate the centroid and center of gravity of a composite solid.
9. Dry friction on two-dimensional rigid bodies:
            a. Define and use the laws of dry friction.
            b. Solve problems involving particles and rigid bodies with frictional surfaces: in equilibrium, in accelerated motion, at impending                     sliding, at impending tipping.
10. Vector algebra operations:
            a. Express a three-dimensional vector in Cartesian vector notation.
            b. Find the dot-product of two vectors with and without using pre-programmed calculator operations.
            c. Find the cross-product of two vectors with and without using pre-programmed calculator operations.
11. Three dimensional forces:
            a. Find the resultant of several forces.
            b. Resolve a force into components parallel and perpendicular to a reference axis, using a dot-product.
            c. Find the angle between two vectors, using a dot-product.
12. Equilibrium of a particle in three dimensions:
            a. Construct the free-body diagram of a particle in equlibrium.
            b. Write and solve equilibrium equations using summation of forces, employing vector algebra operations.
13. Moment of a force about a point in three dimensions:
            a. Find the moment of a force about a point using a cross-product.
            b. Calculate the moment of a couple.
            c. Replace a system of forces by an equivalent force and couple moment at a given point.
14. Equilibrium of a rigid body in three dimensions:
            a. Construct the free-body diagram of a rigid body in equilibrium.
            b. Recognize statically determinate and indeterminate rigid bodies.
            c. Write and solve equilibrium equations using summation of moments about a point, summation of moments about a line, and/or                 summation of forces, employing vector algebra operations.
15. Graphical calculus and beam diagrams:
            a. Define and use the laws of graphical calculus.
            b. Sketch the loading diagram for a beam with transverse loads.
            c. Use graphical calculus to sketch the internal shearing force diagram and calculate shear at any point and maximum shearing                     force.
            d. Use graphical calculus to sketch the internal bending moment diagram and calculate moment at any point and maximum                             bending moment.
COMPETENCIES AND SKILLS:
The student will be able to:

1. Draw a free-body diagram of an object, group of connected objects, or part of an object.
2. Calculate the support reactions on a two or three-dimensional rigid body.
3. Calculate the forces exerted on one member of a structure by another.
4. Use a scientific calculator to solve algebraic and trigonometric equations.
5. Communicate analysis and results clearly: orally, in writing, and through diagrams and calculations.