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# ENG 210 - Engineering Mechanics: Statics

3 Credits, 3 Contact Hours
3 lecture periods 0 lab periods

Engineering analysis of static mechanical systems. Includes statics of particles, rigid bodies and equilibrium, distributed forces, analysis of structure, forces in beams and cables, friction, and moments of inertia.

Prerequisite(s): MAT 231  and PHY 210IN .

Course Learning Outcomes
1. Demonstrate mastery to construct free-body diagrams for particles which are acted on by concurrent force systems.
2. Demonstrate the ability to construct free-body diagrams of rigid boy and identify reactions for different types  of supports.
3. Demonstrate the ability to compute the forces in the members of statically determinate trusses using the method of joints and the method of sections.
4. Demonstrate the ability to compute the forces and moments acting on the members of statically determinate frames and machines.
5. Demonstrate the ability to compute the shear forces and bending moments in a beam and draw shear force and bending moment diagrams.
6. Demonstrate the ability to compute the moment of inertia or second moment of area for complex cross sections.

Performance Objectives:
1.         Apply the appropriate units of measurement to statics problems and check the dimensional integrity of their solutions.

2.         Define force and moment vectors and obtain components and resultants.

3.         Apply scalar and vector algebra to the principles of statics.

4.         Construct free-body diagrams for bodies which are acted on by concurrent force systems.

5.         Specify equilibrium equations and conditions in two and three dimensions.

6.         Compute unknown forces, resultants, weights, angles, etc. for bodies which are acted on by concurrent force systems (2D or 3D) using ∑Fx=0, ∑Fy=0, and ∑Fz=0.

7.         Compute the moment produced by a system of forces about a specified point for 2D problems.

8.         Compute the moment produced by a system of forces about a specified point for 3D problems.

9.         Compute the reaction forces and moments at supports and connections for statically determinate bodies using ∑Fx=0, ∑Fy=0 and ∑M=0.

10.      Apply the principle of transmissibility to the conditions of equilibrium of a rigid body.

11.      Compute the moment of force about given axis, which pass through the origin of chosen rectangular coordinates.

12.      Compute the moment of force about given axis, which doesn’t pass through the origin of chosen rectangular coordinates.

13.      Calculate the angle formed by two given vectors.

14.      Apply properties of couples to solve the problems in statics.

15.      Replace a force with an equivalent force-couple system at a specified point.

16.      Replace a force with a force-couple system with a single equivalent force.

17.      Move a force-couple system from point A to point B.

18.      Reduce a given force system to a single force.

19.      Reduce a given force system to a wrench.

20.      Construct free-body diagrams of rigid body; identify reactions for different type of supports.

21.      Construct free-body diagrams for two-force body and three-force rigid bodies.

22.      Compute the location of the centroid for complex areas using tabulated solutions for the centroids of simple areas (rectangles, semicircles, triangles, etc.); calculate the first moment of area.

23.      Compute the location of the centroid of an area bounded by analytical curves.

24.      Compute the resultant and line of action for a distributed force applied to a beam.

25.      Compute the resultant of the pressure forces on submerged surfaces.

26.      Compute the forces in the members of statically determinate trusses using the method of joints and the method of sections.

27.      Compute the forces and moments acting on the members of statically determinate frames and machines.

28.      Compute the shear forces and bending moments in a beam.

29.      Draw shear force and bending moment diagrams.

30.      Compute the friction forces; apply laws of dry friction.

31.      Construct free-body diagrams for systems with friction forces.

32.      Compute the moment of inertia or second moment of area (I) for complex cross sections using tabulated solutions for simple areas (rectangles, semicircles, triangles, etc.).

Outline:
1. Statics of Particles
1. Force on a particle/resultant of two forces
2. Vectors
4. Resultant of several concurrent forces
5. Resolution of a force into components
6. Rectangular components of force unit vectors
7. Addition of forces by summing X and Y components
8. Equilibrium of a particle
9. Free body diagrams
10. Rectangular components of a force in space
11. Addition of concurrent forces in space
12. Equilibrium of a particle in space
1. Rigid Bodies: Equivalent Systems of Forces
1. External and internal forces
2. Principle of transmissibility
3. Vector product of two vectors
4. Vector products expressed in terms of rectangular components
5. Moment of a force about a point
6. Varignon’s theorem
7. Rectangular components of the moment of a rorce
8. Scalar product of two vectors
9. Mixed triple product of three vectors
10. Moment of a force about a given axis
11. Moment of a couple
12. Equivalent couples
14. Reduction of a system of forces to one force and one couple
15. Equivalent system of forces
16. Further reduction of a system of forces
17. Reduction of a system of forces to a wrench
2. Equilibrium of Rigid Bodies
1. Reactions at supports and connections for two dimensional structure
2. Equilibrium of a rigid body in two dimensions
3. Statically indeterminate reactions
4. Equilibrium of a two-force body
5. Equilibrium of a three-force body
6. Equilibrium of a rigid body in three dimensions
7. Reactions at supports and connections for three dimensional structure
3. Distributed Forces: Centroids and Centers of Gravity
1. Center of gravity of a two dimensional body
2. Centroids of areas and lines
3. First moments of areas and lines
4. Centroids of composite plates and wires
5. Centroids of areas bounded by analytical curves
6. Theorems of Pappus-Guldinus
8. Forces on submerged surfaces
4. Analysis of Structure
1. Simple trusses
2. Analysis of trusses by method of joints
3. Analysis of trusses by method of sections
4. Analysis of frames
5. Analysis of frames with multiforce members
6. Analysis of frames which cease to be rigid when detached from their supports
7. Analysis of machines
5. Forces in Beams and Cables
1. Internal forces in members