# Engineering Mechanics, Statics

EGR 215## Course Description

Prerequisite: MTH 261 and PHY 211 both with a grade of "C" or better. Develops skill in analyzing machine elements and structures, which are in static equilibrium. Solves forces and moments in 2D and 3D problems using vector calculus, integration, and algebra/trigonometry techniques. Includes concepts of centroids and moments of inertia and applies to mechanical linkages, disks and shafts, beams in bending, screw threads, trusses, frames, and vehicles. (45-0)

## Outcomes and Objectives

### Demonstrate logic reasoning and the efficient use of tools to solve statics problems.

#### Objectives:

- Formulate a step-by-step approach to the complete understanding of the problem and its final solution.
- Develop a Free Body Diagram (FBD) of the component studied such as robotics and automation.
- Identify all pertinent variable son the FBD, or on sketches.
- Extract from the engineering mechanics body of knowledge the theory and formulas relating the variables of the problem in question.
- Make assumptions about variables not specified.
- Solve the problem, obtaining a single answer or a range of acceptable answers, using a hand calculator or a computer.

### Analyze friction problems.

#### Objectives:

- Differentiate between coefficient of friction and angle of friction.
- Calculate forces in wedge problems.
- Calculate forces or dimensions in screw thread problems.
- Analyze friction in journal bearings.
- Analyze friction in thrust bearings.
- Calculate forces in belt drives.

### Manipulate vectors in 2D and 3D space as methodology for setting up a problem forultimate solution.

#### Objectives:

- Differentiate between scalars and vectors.
- Calculate the components of a vector with respect to Cartesian Coordinates in 2D or 3D space.
- Find the resultant vector from given components with respect to Cartesian Coordinates in 2D or 3D space.
- Calculate the dot product of 2 vectors in space.
- Calculate the cross product of 2 vectors in space.
- Calculate the mixed triple product of 3 vectors in space.

### Analyze a system of forces applied at a point on an object in 2D or 3D space.

#### Objectives:

- Develop a FBD of a system of forces, showing all forces as vectors.
- Solve for an unknown force using the conditions of equilibrium.
- Calculate unknown forces of a 2D system using components.
- Calculate unknown forces of a 3D system using vector manipulation.

### Analyze moments or couples applied on an object.

#### Objectives:

- Describe the moment vector in 3D space.
- Calculate the moment of a force applied at a distance from the point in question.
- Determine the moment of a force about a line in 3D space.
- Calculate the moment of a couple.
- Develop equivalent systems of forces and couples.

### Analyze an object known to be in equilibrium.

#### Objectives:

- Calculate unknown forces of an object in equilibrium.
- Identify redundant supports in a statically-indeterminate object.
- Identify improper supports in a statically-indeterminate object.
- Identify 2-Force or 3-Force members in a system of objects to simplify the solution.

### Analyze structures or a system of members in equilibrium.

#### Objectives:

- Calculate the force and its sense (compression or tension) of a specified member of a 2D truss by the method of joints.
- Calculate the force and its sense of a specified member of a 2D truss by the method of sections.
- Calculate the force in the members of a 3D truss.
- Calculate unknown forces or dimensions of a frame or machine known to be n equilibrium.

### Find the centroid or center of mass of an object.

#### Objectives:

- Calculate the centroid of a system of line segments.
- Calculate the centroid of an area by considering it as a composite of simple geometric shapes.
- Calculate the centroid of an area using the integration method.
- Calculate the center of mass of a 3D object using the composite method.
- Calculate the center of mass of a 3D object using the integration method.
- Calculate the surface area of a body of revolution using the Pappus Theorem.

### Find the moment of inertia of an object.

#### Objectives:

- Find the moment of inertia of an area bout its principle axes.
- Find the moment of inertia of an area about any axis in space using the parallel-axis theorem.
- Find the moment of inertia or mass moment of inertia by the method of integration.
- Identify what kind of engineering problems make use of the moment of inertia or the mass moment of inertia.

### Analyze systems, which have applied distributed forces.

#### Objectives:

- Calculate the internal moment at some point in a beam in bending.
- Calculate the internal shear forces in a beam in bending.
- Develop the Shear Force Diagram of a beam in bending.
- Develop the Bending Moment Diagram of a beam in bending.
- Determine the force on a body exposed to liquid static pressure.