Professor in Agricultural and Biomedical Engineering
 

University of Puerto Rico Mayagüez Campus
College of Engineering
General Engineering Department   
                   

Related Web sites 

http://www.upr.edu/
http://www.uprm.edu/
http:/ing.uprm.edu/
http://ge.uprm.edu/
http://www.ece.uprm.edu/inelicom/index.php
http://www.ece.uprm.edu/~m_goyal/home.htm

Contact:    m_goyal@ece.uprm.edu
 

|| Student Projects in Engineering Biomechanics: Fluid Mechanics,
  Mechanics of Materials and Statics  ||

DOWNLOAD FREE BOOK ON
 "RIEGO POR GOTEO"

For list of all courses offered by General Engineering Department, you may refer to: http://ge.uprm.edu/

 INGE3031: STATICS

1. General Information: 

Course Number:        INGE 3031 (GEEG 3031)
Course Title:             Engineering Mechanics: Statics                                                                      
Credit Hours:             3

2. Course Catalog Description:

Analysis of force systems, the laws of equilibrium, analysis of simple structures, distributed loads, friction, centroids and moments of inertia.

3. Pre-requisites:

MATE 3031 (MATH 3031) or MATE 3144 (MATH 3144) or MATE 3183 (MATH 3183)

4. Eligibility:

This course is open to chemical, civil and surveying, industrial, and mechanical engineering students.

5. Textbook and other Required Material:

Vector Mechanics for Engineers, F. P. Beer and E.R. Johnston, 7th Edition, McGraw-Hill, 2003.

References:

Engineering Mechanics (Statics), R. C. Hibbeler, 8^th Ed. Prentice Hall, 1998.        
Engineering Mechanics (Statics), Pytel Andrew, Kiusalaas Jaan.  NY, 2^nd Edition, NY: Harper Collins 1998.

6. Course Objectives and Student Learning Outcomes:

Upon successful completion of this course the student shall be able to:

• Describe position, forces, and moments in terms of vector forms in two and three dimensions.
• Determine rectangular and nonrectangular components of a force.
• Determine the resultant of a force system including distributed forces.
• Simplify systems of forces and moments to equivalent systems.
• Draw complete free-body diagrams and write appropriate equilibrium equations from the free-body diagram, including the support reactions on a structure.
• Apply the concepts of equilibrium to evaluate forces in trusses, frames and machines.
• Determine the internal forces in a structure.
• Analyze systems that include frictional forces.
• Calculate centers of gravity and centroids, and moments of inertia .

The objectives of the course will be assessed using exams, quizzes and short assignments.  Other assessment tools such as special reports and projects could be used at the professor’s discretion.

7. Department/Campus Policies:

Please refer to the Bulletin of Information for Undergraduate Studies.

8. Topics Covered:

Chapter 1:   General  Principles 

Chapter 2:   Concurrent Force Systems

      - Classification of forces ; Principle of transmissibility ;  Resolution of forces into components in various coordinate systems

Chapter 2:     Equilibrium of Particles              

       - Equations of Equilibrium ;  Free Body Diagrams

Chapter 3:  Equivalent Force and Moment Systems                                           

       - Moments and couples; Resolution of a force into a force and couple; Simplification of a force system: Resultants

Chapter 5:  Center of Gravity and Centroids

       - Centroids of volume, areas and lines; Centroids of composite bodies;   Distributed        Forces                                                                                

Chapter 4: Equilibrium of Rigid Bodies                                                             

        - Equations of Equilibrium;  Free Body Diagrams

Chapter 6:  Analysis of Engineering Structures                                                  

        - Analysis of Trusses using the method of joints and method of sections; Frames and machines.

Chapter 7:  Internal Forces                                                                              

        - Axial force and torque in bars and shafts;  Axial force, shear force and bending moments in multiple forced members

Chapter 9: Second Moments of Area and Moment of Inertia                              

        - Parallel axis theorem;  Method of integration; Composite area

Chapter 8: Friction  

        - Dry friction

||  Back to top ||

 INGE3032: DYNAMICS 

1. General Information:

Course Number:           INGE 3032 (GEEG 3032)                                                                         
Course Title:                 Engineering Mechanics: Dynamics                                                             
Credit hours:                 3

2. Course Catalog Description:

Kinematics of particles and rigid bodies: relations among force, mass and acceleration; kinetics of particles and rigid bodies; work and energy; impulse and momentum.

3. Pre-requisites:

INGE 3031 (GEEG 3031) and (FISI 3161 (PHCS 3161) or FISI 3171 (PHCS 3171).

4. Eligibility:

This course is opent to all engineering students.

5. Textbook and other Required Material:

Vector Mechanics for Engineers, F. P. Beer and E.R. Johnston, 7th Edition, McGraw-Hill, 2003.

References:

Engineering Mechanics (Dynamics), R. C. Hibbeler, 8^th Ed. Prentice Hall, 1998.                     
Engineering Mechanics (Dynamics), Pytel Andrew, Kiusalaas Jaan.  NY, 2^nd Edition, 
NY: Harper Collins 1998.

6. Course Objectives and Student Learning Outcomes:

Upon successful completion of this course the student shall be able to:

• Determine the kinematic relationships between position, velocity, and acceleration for two-dimensional motion of systems of particles and rigid bodies.
• Calculate the velocity and acceleration of a particle in rectangular, polar and normal/tangential coordinate systems.
• Relate the velocity and acceleration of points in a rigid body using the absolute and relative motion approaches.
• Determine the mass moments of inertia of rigid bodies.
• Draw free body and kinetic diagrams for particles and rigid bodies.
• Apply Newton's second law in two dimensions.
• Analyze the two dimensional motion of particles and rigid bodies using: principle of work and energy; impulse and momentum, both linear and angular.

The objectives of the course will be assessed using exams, quizzes and short assignments.  Other assessment tools such as special reports and projects could be used at the professor’s discretion.

7.Department/Campus Policies:

Please refer to the Bulletin of Information for Undergraduate Studies.

8. Topics Covered:

Chapter 11: Kinematics of Particles                                                                  

Position, Velocity and Acceleration; Rectilinear Motion; Curvilinear Motion;   Relative Motion.

Chapter 12:  Kinetics of Particles: Newton’s Laws                                     

Equations of Motion for a Single Particle and a System of Particles; Rectilinear Motion; Curvilinear Motion.

Chapter 13:  Work and Energy Method for Particles                                         

      Principle of Work and Energy;   Power and Efficiency; Conservation of Energy

Chapter 14: Impulse and Momentum for Particles                                      

Chapter 15:  Kinematics of Rigid Bodies      

Translation and Rotation;   General Plane Motion.

Chapter 16: Kinetics of Rigid Bodies      

      Moment of Inertia; Equations of Motion; Translation and Rotation; General Plane Motion.

Chapter 17:   Work and Energy Methods for Rigid Bodies in Plane Motion  

||  Back to top ||

 INGE3035: STATICS/DYNAMICS 

1. General Information:

Course Number:            INGE 3035 (GEEG 3035)                                                                                                                    
Course Title:                  Engineering Mechanics: Statics and Dynamics                                                                           
Credit Hours:                 3

2. Course Catalog Description:

Analysis of force systems; the laws of equilibrium; friction; centroids and moments of inertia. Kinematics and dynamics of particles and rigid bodies.

3. Pre-requisites: MATE 3031( MATH 3031) or MATE 3144 (MATH 3144) or MATE 3183 (MATH 3183);

Co-requisite: FISI 3161 (PHCS 3161) or FISI 3171 (PHCS 3171)

4. Eligibility:

This course is open to electrical and computer engineering students.

5. Textbook and other Required Material:

Vector Mechanics for Engineers, F. P. Beer and E.R. Johnston, 7th Edition, McGraw-Hill, 2003.

References:

Engineering Mechanics (Statics & Dynamics), R.C. Hibbeler, 8^th Ed. Prentice Hall, 1998.                         
Engineering Mechanics (Statics & Dynamics), Pytel Andrew, Kiusalaas Jaan.  NY, 2^nd Edition, 
NY: Harper Collins 1998.

6. Course Objectives and Student Learning Outcomes:

Upon successful completion of  this course the student shall be able to:

• Describe position, forces, and moments in terms of vector forms in two and three dimensions.
• Determine rectangular and nonrectangular components of a force.
• Determine the resultant of a force system including distributed forces.
• Simplify systems of  forces and moments to equivalent systems.
• Draw free body and kinetic diagrams for particles and rigid bodies.
• Compute support reactions on a structure.
• Analyze systems that include frictional forces.
• Calculate centers of gravity and centroids.
• Determine the kinematics relationships between position, velocity, and acceleration for two-dimensional motion of systems of particles and rigid bodies.
• Calculate the velocity and acceleration of a particle in rectangular, and normal/tangential coordinate systems.
• Relate the velocity and acceleration of points in a rigid body using the relative motion approach.
• Determine the mass moments of inertia of rigid bodies.
• Apply Newton's second law in two dimensions.
• Analyze the two dimensional motion of particles and rigid bodies using the work and energy principle.

The objectives of the course will be assessed using exams, quizzes and short assignments.  Other assessment tools such as special reports and projects could be used at the professor’s discretion.

7. Department/Campus Policies:

Please refer to the Bulletin of Information for Undergraduate Studies.

8. Topics Covered:

STATICS

Chapter 1:  General Principles                                                                    

Chapter 2: Concurrent Force Systems                                                                 

       Forces and their characteristics;  Resultant of Concurrent Forces; Resolution of a Force into Components.  

Chapter 2:   Equilibrium of Particles    

       Equations of Equilibrium; Free Body Diagram                                                 

Chapter 3: Equivalent Force and Moment Systems                                                

       Moments and Couples;   Resolution of a Force into a Force and a Couple;   Simplification of a Force System.

Chapter 5: Distributed Forces, Centroids and Center of Gravity                    

       Center of Mass and Center of Gravity; Centroids of Volumes, Areas and Lines;  Centroids of Composite Bodies;   Distributed Loads on Beams.                                                            

Chapter 4: Equilibrium of Rigid Bodies                                                               

       Free Body Diagrams;   Equilibrium in Two Dimensions.

DYNAMICS:

Chapter 11: Kinematics of Particles                                                                    

       Position, Velocity, and Acceleration;  Rectilinear and Curvilinear Motion;  Relative Motion.

Chapter 12: Kinetics of Particles: Newton's Laws                                         

       Equation of Motion.

Chapter 13: Kinetics of Particles: Work and Energy Methods                                 

       Work of a Force;   Principle of Work and Energy.

Chapter 15: Kinematics of Rigid Bodies                                                               

       Translation; Rotation about a Fixed Axis; General Plane Motion.                       

Chapter 16: Kinetics of Rigid Bodies: Newton's Laws laws                        

       Equations for Plane Motion; Moments of Inertia; Translation, Rotation and General Plane.                                             

Chapter 17: Kinetics of Rigid Bodies: Work and Energy Methods                        

       Work of Forces and Couples Acting on Rigid Bodies;  Kinetic Energy of Rigid Bodies in Plane Motion;   Principle of Work and Energy.

||  Back to top ||

 INGE4015: FLUID MECHANICS 

1. General Information:

Course Number:           INGE 4015 (GEEG 4015)                                                                         
Course Title:                Fluid Mechanics                                                                                         
Credit Hours:               3

2. Course Catalog Description:

Elements of mechanics of fluids and fluid statics. Development of the fundamental equations of fluid mechanics and it applications. Introduction to dimensional analysis and similitude.  Motion of ideal and real fluids including internal and external viscous flows. Introduction to the use of hydraulic machinery.

3. Pre-requisites:

INGE 3032 (GEEG 3032) and MATE 3063 (MATH 3063) or MATE 3185 (MATH 3185)

4. Textbook and other Required Material:

Fluid Mechanics, White F.M., 4^th Ed., 1999, McGraw-Hill.

References:

Mechanics of Fluids, Potter M.C., Wiggert D.C. Prentice-Hall, Inc. (1997)
Engineering Fluid Mechanics, Robertson, J.A., Crowe, C.T., , 6^th Ed., Wiley & Sons, 1997. 
Introduction to Fluid Mechanics, Fox, R. and MacDonalds, A., 4^th., Ed, Wiley and Sons Inc., 1999.      
Fluid Flow, Sabersky, R., Acosta, A. and Hauptmann, E., 3 ^th  Ed., MacMillan Pub. Co., 1999. 1999.       
Fluid Mechanism ,Streeter, V., Wylie, B. and Bedford, K., , 9^th Ed., McGraw-Hill, 1998.

5. Course Objectives and Student Learning Outcomes:

The Fluid Mechanics course aims at the following educational objectives:

• Knowledge and understanding of the definitions of the most important fluid properties in engineering applications.
• Develop understanding and providing analytical tools to solve problems of forces on submerged surfaces.
• Develop basic understanding of the fundamental equations of fluid mechanics.
• Apply the fundamental equations of fluid mechanics to solve fluid flow problems including: Analysis and design of simple pipe systems; analysis of hydrodynamic forces in submerged objects; introduction of turbomachinery in fluid systems.

6. Department / Campus Policies

Please refer to the Bulletin of Information for Undergraduate Studies.

7. Topics Covered:

Basic Definitions and Fluid Properties

Fluid Statics

Hydrostatic Forces on Submerged Surfaces

Fluids in Motion

      Dynamics of Fluid Particles;  Bernoulli’s Equation

Fundamental Equations

      System and Control Volume Definitions; Reynolds Transport Theorem; Mass Conservation; The Energy Equation; Linear Momentum Equation; Angular Momentum Equation

Dimensional Analysis and Similitude

Internal Flows

      Developed FlowLaminar;  Flow in Pipes; Turbulent Flow in Pipes; Energy Losses in Pipes; Pipe Systems with Pumps and Turbines;  Uniform Turbulent Flow in Open Channels

External Flows

      Drag and Lift Forces; Flow Separation; Laminar Boundary Layer Flow; Turbulent Boundary Layer Flow; Von Karman Solution of Boundary Layer Flows;

Compressible Flow

      Isentropic Flow

Turbomachinery

||  Back to top ||

             INGE4016: FLUID MECHANICS LABORATORY 

1. General Information:

Course Number:                       INGE 4016 (GEEG 4016)                                                         
Course Title:                             Fluid Mechanics Laboratory                                                         
Credit Hours:                            1

2. Course Catalog Description:

Laboratory work supplementing classroom instruction in mechanics of fluid phenomena, measuring devices and techniques, and the testing of fluid machinery.

3. Co-requisites:

INGE 4015 (GEEG 4015)

4. Textbooks and other Required Material:

Laboratory Manual by Professor Walter Silva.

5. Course Objectives and Student Learning Outcomes:

1.  Experimentation, observation, and analysis of physical phenomena in Fluid Mechanics.

2. Training students in measurement of the physical properties of fluids

3. Provide experience in collection, analysis, interpretation, and presentation of experimental data.  Precision analysis and equipment limitations.

6. Department / Campus Policies

Please refer to the Bulletin of Information for Undergraduate Studies.

7. Topics Covered:

        Hydrostatic forces on submerged surfaces.

        Error analysis and uncertainty in experimental measurements.

        Discharge and flow velocity measurements.

        Friction losses in closed conduits.

        Boundary layer flow.

        Drag forces in submerged bodies.

        Hydraulic turbomachinery (pumps/turbines).

        Sharp crested weirs.

        Isentropic flow in nozzles.

        Hydraulic jump.

||  Back to top ||

                  INGE4011: MECHANICS OF MATERIALS I 

INGE 3031 (GEEG 3031) and MATE 3032 (MATH 3032) or MATE 3184 (MATH 3184) and a minimum of third year enrollment in a discipline.

Mechanics of Materials , James M. Gere, 5th ed., 2001, Brooks/Cole Thomson Learning

Mechanics of Materials, R.C. Hibbeler, 3rd. Ed.,1997, McMillan Publishing Co. 
Mechanics of Materials , F.P. Beer & E.R.Johnston, 2nd. Ed., 1992, McGraw-Hill, Inc.
Mechanics of Materials, by R.R. Craig, 1st. Ed., 1996, John Wiley and Sons 
Mechanics of Materials, - by F. Riley & L. Zachary - First Edition, 1989, John Wiley and Sons.

Develop a thorough understanding of the relations between the external loads applied to a non-rigid body and the  stress-strains produced in the body.

· Define the concepts of stress, strain due to elastic and plastic deformations.

· Identify the mechanical properties of materials.

· Apply Hooke’s law and know its limitations.

· Calculate stress (normal and shear) in a structure component loaded in various ways.

· Analyze axially loaded members.

· Use stress concentration factors to find stresses in axially loaded members.

· Analyze deformations in structures due to thermal effects.

· Determine stresses and/or strains in torsional member.

· Write equations of shear and bending moment in terms of position and draw the corresponding diagrams for beams subjected to some combination of concentrated loads, distributed loads, and moments.

· Calculate normal and shearing stresses in beams.

· Design members using strength criteria.

The objectives of the course will be assessed using exams, quizzes and short assignments. Other assessment tools such as special reports and projects could be used at the professor’s discretion.

S. No.      Title Articles with Suggested Problems

4              Allowable Stresses and Allowable Loads:  1.6,1.7,1.8 1.6-2,3,9,1.7- 3,7,10, 1.8-1,2,4,12

19           Relationships Between Loads, Shear Forces, and Bending Moments:    4.4

20           Shear-Force and Bending-Moment Diagrams:  4.5 4.5-1,2,4,5,7,8,9,10,12, 15,18,
               21 through 30

Analysis of statically determinate and indeterminate beams; three moments theorem; stresses due to combined loads; column theory, dynamic loads.

Mechanics of Materials , James M. Gere, 5th ed., 2001, Brooks/Cole Thomson Learning

Mechanics of Materials, R.C. Hibbeler, 3rd. Ed.,1997, McMillan Publishing Co. 
Mechanics of Materials , F.P. Beer & E.R.Johnston, 2nd. Ed., 1992,McGraw-Hill, 
Mechanics of Materials, by R.R. Craig, 1st. Ed., 1996, John Wiley and Sons 
Mechanics of Materials, - by F. Riley & L. Zachary - First Edition, 1989, John Wiley and Sons.

Develop a thorough understanding of the analysis of plane stress-strain of bodies, deflection of determinate and indeterminate beams, stresses due to combined loading, and column theory.

· Calculate the principal stress and strains in a structure loaded in various ways.

· Solve problems using stress transformation and Mohr’s circle.

· Apply Hooke’s law for plane stress and plane strain.

· Calculate stresses in thin-walled spherical or cylindrical pressure vessels.

· Calculate the stresses produced by combined axial, bending and torsional loads.

· Calculate the deflections of statically determinate beams, using the elementary differential equations of the deflection curve, superposition, moment-area method, energy methods, and   Castigliano’s theorem.

· Calculate the reactions and deflections of statically indeterminate beams, using the solution of the elementary differential equation of the deflection curve, and superposition.

· Apply Euler’s equation to solve buckling and stability problems for various end conditions.

· Analyze columns subjected to eccentric axial loads.

The objectives of the course will be assessed using exams, quizzes and short assignments. Other assessment tools such as special reports and projects could be used at the professor’s discretion.

S. No.   Title Articles with suggested with problems

3             Mohr's Circle for Plane Stress:  7.4 7.4-1, 4, 6, 8, 9, 19

12           Deflection by Integration of Bending Moment Equation: 9.3 9.3-1, 4,    5, 9, 11, 13,18-19

18           Types of Statically Indeterminate Beams: Analysis by the Differential Equations of
               the Deflection Curve: 10.1, 2,3 10.3-1, 2,5,6,9

 Biofluid Dynamics of Human Body Systems (In preparation)

Principles of Biomedical Engineering (In preparation)

|| Student Projects in Engineering Biomechanics: Fluid Mechanics,
  Mechanics of Materials and Statics  ||
||  Biofluid Dynamics   ||  Education/employment  ||   Teaching  || 
||  Awards  ||  Societies || University of Puerto Rico, Mayaguez ||
||  Courses ||Microirrigation ||