ChabotCollege

Course Outline for Engineering 36, Page 1

Fall 2010

ChabotCollegeFall 2010

Course Outline for Engineering 36

ENGINEERING MECHANICS - STATICS

Catalog Description:

36–Engineering Mechanics - Statics3 units

Force systems under equilibrium conditions; vector properties of forces, moments, couples, and resultants; rigid body structures; hydrostatics; shear and bending-moment diagrams; friction; centroids; area/mass moments of inertia. Graphical, algebraic, and numerical (computer) solutions of vector mechanics problems. Prerequisite: Physics 4A and Engineering 25 (both completed with a grade of "C" or higher). Strongly recommended: Mathematics 2 (concurrent enrollment encouraged). 2 hours lecture, 3 hours laboratory.
[Typical contact hours: lecture 35, laboratory 52.5]

Prerequisite Skills

  1. analyze and solve a variety of problems often using calculus in topics such as:
  1. addition, subtraction, dot product and cross product of vectors;
  2. linear and rotational kinematics;
  3. dynamics;
  4. momentum;
  5. work, kinetic energy, and potential energy;
  6. rotational kinematics and dynamics;
  7. statics;
  8. gravitation;
  9. oscillations;
  1. operate standard laboratory equipment;
  2. analyze laboratory data;
  3. write comprehensive laboratory reports.
  4. analyze engineering/science word problems to formulate a mathematical model of the problem;
  5. express in MATLAB notation: scalars, vectors, matrices;
  6. perform, using MATLAB or EXCEL, mathematical operations on vectors, scalars, and matrices
  1. addition and subtraction;
  2. multiplication and addition;
  3. exponentiation;
  1. compute, using MATLAB or EXCEL, the numerical-value of standard mathematical functions
  1. trigonometric functions;
  2. exponential functions;
  3. square-roots and absolute values;
  1. create, store, and run MATLAB script files;
  2. import data to MATLAB for subsequent analysis from data-sources
  1. data-acquisition-system data-files;
  2. spreadsheet files;
  1. construct graphical plots for mathematical-functions in two or three dimensions;
  2. formulate a fit to given data in terms of a mathematical curve, or model, based on linear, polynomial, power, or exponential functions
  1. assess the goodness-of-fit for the mathematical model using regression analysis;
  1. apply MATLAB to find the numerical solution to systems of linear equations
  1. uniquely determined;
  2. underdetermined;
  3. overdetermined;
  1. perform using MATLAB or EXCEL statistical analysis of experimental data to determine the mean, median, standard deviation, and other measures that characterize the nature of the data ;
  2. compute, for empirical or functional data, numerical definite-integrals and discrete-point derivatives;
  3. solve numerically, using MATLAB, linear, second order, constant-coefficient, nonhomogenous ordinary differential equations;
  4. assess, symbolically, using MATLAB
  1. the solution to transcendental equations;
  2. derivatives, antiderivatives, and integrals;
  3. solutions to ordinary differential equations;
  1. apply, using EXCEL, linear regression analysis to xy data-sets to determine for the best-fit line the: slope, intercept, and correlation-coefficient;
  2. draw using MATLAB or EXCEL two-dimensional Cartesian (xy) line-plots with multiple data-sets (multiple lines);
  3. draw using EXCEL qualitative-comparison charts such as Bar-Charts and Column-Charts in two or three dimensions;
  4. perform, using MATLAB and EXCEL, mathematical-logic operations;
  5. plan, conceptually, computer-solutions to engineering/science problems using psuedocode and/or flow-chart methods;
  6. compose MATLAB script files that employ FOR and WHILE loops to solve engineering/science problems that require repetitive actions.

Expected Outcomes for Students

Upon completion of the course the student should be able to:

  1. perform vector-mathematical operations
  1. addition/subtraction
  2. dot product, cross product
  3. mixed triple product;
  1. express a vector in terms of its Cartesian components;
  2. draw free-body diagrams to depict the forces acting on points, rigid bodies, and mechanical devices;
  3. distinguish between internal and external forces;
  4. state the principle of transmissibility;
  5. compute the moment of a
  1. force about a point
  2. force about an axis
  3. couple;
  1. solve for the reaction forces at the supports of force-loaded 2D or 3D rigid-bodies;
  2. identify statically indeterminate support reactions;
  3. state the conditions for static equilibrium of a 2D or 3D rigid body;
  4. use vectors and vector mechanics to solve for unknown forces and moments acting on points and rigid bodies;
  5. compute the center of gravity for 2D and 3D bodies;
  6. compute the centroid of lines, areas, and volumes by
  1. composition of standard forms
  2. mathematical integration;
  1. compute the first-moment of areas and lines;
  2. evaluate the hydrostatic forces applied to submerged rigid bodies;
  3. trusses
  1. determine the force reactions at the supports
  2. compute the forces in truss-members
  1. analyze machines to determine the transformation and/or modification of the applied forces
  2. assess forces in loaded beams
  1. evaluate reaction forces
  2. compute shear-forces and bending-moments
  3. draw shear and bending moment diagrams;
  1. assess forces in loaded cables
  1. compute shape and tension for cables with

1)concentrated live-loads

2)distributed live-loads

3)dead-load (cable weight) only;

  1. explain the coefficient of friction;
  2. compute the friction force on a rigid body given the force-loading and coefficient of friction;
  3. solve problems involving dry and belt friction;
  4. compute the second-moment (moment of inertia) for
  1. areas
  2. volumes
  3. masses;
  1. apply the Parallel Axis Theorem to the calculation of moments of inertia to compute the:
  1. radius of gyration
  2. polar moment of inertia
  3. product of inertia;

Course Content (Lecture):

  1. Vector mathematical operations
  2. addition, subtraction, negation
  3. dot-product, cross-product
  4. mixed triple product
  5. The Principle of static equilibrium: ΣF = 0
  6. Newton’s First Law of Motion
  7. decomposition of force vectors into Cartesian components
  8. unit vectors
  9. Statics of particles in two or three dimensions
  10. space (dimensional) diagram
  11. free body diagrams

1)internal vs. external forces

  1. Equivalent system of forces
  2. moment of a force about a point or axis
  3. moment of a force-couple
  4. equivalent force systems: forces only, moments and forces
  5. varignon’s theorem
  6. Statics of rigid bodies
  7. constructing free-body diagrams
  8. line-of-action and the principle of transmissibility
  9. equilibrium of two-force and three-force bodies
  10. force reactions at supports and connections in two and three dimensions
  11. determinate and indeterminate reaction systems
  12. support-reaction types

1)ball

2)rough surface roller

3)ball-and-socket

4)universal joint

5)fixed support

6)hinge and bearing

7)pin and bracket

  1. Distributed forces: centroids and centers of gravity
  2. first moment of areas and lines
  3. theorem of Pappus-Guldinus
  4. Forces on Submerged Surfaces
  5. hydrodstatic-pressure versus fluid-depth
  6. free body diagrams for submerged bodies
  7. center of pressure location using the first moment of areas
  8. resultant of hydrostatic forces
  9. Analysis of structures:
  10. trusses: forces in members

1)method of joints;

2)method of sections

  1. frames and machines: transmission and transformation of forces
  1. Forces in beams and cables:
  2. shear and bending-moment diagrams for point-loaded and distributed-loaded beams
  3. cables with concentrated and distributed force-loads
  4. Friction:
  5. laws of dry friction
  6. coefficient of sliding and static friction
  7. angle of friction
  8. friction forces: F = µN
  9. free-body diagrams that include friction forces
  10. belt friction forces and the angle of wrap
  11. Moments of Inertia:
  12. second moment
  13. radius of gyration
  14. product of inertia
  15. parallel-axis theorem
  16. moments of inertia for composite areas/masses

Course Content (Laboratory):

  1. Instructor presents, describes and discusses detailed analysis and solution of textbook engineering mechanics for systems and/or structures in static equilibrium (problem-solving tutorials)
  2. Students work in small teams to solve textbook problems in engineering mechanics for systems and/or structures in static equilibrium (problem-solution generation). Students follow this general engineering mechanics problem solution process
  3. draw space diagram(s) to interpret the physical situation
  4. draw Free Body Diagram(s) (FBDs) to isolate structural components and the forces and/or moments applied to the component which illustrates the interaction of the component and the forces/moments
  5. construct a mathematical model for the situation depicted in the diagrams
  6. solve the mathematical model for the quantity of interest using one, or more of:

1)graphical/geomtrical measurements using scaled hand or CAD diagrams

2)scientific calculator

3)numerical processing software such as MSExcel

4)mathematical processing software such as MATLAB

  1. Accurately and precisely state the answer in terms of magnitude, direction, and units-of-measure as required by the problem

Methods of Presentation:

  1. Formal lectures using PowerPoint and/or WhiteBoard presentations
  2. Computer demonstrations
  3. Reading from the text
  4. Laboratory use of computers
  5. Class discussion of problems, solutions, and student’s questions
  6. Engineering-MechanicsProblem Solving tutorials

Assignments and Methods of Evaluating Student Progress:

  1. Typical assignments
  2. Read chapter-7 in the text on the analysis of shear-forces and bending-moments in structural beams
  3. Complete exercises from the text book, or those created by the instructor

1)Given a composite mass, calculate the moment of inertia (second moment) about the axis shown in the diagram in the text.

2)A set of Slab-tongs uses a scissor mechanism as shown in the diagram at right. For a 960 lb concrete slab, determine the force on the faces of the tongs at points E & F

3)A 0.6 lb cylinder C rests on cylinder D as shown in the diagram at right. The coefficient of static friction, µs, is the same for points A & B. Use MATLAB software to determine for µs in the range of 0-0.4, the largest counterclockwise couple M that can be applied to cylinder D if it is NOT to rotate.

  1. Methods of evaluating student progress
  2. weekly homework assignments
  3. examinations
  4. final examination

Textbook(s) (Typical):

Statics: Analysis and Design of Systems in Equilibrium, Update Edition, Sheri D. Sheppard, Benson H. Tongue, 2007, John-Wiley

Engineering Mechanics: Statics, 12/E, Russell C. Hibbeler, 2010, Prentice Hall

Vector Mechanics for Engineers: Statics, 9th Edition, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, David Mazurek, McGraw-Hill, 2010,

Engineering Mechanics - Statics, 6th Edition, J. L. Meriam, L. G. Kraige, 2007, John-Wiley

Engineering Mechanics: Statics, 5/E, Anthony M. Bedford, Wallace Fowler, 2008, Prentice Hall

Engineering Mechanics: Statics, 1st Edition, Michael Plesha, Gary Gray, Francesco Costanzo, McGraw-Hill, 2010

Special Student Materials:

None

Bruce Mayer, PE • C:\WorkingFiles\Bruce_Files\Chabot\Curriculum_Analysis\Curriculum_Proposal_Fa09\ENGR36_Outline02_090822.doc

Revised 08/22/2009