Chabot College
Fall 2005
Replaced Fall 2010
Course Outline for Engineering 36
ENGINEERING MECHANICS - STATICS
Catalog Description:
36 – Engineering Mechanics - Statics
3 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). (Formerly Engineering 35.) 2 hours
lecture, 3 hours laboratory.
[Typical contact hours: lecture 35, laboratory 52.5]
Prerequisite Skills:
Before entering the course the student should be able to:
1. analyze and solve a variety of problems often using calculus in topics such as:
a. addition, subtraction, dot product and cross product of vectors;
b. linear and rotational kinematics;
c. dynamics;
d. momentum;
e. work, kinetic energy, and potential energy;
f. rotational kinematics and dynamics;
g. statics;
h. gravitation;
i. fluids;
j. waves;
2. operate standard laboratory equipment;
3. analyze laboratory data;
4. write comprehensive laboratory reports.
5. analyze engineering/science word problems to formulate a mathematical model of the problem;
6. express in MATLAB notation: scalars, vectors, matrices;
7. perform, using MATLAB or EXCEL, mathematical operations on vectors, scalars, and matrices
k. addition and subtraction
l. multiplication and addition
m. exponentiation;
8. compute, using MATLAB or EXCEL, the numerical-value of standard mathematical functions
a. trigonometric functions
b. exponential functions
c. square-roots and absolute values
9. import data to MATLAB for subsequent analysis from data-sources
a. data-acquisition-system data-files
b. spreadsheet files;
10. construct graphical plots for mathematical-functions in two or three dimensions;
11. formulate a fit to given data in terms of a mathematical curve, or model, based on linear, polynomial,
power, or exponential functions
a. assess the goodness-of-fit for the mathematical model using regression analysis;
12. apply MATLAB to find the numerical solution to systems of linear equations
a. uniquely determined
b. underdetermined
c. overdetermined;
13. 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 ;
14. computer, for empirical or functional data, numerical definite-integrals and discrete-point derivatives
15. solve numerically, using MATLAB, linear, second order, constant-coefficient, nonhomogenous ordinary
differential equations;
16. assess, symbolically, using MATLAB
Chabot College
Course Outline for Engineering 36, Page 2
Fall 2005
17.
18.
19.
20.
21.
a. the solution to transcendental equations
b. derivatives, antiderivatives, and integrals
c. solutions to ordinary differential equations;
apply, using EXCEL, linear regression analysis to xy data-sets to determine for the best-fit line the:
slope, intercept, and correlation-coefficient;
draw using MATLAB or EXCEL two-dimensional Cartesian (xy) line-plots with multiple data-sets
(multiple lines);
draw using EXCEL qualitative-comparison charts such as Bar-Charts and Column-Charts in two or three
dimensions;
perform, using MATLAB and EXCEL, mathematical-logic operations
compose EXCEL Visual-Basic MACRO programs/functions to automate repetitive spreadsheet tasks.
Expected Outcome for Students:
Upon completion of the course, the student should be able to:
1. perform vector-mathematical operations
a. addition/subtraction
b. dot product, cross product
c. mixed triple product;
2. express a vector in terms of its Cartesian components;
3. draw free-body diagrams to depict the forces acting on points, rigid bodies, and mechanical devices;
4. distinguish between internal and external forces;
5. state the principle of transmissibility;
6. compute the moment of a
a. force about a point
b. force about an axis
c. couple;
7. solve for the reaction forces at the supports of force-loaded 2D or 3D rigid-bodies;
8. identify statically indeterminate support reactions;
9. state the conditions for static equilibrium of a 2D or 3D rigid body;
10. use vectors and vector mechanics to solve for unknown forces and moments acting on points and rigid
bodies;
11. compute the center of gravity for 2D and 3D bodies;
12. compute the centroid of lines, areas, and volumes by
a. composition of standard forms
b. mathematical integration;
13. compute the first-moment of areas and lines;
14. evaluate the hydrostatic forces applied to submerged rigid bodies;
15. trusses
a. determine the force reactions at the supports
b. compute the forces in truss-members
16. analyze machines to determine the transformation and/or modification of the applied forces
17. assess forces in loaded beams
a. evaluate reaction forces
b. compute shear-forces and bending-moments
c. draw shear and bending moment diagrams;
18. assess forces in loaded cables
a. compute shape and tension for cables with
1) concentrated live-loads
2) distributed live-loads
3) dead-load (cable weight) only;
19. explain the coefficient of friction;
20. compute the friction force on a rigid body given the force-loading and coefficient of friction;
21. solve problems involving dry and belt friction;
Chabot College
Course Outline for Engineering 36, Page 3
Fall 2005
22. compute the second-moment (moment of inertia) for
a. areas
b. volumes
c. masses;
23. apply the Parallel Axis Theorem to the calculation of moments of inertia to compute the:
a. radius of gyration
b. polar moment of inertia
c. product of inertia;
Course Content:
1. Vector mathematical operations
a. addition, subtraction, negation
b. dot-product, cross-product
c. mixed triple product
2. The Principle of static equilibrium: ΣF = 0
a. Newton’s First Law of Motion
b. decomposition of force vectors into Cartesian components
c. unit vectors
3. Statics of particles in two or three dimensions
a. space (dimensional) diagram
b. free body diagrams
1) internal vs. external forces
4. Equivalent system of forces
a. moment of a force about a point or axis
b. moment of a force-couple
c. equivalent force systems: forces only, moments and forces
d. varignon’s theorem
5. Statics of rigid bodies
a. constructing free-body diagrams
b. line-of-action and the principle of transmissibility
c. equilibrium of two-force and three-force bodies
d. force reactions at supports and connections in two and three dimensions
e. determinate and indeterminate reaction systems
f. 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
6. Distributed forces: centroids and centers of gravity
a. first moment of areas and lines
b. theorem of Pappus-Guldinus
7. Forces on Submerged Surfaces
a. hydrodstatic-pressure versus fluid-depth
b. free body diagrams for submerged bodies
c. center of pressure location using the first moment of areas
d. resultant of hydrostatic forces
8. Analysis of structures:
a. trusses: forces in members
1) method of joints;
2) method of sections
b. frames and machines: transmission and transformation of forces
Chabot College
Course Outline for Engineering 36, Page 4
Fall 2005
9. Forces in beams and cables:
a. shear and bending-moment diagrams for point-loaded and distributed-loaded beams
b. cables with concentrated and distributed force-loads
10. Friction:
a. laws of dry friction
b. coefficient of sliding and static friction
c. angle of friction
d. friction forces: F = µN
e. free-body diagrams that include friction forces
f. belt friction forces and the angle of wrap
11. Moments of Inertia:
a. second moment
b. radius of gyration
c. product of inertia
d. parallel-axis theorem
e. moments of inertia for composite areas/masses
Methods of Presentation:
1. Formal lectures using PowerPoint and/or WhiteBoard presentations
2. Computer demonstrations
3. Class discussion of problems, solutions and student’s questions
Chabot College
Course Outline for Engineering 36, Page 5
Fall 2005
Assignments and Methods of Evaluating Student Progress:
1. Typical assignments
a. Read chapter-7 in the text on the analysis of shear-forces and bending-moments in structural
beams
b. 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.
2. Methods of evaluating student progress
a. weekly homework assignments
b. examinations
c. final examination
Textbook(s) (Typical):
Vector Mechanics for Engineers: Statics, 7/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R.
Eisenberg, William E. Clausen, George H. Staab, McGraw-Hill, 2004
Engineering Mechanics - Statics, 10/E, Russell C. Hibbeler, Prentice Hall, 2004
Engineering Mechanics - Statics, 4/E, Anthony M Bedford, Wallace Fowler, Prentice Hal, 2005
Engineering Mechanics , Volume 1, Statics, J. L. Meriam, L. Glenn Kraige, John Wiley, 2001
Special Student Materials:
1. MATLAB Software
Bruce Mayer, PE • Course_Outline_ENGR36_041001.doc
New ENGR25 PreReq, MATH2 CoReq, Updated content, ReNumber from ENGR 35 Jul04