U.P. College of Engineering, Institute of Civil Engineering
ES 11 Statics of Rigid Bodies COURSE SYLLABUS st
1 Semester, AY 2014-2015 Course Description : Fundamental principles of mechanics and their applications to the simpler engineering problems involving static equilibrium; Forces and Moments, their components and resultants, and their vector representation; System of discrete as well as continuously distributed forces; Frames, trusses, cables, friction; First and second moments of length, area, volume, and mass. Course goals: After completing this course, a student must be able to 1. Appreciate the fundamental concepts related to engineering mechanics 2. Gain knowledge on geometric properties of areas and volumes 3. Understand the effects of external forces on rigid bodies in static equilibrium 4. Understand internal forces in plane trusses, beams and frames 5. Develop the ability to analyze particles and rigid bodies in static equilibrium : Math 54, Physics 71 Prerequisites Textbook : Vector Mechanics for Engineers: Statics 10th ed. (SI Units) by Beer, Johnston, & Mazurek Additional References : Engineering E ngineering Mechanics: Statics 3rd ed. by Bedford and Fowler; Engineering Mechanics: Statics SI ed. by Hibbeler; Statics of Rigid Bodies SI ed. by E.S. Pacheco, 1993 Course Schedule Week
Lec No. Lecture Topic
Aug 7 – 7 – 8 8
1
Aug 11 – 11 – 15
2
Aug 18 – 18 – 22 22 Aug 25 – 25 – 29
Textbook References
Lab No.
Fundamental Concepts Force Vectors
Preface, Sec. 1.1-1.5 Sec. 2.1-2.8, 2.12-2.14
Lab 0
Free Body Diagram and Particle Equilibrium
Sec. 2.9-2.11, 2.15
Lab 1a, 1b
(No ES 11 classes this week)
3
Vector Operations
Sec. 2.3-2.4,3.4-3.5,3.9-3.10
Lab 2a, 2b
Sep 1 – 1 – 5 5
4
Moment of a Force, Couples and their Moment
Sec. 3.1-3.3,3.6-3.7,3.11 Sec. 3.12-3.15
Lab 3a, 3b
Sep 8 – 8 – 12
5
Equivalent Force Systems
Sec. 3.16-3.18, 3.20
Lab 4a, 4b
Sep 15 – 15 – 19
6
Equilibrium of Rigid Bodies
Sec. 4.1-4.9
Lab 5a, 5b
Sep 22 – 22 – 26
7
Dry Static Friction, Belt Friction
Sec. 8.1-8.5, 8.10
Lab 6a, 6b
Sep 29 – 29 – Oct 3
8
Centroid and Center of Gravity – Gravity – 2D Bodies
Sec. 5.1-5.6, 5.10-5.12
Lab 7a, 7b
Oct 6 – 6 – 10
9
Centroid and Center of Gravity – Gravity – 3D 3D Bodies Distributed Loads: Loads on Beams and Hydrostatic Forces
Sec. 5.8, 5.9
Lab 8a, 8b
Oct 13 – 13 – 17
10
Area Moment of Inertia
Sec. 9.1-9.7
Lab 9a, 9b
Oct 20 – 20 – 24
11
Mass Moment of Inertia
Sec. 9.11-9.15
Lab 10a, 10b
Oct 27 – 27 – 31
12
Internal Forces, Beams, Shear and Bending Moment Diagrams Sec. 7.3-7.6
Lab 11a, 11b
Nov 3 – 3 – 7
13
Beams, Shear and Bending Moment Diagrams (continued)
Sec. 7.3-7.6
Lab 12a, 12b
Nov 10 – 10 – 14
14
Trusses
Sec. 6.1-6.5, 6.7-6.8
Lab 13a, 13b
Nov 17 – 17 – 21
15
Frames
Sec. 6.9-6.11
Nov 24 – 24 – 28 28
Lab 14a, 14b Lab 15a, 15b
(No lecture classes this week)
Schedule of Exams:
FIRST LONG EXAM
September 15, 2014, Monday 4-6pm [Lectures 1-4]
SECOND LONG EXAM
October 6, 2014, Monday 4-6pm [Lectures 5-7]
THIRD LONG EXAM
November 3, 2014, Monday 4-6pm [Lectures [Lectures 8-11]
FOURTH LONG EXAM
December 1, 2014, Monday 4-6pm [Lectures 12-15]
FINAL EXAM
December 9, 2014, Tuesday, 1-4pm
MAKE-UP EXAM
December 9, 2014, Tuesday, 5-7pm
Second Semester important dates : Start of Classes – Classes – Aug Aug 7 (Thurs); Last Day for Dropping – Dropping – Nov Nov 6 (Thurs); End of Classes – Classes – Dec Dec 5 (Fri); Holidays that would affect classes : Quezon City Day – Day – Aug Aug 19 (Tue); Ninoy Aquino Day – Day – Aug Aug 21 (Thurs)
Useful Information:
Lecturer:
Consultation Time/Place:
Lab Instructor:
Consultation Time/Place: 1 of 7 st
Ver. 07/30/2014, AY2014-2015, 1 Semester
CLASS POLICIES Attendance. Attendance is required. A student who is absent in more than 3 lecture meetings OR in more than 6 lab meetings, whether excused or unexcused, should drop the course on or before February 20, 2014. Otherwise, he/she will be given a grade of 5.0, unless his/her standing is passing AND most of the incurred absences are due to valid reasons, in which case he/she will be given a “forced DRP”. In case there is an equal number of excused and unexcused absences, the first three absences will be considered in the decision. If the student is absent due to a valid excuse, supporting documents (e.g. medical certificate) should be presented to the lecturer and/or lab instructor within one week of the student’s return to class. Only the following are considered valid excuses: medical illness, death of an immediate family member, and competitions or trainings endorsed by the department or the University. Students must attend the lab and lecture sections in which they are officially enlisted. ATTENDANCE POLICY WILL BE STRICTLY IMPLEMENTED.
During the lecture class, the lecturer may give a seatwork or quiz that may serve as an attendance check. Any student who misses the attendance check will be marked ABSENT, unless he/she approaches the lecturer immediately at the end of that lecture class. Course Requirements. Students will be evaluated based on their performance in 15 sets of lab work (LW), 4 long exams (LE), & a final exam (FE). Lab work (LW) is designed to challenge the students in using the concepts of Statics in solving simple engineering problems. It is divided into two-1.5 hour-sessions per week, namely Lab-A, and Lab-B (the first and second sessions, respectively).
Lab-A: Students will INDIVIDUALLY solve one average and one difficult problem per lab session. The two problems will be given at the same time. The first one hour and fifteen minutes of the lab session will be allotted for solving the problems. At the end of the allotted period, the student’s papers will be collected, and the last fifteen minutes of the lab session will be devoted to discussion of the lab problems. Each problem will be graded “all-or-nothing” i.e., the student gets a grade of 100 if the solution and answer are correct, and zero if incorrect. If the student gets a grade of 100 for BOTH problems, he/she is exempted from attending Lab-B for that week. Lab-B: Students are given a second chance to solve problems and get the score of 100 during this second lab session. Students will be given a new set of problems to solve (on the same topic). Same procedure and grading is applied as in Lab-A.
The student’s lab score for the week will be taken from t he lab session (Lab-A or Lab-B) where the student got a higher score. In case of suspension of classes or holidays, LW will become a “take home” work, and students must submit their work the day after the problems are distributed, or during the deadline set by the lab instructors. Each long exam (LE) has 4 parts: Part I is a 10-item multiple choice-type subtest, and Parts II to IV are problem solving. Below are policies pertaining to long exams: 1. Submit answer sheets to your lab instructors a day before the exam, or earlier. Use long yellow pad for answer sheets. Late submission of answer sheets will result in a 5% deduction in LE grade. 2. Answer the exam alone and to the best of your knowledge. 3. Write only on one side of the answer sheet and start each part of the exam on a new sheet. 4. Use black or blue ink pen. Solutions written in pencil will not be considered for rechecking. 5. Do not use correction fluid or correction tape in your solutions. 6. Write your name, student number, section, exam number, date, a nd page number on each sheet. 7. Complaints/queries will be entertained only within a week after the results are returned. 8. Students are allowed to make-up for only one LE that has a valid excuse. The final exam (FE) is a 40- to 50-item multiple-choice exam covering all topics. No make-up final exam will be administered. Any student who is not exempted and did not take the FE for VALID reasons (see the paragraph on Attendance) will be given a grade of INC if his/her pre-final grade is passing. Electronic devices, e.g. cellular phones, laptops, tablets, and audio players, must be turned off and kept inside the bag during lecture classes, lab classes, and exams. 2 of 7 st
Ver. 07/30/2014, AY2014-2015, 1 Semester
Grading System Grading of lab work per session (LW) = (grade for average problem + grade for difficult problem) ÷ 2 Grade for each long exam ( LE) = 20% Multiple Choice + 20% Easy Problem + 20% Average Problem + 20% Difficult Problem + 20% Average of LW with topics covered in the LE Pre-final Grade = (LE1 + LE2 + LE3 + LE4) ÷ 4
Exemption from taking the Final Exam: If pre-final grade is 72% or better , and no LE score is lower than 60%. If exempted, the pre-final grade becomes the final grade. For students taking the final exam, final grade will be as follows: Final Grade = 0.70 x (Pre-final Grade) + 0.30 x (Final Exam Score) Grading Scale (Note: This is a pass or fail course.) Final Grade 92-100 88-below 92 84-below 88 80-below 84 76-below 80
Equivalent Grade 1.00 1.25 1.50 1.75 2.00
Final Grade 72-below 76 68-below 72 64-below 68 60-below 64 Below 60
Equivalent Grade 2.25 2.50 2.75 3.00 5.00
Intellectual dishonesty. Intellectual dishonesty is any fraudulent act performed by a student to achieve academic advantage or gain for oneself or others, including but not limited to:
1. 2. 3. 4. 5. 6. 7. 8.
Copying or providing the means to copy a classmate’s exam answers, homework, laboratory experiments, etc.; Allowing a classmate to copy f rom one’s own exam answers, homework, laboratory experiments, etc.; Possession and/or use of cheat devices during an examination; Plagiarism, which shall be defined as the taking and use of another person’s ideas, writings, inventions and similar intellectual products as one’s own without knowledge, consent and/or accreditation; Deception, which shall be defined as providing false information concerning an academic activity; Allowing another person to take an examination in one’s name, and/or impersonating another student or allowing someone to impersonate oneself in an academic activity; Manipulating a corrected exam paper; and Any other form of cheating or any act of dishonesty in relation to academic activity.
Any student found guilty of committing intellectual dishonesty will be penalized in accordance with prevailing University rules and regulations. According to the UP Faculty Manual:
1. 2.
Any student found guilty of any form of cheating or intellectual dishonesty shall be penalized with suspension for not less than one (1) year. Students found guilty of cheating/dishonesty shall be barred from graduating with honors, even if their weighted average is within the requirement for graduation with honors.
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Ver. 07/30/2014, AY2014-2015, 1 Semester
ES 11 Detailed Course Outline: Lesson Objectives and Topics Class Sessions
Lecture 1 Lab 1A/1B
Lecture 2 Lab 2A/2B
Lesson Objectives After the lecture and laboratory, the students must be able to: 1. Define mechanics and statics 2. Identify and explain each of the fundamental concepts and principles used in mechanics 3. Define forces and completely illustrate force vectors (two-dimensional [2D] and three-dimensional [3D]) 4. Define particles and illustrate forces acting on particles; define coplanar and concurrent forces 5. Add force vectors (calculate the resultant) using parallelogram law and triangle rule 6. Define unit vectors that point to the direction of an axis 7. Resolve vectors into rectangular components (2D and 3D) or along any set of given axes 8. Add force vectors by summing up rectangular components (2D an 3D)
1. 2. 3. 4. 5. 6. 7. 8.
Lecture 3 Lab 3A/3B
Lecture 4
1. 2. 3. 4. 5. 1. 2.
Lab 4A/4B 3. 4.
5. 6.
7.
8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
Recall Newton’s first law of motion Define particle equilibrium Define free-body diagram (FBD) Draw FBD of a particle acted upon by forces Draw multiple FBDs Express equilibrium condition graphically and mathematically Learn to set-up equilibrium equations Solve problems involving the equilibrium of a particle Learn (or review) different operations involving multiplication of vectors Calculate vector-product Calculate dot product Explain the projection of a vector on an axis Calculate mixed-triple product Define rigid bodies Differentiate between external and internal forces on rigid bodies Understand the principle of transmissibility Define moment of a force about a point (MOFP) and its illustrate its 2D and 3D vector representation Explain the external effect of moments on the rigid body using right-hand rule Calculate MOFP as product of force and perpendicular distance and as vector product o f position vector and force vector. Explain the Varignon’s Theorem and its application in obtaining the resultant of several concurrent forces Determine the resultant moment about a point of several forces acting on a rigid body Define and illustrate “lambda” or the unit vector defining the direction of an axis or line Define the moment of a force about a line or axis (MOFL) and illustrate its vector representation Calculate MOFL as mixed triple product of lambda, position vector, and force vector Determine the resultant moment about a line of several forces acting on a rigid body Determine the perpendicular distance between a force and a line using the MOFL Define a couple Calculate the moment due to a couple and illustrate its vector representation Explain equivalent couples Determine the resultant moment due to couples acting on a rigid body
Topic
Fundamental Concepts Definition of mechanics Fundamental concepts and principles Statics of Particles Forces on a particle Resolution into components Resultant of forces acting on a particle
Free Body Diagram and Particle Equilibrium
References and Suggested Problems
Chap. 1.1-1.5, 2.1-2.8, 2.12-2.14 Prob. 2.2, 2.3, 2.5, 2.10, 2.23, 2.25, 2.28, 2.38, 2.71, 2.75, 2.85
Chap. 2.9-2.11, 2.15 Prob. 2.43, 2.45, 2.46, 2.47, 2.57, 2.61, 2.99, 2.107, 2.111, 2.121
Vector Operations Vector, scalar and mixed-triple products
Chap 2.3-2.4,3.43.5,3.9-3.10 Prob. 3.15, 3.35, 3.36, 3.39, 3.45, 3.46
Moment of a Force Moment of a force about a point Moment of a force about a line Couples and their moment
Chap. 3.1-3.3,3.63.7,3.11, 3.12-3.15 Prob. 3.1, 3.2, 3.3, 3.8, 3.11, 3.12, 3.48, 3.59, 3.60, 3.61 Prob. 3.68, 3.69, 3.70, 3.71, 3.73, 3.75, 3.76, 3.78, 3.80
FIRST LONG EXAM
4 of 7 st
Ver. 07/30/2014, AY2014-2015, 1 Semester
Class Sessions
Lecture 5
Lesson Objectives
1. 2.
Lab 5A/5B 3. 4. 5. 6. 7. Lecture 6 Lab 6A/6B
Lecture 7 Lab 7A/7B
Explain equivalence of force systems by external effect Resolve a force vector with an equivalent force-couple system at any other point Reduce a system of forces to a resultant force-couple Define and illustrate equivalent force systems Calculate the angle between resultant force vector and resultant couple vector Identify types of force systems that allow further reduction of systems of forces into a single force. Reduce a system of forces to a single force.
1.
Recognize different types of supports/connections used to hold structures in place (2D and 3D) 2. Identify and draw all reaction force and moment components for different types of support (2D and 3D) 3. Draw the free body diagram of a rigid body acted upon by forces and moments 4. Define equilibrium of rigid bodies 5. Give the number of equilibrium equations and set up the equations for a rigid body acted upon by a force system (2D and 3D) 6. Recognize situations defined as statically determinate, statically indeterminate, or partially constrained. 7. Define two-force body and three force-body in equilibrium 8. Identify two-force and three-force bodies in a multi-FBD problem 9. Solve for unknown quantities in an equilibrium problem (2D and 3D) 1. Define static friction 2. Explain the laws of dry friction 3. Explain the meaning of maximum static friction and impending motion 4. Compute the angle of static or kinetic friction, and angle of friction in general 5. Draw the friction force with correct direction on the FBD 6. Solve for unknown quantities in equilibrium problems involving friction. 7. Solve friction problems involving wedges 8. Determine whether or not a body will move when a force system acting on the body is given Derive the belt friction formula 9. Determine which side of the frictionless belt has larger tension 10. Determine the angle of contact in radians from the sketch of belt/drum or pulley
Topic Equivalent Force Systems (Resultant of force systems acting on rigid bodies)
Equilibrium of Rigid Bodies
References and Suggested Problems Chap 3.16-3.18, 3.20
Prob. 3.82, 3.83, 3.85, 3.88, 3.90, 3.91, 3.121, 3.122, 3.142
Chap 4.1-4.9 Prob. 4.3, 4.5, 4.10, 4.69, 4.75, 4.89, 4.107, 4.115, 4.139
Dry Static Friction Laws of dry friction Wedges Belt Friction
Chap 8.1-8.5, 8.10 Prob. 8.1, 8.4, 8.5, 8.6, 8.14, 8.15, 8.53, 8.54, 8.56, 8.65, 8.103, 8.105, 8.119, 8.120, 8.122
SECOND LONG EXAM
5 of 7 st
Ver. 07/30/2014, AY2014-2015, 1 Semester
Class Sessions
Lecture 8 Lab 8A/8B
Lecture 9
Lesson Objectives
1.
Determine by integration the first moment of an (a) area, and (b) line, about an axis 2. Explain the geometric interpretation of a centroid in relation to the first moment of area. 3. Give the location of the centroid of a triangle, quarter circle, semi-circle, parabolic area, spandrel, quarter circular arc, semi-circular arc, and general arc. (Remember: Take note of the reference axes from which the centroids given in the book were derived.) 4. Give the location of centroid of an area by integration. 5. Give the location of centroid of composite areas and lines. 6. Define center of gravity 7. Differentiate centroid from center of gravity. 8. Determine the center of gravity of plates and thin wires. 9. Determine the centroid of a volume (volumes of revolution). 10. Determine the center of gravity of 3D bodies 11. Determine the center of gravity of composite bodies
Centroid and Center of Gravity Areas and lines Volumes and masses
1. 2.
Define distributed loads Replace distributed loads on beams with equivalent concentrated loads. Determine the location of the equivalent concentrated load on beams Determine unknown quantities for a beam in equilibrium, subjected to distributed loading and concentrated loads Determine the resultant hydrostatic pressure on a submerged rectangular surface
Distributed Loads Loads on Beams Hydrostatic Force
Define the second moment or moment of inertia of an area Differentiate the second moment from the first moment Obtain the moment of inertia of an area about an axis lying on its plane by integration Obtain the moment of inertia of an area about an axis perpendicular to the plane or obtain the polar moment of inertia Give the formula for the moment of inertia of a rectangle, triangle, circle, semi-circle, and quarter circle about the centroidal axis, or any axis parallel to it. Define radius of gyration and solve for it given the area and AMOI State and use the parallel axis theorem Obtain the moment of inertia of a composite area about a prescribed axis.
Area Moment of Inertia
Define the mass moment of inertia Obtain the mass moment of inertia of a thin plate about (a) an axis lying on the middle surface of the plate, and (b) an axis perpendicular to the plate Give the formula for the mass moment of inertia of a sphere about an axis through the center, a slender rod about an axis perpendicular to the rod and passing through its center of mass, and a circular disk about an axis perpendicular to the disk and passing through its center Compute the radius of gyration given the mass and mass moment of inertia State and use the parallel axis theorem for mass moment of inertia Determine the mass moment of inertia by integration Obtain the mass moment of inertia of a composite area about a prescribed axis.
Mass Moment of Inertia
Lab 9A/9B 3. 4.
5.
Lecture 10
1.
Lab 10A/10B
2. 3. 4.
5.
6. 7. 8.
Lecture 11
Topic
1. 2.
3.
4. 5. 6. 7.
References and Suggested Problems Chap 5.1-5.6, 5.10-5.12
Prob. 5.3, 5.6, 5.15, 5.37, 5.44, 5.48, 5.96, 5.98, 5.103
Chap 5.8-5.9 Prob. 5.66, 5.72, 5.74, 5.75, 5.76, 5.78, 5.84, 5.89, 5.93
Chap 9.1-9.7 Prob. 9.2, 9.3, 9.4, 9.9, 9.11, 9.14, 9.15, 9.36, 9.46, 9.47
Chap 9.11-9.15 Prob. 9.115, 9.116 , 9.121, 9.138, 9.142, 9.145, 9.131, 9.122, 9.124
THIRD LONG EXAM
6 of 7 st
Ver. 07/30/2014, AY2014-2015, 1 Semester
Class Sessions
Lesson Objectives
Lecture 12 & 13
1.
Lab 12A/12B Lab 13A/13B
2.
3. 4. 5.
6. 7. 8. 9.
Lecture 14
1. 2.
Lab 14A/14B 3.
4.
Lecture 15
1.
Lab 15A/15B
2.
3.
Topic
Differentiate and explain external forces and internal forces with respect to members forming a structure State the three types of internal forces that can appear in a member acted upon by a general coplanar force system Determine the internal forces at any section of a given member Define a beam and identify types of loading for a beam Classify beams either as statically determinate or indeterminate, depending on type of support State the convention for positive shear and positive bending moment for beam analysis Draw shear and bending moment diagrams by cutting through critical sections of a beam State the mathematical relations among load, shear, and bending moment Draw shear and bending moment diagrams with the aid of mathematical relations among load, shear, and bending moment
Internal forces in members
References and Suggested Problems Chap 7.1-7.6
Prob. 7.29, 7.35, 7.37, 7.39, 7.40, 7.42, 7.75, 7.76, 7.87
Shear and Bending Moment Diagrams for Beams
Define a simple truss State the assumptions made in the analysis of trusses Determine the magnitude and type of axial force (tensile or compressive) in any member of a truss using the method of joints. Determine the magnitude and type of axial force (tensile or compressive) in any member of a truss using the method of sections.
Trusses
State the principal difference between a truss and a frame Given a structure where a pin connects three or more members, draw the FBD of each of the members Determine the forces acting on any member of a frame.
Frames
Chap 6.1-6.5, 6.7-6.8 Prob. 6.4, 6.9, 6.13, 6.45, 6.51, 6.53, 6.57, 6.61, 6.63
Chap 6.9-6.11 Prob. 6.75, 6.78, 6.79, 6.82, 6.89, 6.94, 6.99, 6.100, 6.101
FOURTH LONG EXAM FINAL EXAM
7 of 7 st
Ver. 07/30/2014, AY2014-2015, 1 Semester
