UNIVERSITY OF ARCHITECTURE, CIVIL ENGINEERING AND GEODESY
TECHNICAL MECHANICS DEPARTMENT
COURSEWORKS
ON
THEORETICAL MECHANICS – PART I
(KINEMATICS & STATICS)
Sofia
2011
CONTENTS
1. General instructions for the semester work preparation ……………………………………. 1
2. List of symbols
…………………………………………………………………………… 2
3. Coursework 1 – Kinematics of the plane motion of rigid bodies ……………………………. 3
4. Coursework 2 – Kinematics of the relative motion of a point ………………………………… 6
5. Coursework 3 – Reduction of a spatial set of forces …..……………………………………… 10
6. Coursework 4 – Reduction of a set of coplanar forces ………………………………………... 14
7. Coursework 5 – Equilibrium of a body acted upon by a spatial set of forces ………………… 18
8. Coursework 6 – Equilibrium of a body – plane problems ………………………….…………. 21
9. Coursework 7 – Equilibrium of Gerber beams …...…………………………………………… 24
10. Coursework 8 – Equilibrium of Three-hinged frames ...……………………………………… 27
11. Coursework 7 – Equilibrium of Plane trusses …….…………………………………………… 30
12. Appendix – Centroids and areas of common geometric shapes …….………………………… 33
GENERAL INSTRUCTIONS FOR THE SEMESTER WORK PREPARATION
I. Instruction for the coursework preparation
1. The courseworks have to be written with a pencil on the one side only of white sheets of paper. The
schemes and diagrams have to be drawn on a suitable scale.
2. A frame is drawn on each sheet of paper to mark the working field. The faculty number of the student
must be written in pen or ball-pen in the bottom right corner and the number of the individual variant
– at the top right corner inside the frame.
3. Every coursework thus prepared must be submitted to the assistant professor for verification and
approval not later than two weeks after typical worked or sample examples have been explained
during classroom work. After approval of all courseworks they are compiled in a file and submitted to
the assistant professor for final validation.
II. Instructions about the courseworks data
1. There are 20 problems to each topic to be resolved by student with correspondent numbers in the
assistant professor’s list. The students with numbers above 20 have to prepare the problems 1, 2, 3
etc., respectively, complying with the additional indication. For example, the student with number
28 has to prepare the problem 8, etc.
2. Most part of the parameters are given as functions of the four digits constituting the student’s faculty
number, say K1, K2, K3, K4. When a faculty number contains less than four digits, for example 198,
then it is written as 0198, so that K1=0, K2=1, K3=9, K4=8. If the faculty number contains five digits,
for example 14523, then the first digit is omitted, so that K1=4, K2=5, K3=2, K4=3.
3. Dimensions, loadings, masses, velocities, accelerations and other parameters to be needed for
problem solutions are given together with the related drawings.
4. Cylinders and wheels, when present in a problem, are supposed to roll without sliding.
5. The analytical and graphical solutions of one and the same problem, where required, are carried out
independently. The space and acceleration or force diagrams of a graphic solution should be plotted
on the same sheet of paper.
LIST OF SYMBOLS
a – acceleration; distance; coefficient
A, B, C, D … – points
b – distance; coefficient
d – distance; coefficient
F, F1, F2 – forces
Ki – digits constituting the faculty number of the student
M, M1, M2 – moments
q – intensity of distributed loading
R – radius
V – velocity
 – angle; angular acceleration
 – coefficient
 – angle; weight per unit volume/area
 – angular velocity
APPENDIX – CENTROIDS AND AREAS OF COMMON GEOMETRIC SHAPES
Shape
Rectangle
Figure
Area [m2]
A  h.b
Right-angled
triangle
A
h.b
2
Isosceles triangle
A
h.b
2
Semicircle
A
Quarter circle
A
 .R 2
2
 .R 2
4