Force is defined as any interaction that, when unopposed, will change the motion of an object. It is a vector quantity that has both magnitude and direction. The parallelogram law of forces states that the resultant of two concurrent forces can be determined by drawing them as the sides of a parallelogram, with the resultant being the diagonal of the parallelogram. Wood has varying mechanical properties depending on whether force is applied parallel or perpendicular to the wood grain, with strength greatest in compression parallel to grain and least in tension perpendicular to grain. Properties like modulus of elasticity also determine a wood member's resistance to bending and deformation.

1. Force System

2. Force
• Force: simplest way to define by thinking
of pull or push.
• Generally force is defined as an action that
tends to disturb a body in static.
• Static; is concerned with the study of
bodies at rest or in equilibrium, under the
action of a force system.

3. Force
• Force is derive from Newton’s first Law of Motion
which states that a body will remain in its state of
rest or in its state of uniform motion in a straight
line unless compelled by an external force to
change that state.
• Force is therefore associated with a change in
motion. i.e; The force of the earth’s gravitational
pull acts vertically downwards on our bodies and
giving us weight; wind forces, which can vary in
magnitude, tend to push us horizontally. Forces
therefore have magnitude and direction.

4. • A force is specified by its magnitude,
direction and position, and therefore a
vector quantity.
• To describe a force completely, need
vector.
• Vector is quantity that has a magnitude,
line of action and direction.

5. A F B
magnitude Direction
Line of action
Since force is a vector it may be represented graphically as shown Figure 2.1,
where the F is considered to be acting on small particle at the point A in a direction
from left to right.
The magnitude of F is represented, to a suitable scale, by the length of the line AB and
its direction by the direction of arrow.
Figure 2.1Representation of a Force by a Vector

6. Movement by Forces
• Movement is the result of the action of
force, or a combination of forces.
• Movement can include such parameters
as distance, speed, time, and acceleration.

7.  Displacement
F 
Displacement F
Figure 3.2 Displacement
 Displacement is the distance through which a body, or a point on the
body, moves as a result of the action of force.

8. Resultant Force /Resultant Vector
• Normally a structure is not subjected to a
single force, but to a combination of
several loads and other forces, in different
directions and locations.

9.  Example : Consider now a cube of material place on horizontal surface and
acted upon by force F1 as shown in Figure 2.3. If F1 is greater than the
frictional force between the surface of the cube, the cube will move in the
direction of F1. Similarly if a force F2 is applied, the cube will move in the
direction of F2. Its follows that if F1 and F2 were applied simultaneously,
the cube would move in some incline direction as it were acted on by a
single inclined force R; clearly R is the resultant of F1 and F2.
Direction of motion
F1 F1
F2 R F2
Figure 3.3 Action of Force on A Cube

10.  When a number of forces (or any vectors) act on an object simultaneously,
the Resultant force (or Resultant vector) is a single force (vector) which ,
if acting alone on the object would have the same effect as the combined
forces (vectors).
Resultant vector = is the vector sum of two or more vectors
A
B

11. Parallelogram of Forces
 The resultant of two concurrent/simultaneous forces, whose lines of action
pass through a single point and lie in the same plane (Fig.3.4 (a)), may be
found using the theorem of parallelogram of force which states that:
If two forces acting at a point are represented by two adjacent sides of a
parallelogram drawn from that point their resultant is represented in
magnitude and direction by the diagonal (slating, sloping) of the
parallelogram drawn through the point.
F1 A (F2) C
F1 R (F1)
 

O F2 O B
F2
(a) (b)
Figure 3.4 Resultant of Two Concurrent Forces

12. F1 A (F2) C
F1 R (F1)
 

O F2 O B
F2
(a) (b)
Figure 3.4 Resultant of Two Concurrent Forces
 Figure 3.4 (b) R is the resultant of F1 and F2. Side BC of the parallelogram
is equal in magnitude and direction to the force F1 represented by the side
OA. Therefore, in vector notation;
R = F2 + F1

13. F1 A (F2) C
F1 R (F1)
 

O F2 O B
F2
(a) (b)
Figure 3.4 Resultant of Two Concurrent Forces
 The same result would be obtained by considering the side AC of the
parallelogram which is equal in magnitude and direction of the force F2 ;
R = F1 + F2

14. F1 A (F2) C
F1 R (F1)
 

O F2 O B
F2
(a) (b)
Figure 3.4 Resultant of Two Concurrent Forces
 The determination of the actual magnitude and direction of R may be
carried out graphically by drawing the vectors representing F1 and F2 to the
same scale (i.e. OB and BC) and then completing the triangle OBC by
drawing vector, along OC, representing R. Alternatively R and  may be
calculated using the trigonometry of triangles (sine and cosine formulae).
R2
= F1
2
+ F2
2
- 2F1F2cos
or
R2
= OB2
+ BC2
- 2OB.BC.cos @ R2
= OA2
+ AC2
- 2OA.AC.cos

15. Sine and Cosine Laws
A
c b
B C
a
The Sine Law The Cosine Law
a = b = c
sinA sinB sinC
alternatively, sinA = sinB = sinC
a b c
c² = a² + b² - 2a.b.cosC
which can also be written as:
a² = b² + c² - 2.b.c.cosA
NOTE: the triangle is labeled as follows:

16. Q1

17. Q1

18. Q2

19. Q2

20. Q3
• Using the law of cosine and law of sine
calculate the magnitude and direction of
the resultant pull on the log from the
concurrent forces of two students i.e Fa =
220kg at 21 degrees and Fb = 120kg at
333 degrees. (The angle of the forces are
measured anti-clockwise from the positive
X-axis which is taken to be 0 degrees).

21. Q3

22. Q4

23. Q4

24. Q5

25. Q5

26. Force/Vector Components
• Force/vector and a reference axis with
+ve and –ve direction.
• Normally used for force that act from two
components or more.
• Component :
1. Component X-axis
2. Component Y-axis

27. Components
Y-axis
X-axis
+ve
+ve
-ve
-ve
200kg
300kg
50kg
Forces and directions

30. Q1

31. Q1

32. Q2. Determine the resultant of four forces applied to the top of the
vertical Post shown in Figure 2.15
40KN
60KN

33. Q2

34. Q3

35. Q3

36. Wood Properties (Bending and Tensile)
• Strength is often defined as the ability to resist
applied stress, and the strength of the material is
synonymous with resistance of the material.
• The strength or mechanical properties of wood
is more complicated because wood is an
anisotropic, heterogeneous material, subject to
species differences, biological variability and
wide array of natural irregularities and defect.

37. Properties How or where this property is important
a) Strength properties
1.Compression strength parallel to the
grain
Determines the load a beam will carry
2. Compression perpendicular to the grain Determine the load a short post or column
will carry.
3. Tension strength parallel to the grain Important for the bottom member in a
wood truss and the design of connections
between structural members.
4. Tension perpendicular to the grain Important in design of the connections
between wood members in a building.
5. Work to maximum load Measure of the energy absorbed by a
specimen as it is slowly bent.
b) Elastic properties
1. Modulus of elasticity Measure of the resistance to bending, i.e.,
directly related to the stiffness of a beam,
also a factor in the strength of a long
column.
2. Modulus of elasticity parallel to the
grain.
Measure of the resistance to elongation or
shortening of a specimen under tension or
compression.
The strength and resistance to deformation of a material are referred to as its
mechanical properties

38. • Wood is very strong
in compression
parallel to grain
because the wood
cells act as tiny
columns or tubes
bonded together,
giving and receiving
support from.

39. • Strength in
compression
perpendicular to grain
is difficult to measure.
Compressive strength
increases with
deformation, reaching
a maximum when the
wood is compressed
to about one third of
its original thickness.

40. 1. Wood is also strong
in tension parallel to
grain. Knots reduce
the strength, but this
is already
considered in setting
design strength
properties.

41. 1. Wood is relatively
weak in tension
perpendicular to
grain. However, it is
rarely required to
take much load in
that direction except
for secondary
stresses in some
curved members.

42. • Wood is very strong in
bending. Shallow beams
have relatively greater
resistance to bending in
comparison to
proportionately deeper
beams. Therefore, depth
effect is considered in
setting design properties.

43. • Longitudinal or
horizontal shear is
often a controlling
factor in beam design.
It is caused by
bending loads,
creating maximum
longitudinal shear
stresses parallel to
grain at the neutral
axis.

44. Stress and Strain