force system

Force System

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.

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.

• 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.

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

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.

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.

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.

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

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

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 F 2

(a) (b)

Figure 3.4 Resultant of Two Concurrent Forces

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

F1 A (F2) C F1 R (F1) O F2 O B F2

(a) (b)


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

F1 A (F2) C F1 R (F1) O F2 O B F2

(a) (b)


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 + F22 - 2F1F2cos

or R2 = OB2 + BC2 - 2OB.BC.cos @ R2 = OA2 + AC2 - 2OA.AC.cos

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:

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).

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-axis2. Component Y-axis

Components

Y-axis

X-axis

+ve

+ve

-ve

-ve

200kg300kg

50kg

Forces and directions

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

40KN

60KN

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.

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

• 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.

• 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.

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

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.

• 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.

• 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.

Stress and Strain

force system

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