Fundamental principles of engineering. BADI Year 1. Fundamental principles. Suppose we design a chair. We need to know how much weight the chair must support.
BADI Year 1
Suppose we design a chair. We need to know how much weight the chair must support.
We could safely make the chair from a solid block of steel, or mahogany. However these would be expensive and rather heavy! (also not very green!)
For elegance and economy we usually choose to use the minimum amount of material. This must be based on an understanding of the stresses imposed on each part of the chair, and the ability of the materials used to withstand these stresses.
We experience mass in two main ways:
NB Mass is not the same as weight! We measure mass in kg but your dumbell (10kg) would weigh nothing in space – however it would have the same amount of matter, and be just as hard to accelerate!
Cant be seen, we experience force
Force is measured in Newtons (N) and 1 Newton is roughly the force exerted by an apple in the earth’s gravitation. (Actually 1kg m s-2: 9.81N is the force exerted by 1kg)
The earth pushes us up by the same amount as gravity attracts us down!
What is making this balancing force and how does it work?
F = 588N
Fr = 588N
When a force is applied to a body the body will be deformed by the force. The body may remain deformed afterwards (like clay) or spring back (like a rubber band).
Deformation is what produces the force that stops us from sinking into the earth. The material we walk on can be elastic (like floorboards) or plastic (like sand).
The work done in deforming the material is
4. Work = Force * distance.
Hooke (1635 – 1703) noted that the length of an elastic* solid changed in exact relation to the force applied.Hooke’s law as applied to a wire under tension
Original length Lo
Wire of cross-sectional area A
Change L in length due to applied force
We define stress as the internal force at a point within the body. There are different ways in which a body can be stressed (see later)5: Stress s = force per unit area s= F / A
We define strain as the relative change in dimension of a body that results from a stress.6: Strain e = change in length / original length Strain e = L / Lo
Hookes Law can be expressed as strain stress.
The constant of proportionality is the elastic modulus.
In this example of a body under tension it is
7: Y = s / e
When a force acts at a distance from a point we call this a solid changed in exact relation to the force applied.moment. The moment of the force F at point P is Fx and acts in the same direction as the force.
We will use this notion later in combining the effect of forces.
PMoment and torque
P solid changed in exact relation to the force applied.Torque
When we use a spanner to turn a nut the force we apply to the handle is opposed by an equal and opposite force (reaction) at the nut.
This pair of forces is called a couple and produces a turning motion - we call this torque.
If point P is fixed in space but free to turn the turning force T is T = Fx and here acts in a clockwise direction.
Notice that moment is a vector, having magnitude and direction, while torque has only magnitude and sense
*Strictly work = force * displacement IN THE DIRECTION OF THE FORCE