Fundamental principles of engineeringBADI Year 1

Fundamental principlesSuppose 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.

So we need to learn some physics!

Fundamental principles 1: Newtons laws (1642 -1727)A body will continue in a state of rest or uniform straight-line motion unless acted upon by a force

The acceleration of a body is dependent on its mass and the total force acting on it F = m a

Every action has an equal and opposite reaction

Mass : the amount of matter in a bodyWe experience mass in two main ways:Through the effort required to lift the body against the earths gravity, andThrough its resistance to acceleration, i.e. its inertia. Try picking up a dumbell and shaking it rapidly. You are attempting to accelerate the dumbell and this takes a lot of force.

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!

ForceCant be seen, we experience force By its effects on our body and the way in which we need to oppose it to maintain our balance. By observing the effect it has on objects around us.

Force is measured in Newtons (N) and 1 Newton is roughly the force exerted by an apple in the earths gravitation. (Actually 1kg m s-2: 9.81N is the force exerted by 1kg)

Forces in equilibriumA man of mass m = 60kg experiences a force of F = 60 * 9.81 N = 588N due to gravity. (2)

If he was able to move freely in any direction (eg jump off roof) he would fall with an acceleration of a = F / M = 60kg / 60 * 9.81N = 9.81m s-2

If he is stationary, standing seated or lying down he is not accelerating. a=0; hence F/m = 0 so F = 0. This shows that the downforce acting on him is exactly balanced by the floor pushing him upwards!

Forces in equilibriumThe earth pushes us up by the same amount as gravity attracts us down!

What is making this balancing force and how does it work?Fr = 588NF = 588N

Restoring forceWhen 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.

Elastic and plasticConcrete is very hard and very elastic. When we walk on it we dont deform it very much, and it springs back when we move on. You can see the effect better if you walk on a trampoline. Hard elastic materials are easy to walk on because the energy used in deforming them is given back when you lift your foot.

Sand or mud are very plastic and you can see the change you have made by stepping on it. Wet sand is harder than dry sand and deforms less so each step uses less work, and makes it easier to walk on then dry sand.

Hookes law as applied to a wire under tension

Hooke (1635 1703) noted that the length of an elastic* solid changed in exact relation to the force applied.

Force FWire of cross-sectional area AOriginal length LoChange L in length due to applied force

StressWe 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

StrainWe 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 lawHookes 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 Youngs modulus

7:Y = s / e

Moment and torqueWhen a force acts at a distance from a point we call this a 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.

Distance xForce F

TorqueWhen 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.

Distance xForce FForce -FNotice that moment is a vector, having magnitude and direction, whiletorque has only magnitude and sense

Summary: concepts and equationsMass kgForce N( F = m * a )EquilibriumWork (Force * distance) * Newton metres or JoulesElastic and plasticStress (s= F / A) Newtons per square meterStrain (e = L / Lo)Youngs modulus (Y = s / e)Moment of a force CoupleTorque (T = Fx)

* Strictly work = force * displacement IN THE DIRECTION OF THE FORCE