Statics

Statics Basics

• Statics is the study of the forces that are both internal and external within a structure
• Statics is a branch of mechanics
• Statics deals with bodies at rest and systems where the momentum does not change
• Dynamics deals with changes in momentum

Forces, Moments, and Couples

• A force can is that which can produce a change in a body's state of motion
• Applying force to a mass will cause acceleration or deceleration
• Forces can be used to do work if energy is available
• Force is a vector quantity needing both magnitude (size) and direction to be fully defined
• Scalar quantities are defined by size only (e.g., temperature, length, time)
• Scale drawings can conveniently represent vectors
• A resultant net force calculation is required when forces act in different directions on a body
• One vector's tail should be moved to the other vector's head when adding vectors without changing magnitude or direction
• Complete the triangle with the resultant vector, where the head of the resultant meets the 'free' head of the vector you wish to add
• Aircraft wings produce an aerodynamic force, called lift, in flight
• Lift has horizontal and vertical components when the aircraft is banked during a turn
• Lift is the resultant force of the vertical and horizontal components
• When an object is in a state of equilibrium, it does not change its state of motion or rest, with the resultant of all forces acting on it being 0
• If a car is being pushed at one end by a person and opposed at the other end by a similar force, the car does not move. The sum of the positive and negative forces is 0

Moments

• The moment of a force is a measure of its tendency to rotate an object about a point
• This is different from the tendency for a body to move (translate) in the direction of the force
• For a moment to develop, force must act to twist the body
• Moment and torque are used interchangeably and measured using similar units, referring to turning effects, but moment applies in static situations while torque applies in dynamic applications
• A spinning motor shaft demonstrates torque, while a lever demonstrates moment
• A formula states moment = force × distance
• As SI and English units can be used in the above calculation, moments are generally expressed in newton-metres (Nm), foot-pounds (ft lb) or inch-pounds (in Ib).

Moment example

• A force of 300 Newtons is applied to the bicycle crank with a length (d) of 170 mm, the moment in newton-metres (Nm) caused about the centre shaft can be worked out by;
  • Adding the formula M = Fxd
  • Converting to correct units
  • Solving the equation; Moment = 300N × 0.170m, Moment = 51Nm

Moments of a wrench

• The torque in Nm exerted by the wrench on the bolt can be calculated by;
• Adding the formula M = Fxd
• Converting to correct units
• Solving the equation; Moment = 20N × 0.25m, Moment = 5Nm
• The torque exerted by the wrench on the bolt is 80 in lb, as Moment = 10 lb × 8 in Moment = 80 in lb

Applying Torque

• By not tightening a screw or bolt to the correct torque, you risk a component or accessory coming loose during operation. This could occur because a bolt or screw is loose from under-torquing or because the threads are damaged/stripped and not holding properly due to over-torquing

Equilibrium Principle

• The principle of moments states that when in equilibrium, the total sum of the anticlockwise moment is equal to the total sum of the clockwise moment
• A system that is stable or balanced is in equilibrium
• A state of equilibrium can be explained by considering two people on a seesaw

Levers

• Either side of a lever has a moment which is the force multiplied by the distance from the fulcrum or pivot (called the arm)
• The system is balanced and the load will be raised when the load moment and the effort moment are equal
• Leverage explained; the smaller effort force moves through a larger arc to raise the heavier load a short distance
• A device used to gain mechanical advantage (MA) in a mechanical machine is an example of a lever

First-Class Lever

• The purpose of a lever is to perform work for a load (L) to be lifted by an effort (E) pivoting around a fulcrum (F)
• The machine has an MA greater than 1, making a crowbar an example as the the load moved is greater than the effort used
• The fulcrum is situated between the load and the effort, but also the load is greater than the effort
• Even if the load arm of a first-class lever is longer than the effort arm the load only needs to be raised a short distance; the MA will be less than 1
• Effort travels a larger distance, hence leverage

Second-Class Lever

• Second-class lever examples; cockpit control levers (throttle or thrust lever) and a simple wheelbarrow
• The load is situated between the fulcrum and the effort
• The effort arm is greater than the load arm, which is why the load is greater than the effort
• The MA of any second-class lever is greater than 1

Third Class Lever

• The effort is between the fulcrum and the load
• The effort is greater than the load and moves through a smaller distance
• An example is the retraction mechanism on aircraft landing gear
• MA is less than 1

Couples of Forces

• A system of two equal forces, which are parallel and act in opposite directions on an object, but not through the same point, resulting in a turning effect, is a Couplings of Forces
• The moment of a couple of forces around the axis is equal to the sum of the moment of each force of the couples; each force exerts an anticlockwise movement
• Described via formula as: Moment of couple = F × perpendicular distance between the two forces
• The moment of a couple of forces is equal to the product of the intensity of the force and the distance between the two forces

Torque requirements example

• If 12 Nm of torque is required at the centre of moments to rotate a valve;
• Check for compatible units of newton-metres and metres
• F is the force applied, 'd' is the distance between applied forces
• Solve the equation for F: Moment of a couple = F × d; 12 Nm = F (Newtons) × 0.4 (metres); F = 30N

Gravity

• Gravity is the invisible force of attraction that exists between two objects
• Gravity attracts all objects to one another with the force of gravity being proportional to the product of the mass of the two objects
• The force of gravity is inversely proportional to the square of the distance between them
• The weight of an object decreases with increasing altitude
• Newton's formula to calculate the force of gravitational attraction between two bodies is: F=G× m1m2/r^2
  • F is the gravitational force acting between the two objects
  • m₁ and m2 are the masses of the two objects
  • r is the distance between the centres of their masses
  • G is the gravitational constant
• Earth's force of attraction is highly noticeable

Weight Measurement

• Weight is the gravitational pull of Earth on a body, exerted in a direction from the body to the centre of Earth or in a vertical direction
• It can be calculated by the formula: W = mg
• W = weight of a body, in newtons (N)
• m = mass of the body, in kilograms (kg)
• g = acceleration of gravity (9.8 m/s² at or near the surface of Earth)
• The newton is the official unit of force in the International System of Units (SI)
• The kilogram (1000 g) is the SI unit of mass
• One newton is the amount of force needed for a mass of 1 kg to accelerate at 1 m/s when acted on by the force
• Acceleration of an object due to gravity near Earth's surface is 9.8 m/s2
• Weight should be identified in newtons as it is 'force of attraction' and the formula is a renamed version of Newton's Second Law (force = mass × acceleration)

Weight vs Mass

• Pound is the English unit of measurement
• The force applied on a mass of 1lb by the acceleration due to gravity is termed a pound
• A pound is a non technical unit of force also called the weight
• Mass is constant at any point of Earth.
• Weight varies at different geographic points.
• Gravity varies across Earth as the planet isn't perfectly spherical or uniformly dense
• Gravity is weaker at the equator due to centrifugal forces produced by the planet's rotation
• Example values of g:
• At the poles: g = 9.83 m/s²
• In France: g = 9.81 m/s²
• At the equator: g = 9.78 m/s²
• On the moon: g = 1.63 m/s²

Weight in France

• The weight in France of a body whose mass is 1 kg is 9.81N
• Using the force of gravity; 9.81 m/s²
• Formula; W = mg = 1 x 9.81
• Which is; W = 9.81N

Centre of Gravity

• CG in physics, is an imaginary point in a body of matter where, for convenience in certain calculations, the total weight of the body may be thought to be concentrated
• CG is useful for predicting the behaviour of objects when acted upon by gravity and other external forces
• Vector representation of gravitational forces is shown with respect to the CG
• Finding CG in objects: The CG is the point where all the mass of the object is concentrated
• No net moment acts on the object when it is supported at its CG
• Suspension of a freely moving object ensures the CG being directly below the suspension point
• Find an object's CG experimentally by hanging it from several points, marking a vertical line. The intersection of two or more vertical lines drawn from the plumb constitutes the item's CG

Aircraft Centre of Gravity

• Aircraft CG is the point at which the aircraft would balance if suspended
• As the location of the CG affects the aircraft's stability, it must fall within the manufacturer's specified limits
• CG is calculated after supporting the aircraft on at least two sets of weighing scales
• Static Balancing of Rotating Components: Even with regular-shaped objects (disc, wheel, or propeller), slight variations in thickness or dimensions can occur due to manufacturing tolerances, wear, or damage
• Because the material density may not be perfectly uniform, this means the CG may not coincide with the geometric centre or axis of rotation
• The CG must be shifted to lie on the axis of rotation; this can be done by adding small masses of material to the light side or removing small masses from its heavy side
• Propeller balancing involves rolling the supporting mandrel (or spindle) freely on a pair of horizontal knife edges with minimal friction
• Stationary propeller in any selected position means perfect balance
• Many components are balanced; wheel assemblies, rotors in helicopters, compressors/turbines, fans, the rotors in generators, magnetos and gyroscopes
• At very high speed, even a tiny imbalance may produce excessive vibration

Conditions of Loading

• Applying a force to an object is known as loading
• There are five fundamental loading conditions: tension, compression, bending, shear and torsion
• Tension: Forces are pulling away or applied to the ends, causing it to stretch
• Compression: Force is squeezing material together

Bending examples

• Bending is a combination of tension and compression (upper portion stretches, lower portion crushes together)
• In flight, an aeroplane experiences bending force; aerodynamic lift tries to raise the wing, causing compression on the top and tension on the bottom
• When the aeroplane is on the ground sitting on its landing gear, gravity tries to bend the wing downward
• This subjects the bottom of the wing to compression and the top wing to tension

Shearing

• An example includes cutting a piece of paper with scissors
• Shear in an aircraft structure is a stress when two fastened pieces of material tend to separate
• A clevis bolt has shear stress acting on it; often used to secure a cable to a part of the airframe, a fork fitting secures the end of the cable, and the fork attaches to an eye on the airframe with the bolt
• The fork is designed to take high shear loads under tension to not slide off the eye. In this way, it doesn't cut through the clevis

Torsion Forces

• Torsional stresses result from a twisting force
• Twisting a wet rag or towel creates torsion forces
• If a torsional loading is applied to a rod fixed at one end, the twisting force will try to slide sections of material over each other, creating compression loading in the twist direction and tension loading opposite the twist

Static and Dynamic Loading

• Static loading refers to a constant force applied to a material, and dynamic/cyclic loading is where the force fluctuates
• How a material is loaded greatly affects its mechanical properties and determines how/if the component will fail, and the amount of warning if any before that occurs.

Stress Term

• The term stress expresses the loading in terms of force applied to a certain cross-sectional area of an object
• Perspective of loading- stress is the applied force or system of forces that tends to deform a body
• Materials perspective- it's the internal distribution of forces that balance and react to applied loads
• The loading condition also affects whether stress distribution is uniform
• A bar experiencing pure tension has a uniform tensile stress distribution
• A bar loaded in bending will have a stress distribition which varies with distance perpendicular to the normal axis

Strain Definition

• Strain is the response of a system to an applied stress causing the material to deform after being loaded with a force
• Engineering strain is the amount of deformation in the direction of the applied force divided by the material's initial length
• Strain results in a unitless number (often denoted as inches per inch or metres per metre)
• Strain distribution may or may not be uniform in a complex structural element

Deformation

• If the stress is small, the material may only strain a small amount and return to its original size, referred to as elastic deformation due to the similarity to elastic
• Elastic deformation occurs only when stresses are lower than a material's critical yield strength
• With stress beyond that limit, the material remains in a deformed condition after load removal, called plastic deformation

Stress-Strain Curve

• Engineers analyze stresses and use resources to find appropriate materials for aircraft components
• The stress-versus-strain curve informs about the material in tension
• Materials are brittle (glass) or ductile (steel or aluminum).
• Brittle materials fracture without bending
• Ductile materials bend and deform without returning to original shape
• Stress-strain graphs/curves for ductile materials:
• Elastic region is linear
• It represents material stretching, and there is a return to original form if stresses are removed
• Yield point
• Material starts to experience plastic deformation
• Larger ductile region
• Ultimate tensile strength (UTS) point
• Material weakens and starts "necking"
• Reduction in the cross-sectional area also occurs
• Breaking strength (or fracture point)
• Where the material breaks completely

Failure Point

• The point where that the two meet as a result is where the materials fail
• A brittle material will break shortly after reaching its yield point because there is no necking that occurs
• Ultimate tensile strength = breaking strength (fracture point)

Fatique

• Moving parts experience vibration, load changes and temperature changes during operation
• Accumulation of loadings may eventually result in fatigue failure (cyclic loading)
• Fatigue failure as common as overload failure within aircraft
• Maximum stress values that cause fatigue are less than ultimate tensile stress of the material and may be below the yield stress limit of the material

Mechanics of Matter

• Solids have specific shapes and definite volumes as molecules are in close proximity with significant force
  • Certain molecules organize into a lattice- molecules connected by rigid bonds, which allow only limited freedom of movement
  • Solids resist shearing

Liquids/Gases

• Both categorized as fluids because they yield to shearing forces
• Bonds exist between the molecules in liquids, but possess fewer bonds than solids
• Molecules are not locked in place; they can move around
• Similar distance properties to solids in terms of molecules
  • Liquids have definite volumes
• Gases are not bonded, can have large separations between molecules, and have neither specific shape nor definite volume (Left) Atoms in a solid are always in close contact with neighboring atoms with strong bonds (Middle) Atoms in a liquid are also in close contact but can slide over one another
• Forces between the atoms strongly resist attempts at compression (Right) Atoms in a gas move about freely and are separated by large distances
• A gas must be held in a closed container to prevent it from expanding freely and escaping Liquids flow (making liquids fluids) as atoms/molecules are free to slide and change neighbors, creating a mutual attraction
• Liquids resist compression Atoms in gases are separated by distances
• In gases, atoms collide, allowing the gases to compress and flow
• Unlike liquids, gases will escape

Density Defined

• Defined as a material’s mass per unit volume of lowercase Greek letter rho (p)
• Density is an important descriptor for a substance
• Density = mass/volume
• Solid densities are comparable with liquids, in that their respective atoms are in contact
• Solids exhibit the lowest densities because atoms in gases are separated by large amounts of empty space
• Solids/liquids: heating/cooling can cause the density to vary (typically the density will decrease as temperature increases, as with water below 4°C
• The International of Pure and Applied Chemistry (IUPAC) uses a standardized value of 0°C and 100 kPa of pressure
• The International of Pure and Applied Chemistry (IUPAC), the International Civil Aviation Organization (ICAO) standard (1013.25 hPa) at 15°C at sea level is used in an aircraft environment

Units Table

• The SI unit of density is kg/m³ (kilogram per cubic metre)
• Cgs unit of density is G/cm³ (water has value of 1)

Pressure Basics

• Pressure is the amount of force applied perpendicular (normal) to a surface per unit of area
• P = pressure
• F = resultant force
• A = surface subjected to the force Formula; Pressure = force over area (N/m2) Every molecule of a solid block (with gravity) has weight and exerts a small force to create pressure

Pressure Measuring

• SI unit is Pascal (Pa) with means newtons per square metre (N/m2) and area is measured in square metres
• Pounds per square inch or more accurately, pound-force (psi) is the non-SI unit
  • Equivalent for SI units - 1 psi approximately equals 6895 N/m² (or 6895 Pa) Solid surface can exert pressure but also liquids and gasses

Air Pressure

• Air pressure is the weight of the atmosphere pressing down on a location
• The air pressure is greatest as low altitudes as a large force of air is above that location
• Atmospheric pressure varies with height

Measuring

• A barometer measures atmospheric pressure
• Evangelista Torricelli invented it

Mercury

• Created in 1643, it used mercury to measure pressure
• If there is an increase in air pressure, the atmosphere pushes mercury up inside the glass tube
• Air pressure lessens, then less force is on Mercury, and the height of mercury lowers
• A method of measurements references height and is given in inches mercury (in Hg)

Aneroid

• Sealed wafers that shrink or spread as pressure levels change
• Wafers push as pressure increases
• As atmospheric pressure decreases, wafers expand
• Changes are transmitted to a mechanical indicator

Pressure reporting

• Mercury barometer records in inches or millimetres of mercury (in Hg or mm Hg)
• Pounds per square inch (psi) are useful, pascal (Pa) is standard

Pressure Example

• Pascals (Pa) is used in AU aviation
• 100 Pa = 1 hectopascal (hPa)
• 1000 Pa= 1 kilopascal (kPa)
• the atmospheres (atm) also expresses pressure
• 1 atm is 101325 PA or 101.325 kPa
• Bars (mb) can also be used to describe pressure

International Standard Atmosphere

• Temperature varies across the globe due to the unequal solar heating on Earth
• Coriolis Effect: Air is twisted to the right and left of the Northern and Southern Hemisphere, respectively
• Moving system pressures result in hypothetical models

Atmospheric model

• The International Civil Aviation Organization (ICAO) introduced the International Standard Atmosphere (ISA) by in 1952 -Lists pressure, temperature and density based on altitude
• Temperature rates decrease with height
• Constant levels of temperature result in the air increasing
• There are 5 parameters
• Pressure - 101.3 kPa/29.9 in Hg
• Temperature - +15 °C
• Temperature lapse rate - 2 °C per 1,000 ft
• Density- 1.225 kg/m3
• Sea level temperature is constant

Gas Under Pressure

• Molecules move in all directions with force
• Can exert force on enclosed container
• These collisions generate a force and cause pressure
• Pressure is applied equally to all surfaces
• Increased particles result in increased pressure

Deodorant Spray

• The temperature of aerosol increases the internal pressure to potentially cause the container to explode
• If the enclosed gas is heated, its particles more around

Pressure Measurement

• Measurements in relation to pressures in 2 places
• One location is the reference, the other is the measurement
• Measured values can be categorized in 3 ways
• absolute pressure
• gauge pressure
• differential pressure

Key points in pressure

• Absolute pressure: pressure taken in a perfect vacuum
• Gauge pressure: pressure taken in atmospheric pressure
• differential pressure: when there's no fixed reference

Formula Applications

• The weather forecast is in absolute pressure
• Atmospheric pressure is 14.696 psia. Adding subscripts results with 1000 mbara -
• Gauge pressures measure at a constant
• Atmospheric pressure or ISA 101,325 Pa or 6 psig with 2 barg
• Pressure is measured relative to what the sealed vessel has
• outside is the external pressure, and the inside is the denotation

Differential

• The difference is the difference in magnitude between the readings
• Ex is; 6 psid or 2 bard

Water Force in Physics

• Both Water and Air are able to move from place to place
• Water is incompressible due to almost constant density
• Air is compressible because its density changes with pressureHydrostatic pressure is by a liquid due to fluid
• If the object is more deep, gravity provides more force Top has the less holes and is greater by more Bottom has the most pressure
• If an object submerged, water applies force and exerts pressure

Pressure At Depth

• A calculation requires; the amount of fluid or density
• The formulas provided are
• Weight of fluid or h20
• Calculation 1 = fluid constant
• Calculation 2 = volume or area
• The units used
• Pascals volume
• Newtons volume
• The most important of the value is what is doesnt display
• Pressure can be different as there are various containers

Pascal's Law

• Pressure= Force times height and is the base of the area
• A force that is measured in Newtons is extereted on the inside. The pressure of the liquid is the under, but it transmitts throughout the the liquaid

Pascal and Gravity

• Law (also referred to as Pascal's principle or the principle of transmission of fluid-pressure) is established by French mathematician Blaise Pascal (1623-1662) which states that the exerted pressure in a liquid will distribute across the vessel's surface equally
• Bramah applied this idea to devlop A hydrualic press, a small input will generate an output.
• The pressure on the 2nd part will travel along the pressure
• a result would be 100lbs of force
• a real eample is a hydraulic jack

Fluid Formations

• Buoyant force in a fluid
• Fluids exert a force on placed fluids or things

The Three stages

• The pressure that creates a force will cause the weight to rise, if it dosent It will stay on top of the liquid
• With increased depths, there comes increased pressures
• Top liquid will apply the lesser pressure
• Bottom liquid will apply the greatest pressure

Achimedes

• It states when the force is constant on the object the weight will be balanced with the fluid.
• In this moment that the force is balanced the density can be calcuolated due to the 2 levels being balanced in the water Archimedes is valid if The material in the circle is on the surface. We can make place of the liquid in submerged Objects must be the same as the others one's on top