Statics Notes PDF

TOPIC 2.1: STATICS A force can be described as that which can produce a change in a body's state of motion. An application of force will:  start  stop  accelerate, or  decelerate, a mass If **energy** is **available**, then forces can be used to do **work**. Sometimes, forces act at diff...

TOPIC 2.1: STATICS A force can be described as that which can produce a change in a body's state of motion. An application of force will:  start  stop  accelerate, or  decelerate, a mass If **energy** is **available**, then forces can be used to do **work**. Sometimes, forces act at different directions on a body. In cases such as these, forces must be resolved to calculate a **resultant net force.** When an object does not change its state of motion or rest, **the resultant of all the forces acting on it is zero,** and it is said to be in a state of **equilibrium**. Moments and Levers Either side of the lever below, has a moment which is the force multiplied by the distance, from the fulcrum, or pivot, (called the arm ) The system is balanced when the load moment and the effort moment are equal. If the effort force is increased, the load will be raised. A lever is an example of a Simple Machine, which is a device used to gain a Mechanical Advantage, MA. MA = Load/Effort. 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). If the load moved is greater than the effort used, the machine has a positive MA. An example of a **first-class** lever is a **CROWBAR** Examples of a **second-class lever** include **cockpit control levers**, such as a throttle or thrust lever, and a simple **wheelbarrow.** The load is situated between the fulcrum and the effort. An example of a **third-class lever** is the retraction mechanism on an aircraft landing Gear The effort is between the fulcrum and the load. Velocity Ratio A Velocity Ratio is the direct ratio of two speeds that may be present in the same system. For example, consider a pulley system that uses an MA of 4. The operator will pull through a metre of rope to raise the load by 0.25m. Therefore, the rope moves 4 times as fast as the load is being raised. COUPLES A 'couple' is a type of moment which is derived from **two equal forces acting in** **parallel but opposite directions on two different points of a body.** The forces are **equal, but act in opposite direction**. The forces produce a '**torque'** or twisting force to the aircraft, causing it to turn. Centre of Gravity (CG) The Centre of Gravity ('CG' or 'C of G') of a body is the point from where the weight appears to act, irrespective of the body's position. The cg of regularly shaped bodies of uniform density is easy to find. It is simply the geometric centre of the bodies. If an irregularly shaped solid is hung first from one point, and then from another point, its CG is the intersection of the verticals passing through these points. STRESS, STRAIN and ELASTICITY **Stress** is the **force acting through a section of solid material** and defined as **force per** **unit area.** **Stress = force/area** **Strain** is the deformation of the material as a result of the stress. If the strain is **less than the material's elastic limit**, the elasticity of the material will allow it to **return to its natural length.** Strain below the elastic limit is directly proportional to the applied stress (Hooke's Law). Doubling stress will double the strain, (below the elastic limit)  **Tension** describes forces that tend to pull an object apart. Flexible steel cable used in aircraft control systems is an example of a component designed to withstand tension loads. **Compression** is the resistance to an external force that tries to push an object together. The weight of an aircraft causes compressive stress to the runway. Aircraft riveting is performed using compressive forces.  **Shear stresses** occur when external forces distort a body so that adjacent layers of material tend to **slide over one another**. Shear stress tries to slice a body apart. Shear stress may also occur in **fluids**, for example a layer of oil or grease between two sliding metal surfaces. **Aerodynamic and gravitationa**l forces try to bend the wing or blade upwards and downwards. Consequently, the top and bottom surfaces of the wing are under **alternating compression and tensile stresses** and must be constructed to withstand the fatigue that could develop from this situation. TORSIONAL STRESS Torsion or torque is a form of shear stress. If a twisting force is applied to a rod that is fixed at one end, the twist will try and slide sections of material over each other. The result is that, in the **direction of the twist, there is compression stress** and in the **direction opposite to the twist, tension stress** develops. Residual Stress ("Locked In Stress") Abrupt or uneven temperature changes tend to cause internal stress. This often occurs when heat-treating metals. This effect often explains why a component fails in service even though its externally applied stress levels are low. PRESSURE and BUOYANCY Both liquids and gases are fluids, therefore the theory behind buoyancy and pressure in liquids, such as water, and gases, such as air, is similar. An important difference to remember, though, is that **liquids are considered** **incompressible,** **that is, have a constant density, while gases are compressible**. Pressure is defined as: Force per unit area Pressure in Fluids Pressure is still defined as Force per unit area, but in a fluid it is caused by the continual bombardment of the molecules against the inside of the container. The pressure exerted by a column of liquid is determined **by the vertical height of the** **column, gravity, and the density of the fluid.** **The pressure** is not affected by the volume or shape of the liquid. Density and Specific Gravity **Density** is defined as the **mass per unit volume** of a substance. When the density of other liquids are compared to water, a table of **comparative densities or specific gravities** can be determined. **Gasoline** has a **specific gravity of 0.72,** which means its **weight is 72% of the same** **amount of water.** Gases are compared to air to obtain an SG. The term Relative Density is used to compare the density of air at different altitudes to sea level The SG of aviation fuel varies due to a variety of factors such as: refining process; storage facilities; ambient conditions. Buoyancy **Archimedes principle** states that an item placed in fluid will displace a volume of fluid equal to its own volume. Furthermore, the object submerged in the fluid is supported by a force equal to the weight of the fluid displaced. This is the **buoyancy force**. Therefore if a body displaces more fluid than its own weight it will float. Lower density materials float on higher density materials. Use of Pressure for MA Pascal's law states ,that when pressure is applied to a confined liquid, **the liquid** **exerts an equal pressure at right angles to the container that encloses it** Pascal's Law can be used to provide Mechanical Advantage, e.g. A Hydraulic Jack Properties of Solids, Liquids and Gases **Solids** have a definite shape and a definite volume which is independent of its container. In a solid the forces (bonds) that keep the atoms or molecules together are strong. Therefore, a solid does not require outside support to maintain its shape. **Both liquids and gases are classified as fluids.** **A liquid is regarded as incompressible, (fixed density) whereas a gas is comparatively** **easy to compress.** A change in volume of a gas can easily be achieved by changes of temperature and/or pressure. A given mass of gas has no fixed volume and will expand continuously unless restrained by a containing vessel.