Module 4 Engineering Mechanics

1. All aircraft are subjected to five major stresses: tension – it resists pulling forces,
compression –it resists the crushing force, bending –combination of compression and
tension forces, shear and torsion (BCTTS)
2. Spar are in wings whereas as Longeron are in fuselage.
3. I- beam spar: web (VC) and cap (horizontal component)
4. Cowl flaps are moveable parts of the cowling that open and close to regulate the engine
temperature.
5. Fowler Flap: Flaps that slide aft to increase the total area of the wing
6. Teetering hinges in a semi‐rigid system allow for movement of the flap up and down
while preventing movement back and forth.
7. Monocoque: Bulk head, formers – they are designed only with the skin or no skin
stiffened
8. Semi-monocoque: they have skin stiffened
a. Stringer (attached between formers and bulkhead), short and light structural
elements.
b. Longeron - used to prevent the bending
c. bulk head -
d. formers –
9. Keelson- It is a large beam placed at fuselage bottom and it is a structural element
through which bending loads are carried out
10. Box beam wing constructions are used on transport category aircraft
11. Wing: Ribs (gives aerodynamic shape, Ribs can be lightened by stamping holes in the
assembly), Spar (gives structural support and support all distributed loads as well as
concentrated weights) and stringer
a. False ribs: They are located entirely forward of the front spar and they are used to
shape and strengthen the wing leading edge. They do not span the entire wing
chord.
12. Fly by wire: it uses electrical and hydraulic power to move the elevator.
13. Winglets (sharklet): they are responsible for breaking vortices thereby reducing the drag
on the airplane.
14. Strain: the degree of deformation of material
15. Stress is a material’s internal resistance, or counterforce, that opposes deformation
16. Conventional type landing gear: Allows for greater clearance between the propeller,
which were longer back then, and loose debris when operating on unpaved runway.
17. NOTAR anti torque system: Stands for “no tail rotor” because it has an engine driven
adjustable fan located in the tail boom
18. Often wings are of full cantilever design. This means they are built so that no external
bracing is needed.
19. Aircraft structure and loads
a. Body force: acting through volume of the body e.g. force due to gravity
b. Surface force: acting through surface of an object e.g. shear force
c. Limit load : (applied load)- largest load expected in normal cycle without any
permanent deformation
d. Ultimate load: (design load) – largest load that structure is able to withstand
without breaking
i. UL= LM*FOS value of FOS is 1.5
ii. FOS is used to increase the safety of the aircraft
 e. Load factor: ratio of aerodynamic forces to the weight of the aircraft.
f. Power plant load: thrust, torque, duct pressure, vibration
g. Air loads acting on the aircraft during flight in the air. E.g. maneuver, gust,
buffet, control deflection
h. Other load: bird strike, actuation, crash, pressurization, fuel pressure, towing
i. Inertial load: acceleration, rotation, dynamic, vibration and flutter
j. When an aircraft flies in the air, it might experience various types of loads such as
lift, drag Thrust, vibration, gust
k. Euler load is defined as the highest compression load, which will not cause the
elastic column buckling. Euler load is also termed as critical load.
i. Euler load = π2EI/(Effective length)2
20. Structure fundamental
a. Stress= F/A - internal resistive force per unit cross section area - produced due
to internal forces
b. Pressure- produced due to external force
c. Strain= change in length / original length
d. Young modulus(Y) and elastic constraints (E) = stress/strain
e. Shear modulus (G) = E / 2(1+μ), elastic constant E and Poisson’s ratio µ
f. Creep: Tendency of some materials to get deform slowly and permanently under
low but sustained stress.
21. Materials
a. Woods: they are easy to fabricate and repair. Disadvantage: moisture sensitivity
b. For high strength, application 7075 aluminium alloy is widely used. 7075 is
alloyed with zinc, copper and magnesium.
c. Magnesium is used in control hinges, wheels, engine mounts. It has good
strength to weight ratio. It can resist the high temperature.

4.1 Applied mechanics: Concept of Particles, rigid and deformable bodies, Concept in Statics and
Static Equilibrium, Forces acting on particle and rigid body, Friction, Newton’s law of motion,
Newton’s Law of Gravitation, Work Energy Theorem, Impulse Momentum Principle.

1. Impulse momentum theorem:

 Impulse =force x time
 Derived from 2nd law of Newton’s
 F=dp/dt here F is the force, p is the momentum and t is the time and dp/dt si the rate of
change of momentum
 Statement: the impulse applied to a body is equal to the change of momentum
i.e. Ft= Pf-Po
 it quantify how long a force acts in a body

2. Work energy theorem

a. W= Kf-Ki here
i. W is the net work done on an object W= Wg (gravity)+Wn (reasonable
force)+Wf (friction)
ii. kf is the final kinetic energy and Ki is the initial KE
b. Application
i. Analysing the situation where rigid body should move under several forces

3. Newton law of motion

 a. First law: if an object is at rest, it remains at rest, or if it is in motion remains in
motion at a constant velocity unless an external force acts on it.
i. It is also called the law of inertia.
b. Second law: The change of motion is proportional to the applied force and takes
place in the direction of the straight line along which that force acts.
i. It explain the measure of force and establishes the fundamental equation of
dynamics.
c. Third law: To every action, there is always an equal and contrary reaction; or the
mutual actions of any two bodies are always equal and oppositely directed along the
same straight line.
4. Principle of conservation of momentum: whenever there is no external force in the system
then the total momentum of the system remains constant.
a. Initial momentum (P1)= Final momentum (P2)
5. Newton’s law of gravitation:
a. Weight on the body = gravitational force acting
b. Computed both for static and dynamics
c. F= G m1m1/r2
d. W = G mMe/r2 where Me is the mass of the earth
e. g=GMe/r2

6. Friction: It is the property of a surface that opposes the relative motion between two
surface
a. F= coefficient of friction x normal force (N)
b. Types
i. Static friction – friction between object at rest and a rough surface on
which it is placed. No relative motion between the contacting
surfaces. Static friction is the value of the limiting friction just
before slipping occurs. The co-efficient of static friction is more
than dynamic friction.
ii. Dynamic friction: Dynamic friction is the force of friction experienced
by a body when it is in motion. It is the value of frictional force after
slipping has occurred
iii. Kinetic friction/ sliding friction – friction between the two relative motion
surfaces. Kinetic friction is always greater than rolling friction
iv. Rolling friction – when the block (circular body) is rolling on a surface
c. Co-efficient of sliding friction for steel is 0.18. When railway wheels
made of steel rolls on rails made of steel, the co-efficient of rolling
friction becomes 0.004.

7. Statics is the branch of mechanics studying forces that act on bodies in static or dynamic
equilibrium.
a. Static equilibrium is a state where bodies are at rest;
i. Example: An iron box on a bench is an example of static equilibrium. Other
instances of static equilibrium include a tower of Jenga blocks, rock balance
sculptures, etc. As long as the components of systems do not disintegrate,
they are in static equilibrium.
b. Dynamic equilibrium is a state where bodies are moving at a constant velocity
(rectilinear motion). In both cases, the sum of the forces acting on them is zero.
1. Equilibrium law:
 a. Two forces are said to be in equilibrium only if the forces
are equal in magnitude, opposite in direction, and are
collinear.

4.2 Theory of elasticity: Stress, Strain, Hook’s Law, Modulus of elasticity, Thermal stress, longitudinal
strain, Lateral strain, Poisson’s ratio, volumetric strain, bulk modulus, strain energy and impact
loading.

1. Stress
a. F/A
b. Longitudinal stress: occurs when the stress is normal to the body surface area
and changes the body length.
1. Tensile stress – occurs when substance is under tension (when
something is being pulled)
2. Compressive stress – a material undergoes causes it to shrink in
volume
c. Bulk stress (volumetric stress)- occurs when the force applied in all the
dimensions
d. Tangential stress: occurs when tension is tangential or parallel to the body
surface.
2. Strain
a. Change in dimension to the original dimension
b. Types
1. Longitudinal strain,
2. Volume strain: EV=dv/v
3. Shearing strain/tangential strain
3. Stress strain curve
a. Elastic line are also called = deflection curve /elastic axis

4. Young’s modulus of elasticity (Y)/ modulus of elasticity

a. It is the amount of stress required to achieve a unit of strain
b. A larger modulus implies the material is harder to deform
c. Y=stress/strain
5. Hooke’s law (Elastic law)
 a. Stress is directly proportional to strain ie σ = Eε where E is the modulus of
elasticity or young’s modulus
6. Potassium when added to gold increases its elasticity thereby making it easy to be
electroplated.
7. Poisson’s ratio = Y/2n – 1
8. While being hammered or rolled, crystals break into smaller units resulting in
increase of their elastic properties
9. Annealing is the process of heating a material and then gradually cooling it. It results
in decrease in elastic property
10. Rigidity modulus is defined as the ratio between tangential stress and shearing strain
11. Air can be compressed easily while water is incompressible and bulk modulus is
reciprocal of compressibility. Therefore, water is more elastic than air.
12. a) Elastic modulus - Y
b) Plastic modulus
c) Poisson’s ratio
d) Stress modulus
13. A material can be beaten into thin plates by its property of malleability.
14. Types of modulus
a. Young’s modulus (E)/ Elastic constant: tensile stress (compressive stress)
to tensile strain (compressive strain)

b. Shear modulus (G) (Rigidity modulus): shearing stress to the shearing

strain

c. Bulk modulus (K): Volumetric stress/Normal stress to the volume strain

15. Relation between E,G and poisons ratio: G=0.5E/1+poission ratio

16. Poisson ratio= lateral strain (transverse strain) / linear strain (longitudinal/axial) (X axis/
Y axis)
4.3 Strength of materials: Centre of Gravity, Centroid, mass & area moment of inertia, polar
moment of inertia, shear force and bending moment, Deflection of Beam, Analysis of Truss,
Torsion of Shaft.

Deflection of simply supported beam

1. Stiffness of a beam = maximum deflection / span length

a. This is the measure of resistance against deflection
2. In Simply supported beam
a. Slope is maximum at the support. And deflection is maximum at the point of
loading
3. Cantilever beam
a. Deflection is zero at the fixed end and free end is maximum.
4. Mohr’s theorem = Ax/EI= deflection at any point
a. X is the distance of g of bending moment
5. Slope = A/EI

Analysis of truss

Twisting moment =T