Mechanics of Solids: Friction and Deformation in Engineering, Lecture notes of Mechanics

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ESO202A: Mechanics

ESO202A: Mechanics

of Solids

of Solids

Examples of deformation

Examples of deformation

of structures

of structures

Friction



Friction is a force that is created

whenever two surfaces move or try

to move across each other.



Friction always opposes the motion

or attempted motion of one surface

across another surface.

Types of friction



There are two main types of friction,

static friction and kinetic friction.



Static friction operates between two

surfaces that aren't moving relative

to each other, while kinetic friction

acts between objects in motion.

Types of friction

In liquids, friction is the resistance

between moving layers of a fluid,

which is also known as viscosity.

In general, more viscous fluids are

thicker, so honey has more fluid

friction than water.

Typical friction coefficients

Surface μ

s

μ

k

Velcro on Velcro 6.0 5.

avg tire-on-dry pavement 0.9 0.

Grooved tire-on-dry pavement 0.8 0.

Glass on glass 0.9 0.

Metal on metal (dry) 0.6 0.

Metal on metal (lubricated) 0.1 0.

Steel on teflon 0.05 0.

Ring subjected to uniform pressure

Ring subjected to uniform pressure



A thin ring of

A thin ring of

internal radius r,

internal radius r,

thickness t and

thickness t and

width b is

width b is

subjected to an

subjected to an

internal pressure p

internal pressure p



Determine the

Determine the

forces in the ring

forces in the ring

and the

and the

deformation of the

deformation of the

ring

ring

Force equilibrium equations

Force equilibrium equations



Equilibrium in y direction gives:

Equilibrium in y direction gives:

∑

∑

F

F

y

y

= p(2 r b) – 2 F

= p(2 r b) – 2 F

T

T



The hoop may be thought of as a flat

The hoop may be thought of as a flat

plate of thickness t, width b and

plate of thickness t, width b and

length 2

length 2

(r+t/2) subjected to a

(r+t/2) subjected to a

tensile force F

tensile force F

T

T

Force Deformation Relation

Force Deformation Relation



The increase in circumference can be

The increase in circumference can be

obtained from the relation:

obtained from the relation:

δ

δ = PL/AE

= PL/AE



The change in circumference of the hoop

The change in circumference of the hoop

is thus:

is thus:

δ

δ

TT

= F

= F

TT

π

π (r+t/2) /(bt)E

(r+t/2) /(bt)E

Where F

Where F

T

T

= prb

= prb

Tension of rope over a drum

Tension of rope over a drum

Frictional forces

Frictional forces

Torque versus rpm Testing of engine

Torque versus rpm Testing of engine

Torque versus rpm Testing of engine

Torque versus rpm Testing of engine



Load is applied on one end of the rope

Load is applied on one end of the rope

while the other end is anchored in a

while the other end is anchored in a

support.

support.



By increasing the total applied force at the

By increasing the total applied force at the

same (maximum) power setting, the

same (maximum) power setting, the

motor rpm will decrease.

motor rpm will decrease.



Rpm can be measured by a tachometer or

Rpm can be measured by a tachometer or

stroboscope.

stroboscope.



Thus torque versus rpm characteristics can

Thus torque versus rpm characteristics can

be obtained.

be obtained.

Applications of friction (Rope wrench)

Applications of friction (Rope wrench)



To torque a smooth bar, use plenty of

To torque a smooth bar, use plenty of

turns of rope to get a grip.

turns of rope to get a grip.



Apply the torque using a lever. To maintain

Apply the torque using a lever. To maintain

the surface finish, you can also use a

the surface finish, you can also use a

cushioning material.

cushioning material.

Deformation of

Deformation of

structures

structures