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Transcript B-Mech-Engg-3-Statics

ME101-Basic Mechanical
Textbook: Engineering MechanicsSTATICS and DYNAMICS
11th Ed., R. C. Hibbeler and A. Gupta
Course Instructor: Miss Saman Shahid
Characteristics of Dry Friction
• Friction can be defined as a force of resistance
acting on a body that prevents or retards
slipping of the body relative to a second body
or surface with which it is in contact.
• This force is always tangent to the surface at
points of contact with other bodies.
Types of Friction
• Fluid Friction: it exists when the contacting
surfaces are separated by a film of fluid (gas or
liquid). The nature of fluid friction is studied in
fluid mechanics since it depends upon knowledge
of the velocity of the fluid and the fluid’s ability to
resist shear forces.
• Dry Friction/Coulomb Friction: it occurs between
the contacting surfaces of bodies when there is
no lubricating fluid.
Shear Force
• If a coplanar force system acts on a member,
then in general, a resultant internal normal
force N, shear force V, and bending moment
M will act at any cross-section along the
Theory of Dry Friction
Consider the effects caused by pulling horizontally on a block of uniform weight W
which is resting on a rough horizontal surface.
The floor exerts a distribution of both normal force and frictional force along the
contacting surface.
For equilibrium, the normal forces must act upward to balance the block’s weight,
and the frictional forces act to the left to prevent the applied force P from moving
the block to the right.
It can be seen that many microscopic irregularities exist between the two surfaces
and, as a result, reactive forces ΔRn are developed at each of the protuberances (a
detailed approach towards friction including the effects of temperature, density,
cleanliness and atomic or molecular attraction between the contacting surfaces)
These reactive forces contributes both a frictional component ΔFn and normal
component ΔNn.
• The distribution of ΔFn indicates that F always act tangent to the
contacting surface, opposite to the direction of P.
• The normal force N is determined from the distribution of ΔNn
and is directed upward to balance the block’s weight.
• Note that N acts a distance x to the right of the line of action of
W. This location which coincides with the centroid (geometric
center) of the loading diagram, is necessary in order to balance
the “tipping effect” caused by P.
Impending Motion
• In cases where h is small or the surfaces of
contact are rather “slippery”, the frictional
force F may not be great enough to balance P,
and consequently the block will tend to slip
before it can tip.
1-Static Friction
• A certain maximum value Fs called the
limiting static frictional force. When
this value is reached, the block is in
unstable equilibrium since any further
increase in P will cause deformations
and fractures at the points of surface
contact, and consequently the block
will begin to move.
• Experimentally, it has been
determined that the limiting static
frictional force Fs is directly
proportional to the resultant normal
force N.
2-Kinetic Friction
If the magnitude of P on the block is increased so that it becomes greater than Fs,
the frictional force at the contacting surfaces drops slightly to a smaller value Fk,
called the kinetic frictional force.
The block will not held in equilibrium (P>Fk); instead, it will begin to slide with
increasing speed.
At P>Fk, then P has the capacity to shear off the peaks at the contact surfaces and
cause the block to “lift” somewhat out of it settled position and “ride” on top of
these peaks.
Once the block begins to slide, high local temperatures at the points of contact
cause momentary adhesion (welding) of these points. The continued shearing of
these welds is the dominant mechanism creating kinetic friction.
Variation of Frictional Force versus
Applied Load
• Frictional force categorized in three different ways:
• F is a limiting static frictional force if equilibrium is maintained,
• F is a limiting static frictional force Fs when it reaches a maximum value
needed to maintain equilibrium,
• F is termed a kinetic frictional force Fk when sliding occurs at the
contacting surface.
• Notice from graph that for very large values of P or for high speeds,
because of aerodynamic effects, Fk and likewise µk begin to decrease.
Types of Friction Problems
• They can be easily classified once free-body
diagrams are drawn and the total number of
unknowns are identified and compared with
the total number of available equilibrium
• There are three types:
1. Equilibrium
2. Impending Motion at All Points
3. Impending Motion at Some Points
1- Equilibrium
• Problems in this category are strictly
equilibrium problems which require the total
number of unknowns to be equal to the total
number of available equilibrium equations.
• After calculation of frictional forces, their
numerical values can be checked to be sure
they satisfy the inequality F<=µN; otherwise
slipping will occur and the body will not
remain in equilibrium.
• In diagram, we must determine the frictional
forces at A and C to check if the equilibrium
position of the two-member frame can be
• If the bars are uniform and have known
weights of 100N each. There are six unknown
force components which can determined from
six equilibrium equations (three for each
2- Impending Motion at All Points
• In this case, the total number of
unknowns will equal the total
number of available equilibrium
equations plus the total number
of available frictional equations
(static or kinetic).
• Consider the problem of finding
the smallest angle at which the
100N bar can be placed against
the wall without slipping.
• Here are five unknowns. For the
solution, there are three
equilibrium equations and two
static frictional equations which
apply at both points of contact.
3- Impending Motion at Some Points
• In this case, the total number of unknowns will
be less than the number of available equilibrium
equations plus the total number of frictional
equations or conditional equations for tipping.
• As a result, several possibilities for motion or
impending motion will exist and the problem
will involve a determination of the kind of
motion which actually occurs.
• For example, consider the diagram, if we wish to
find horizontal force P needed to cause
movement. There are total seven unknowns.
• For a unique solution, we must satisfy the six
equilibrium equations (three for each member)
and only one of two possible frictional
• This means that as P increases it will either
cause slipping at A and no slipping at C or viceversa.
• Consider pushing on the uniform crate that has a weight W and sits
on the rough surface. If the magnitude of P is small, the crate will
remain in equilibrium. As P increases the crate will either be on the
verge of slipping on the surface, or if the surface is very rough (large
µ) then the resultant normal force will shift to the corner, x=b/2 and
the crate will tip over.
• The crate has a greater chance of tipping if P is applied at a greater
height h above the surface, or if the crate’s width b is smaller.
Example 8.1
• The uniform crate
shown has a mass of
20kg. If a force
P=80N is applied to
the crate, determine
if it remains in
equilibrium. The coefficient of static
friction is 0.3.