ME 101: Engineering Mechanics
A. Narayana Reddy
Department of Mechanical Engineering,
Indian Institute of Technology Guwahati,
Guwahati - 781039, India.
Sample free-body diagrams
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Sample free-body diagrams
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Complete the following free-body diagrams
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Complete the following free-body diagrams
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Complete the following free-body diagrams
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Complete the following free-body diagrams
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Draw the free-body diagrams
(b)
(a)
(d)
(c)
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Engineering structures
Engineering structures are made of several connected
memebrs. The members are assumed to be rigid bodies in
this discussion.
There is force applied by one member on another and vice
versa if the two members are interconnected.
Newton’s third law states that forces of action and
reaction between two connecting bodies must have same
magnitude, line of action, and opposite in direction.
Engineering structures are classified into three categories.
Trusses - Contain all two-force members.
Frames - Contain at least one multi-force member.
Machines - Strcure contain moving parts and used for
transmit the motion and also to modify forces.
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Definition of a truss
A truss consists of straight members connected at
joints. No member is continuous through a joint.
Bolted, riveted, or welded connections are
assumed to be pinned together. Force acting at
the member reduce to a single force and no
couple. Only two-force members are considered.
The forces are applied only at the joints.
When forces tend to pull the member apart, it is
in tension. When the forces tend to compress the
member, it is in compression.
Plane truss - Members lie in a single plane.
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Definition of a truss
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Applications of trusses
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Simple trusses
A rigid truss will not collapse under the application of a load.
Basic element of plane truss is the triangle.
The polygon formed by four or more bars is a nonrigid frame.
Nonrigid frame can be made as a stable structure by adding extra
memebrs.
A simple truss is constructed by successively adding two members and
one connection to the basic triangular truss.
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Analysis of Trusses
If the truss is in equilibrium then the forces are in balance at every point on
the truss and in particular at every joint.
Method of joints
Satisfying the equilibrium equations at every joint of truss.
If the truss is in equilibrium then every part or segment is also in equilibrium.
Method of sections
The equilibrium is used for the part of truss. This is useful for getting force in
a member of interest without solving all joints.
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Method of joints
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Example
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Example
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Example
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Example
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Example
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Joints under special loading conditions
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Statically indeterminate truss
Statically indeterminate truss
External redudancy
Internal redundancy
External redundancy:
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Internal redundancy
Internal redundancy
The members in a truss is more than that are required to maintain the
equilibrium. This is also known as degree of internal indeterminacy.
Let n be number of joints in a given truss.
Let m be number of members in a given truss.
Therefore, we can form 2n equations as force is balanced at every joint along
x and y direction. On the other hand, we have m + 3 unknowns as axial force
in m members along with three reaction forces.
Thus, the necessary condition for internal static determinacy is given by
m + 3 = 2n.
The Maxwell’s rule:
m + 3 = 2n. → statically determinate internally
m + 3 > 2n. → statically indeterminate internally
m + 3 < 2n. → unstable
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Internal redundancy
The criterion m + 3 = 2n is necessary condition but not sufficient condition.
In other words, if the truss is statically determinate internally then that must
satisfy the criterion m + 3 = 2n. But all the structures that satisfy the
condition m + 3 = 2n is not necessarily statically determinate internally.
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Necessity of redundancy
Why to provide redundant members?
To maintain allignment of two members during construction.
To increase stability during construction.
To prevent buckling of compressive members.
To provide support if the direction of loding is changed.
Redundant members can act as backup members if some members are
failed during loading.
Analysis of truss with redundant members is difficult but possible.
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Example
Determine the force in members FH, GH and GI.
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Method of sections
Caution
The section of truss must be consider such that there are only three unknown
force members are on the section as we have three equilibrium equations.
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Example
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Example
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Example
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Example
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Example
Calculate the forces induced in members KL, CL, and CB by the 200 kN load on
cantilever truss.
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Space trusses
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Space trusses
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Example
Determine the forces acting in members of
the space truss
Solution:
At joint A:
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Example
At joint B:
At joint C and D:
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