Static-Determinacy-Stability.

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TYPES OF FORCES
 Internal Forces
 External Forces
Internal forces are the forces and couples
exerted on a member or portion of the
structure by the rest of the structure.
External forces are the actions of other
bodies on the structure under
consideration. For the purposes of analysis,
it is usually convenient to further classify
these forces as applied forces and reaction
forces.
TYPES OF SUPPORTS 4
S T A B I L I T Y

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TYPES OF STABILITY
 Internal Stability
A structure is considered to be internally stable,
or rigid, if it maintains its shape and remains a
rigid body when detached from the supports.
Conversely, a structure is termed internally
unstable (or nonrigid) if it cannot maintain its
shape and may undergo large displacements
under small disturbances when not supported
externally.
 External Stability
External stability evaluates if there are
enough support reactions to prevent the
structure from moving as a rigid body.
OVERALL STABILITY
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Overall Stability = Internal Stability +
External Stability
DETERMINACY OF STRUCTURE
 Statically Determinate
o When the unknown forces can be computed using equilibrium equations
o A structure which has enough connections to be stable
 Statically Indeterminate
o When the number of unknown forces is more than the equilibrium equations
o A structure which has more than enough connections to be stable
DETERMINACY OF STRUCTURE

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I M P O R T A N T
C O N C E P T S
IMPORTANT CONCEPTS
1) Stable / Unstable
A stable structure is one that will not collapse when disturbed. Stability is the
capability for a structure to recover equilibrium.
In general, there are many ways that a structure may become unstable, including
buckling of compression members, yielding/rupture of members, or nonlinear geometric
effects (like so-called P-Delta effects); however, in linear structural analysis, our
main concern is instability caused by insufficient reaction points or poor layout of
structural members.
An unstable structure generally cannot be analyzed. Therefore, it is useful to know
if a structure is stable or unstable before you conduct a structural analysis.
IMPORTANT CONCEPTS
2) Internally Stable
A stable structure is one that will not collapse when disturbed. Stability is the
capability for a structure to recover equilibrium.
An internally stable structure is one that would maintain its shape if all the
reaction supports were removed. A structure that is internally unstable may still
be generally stable if it has sufficient external support reactions.
IMPORTANT CONCEPTS
3) External Determinacy
In an externally statically determinate structure, all of the external reaction force
components may be calculated using only static equilibrium (i.e. using the three
equilibrium equations in 2D). A structure for which the external reactions
component forces cannot be calculated using only equilibrium is called externally
statically indeterminate.
In an internally statically determinate structure, all of the external reaction
component forces and internal forces may be calculated using only static
equilibrium. A structure for which the internal forces cannot be calculated using
only equilibrium is internally statically indeterminate.
4) Internal Determinacy

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IMPORTANT CONCEPTS
5) Redundant Forces
Indeterminate structures have more unknown forces than you can solve using the
three equilibrium equations alone (or six equilibrium equations in 3D). These
extra unknown forces are called redundant forces or redundants.
The degree of indeterminacy for a structure is equal to the number of redundant
forces. An indeterminate structure with 2 redundants may be said to be statically
indeterminate to the second degree or "2 S.I."
6) Degree of Determinacy
For indeterminate structure, the degree of external indeterminacy can be
written as
DETERMINACY OF
INTERNALLY STABLE
Where;
r = no. of reactions
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For indeterminate structure, the degree of external indeterminacy can be
written as
DETERMINACY OF
INTERNALLY UNSTABLE
Where;
r = no. of reactions
fi = no. of internal forces
nr = no. of rigid members
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As this figure indicates, these reactions, which would have been sufficient to
fully constrain an internally stable or rigid structure, are not sufficient for this
structure.
INTERNALLY UNSTABLE

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In order for the structure to be made externally stable;
The roller support at A can be replaced by a hinged support to prevent the
horizontal movement of end A of the structure.
INTERNALLY UNSTABLE
EXAMPLE
Determine whether each of
the beams and frames below
are internally stable or
unstable and determinate,
indeterminate, or unstable.
If it is indeterminate, what
degree is it indeterminate?
INTERNALLY UNSTABLE
STATICALLY UNSTABLE EXTERNALLY
INTERNALLY STABLE
STATICALLY INDETERMINATE EXTERNALLY
AT 2ND DEG
EXAMPLE
Determine whether each of
frames is determinate,
indeterminate, or unstable.
If it is indeterminate, what
degree is it indeterminate?
INTERNALLY UNSTABLE
STATICALLY DETERMINATE
EXTERNALLY
INTERNALLY UNSTABLE
STATICALLY DETERMINATE
EXTERNALLY
DETERMINACY AND
STABILITY OF TRUSS

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WHAT IS TRUSS?
 Truss is a structure composed of
slender members joined together at
their end points.
 The members commonly used in
construction consist of wooden struts,
metal bars, angles, or channels.
 The joint connections are usually
formed by bolting or welding the
ends of the members to a common
plate, called a gusset plate.
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COMMON BRIDGE TRUSSES
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ASSUMPTIONS FOR ANALYSIS OF
TRUSSES
 All members are connected only at their ends by frictionless hinges
in plane trusses and by frictionless ball-and-socket joints in space
trusses.
 All loads and support reactions are applied only at the joints.
 The centroidal axis of each member coincides with the line
connecting the centers of the adjacent joints.
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INTERNAL STABILITY (TRUSS)
The term internal used in truss refers to the number and arrangement
of members contained within the truss.
The instability due to insufficient external supports or due to
improper arrangement of external supports is referred to as external.
The triangular truss is called the basic truss element.

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INTERNAL STABILITY (TRUSS)
Where;
m = no. of members
j = no. of joints
NOTE: It is very important to realize that although the foregoing
criterion for internal stability is necessary, it is not sufficient to ensure
internal stability. Members must also be properly arranged to ensure
rigidity of the entire truss.
If a truss contains a sufficient number of members, but they are not
properly arranged, the truss is said to have critical form.
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INTERNAL STABILITY (TRUSS)
INTERNALLY STABLE
INTERNALLY UNSTABLE
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EXTERNAL STABILITY (TRUSS)
A structure (or truss) is externally unstable if all of its reactions are concurrent or
parallel.
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For indeterminate structure, the degree of external indeterminacy can be
written as
DETERMINACY (TRUSS)
Where;
r = no. of reactions
m = no. of members
j = no. of joints

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EXAMPLE
(1)
(2)
INTERNALLY STABLE
STATICALLY DETERMINATE
EXTERNALLY
INTERNALLY STABLE
STATICALLY INDETERMINATE
EXTERNALLY AT 4TH DEG
ANSWER LABORATORY
EXERCISE NO. 2