Determinate and indeterminate structure-(Video-Youtube)
Determinacy,
a structure can be called determinate if the equilibrium equation provides
enough and sufficient condition for equilibrium. if all forces for a structure
can be determined using equilibrium equations only, this structure is
determinate, but if the unknown forces are more and cant be determined using
equilibrium equations then this structure is indeterminate. in general we can
determine if a structure is statically determinate or indeterminate by drawing
free body diagram for a structure or part of it and comparing a number of
unknown forces and moment component with number of available equation of
equilibrium. for coplanar structures, we have
three equilibrium equations, if n is the total number of parts, and r is
the number of unknown forces and moment component then. if r = 3 times n, the
structure is determinate. and if r
bigger than 3 times n, the structure is indeterminate .
statically
indeterminate structure cant be solved using equilibrium equations, solving of
a statically indeterminate structure by relating loads and reactions with slope
and displacement at different point of structure, this known as compatibility
equations, Compatibility equations involve the geometric and physical
properties of the structure. the figure here showing some examples of
statically determinate and indeterminate structures. The first beam has 3
unknown reactions, we have 2 vertical forces and one horizontal force as shown
in this figure. So r=3, the beam consist of one part so n=1. So r= 3 times n
and the beam is determinate. We can apply same principle for the remaining
beams. For this beam we have 10 unknow reaction, moment, vertical and
horizontal forces near the fixed support. And 2 horizontal and vertical forces
for the internal hinge. Hinge can’t carry moment unlike the fixed support.
Therefore r=10, the beam composed of 3 parts. So r is less than 3 times n and
the beam is indeterminate. For frames members are connected together by rigid
joint, therefore we can determine if the structure is statically determinate or
indeterminate by cutting of members into parts as shown in this figure. forces at cut point should be counted one
time only. this figure showing a bridge. this bridge consist of one span, this
will have three unknown forces at both support. So r=3 and n=1. N is the number
of structure parts. So n is equal 3
times 1 and the structure is determinate. This figure showing a bridge with two
continuous span. We have 3 supports. for this bridge we have four reactions as
shown in this figure. In total we have 6 unknown reaction. N for this bridge =
1. Therefore r is more than 3 times n and the structure is indeterminate. if r
is lesser than 3 times n. let assume that this birdge is setting on two roller
support. so we have only vertical forces and no horizontal forces. so r=2 and
it is lesser than 3 times n. but if the bridge is seated on two roller, is it
going to be stable. the answer is no because the bridge will be sliding because
the horizontal force is not resisted. so if r is lesser than 3 times n, the
structure will not be stable.
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