STRUCTURAL ANALYSIS:
In structural analysis we only analyse the structure and we design the structure in STRUCTURAL DESIGN. in structural analysis we analyse the structure only .
for analyse we have to understand it is STATICALLY INDERMINATE STRUCTURE OR STATICALLY INDETERMINATE STRUCTURE.
if it is statically indeterminate structure then it belong to STRENGTH OF MATERIAL
and it is statically inderminate structure then it belong to STRUCTURAL ANALYSIS.
STATIC EQUILIBRIUM EQUATION:
Static equilibrium equation deals with balancing forces .
such as
- summation of horizontal forces
- summation of vertical forces
- summation of moment
COMPATIBILITY CONDITION :
If the statically equilibrium equation is not sufficient for balancing the forces then compatibility condition is used.
it noting but balancing rotation /angular
STATICALLY DETERMINANT STRUCTURE:-
If the no of unknown forces of a given structure are equal to number of equilibrium equation is known as statically determinant structure.
e.g. simply supported beam, three hinged arches ,double over hanging beam.
STATICALLY INDEERMINANT STRUCTURE:
If the no of unknown forces of a given structure are more than the number of equilibrium is known as statically indeterminant structure.
e.g. proper cantiliver beam, fixed beam,continuous beam,two hinged arches.
we have formula
Ds=Dse+Dsi
Ds= static indeterminancy
Dse= external indeterminancy
Dsi=internal inderminancy
IF
Ds=0 statically determinate structure
Ds > 0 stically indetermined sructure
Ds <0 unstable
first of all we have to study
EXTERNAL INDETERMINANCY (Dse)
if
Dse=0 externally determined structure (r=s)
Dse >0 externally indeterminant strucure (r>s)
Dse < 0 externally unstable.
where,
Dse = r - s
where ,
r= no of reaction
s = no of equilibrium
INTERNALLY INDETERMINANCY (Dsi)
IF,
Dsi = 0 internally determined structure
Dsi > 0 internally indetermined sructure
D se < 0 internally unstable
for rigid jointed frame;
Dsi=3C --for plane frame
Dsi=6C -- FOR space frame
where ,
C = no of cuts required to open a closed configuration
or
no of closed boxces
for pin jointed frames:
Dsi= m-(2j-3) for plane frame
Dsi= m-(3j-6) for space frame
DIFFERENCE BETWEEN STATICALLY DETERMINED AND INDETERMINED STRUCTURE
DETERMINATE
- Equilibrium equation are sufficient .
- compatibility condition are not required
INDETERMINATE
- Equilibrium equation are not sufficient
- compatibility equation are required.
- stresses will develop due to change in temperaturel,sinking of support and lack of fit
LACK OF FIT:
DEF: if the actual length of member more/less than the designed length is known as lack of fit.
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