structural analysis: statically determinant & inderminant structure.

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

1. Equilibrium equation are sufficient .
2. compatibility condition are not required

3. stresses will not develope due to change in temperature sinking of support and lack of fit.  

INDETERMINATE

1. Equilibrium equation are not sufficient
2. compatibility equation are required.
3. 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.