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What is indeterminate structure? The structure which can not be analysed

by the equations of static equilibriums alone are called indeterminate structures.

This kind of structure consist of more members and more restraints.

Why Stiffness Method should use

The ability to automate the solution process.

Implementation in a computer program is possible.

Stiffness method is used for solving problems related with,

Beams Frames Trusses

Stiffness Method: The stiffness method is defined as the end

moment required to produce a unit rotation at one end of the member while the other end is fixed.

Degree Of Freedom (DOF): Number of directions that the joints can

move.

Degree of freedom for different structural system

Structure Type Translational Rotational Total

Beam 1 1 2

Plane Truss 2 0 2

Plane Frame 2 1 3

Degree of Kinematic Indeterminacy (DOKI): Total number of degree of freedom of the

structure. i.e. degree of freedom at all the joints less

than no of restraints at supports. DOKI=(Number of joints)*(Number of

DOF/joints)-Number of restraints.

The steps to be followed in performing

a stiffness analysis can be summarized as:

I. Determine degree of kinematic indeterminacy.

II.Apply restraints and make it kinematically determine.

III. Apply loads on the fully restraint structure and calculate forces.

IV. Apply unknown displacement to the structure one at a time keeping all other displacements zero and calculate forces corresponding to each degree of freedom.

V. Equilibrium equations are written and solved in matrix form and obtain the value of unknown displacements.

VI. All the member-end forces are calculated.

Equilibrium equation: Pm+Ku=PjHere,Pm=Member force MatrixK=Stiffness Matrixu=Unknown displacementPj=Joint Load Matrix

EXAMPLES

Formulate the stiffness matrix for a beam shown with co-ordinates in fig

Thank you