• Md.Tawfiq Rahman• Student ID : 10.01.03.080.• Section: B• Year :4th • Semester: 2nd • Course No : CE-416.• Course Title: Pre-stressed Concrete Lab

AHSANULLAH UNIVERSITY OF SCIENCE & TECHNOLOGY

SOLVING STATICALLY INDETERMINATE STRUCTURE : STIFFNESS METHOD

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.

Analysis MethodI. Moment distribution methodII. Slope deflection methodIII. Matrix method- Stiffness method - Flexibility methodIV. Column Analogy MethodV. The Method of Consistent DeformationVI. Energy Method

Here I will discuss about Stiffness Method

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.

DOKI :1

DOKI:2

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

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