Solving Statically Indeterminate Structure: Stiffness Method
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Solving Statically Indeterminate Structure: Stiffness Method

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Md.Tawfiq Rahman ...

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

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  • 1. • • • • • • • Md.Tawfiq Rahman Student ID : Section: B Year :4th Semester: 2nd Course No : CE-416. Course Title: Pre-stressed Concrete Lab
  • 2. 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.
  • 3. Analysis Method I. Moment distribution method II. Slope deflection method III. Matrix method- Stiffness method - Flexibility method IV. Column Analogy Method V. The Method of Consistent Deformation VI. Energy Method
  • 4. Here I will discuss about Stiffness Method
  • 5. Why Stiffness Method should use The ability to automate the solution process. Implementation in a computer program is possible.
  • 6. • Stiffness method is used for solving problems related with,  Beams  Frames  Trusses
  • 7. • 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.
  • 8. Degree of freedom for different structural system Structure Type Translational Rotational Total 1 1 2 Plane Truss 2 0 2 Plane Frame 2 1 3 Beam
  • 9. • 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.
  • 10. 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.
  • 11. 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.
  • 12. 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.
  • 13. • Equilibrium equation: Pm+Ku=Pj Here, Pm=Member force Matrix K=Stiffness Matrix u=Unknown displacement Pj=Joint Load Matrix
  • 14. THANK YOU