This document discusses stiffness method for analyzing indeterminate structures. It defines stiffness method as the end moment required to produce a unit rotation at one end of a member while fixing the other end. It also defines degree of freedom and degree of kinematic indeterminacy. The steps of stiffness method are outlined, which include determining degree of kinematic indeterminacy, applying restraints, calculating member forces, applying displacements one at a time to write equilibrium equations in matrix form, and solving the equations to obtain displacements and member forces. Stiffness method can be used to analyze beams, frames, and trusses and is suitable for automation in computer programs.

1. •
•
•
•
•
•
•
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

3. 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.

4. 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

5. Here I will discuss about
Stiffness Method

6. Why Stiffness Method should use
The ability to automate the solution process.
Implementation in a computer program is
possible.

7. • Stiffness method is used for solving
problems related with,
 Beams
 Frames
 Trusses

8. • 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.

9. 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

10. • 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.

12. 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.

13. 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.

15. 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.

16. • Equilibrium equation:
Pm+Ku=Pj
Here,
Pm=Member force Matrix
K=Stiffness Matrix
u=Unknown displacement
Pj=Joint Load Matrix

18. THANK YOU