Perbandingan Metode kekakuan Vs Fleksibilitas

Stiffness Vs Flexibility

1. STIFFNESS vs FLEXIBILITY
Yoyong Arfiadi
1
DEPARTMENT OF CIVIL ENGINEERING,
FACULTY OF ENGINEERING

2. FLEXIBILITY vs. STIFFNESS METHODS
Force method vs. Displacement
(overview)
•Redundant Forces vs. Degree of freedom
2
q

3. FLEXIBILITY (FORCE) METHOD
3
3 m + r = 6+ 4 = 10
3 j = 9
Static indeterminacy = 1
Take R
B
as redundant force
D
B2
=
R
B
x L
3
________
48 E I
D
B1
=
5 qx L
4
________
384 E I
q
q
Compatibility condition at support B: D
B1
= D
B2
R
B
can be obtained

4. Solution is not unique!
4
That is not the only solution!
Release R
C
Release R
B

5. STIFFNESS (DISPLACEMENT) METHOD
5
q
DOF = 5
The number of solution
increase compared to
flexibility method
However, the solution is
unique
The only solution

6. FLEXIBILITY (FORCE) METHOD
6
Solution 1
Solution 2
Solution 3
Solution 4
?
q
q
q q
H
H
H
H

7. STIFFNESS (DISPLACEMENT) METHOD
7
The only solution!

8. 8

10. 10
OTHER SOLUTIONS?

11. Diplacementmethod
11
The only solution!

12. Stiffness methods become popular compared to flexibility:
12
Unless artificial intelligence method is developed
•unique solution
•modular
Relatively easy to program

13. 13
•In modern era it is uncommon to use
hand calculation in doing structural
analysis
•Most students (and engineers) prefer
to use sophisticated computer program
in order to get the final results
•It is now very easy to analyze the
structures with thousands degrees of
freedom within a coupled minutes

14. •Input data
•Although the users do not really
understand the program, inputting can
be done
•The results can be obtained
•For users/students who have ‘minimum
knowledge’ in structural engineering,
interpreting the results can be very
difficult because the calculation process
was done by computers
14
The final design can be dangerous

15. •because in stiffness matrix method involves several matrix operations and manipulations
the use of computer is unavoidable
•otherwise the problem that is discussed in class is a very simple structure
15
q
H
2 members
3 DOFs
3 members
3 DOFs

16. 16
Hand calculation?

17. 17
There is a need to have a computer program such that the step-
by-step process is defined by the user, yet the matrix
computation is done by computers
Computer program for academic purpose (teaching and learning)
students/young engineers

18. 18