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# PPT: Matrix Method Notes | EduRev

## GATE : PPT: Matrix Method Notes | EduRev

``` Page 1

METHODS TO SOLVE INDETERMINATE PROBLEM
2
Displacement methods
Force method
Small degree
of statical
indeterminacy
Large degree
of statical
indeterminacy
Displacement method
in matrix formulation
Numerical methods
Page 2

METHODS TO SOLVE INDETERMINATE PROBLEM
2
Displacement methods
Force method
Small degree
of statical
indeterminacy
Large degree
of statical
indeterminacy
Displacement method
in matrix formulation
Numerical methods
•
bulky calculations (not for hand calculations);
•
structural members should have some certain
number of unknown nodal forces and nodal
displacements; for complex members such as curved
beams and arbitrary solids this requires some
discretization, so no analytical solution is possible.
METHODS
3
•
very formalized and computer-friendly;
•
versatile, suitable for large problems;
•
applicable for both statically determinate and
indeterminate problems.
Page 3

METHODS TO SOLVE INDETERMINATE PROBLEM
2
Displacement methods
Force method
Small degree
of statical
indeterminacy
Large degree
of statical
indeterminacy
Displacement method
in matrix formulation
Numerical methods
•
bulky calculations (not for hand calculations);
•
structural members should have some certain
number of unknown nodal forces and nodal
displacements; for complex members such as curved
beams and arbitrary solids this requires some
discretization, so no analytical solution is possible.
METHODS
3
•
very formalized and computer-friendly;
•
versatile, suitable for large problems;
•
applicable for both statically determinate and
indeterminate problems.
FLOWCHART OF MATRIX METHOD
4
Classification
of members
Stiffness matrices
for members
Transformed
stiffness matrices
Stiffness matrices are
composed according to
member models
Stiffness matrices are
transformed from local to global
coordinates
Final equation
F = K · Z
Stress-strain state
of structure
Unknown displacements and
reaction forces are calculated
Stiffness matrices of separate
members are assembled into a
single stiffness matrix K
Page 4

METHODS TO SOLVE INDETERMINATE PROBLEM
2
Displacement methods
Force method
Small degree
of statical
indeterminacy
Large degree
of statical
indeterminacy
Displacement method
in matrix formulation
Numerical methods
•
bulky calculations (not for hand calculations);
•
structural members should have some certain
number of unknown nodal forces and nodal
displacements; for complex members such as curved
beams and arbitrary solids this requires some
discretization, so no analytical solution is possible.
METHODS
3
•
very formalized and computer-friendly;
•
versatile, suitable for large problems;
•
applicable for both statically determinate and
indeterminate problems.
FLOWCHART OF MATRIX METHOD
4
Classification
of members
Stiffness matrices
for members
Transformed
stiffness matrices
Stiffness matrices are
composed according to
member models
Stiffness matrices are
transformed from local to global
coordinates
Final equation
F = K · Z
Stress-strain state
of structure
Unknown displacements and
reaction forces are calculated
Stiffness matrices of separate
members are assembled into a
single stiffness matrix K
STIFFNESS MATRIX OF STRUCTURAL MEMBER
5
Stiffness matrix (K) gives the relation between vectors
of nodal forces (F) and nodal displacements (Z):
Page 5

METHODS TO SOLVE INDETERMINATE PROBLEM
2
Displacement methods
Force method
Small degree
of statical
indeterminacy
Large degree
of statical
indeterminacy
Displacement method
in matrix formulation
Numerical methods
•
bulky calculations (not for hand calculations);
•
structural members should have some certain
number of unknown nodal forces and nodal
displacements; for complex members such as curved
beams and arbitrary solids this requires some
discretization, so no analytical solution is possible.
METHODS
3
•
very formalized and computer-friendly;
•
versatile, suitable for large problems;
•
applicable for both statically determinate and
indeterminate problems.
FLOWCHART OF MATRIX METHOD
4
Classification
of members
Stiffness matrices
for members
Transformed
stiffness matrices
Stiffness matrices are
composed according to
member models
Stiffness matrices are
transformed from local to global
coordinates
Final equation
F = K · Z
Stress-strain state
of structure
Unknown displacements and
reaction forces are calculated
Stiffness matrices of separate
members are assembled into a
single stiffness matrix K
STIFFNESS MATRIX OF STRUCTURAL MEMBER
5
Stiffness matrix (K) gives the relation between vectors
of nodal forces (F) and nodal displacements (Z):
EXAMPLE OF MEMBER STIFFNESS MATRIX
6
Stiffness relation for a rod:
Stiffness matrix:

( )
i j i
EA
F x x
L
= - · -
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## Structural Analysis

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