Prepared by:Mohd Raizamzamani bin Md Zain

INTRODUCTION OF DETERMINATEAND INDETERMINATE STRUCTURES

OUTLINEDeterminate and Indeterminate Structures:

q Analysis of beamsq Analysis of trussesq Analysis of frames

LEARNING OUTCOMESWEEK 1

At the end of this chapter, students should be able to:

q identify types of frame structures and structural idealization

q define static and kinematic indeterminacy of structures

STRUCTURE

Stable Unstable

Statically Determinate StaticallyIndeterminate

Statically Geometrically

External Internal

Types of Framed Structures:q beamsq trussesq frames

Static indeterminacy

Static indeterminacy is the excess of unknown actions(generalized applied and reactional forces) ascompared to the number of equations staticequilibrium available. The number of excess ofunknown actions represents the degree of staticindeterminacy (or redundant).q External indeterminacy occurs at the supports.q Internal indeterminacy occurs in the members of

the structure.

a. Plane truss. Space truss

d = m + r - nj

where,d = the degree of static indeterminacy,m = no. of member,r = no. of reaction,j = no. of joint.Plane truss n = 2, space truss n = 3.(If d = 0 it is statically determinate)

b. Beam and Plane Frame

d = 3m + r – 3j

EXERCISE 1

Kinematic Indeterminacy

q In the stiffness method, the displacements of the jointsbecome the unknown quantities.

q Therefore, kinematic indeterminacy becomes important.q When loads are applied on structure, each joint will

undergo displacements (translation and rotation).q Some displacements may be known, others unknown.

q The number of unknown joint displacements is thedegree of kinematic indeterminacy or the number ofdegrees of freedom for joint displacement.

Joint B has 2 degrees of freedom (rotation andtranslation). It is normal to neglect axial deformationand thus no translation. So joint B has only one degreeof freedom (rotation).

Seven degree of freedom if include axial deformation.Four degree of freedom if ignore axial.

A B

A

B C

D

Kinematically determinate (zero degree of freedom).

Joints A, B, C and D each has 2 degrees of freedom.E and F have zero and one degree of freedomrespectively. Thus, the truss has a total of ninedegrees of freedom for joint translation or the truss iskinematically indeterminate to the ninth degree.

A B

D

A B C

E F

Analysis ofindeterminate

structure

Staticindeterminacy

Kinematicindeterminacy

FlexibilityMethod

Degree of staticindeterminacy(Redundant)

N.A

StiffnessMethod

N.A Degree offreedom (DOF)

Summary

ThankYou