Degree of static indeterminacy of trusses PDF

Preview

Summary

BASICS OF PIN CONNECTED STRUCTURES...

Description

ANALYSIS OF STRUCTURE :

1. ALL OF ITS EXTERNAL SUPPORT REACTIONS, 2. ALL OF ITS INTERNAL MEMBER FORCES , AND 3.

KNOWING THE ABOVE TWO, THE DISPLACEMENT OF ITS VARIOUS JOINTS AND MEMBER DEFORMATIONS MAY THEN BE DETERMINED.

1

Statical Indeterminacy Pin connected structure where usual assumptions are made related to loading, member configurations, and material behaviour, ℎ . . Number of Internal Member Forces = 1 ×

=

,

Where , m is the number of members in the truss 1

Statical Indeterminacy ℎ

ℎ ,ℎ ℎ

ℎ

,ℎ .

Number of total independent equations of equilibrium = 2 , ℎ = ℎ

ℎ ℎ . Thus,

3 ℎ

Number of independent equations of equilibrium available for evaluating internal member forces = 2 × − 3 Number of independent equations of equilibrium available for evaluating ex =3 1

Statical Indeterminacy Number of Joints = Number of External Support Reactions = Number of Internal Member Forces = 1 × Total Number of unknowns =

=

+

Number of total independent equations of equilibrium = 2 ×

ℎ , ,

. 1

Statical Indeterminacy 1.

+

>2×

More unknowns than available equations of equilibrium ≡ Statically Indeterminate 2.

+ =2×

Total Unknowns = available equations of equilibrium ≡ Statically Indeterminate 3.

+...