Structure Analysis I

Structure Analysis I

Lecture 3

Analysis of Statically

Determinate Structures

Idealized Structure

•In real sense exact analysis of a structure can never be carried out.

Support connection

• Pin support and pin connection

• Fixed support & fixed connection

• Roller support

Support for coplanar structures

Idealized Structure

Equation of Equilibrium

• In x-y plane

0

0

0

o

y

x

M

F

F

Internal loading

Determinacy & Stability

• Determinacy: when all the forces in structure can be determined from equilibrium equation , the structure is referred to as statically determinate. Structure having more unknown forces than available equilibrium equations called statically indeterminate

• If n is number of structure parts & r is number of unknown forces:

r = 3n, statically determinate r > 3n, statically indeterminate

Classify determinate & indeterminate structure

eDeterminat Statically )1(33

1

3

n

r

degree 2

ateindetermin Statically )1(35

1

5

nd

n

r

edeterminat Statically )2(36

2

6

n

r

degree 1

ateindetermin Statically )3(310

3

10

st

n

r

degree 1 ate,indetermin Statically )2(37

2

7

st

n

r

degree 4

ateindetermin Statically )2(310

2

10

th

n

r

• StabilityPartial Constraints

case loading with thisunstablesatisfied benot will0 xF

• Improper ConstraintsThis can occur if all the support reactions are

concurrent at a point.

0dP

• This can occur also when the reactive forces are all parallel

In Generalr < 3n, Then the structure is Unstable r >= 3n, Also, Unstable if member reactions

are concurrent or parallel or some of the components form a collapsible mechanism

Classify The structure Stable or Unstable

Sable )1(33

1

3

cases no special

n

r

Sable )2(38

2

8

cases no special

n

r

Unsable Bar concurrent are reactions three the)1(33

1

3

n

r

Unsable )3(37

3

7

n

r