Structural Analysis-IStructural Analysis-I

DrDr. . Ali Ali TayehTayehSecond Second SemesterSemester

2010-2010-20112011

Lecture 3Analysis of Statically

Determinate Structures

Support connectionPin support and pin connection

Fixed support & fixed connection

Roller support

Support for coplanar structures

Idealized Structure

Equation of EquilibriumIn 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

Stable )1(33

1

3

cases no special

n

r

Stable )2(38

2

8

cases no special

n

r

Unstable Bat concurrent are reactions three the)1(33

1

3

n

r

Unstable )3(37

3

7

n

r

Classify determinate & indeterminate structure, If indeterminate, specify the degree of indeterminacy. Classify The structure Stable or Unstable

Indeterminate to the 2ed degree. Stable

Indeterminate to the 3rd degree. Stable