DETERMINACY

Equilibrium, Determinacy and Stability

Ahmad Shufni Othman

July 2012

DETERMINACY

• Support Connections

– Pin connection (allows slight rotation)

– Roller support (allows slight translation)

– Fixed joint (allows no rotation/translation)

Idealized Structure

DETERMINACY

Idealized Structure

DETERMINACY

• In reality, all connections and supports are modeled with

assumptions. Need to be aware how the assumptions will affect the

actual performance

Idealized Structure

DETERMINACY

– No thickness for the components

– The support at A can be modeled as a fixed support

Idealized Structure

DETERMINACY

Review of support conditions

DETERMINACY

Types of Beams • Depends on the support configuration

M

Fv

FH Fixed

FV FV

FH

Pin

Roller

Pin Roller

FV FV

FH

DETERMINACY

Statically Indeterminate Beams

Can you guess how we find the “extra” reactions?

Continuous Beam

Fixed Beam

Propped Cantilever

Beam

DETERMINACY

Combined Beams

A combination beam can

be either statically

determinate or

indeterminate. These two

beams are statically

determinate, because the

hinge provides another

location, where the moment

is equal to zero.

DETERMINACY

Reactions at Supports and Connections for a Two-Dimensional Structure

• Reactions equivalent to a force with known line of action.

DETERMINACY

Reactions at Supports and Connections for a Two-Dimensional Structure

• Reactions equivalent to a force of unknown direction and magnitude.

• Reactions equivalent to a force of unknown direction and magnitude and a couple of unknown magnitude

DETERMINACY

DETERMINACY

DETERMINACY

What do we understand by determinate and indeterminate structures?

0

0

0

o

y

x

M

F

F

Equilibrium and Determinacy

Determinate: Forces and Moments are determined by equilibrium equations

DETERMINACY

– If the reaction forces can be determined solely from the equilibrium EQs

STATICALLY DETERMINATE

– If No. of unknown forces > equilibrium EQs

STATICALLY INDETERMINATE

–Can be viewed globally or locally (via free body diagram)

Equilibrium and Determinacy

DETERMINACY

– For a 2D structure

– Where,

– The additional EQs needed to solve for the unknown forces are referred to as compatibility EQs

ateindetermin statically ,3

edeterminat statically ,3

nr

nr

No. of unknown forces

No. of components (members)

acyindetermin of degree 3 nr

Equilibrium and Determinacy

DETERMINACY

1F

P wA B

P wA B

3 EQs 3 unknown reactions

Stable Structures!

3F2F

1F

2FAM

determinate structure

Equilibrium and Determinacy

DETERMINACY

3F

1F 2F 3F

P wA B

Stable Structures?

1F

2FAM

P wA B

Stable Structures?

Not properly supported

INDETERMINATE stable 1 degree indeterminancy

3 unknown reactions

3 EQs

Equilibrium and Determinacy

4 unknown reactions

3 EQs

DETERMINACY

3F

1F

2FAM

P wA B

Stable Structures ! Stable Structures ?

1F

2FAM

3F

5F

4F

4F

6 equilibrium conditions

6 unknown forces

Equilibrium and Determinacy

DETERMINACY

3F

P wA B

3F4F

5F

4 equilibrium conditions

4 unknown forces

C

3 equilibrium

conditions

0cb

cM

+ 1F

2FAMC

Equilibrium and Determinacy

DETERMINACY

Determinacy (Recap.)

acyindetermin of degree : 3nr

Equilibrium and Determinacy

DETERMINACY

Discuss the Determinacy

DETERMINACY

Discuss the Determinacy

DETERMINACY

Discuss the Determinacy

DETERMINACY

Discuss the Determinacy

DETERMINACY

Discuss the Determinacy

DETERMINACY

Stability

DETERMINACY

Discuss the Stability

DETERMINACY

Discuss the Stability

DETERMINACY

Discuss the Stability

DETERMINACY

To be

continued ……