1

Example: Jib Crane

P

L

L

AB

C

1

2

Moment Diagram

PL

PL

2

Deflections?

P

A1

3 22, ,

2B Bx B y

PL PL PLu uEI EI EA

θ= = = −

C

2

Byu

Bxu

2Bθ 1

Bθ

31

21 1

Effect ofEffect of endEnd rotationCantilever beamdeflection

( )2

( ) (3 )6

Bx x

y B

PLu x uEI

Px PLu x L x xEI EA

θ

= =

= − − − −

3

31

2

3

Ax

Ay B

PLuEI

PL PLu LEI EA

θ

=

= − − −

Byu

BxuMB=-PL

P

Relating 1 2andB Bθ θ

P

AB

C

1

2Stiff Joint

1 2=B Bθ θ

2Bθ

1Bθ P

AB

C

1

2Pin Joint

356

Ay

PL PLuEI EA

= − − Mechanism

Full moment connection

3

Intermediate Joint

P

A

B

C

1

2( )2 1

B B BM θ θ= Γ −

2Bθ

1Bθ

Torsional spring, stiffness (Force×Length) Γ

21

21

B B

B

PLM PLEI

PL PLEI

θ

θ

⎛ ⎞= − = Γ −⎜ ⎟

⎝ ⎠

⇒ = +Γ

356

Ay

PL PL PLuEI EA

= − − −Γ

P

MB1

1BV

1BN

Bending dominates

P

AB

C

1

2

1 2=B Bθ θ

2Bθ

1Bθ

3 3 3

2

5 5 6 516 6 5 6

Ay

PL PL PL I PLuEI EA EI AL EI

⎛ ⎞= − − = − + ≈ −⎜ ⎟⎝ ⎠

Full moment connection

2

6 15

IAL

If the beam is much longer than its cross section dimension