*Collapse of Frames & Grillage Structures (Topic 3)

(1)

* Collapse of Frames & Grillage Structures ( Topic 3 )

Advanced Local Structural Design & Analysis of Marine Structures

OST

Since 2015

OST

Since 2015

(2)

Page 2/23

OST

Since 2015

OST

Since 2015

[Part I] Plastic Design of Structures

– Plastic theory of bending (Topic 1) – Ultimate loads on beams (Topic 2)

– Collapse of frames and grillage structures (Topic 3)

[Part II] Elastic Plate Theory under Pressure

– Basic (Topic 4)

– Simply supported plates under Sinusoidal Loading (Topic 5) – Long clamped plates (Topic 6)

– Short clamped plates (Topic 7)

– Low aspect ratio plates, strength & permanent set (Topic 7A)

[Part III] Buckling of Stiffened Panels

– Failure modes (Topic 8)

– Tripping (Topic 9) + Post-buckling strength of plate (Topic 9A) – Post-buckling behaviour (Topic 10)

[Theory of Plates and Grillages]

Adv. Local Structural Design & Analysis of Marine Structures (Overview)

(3)

OST OST

The aim of this lecture is:

• To equip you with the knowledge and understanding of various collapse modes of frame and grillage structures.

Objectives

(4)

OST

Since 2015

OST

Since 2015

Learning Outcome

At the end of this lecture, you should be able to:

– Identify various collapse modes of frame and grillage structures.

– Determine the ultimate loads on frame and grillage structures.

– Design structure against bending collapse .

(5)

OST OST

• Structures are composed of various structural components such as beams and girders, longitudinals and transverses,

• Therefore, there are a number of possible failure modes.

• In order to identify the ultimate strength of a structure, loads causing these failure modes must be considered.

Introduction

(6)

Page 6/23

OST

Since 2015

OST

Since 2015

• The mechanism method used to analyse simple beams and continuous beams can be applied for frame and grillage structures.

• The frame structure is arrangement of members in more than one plane.

• For frames of limited height, axial stresses tend to be small enough to be neglected and those members are treated as beams.

• The grillage structure is a set of intersecting beams, which carry loads normal to the plane of the structure.

Frame and Grillage Structures

• All possible collapse mechanisms are needed to establish the smallest load at which the structures collapse.

• This is because frame and grillage structures are more complicate than beams,

• It is essential NOT to miss any collapse modes.

(7)

Page 7/23

OST OST

Frame and Grillage Structures

• Sway mode of failure

(a) Portal frame with vertical and horizontal point loads

Internal work = 4M _p



_h

External work =

h h

h

HL

H  = 

By the principle of virtual work

h p h

h M

HL



= 4





h

p L

M H = 4 /



(8)

Page 8/23

OST

Since 2015

OST

Since 2015

Frame and Grillage Structures

• Vertical mode of failure

(a) Portal frame with vertical and horizontal point loads

Internal work = External work =

( )

4M _p



_b = M _p



_b + 2

 

_b + _b

b b b

V L

V 

= 2

b p b

b M

V L  4 

2 =



b

p L

M V = 8 /



(9)

Page 9/23

OST OST

(b) Ship frame structures

Weak frame and side impact

(10)

Page 10/23

OST

Since 2015

OST

Since 2015

• Assume that transverse and longitudinal have the same strength

(c) Grillage structure with fixed end transverse beams and simply supported longitudinal

(11)

Page 11/23

OST OST

• Failure mode 1 : Local collapse

4M _p



1

1 1

1

1 ^W 2^L

W_p = _p

1 1

1 4

2  _p

p L M

W =



L M

W = 8 /



(12)

Page 12/23

OST

Since 2015

OST

Since 2015

Frame and Grillage Structures

• Failure mode 2 : Overall collapse

2 2

1 . 5 

 = L

2 2

2

L  L 

d = = 

₂

= 

₂

From displacement diagram, we have

(13)

Page 13/23

OST

Since 2015

OST

Since 2015

• Failure mode 2 : Overall collapse

2 2

2 2 4 10

2M _p



+  M _p



= M _p



2 2

2



1.5W L



W_p = _p

2 2

2 10

5 .

1 W_p L



= M _p



 W_p 20 M _p / L

2 =



2



 =

2 2

1 . 5 

 = L

(14)

Page 14/23

OST

Since 2015

OST

Since 2015

Frame and Grillage Structures

• Hence, the smallest ultimate load W_p is 20M_p / 3L.

W_p2 = 20M_p / 3L W_p1 = 8M_p /L

L M

W_p _p / 3

20

2 =



>

(15)

Page 21/23

OST OST

• We have investigated the Collapse of frames & grillage structures.

Learning Outcomes (Final Review)

• Now we are able to:

– Identify various collapse modes of frame and grillage structures.

– Determine the ultimate loads on frame and grillage structures.

– Design structure against bending collapse.

• Details can be referred to topics 3 in the lecture notes.

(16)

Page 22/23

OST

Since 2015

OST

Since 2015

[Part I] Plastic Design of Structures

– Plastic theory of bending (Topic 1) – Ultimate loads on beams (Topic 2)

– Collapse of frames and grillage structures (Topic 3)

[Part II] Elastic Plate Theory

– Basic (Topic 4)

– Simply supported plates under Sinusoidal Loading (Topic 5) – Long clamped plates (Topic 6)

– Short Clamped plates (Topic 7)

– Additional (Low aspect ratio plates, strength & permanent set)

[Part III] Buckling of Stiffened Panels

– Failure modes (Topic 8) – Tripping (Topic 9)

– Post-buckling behaviour (Topic 10)

[Theory of Plates and Grillages]

Adv. Marine Structures / Adv. Structural Design & Analysis (Next class)

(17)

Page 23/23

OST OST

Kam Sa Hab Ni Da

Questions?