Topic C7 Plastic Design of Steel Struct-2008

Unit CIV4235 Advanced Structural Design C7.1 Topic C7 - Plastic Design of Steel Structures to AS4100

Department of Civil Engineering Date: 7-2008

Topic C7: PLASTIC DESIGN OF STEEL STRUCTURES TO AS4100

TABLE OF CONTENTS

Preview.............................................................................................................. 2

INTRODUCTION ................................................................................................ 2

OBJECTIVES ..................................................................................................... 2

READINGS........................................................................................................ 2

Principles of plastic design................................................................................ 3 Example ...................................................................................................... 3 Plastic design using mechanism method.................................................... 3 Solution....................................................................................................... 5

Limit states requirements for plastic design to AS4100 ................................... 5

Web slenderness requirements (AS4100 - 5.10.6)............................................ 5

Combined actions requirements (AS4100 - 8).................................................. 7

CONNECTIONS (AS4100 - 9.1.2.4, 4.5.3)......................................................... 8

SHEAR CAPACITY (AS4100 - 5.11) .................................................................. 8

MOMENT AMPLIFICATION FACTOR................................................................... 9

SERVICEABILITY LIMIT STATES REQUIREMENT................................................. 9



Preview

Introduction The principles of plastic design and its relationship with plastic analysis are explained. The limit states requirements for plastic design as stipulated in AS4100 are discussed. The requirements to deal with second-order effect for plastic design are also given. The serviceability limit state requirement in plastic design is given.

Objectives Having successfully completed this topic, the learner should be able to • Design structures which satisfy the requirements stipulated in As4100 .

Readings

Required

Notes for this topic

Suggested

• Chapters 3 & 4, Plastic Design to BS5950, Davies & Brown.

• AS4100 – 1998.



Principles of plastic design The following example demonstrates the advantage of using plastic design method over the elastic one.

Example Compare elastic and plastic designs for the fixed-end beam shown in Figure C7.1.

Elastic design

Maximum elastic moment, M*, at support

= wL2/12 = 175kNm

Use Grade 300, 310UB40.4 (φMs = 182kNm)

Plastic design

Plastic moment, Mp = wL2/16 = 131kNm

Use 250UB37.3, Grade 300 (φMs = 140kNm)

Saving in weight = (40.4 - 37.3)/40.4 = 7.6%

Plastic design using mechanism method The design of a structure using plastic method is a reverse of the process for Plastic analysis.

Plastic analysis: The collapse load Pw is a function of moment capacity Mp (given).

E.g. a fixed end beam with a point load at mid-span :L

MP p

w8

= .

Plastic design: The plastic moment Mp is a function of design loads P (given).

For the fixed end beam example, 8

PLM P = .

L = 10m

w = 21kN/m

Figure C7.1



For a structure with more than 1 possible collapse mechanism, Plastic analysis - Collapse load is the smallest Pw of all collapse mechanisms. Plastic design - Design moment capacity is the largest Mp of all collapse mechanisms. This is shown in Figure C7.2.

Example Choose a suitable section for the portal frame shown in Figure C7.3. All members are of the same size.

Mechanism 1 Mechanism 2

Mechanism 3

Moment capacity Mp

Pw

Load

Figure C7.2

200kN

67kN 5m 5m

5m Pin-joint

Figure C7.3



Solution (a) Beam mechanism 200(5θ) = Mp (4θ)

Mp = 250 kNm

(b) Sway mechanism 67(5θ) = Mp (2θ)

Mp = 167 kNm

(c) Combined mechanism 67(5θ) + 200(5θ)= Mp (4θ)

Mp = 334 kNm

∴(c) is critical, Mp required = 334 kNm

From DCT, Use 460UB67.1, Grade 300.

Limit states requirements for plastic design to AS4100 Some limitations to the use of plastic design have been described in Section 1.4. In additions, the following requirements need to be met.

Web slenderness requirements (AS4100 - 5.10.6) To ensure that the plastic hinge can be fully developed without excessive compression (as a result of pure bending) in the web which may fail prematurely due to local buckling,

82250

1 ≤y

w

ftd

where d1 = clear height of web, and tw = thickness of web.



In addition, if a design bearing load, P*b, (such as a secondary beam sitting on a

main beam) or a design shear force, V* is

10** w

bVVorP φ

≥

where φVw is the shear force capacity of the web, then load bearing stiffeners should be provided as shown in Figure C7.4.

When load bearing stiffeners are required, they are designed in accordance with AS4100 – 5.14: (a) The stiffener must be compact (AS4100 - 5.2.2) to ensure no local buckling.

That is,

spy

sf

td λλ <=

2501 from AS4100 - Table 5.2.

(b) The stiffener is designed to carry the greater of P*b or V* as an axial

compression member.

Plastic hinge is to form within this length

*bP or

d1/2 d1/2

Figure C7.4

“Elasto-plastic behaviour of steel frame works”. Boeraeve Ph., Lognard B., Janss J., Gerardy JC., Schleich JB., J. Const. St. Res., 27, 1993, 3-21



Combined actions requirements (AS4100 - 8) In plastic design, the effect of the combined actions of bending moment and axial force is most significant. The following applies mainly to members made of I-sections. (i) In-plane member capacity (AS4100 – 8.4.3.4)

Moment capacity

The plastic moment capacity of any member is reduced by the presence of axial force. The theoretical derivation of the equations has been given in Section 4. Writing sp MM φ= and sp NN φ= , then the reduced plastic

moment capacity, prMφ , is

sxs

sxprx MNNMM φφ

φφ ≤⎟⎟⎠

⎞⎜⎜⎝

⎛−=

*118.1 for bending about the x-x axis

sys

sypry MNNMM φφ

φφ ≤⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

2*119.1 for bending about the y-y axis.

Member slenderness To ensure that the full moment capacity can be maintained when the

collapse mechanism develops, check (AS4100 - 8.4.3.2)

2* 40.060.0

⎥⎥⎦

⎤

⎢⎢⎣

⎡ +≤

oLs

m

s NNNN βφ

when 15.0*≤

sNNφ

(A)

and

⎥⎥⎦

⎤

⎢⎢⎣

⎡

++

−+≤

oLsm

oLsm

s NNNN

NN

ββ

φ 11*

when 15.0*>

sNNφ

(B)

where

βm = ratio of smaller to larger end moments

NOL = π2EI/L2

L = actual length of member

If (B) is not satisfied, the member shall not contain plastic hinge and

should be designed elastically according to AS4100 - 8.4.2.



Web slenderness

To ensure that no local buckling occurs to the web due to both bending moment and axial force, check

( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡−≤

137

25060.0 1

* y

ws

f

td

NNφ

for webs where 82250

45 1 ≤≤ y

w

ftd

or

( )

0.14.27

25091.1 1

*≤

⎥⎥⎦

⎤

⎢⎢⎣

⎡−≤

y

ws

f

td

NNφ


25 1 << y

w

ftd

or

0.1*≤

sNNφ


1 ≤y

w

ftd

For the case where 82250

1 >yft

d (local buckling occurs even under

pure bending), the member has to be designed elastically according

to AS4100 - 8.4.2.

Connections (AS4100 - 9.1.2.4, 4.5.3) For full strength connection, it should have a strength capacity not less than that of the connecting members. This assumption has been made when connections are designed in accordance with AS4100 – 9. The rotation capacity at any of the plastic hinge should not be exceeded. If the materials of the steel members satisfy the ductility requirements given in Section 1.4, it is unlikely that the rotation capacity of any plastic hinge in a simple or moderately complex structure will be exceeded when all other design requirements are satisfied.

Shear capacity (AS4100 - 5.11) Same as elastic design.



Moment amplification factor Bending moment is amplified due to the P-δ and P-Δ (second-order) effects. These effects are accounted for in the plastic analysis by the use of an amplification factor δp. The significance of the second-order effects depends on the elastic buckling load factor λc. (a) For λc ≥ 10, second order effects can be ignored.

(b) For 5 ≤ λc < 10, Mp is amplified by the factor δp in a rigid plastic analysis

where

c

p

λ

δ 11

9.0

−= .

The above equation is equivalent to reducing the plastic collapse load by the same factor. Hence, for an elastoplastic analysis,

True collapse load = p

cδα .

(c) For λc < 5, a second-order plastic analysis (advanced analysis) has to be carried out.

Serviceability limit states requirement This is mainly concerned with the deflection limit of the structure. For certain types of structures, such as portal frames, subject to high wind loads, deflection is often excessive and could be the main factor governing the design. The check for serviceability is usually carried out in the same way as for elastic design. That is,

Δ≤δ

where δ is the maximum deflection obtained from elastic analysis and Δ is the deflection limits from AS4100 – Appendix B.

When deflection check is performed, a traditional assumption for plastic design is that no plastic hinge should form when the structure is subject to service load. This assumption is debatable.

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Topic C7 Plastic Design of Steel Struct-2008