Classification of Cross-Section - PowerPoint Presentation

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Classification of Cross-Section

Introduction

To

determine strength

of the structural steel component, it requires the designer to

consider the cross-sectional

behaviour

and the overall member

behaviour

.

Purpose of classification : to identify the extent to which

the resistance and rotation capacity of cross sections is limited

by its local buckling resistance.

Clause 5.5.1 and 6.2 cover the cross-sectional aspects of the design process

In EC3, cross-sections are placed into one of four

behavioural

classes depending upon the material yield strength, the width to thickness ratios (

b/t

f

or

d/t

w

) of the individual compression parts (e.g. web and flanges) within the cross-section and the loading arrangement.

Local buckling

Local buckling exhibit local deformation of outstand

E.g. a flange of I beam

Local buckling occurs when the flange outstand to thickness ratio (

b/t

f

) is high

Called flange buckling

The web is also subjected to compressive stresses from bending with a limiting to

d/t

w

ratio beyond which web will buckle even though the axis of the axis remain straight

Called web buckling

Definition of classes

EC3 classified four classes

In hot rolled design the majority of standard cross-section will be class 1, 2 or 3.

The four

behavioural

classes of cross-section defined by EC3

Assessment of Individual parts

Each compressed (or partially compressed) element is assessed individually against the limiting width to thickness ratios for Class 1,2 and 3 elements as defined in Table 5.2 of EN 1993-1-1.

An element that fails to meet the class 3 limits should be taken as Class 4.

The limiting width to thickness ratios are modified by a factor

ε

that is depend upon material yield strength

Where

f

y

is the nominal yield strength of steel

*The section classification based upon the weaker element

Definition of compression width c for common cases a) outstand flanges b) internal compression parts

Overall Cross-Section Classification

EC3 allows the overall cross-section classification to be defined in one or two ways:

The overall classification is taken as

the highest

( least

favourable

)

class

of its component parts, with the exceptions that Cross-sections with class 3 webs and class 1 or 2 flanges may be classified as Class 2 cross-sections with an effective web (

Clause 6.2.2.4 of EC3-1-1)In the case where the web is assumed to carry shear force only (and not to contribute to the bending or axial resistance of the cross-section, the classification may be based on that of the flanges ( not allow for class 1)

The overall classification is defined

by quoting both the flange and web classification.

Class 4 cross-section

Class 4 sections

contain slender elements

that are susceptible to local buckling in the elastic material range

Allowance for the reduction in resistance of Class 4 cross-section as a result of local buckling is made by

assigning effective width

to the class 4 compression element.

Calculation not

include in Part 1-1

, instead is directed to Part 1.3 for cold form sections, to Part 1.5 for hot-rolled and fabricated sections and to Part 1.6 for circular hollow section.

Example 2.1

Cross section classification

Q

Determine the classifications and resistance

N

c,Rd

for a 254 x 254 x 73 UC in pure compression, assuming grade S355 steel

A

Outstand flanges

(Table 5.2, sheet 2)

c

f

= (b-t

w

-2r)/2

=110.3mm cf/tf = 110.3/14.2 = 7.77 Limit for class 2 flange 10

ε = 10 x 0.81 = 8.14 > 7.77 Hence flanges are Class 2

Web-internal compression part

(Table 5.2 sheet 1)

c

w

= (h-2t

f

-2r)

=200.3 mm

c

w

/

t

w

=

200.3/8.6 = 23.29

Limit for Class 1 web, 33

ε

= 26.85 > 23.29

Hence web are

class 1



Overall cross-section classification is therefore Class 2

Classification under combined bending and axial force

Should be classified based on the actual stress distribution of the combined loadings

For simplicity , initial check carried out under the severe loading condition of pure axial compression.

If the section classified as Class 1 or 2, nothing to be gained by conducting additional calculations with the actual pattern of stress

If the classification is Class 3 or 4, it is advisable for economy to conduct a more precise classification under combined loading

Example 2.2

Cross-section classification under combined bending and compression

Q

A member is to be designed to carry combined bending and axial load. In the presence of a major axis (y-y) bending moment and an axial force of 300kN, determine the cross-section classification of a 406 x 178 x 54 UB in grade S275 steel

Cross-section classification

(Clause 5.5.2)

Outstand flanges

(Table 5.2, Sheet 2)

Limit for class 1 flange =

9

ε

= 8.32

8.32>6.86 flanges are

class 1

Web internal compression part

(Table 5.2,Sheet 1)

Limit for Class 3 web = 42

ε

= 38.8

38.8 > 46.81 web is

Class 4

Overall cross-section classification is therefore

Class 4.

More precise approach (cross section classification under combined loading)-

clause 5.5.2

Flange classification remains as Class 1.

Web- internal part in bending and compression (Table 5.2 sheet 1)

From Table 5.5 (sheet 1), for a class 2 cross-section:

where

α

may be determined from equation below, for I and H section where the neutral axis lies within the web.

limit for a class 2 web = 456

ε

/13

α

-1 = 52.33

52.33 > 46.81 web is

class 2

Overall cross section classification under the combined loading is therefore

Class 2

. Conclusion:

For this section, a maximum axial force of 411 kN may be sustained in combination with a major axis bending moment, whilst remaining within the limits of a Class 2 section

Tutorial 1

Q

A welded I section is to be designed in bending. Determine the classification for a welded section with 200

x 20

mm flanges and a 600 x 6 mm web. Assuming grade S275 steel