lecture-6

11

University of Sheffield

Department of Civil & Structural Engineering

4. Design of Steel Structures to Eurocode 3

22



Introduction to Eurocode 3

Eurocode 3 applies to the design of buildings and civil engineering works in steel

It is based on limit state principles and comes in several parts as shown in following:

EN 1993-1 Design of Steel Structures: General rules and rules for buildings.

EN 1993-2 Design of Steel Structures: Steel bridges.

EN 1993-3 Design of Steel Structures: Towers, masts and chimneys. EN 1993-4 Design of Steel Structures: Silos, tanks and pipelines.

33



EN 1993-5 Design of Steel Structures: Piling.

EN 1993-6 Design of Steel Structures: Crane supporting structures.

EN 1993-1 “General rules and rules for buildings” comprises of 12 parts.

44



EN 1993-1-1, (EC3) gives a general basis for the design of buildings and civil engineering works in steel

The arrangement of sections within EC3 is based on design criteria such as deflection, tension, compression, bending, shear, buckling etc, rather than on individual element types, such as beams, columns, etc

EC3 is organised into seven chapters.

There are a number of Annexes within EC3

These may be ‘normative’, in which case they have the same status as the chapters of EC3 to which they relate, or ‘informative’

Informative annexes are not mandatory but provide useful information

55



Principles and application rules (clause 1.4, EC3)

The clauses in EC3 have been divided into principles and application rules

Principles encompass statements, definitions, requirements and analytical methods for which there is no permitted alternative

Application rules are generally recognized rules which follow the principles, but for which EC3 permits the use of alternative techniques

66



Symbols (clause 1.6, EC3)

A complete list of symbols is included in EC3

Subscripts can be arranged in sequence as necessary, separated by a comma – for example:

Npl,Rd design plastic resistance to normal forces of the gross cross-section

77



Basis of design

Serviceability limit state

Ultimate limit state

EC3 uses limit state principles and for design purposes considers the two principal categories of limit states:

The ultimate limit state is concerned with the resistance of the structure to collapse

This is generally checked by considering the strength of individual elements subject to forces determined from a suitable analysis

The overall stability of the structure must be checked

88



The ultimate limit state is examined under factored load conditions

The effects on individual structural elements will be determined by analysis, and each element then treated as an isolated component for design

99



Serviceability limit state

The calculated deflection is valuable as an index of the stiffness of a member or structure.

Calculations of deflection should relate to elastic behaviour of the structure.

Calculated deflections should be compared with specified maximum values.

The dynamic effects to be considered at the serviceability limit state are vibration caused by machinery and self-induced vibrations.

Resonance can be avoided by ensuring that the natural frequencies of the structure (or any part of it) are sufficiently different from those of the excitation source.

1010



Actions (clause 2.3.1, EC3) Actions is the Eurocode terminology for loads and

imposed deformations

Dead and imposed loads are generally referred to in EC3 as permanent and variable actions respectively

The design values of actions (Fd) are obtained by

kFd FF Fk is the characteristic actions

is partial safety factor for actions (1.35 for permanent and 1.5 for variable actions)

F

1111



Design strength (clause 2.4.1, EC3)

Design strengths, , are obtained by dX

mkd XX /kX is the characteristic strengths

m is the partial safety factor for materials

dRDesign resistance, for the member is given by

Mkd RR /is the cross-section resistance kR

M is the partial safety factor for the resistance

1212



Characteristic strength (clause 3.2.1, EC3)

Nominal values of yield strength, for hot rolled structural steel yf

1313



In EC3 the partial safety factor, is applied to structures and components

MPartial safety factors (clause 2.4.3 and 6.1(1), EC3)

The values for partial safety factors should be those given below:

Resistance of cross-section, 0.10 M

0.11 M Resistance of member to buckling (assessed by

checks in clause 6.3),

Resistance of cross-sections in tension to fracture,

25.12 M

1414



Material coefficients (clause 3.2.6, EC3)

The material coefficients to be adopted in EC3 are as following:

Modulus of elasticity 2/210000 mmNE

Shear modulus 2/81000)1(2

mmNE

G

Poisson’s ratio 3.0

Coefficient of linear thermal expansion C /1012 6

Density 3/7850 mk g

.

1515



Section classification (clause 5.5 and 6.2, EC3)

Outstand

WebInternal

Web

Flange

Internal

Flange

Rolled I-section Hollow section

Flange

Welded box section

InternalOutstand

InternalWeb

Some are internal- webs of open beams - flanges of boxes

Some are outstand- flanges of I beams- legs of angles and Tees

Rolled or welded sections may be considered an assembly of individual plate elements

1616



Basis of section classification

Outstand

WebInternal

Web

Flange

Internal

Flange Rolled I-section Hollow section

Flange

Welded box section

InternalOutstand

InternalWeb

As the plate elements are relatively thin, when loaded in compression they may buckle locally.

The tendency of any plate element within the cross section to buckle may limit the axial load carrying capacity, or the bending resistance of the section, by preventing the attainment of yield.

Avoidance of premature failure arising from the effects of local buckling may be achieved by limiting the width-to-thickness ratio for individual elements within the cross section.

1717



Classification of cross-sections

EC3 defines four classesfour classes of cross section.

The class into which a particular cross section falls depends upon: slendernessslenderness of each element (defined by a

width-to-thickness ratio). the compressive stress distributionstress distribution.

Classes are defined in terms of performanceperformance requirementsrequirements for resistance of bending bending momentsmoments..

1818



Class 1 cross sectionsClass 1 cross sections

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance

Rotation Capacity Class

1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4

Plastic momenton gross section


Elastic momenton gross section

Plastic moment oneffective section

Mpl

Mpl

Mpl

Mpl

Mel elastic moment resistance of cross-sectionMpl plastic moment resistance of cross-sectionM applied moment rotation (curvature) of section

rotation (curvature) of section required to generate fully plastic stress distribution across section

pl

pl

rot

pl

pl

pl

pl

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl



pl

pl

rot

pl

pl

pl

pl

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl



pl

pl

rot

pl

pl

pl

pl

1919



fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl



pl

pl

rot

pl

pl

pl

pl

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl



pl

pl

rot

pl

pl

pl

pl

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl

Mel elastic moment resistance of cross-sectionMpl plastic moment resistance of cross-sectionM applied moment rotation (curvature) of section rotation (curvature) of section required to generate fully plastic stress distribution across section

pl

pl

rot

pl

pl

pl

pl


2020



fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl



pl

pl

rot

pl

pl

pl

pl

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl



pl

pl

rot

pl

pl

pl

pl

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl



pl

pl

rot

pl

pl

pl

pl


2121



fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl



pl

pl

rot

pl

pl

pl

pl

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl



pl

pl

rot

pl

pl

pl

pl

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

fy

Moment

LocalBuckling

Mel

fy

Moment

LocalBuckling

Mel

Model ofBehaviour

MomentResistance


1

1

1

1

1

1

1

1

Sufficient

Limited

None

None

MMpl

MMpl

MMpl

MMpl

1

2

3

4





Mpl

Mpl

Mpl

Mpl



pl

pl

rot

pl

pl

pl

pl


2222



Assessment of individual parts

(d)

(c)

(b)(a)

Simply supported onall four edges

t

L

b

Simply supportededge

Freeedge

b

L1

2

3

4

5

1 2 30 4 5

Plate aspect ratio L / b

Buckling coefficient k

b

L Free

Exact

k = 0.425 + (b/L)2

0.425

Behaviour of plate elements in compression

2323



Maximum width-to-thickness ratios for compression parts (Table 5.2, EC3)

In EC3 each compressed (or partially compressed) element is assessed individually against the limiting width-to-thickness ratios for Class 1, 2 and 3 elements defined in Table 5.2 of EC3 (see Table 4.4).

It should be noted that the factor is given by

5.0

235

yf

2424



Definition of compression width c for common cases: (a) Outstand flanges. (b) Internal compression parts

The compression widths c defined in sheets 1 and 2 always adopt the dimensions of the flat portions of the cross-sections, i.e. root radii and welds are explicitly excluded from the measurement, this was not the case in the ENV version of EC3 or BS 5950

2525



Overall cross-section classification Once the classification of the individual parts of the cross-

section is determined, EC3 allows the overall cross-section classification to be defined in one of two ways:

The overall classification is taken as the highest (least favourable) class of its component parts.

The overall classification is defined by quoting both the flange and the web classification.

2626



Work example WE 6-1:

Classify the hot rolled sections, 406x178x54UB, assuming in S275 and S355 steel and subjected to bending only. The section properties are:

m mh 6.4 0 2 m mb 7.1 7 7 mmt f 9.10

mmt w 7.7 m mr 2.1 0

2727



2828



2929



3030



Introduction to Introduction to

Design ofDesign of

Restrained BeamsRestrained Beams

3131



Fully laterally restrained beams

Beams which are unable to Beams which are unable to move laterally are termed move laterally are termed

"restrained""restrained"

Beams which are unable to Beams which are unable to move laterally are termed move laterally are termed

"restrained""restrained"

Unaffected by out-of-plane Unaffected by out-of-plane buckling buckling

(lateral-torsional instability)(lateral-torsional instability)

Unaffected by out-of-plane Unaffected by out-of-plane buckling buckling

(lateral-torsional instability)(lateral-torsional instability)

3333



Beams may be considered restrained if: Full lateral restraint is provided by positive attachmentpositive attachment of a

floor system to the top flange of a simply supported beam -Many designers consider the friction generated between a

concrete slab and steel beam to constitute a positive attachment -

adequate torsional restraint of the compression flange is provided, for example by profiled roof sheeting

closely spaced bracing elements are provided such that the minor axis slendernessminor axis slenderness is low

Sections bent about their minor axis cannot fail by lateral torsional instability and it is unlikely that sections with high torsional and lateral stiffness (eg RHS) will fail in this way.

Fully laterally restrained beams

3434



In a simple single span, failure occurs when design value of the bending moment MMEdEd exceeds design moment resistance of the cross-section MMc,Rdc,Rd.

EC3 sets this limit as a shear force of 50% of the plastic shear resistance

Magnitude depends on section shapesection shape, material material strengthstrength and section classification.section classification.

Where shear force on cross-section is smallsmall its effecteffect on the resistance moment may be neglected.neglected.

RdcEd MM ,

3535



Class 1 and 2 cross-sections: moment resistance is the design plastic resistance moment.

Class 3 cross-sections: moment resistance is the design elastic resistance moment.

0

,,,

M

yplRdplRdc

fWMM

0

.min,,,

M

yelRdelRdc

fWMM

class 4 cross-section, the design local buckling resistance.

0

.min,,

M

yeffRdc

fWM

maxmin,el d/IW

dmax = maximum distance from the centroid to the edge of the section

3636




Calculate the moment of resistance, , of the section 152x152x23UC in grade S355 steel (ignoring the influence of shear force), The section properties

are:

RdcM ,

m mh 4.1 5 2 m mb 2.1 5 2 mmt f 8.6

mmt w 8.5 m mr 6.73182 cmW p l

3164 cmW el

3737



3838



3939



Beams with holes in the tension flange at the critical cross-sectionBeams with holes in the tension flange at the critical cross-section Check that ratio of net area/gross area of the flange is not

so small that the section would rupture on the net sectionrupture on the net section before the gross section yielded.gross section yielded.

Bolt holes in the tension zone of the web

should be considered similarly

Holes in the compression zone (both web and flange) may

be ignored unless oversized or slotted

02. ///9.0 MMuyfnetf ffAA

This check will be satisfied provided.

If not, a reduced flange area may be assumed which satisfies the limit.

02

.9.0

M

yf

M

unetf fAfA

4040



Continuous (statically indeterminate) structures

The design moment resistance at the point of maximum moment obtained from an elastic analysis will not normally

lead to collapse

Redistribution of moments enables the structure to withstand loads beyond that which produces the first hinge until eventually sufficient hinges have formed to turn the structure into a mechanism

Load F Elastic - plasticF F

F F

L/2 L/2 L/2 L/2

Plastic

Behaviouraccording tosimple plastictheory

Actual behaviour

F F

Elastic

A B C

F F

L L

Fc

F1st hinge

Fyield

Deflection under load

Load deflection curve for a statically indeterminate beam

4141



Resistance of cross-sections – shear (clause 6.2.6, EC3)

The pattern of shear stress in an I section assuming elastic behaviour

max

V

ht

3

2

h

Cross - section

b

h

Cross - section

Variation of shearstress

Variation of shearstress

t f

tw

Vhb

4I

max

Vhb

2I

h

4b

1

Vhb

2I

The design value of the shear force, , at each cross-section should satisfy

EdV

RdcEd VV ,

As almost all the shear force is carried by the web and since the variation in shear stress through the web is quite small it is sufficiently accurate for design to assume an average shear stress over the web.

4242



MO

yvRdpl

fAV

)3/(

,

vAWhere is the shear area, for general structural cross-sections are given in clause 6.2.3(3). vA

Plastic shear resistance, of the shear area ( ) is given by:

RdplV , vA

The most common ones are shown below:

Rolled I and H sections, load parallel to the web:

wwfwfv thbuttrttbAA 22

Rolled channel sections, load parallel to the web:

fwfv trttbAA 2

4343



Welded I, H and box sections, load parallel to the web:

wwv thA

Welded I, H, channel and box sections, load parallel to the flanges:

wwv thAA

Rolled rectangular hollow section of uniform thickness, load parallel to the depth:

hbAhAv /

4444



Rolled rectangular hollow section of uniform thickness, load parallel to the width :

Circular hollow section and tubes of uniform thickness:

hbAbAv /

/2AAv

4545



Shear buckling need not be considered provided:

for an unstiffened web

for a stiffened web

where is the buckling factor defined in Annex A.3 of EN 1993-1-5.

k

72w

w

t

h

kt

h

w

w 72

4646



Calculate the plastic shear resistance, , for the class 1 section 610x229x101UB in grade S355 steel. The section properties are:

RdplV ,


m mh 6.6 0 2 m mb 6.2 2 7 mmt f 8.14

mmtw 5.10 m mr 7.1 2212900 mmA

441075780 mmI

4747



4848



Resistance of cross-sections – bending and shear (clause 6.2.8, EC3)

If the design shear force exceeds 50% of the plastic exceeds 50% of the plastic shear resistanceshear resistance, the design moment resistance of the cross-section is reduced.

4949



Design plastic moment is calculated using a reduced reduced strength for the shear area, strength for the shear area, given bygiven by:

yyr ff )1(

)5.0(12

,

2

,RdplEd

Rdpl

Ed VVforV

V

The reduced design plastic resistance moment allowing for the shear force may alternatively be obtained as follows for equal flanged section, bending about major axis:

RdVyM ,,

RdcyM

y

w

wyplRdVy M

f

t

AWM ,,

0

2

,,, 4

www thA where

5050



Deflections (clause 7.2.1, EC3)

Deflections and vibrations must be limited to avoid: adverse affects to the appearance impaired use of the structure discomfort to the occupants damage to the finishes and contents of a building.

Acceptable limits for deflections should be agreed between the client, designer and competent authorities.

5151



Vertical deflection limits

Numerical values for deflections limits are not provided in both EC3 and EN 1990.

The UK National Annex may define similar limits to those given in Table 4.6, and is likely to propose that permanent actions be taken as zero in serviceability checks, essentially reverting to the practice in BS 5950, which is to check deflections under unfactored imposed loading.

5252



Design procedure for restrained beams:

(1) Perform structural analysis and calculate design loads on the beam for both ultimate limit state and serviceability limit state.

(2) Determinate maximum design bending moment and shear force along the beam for ultimate limit state.

(3) Select a suitable beam-section.

y

MEdupl f

MW 0.

5353



Web Flange Flange WebAxisx-x

Axisy-y

Axis x-x Axis y-yAxisx-x

Axis y-yAxisx-x

Axis y-y

h b s t r d b/2t d/s Ix Iy rx ry Zx Zy Sx Sy u x H J A

kg/m mm mm mm mm mm mm cm4 cm4 cm cm cm3 cm3 cm3 cm3 dm6 cm4 cm2

838x292x176 175.9 834.9 291.7 14 18.8 17.8 761.7 7.76 54.4 246000 7799 33.1 5.9 5893 535 6808 842 0.856 46.5 13 221 224

762x267x197 196.8 769.8 268 15.6 25.4 16.5 686 5.28 44 240000 8175 30.9 5.71 6234 610 7167 959 0.869 33.2 11.3 404 251

762x267x173 173 762.2 266.7 14.3 21.6 16.5 686 6.17 48 205300 6850 30.5 5.58 5387 514 6198 807 0.864 38.1 9.39 267 220

762x267x147 146.9 754 265.2 12.8 17.5 16.5 686 7.58 53.6 168500 5455 30 5.4 4470 411 5156 647 0.858 45.2 7.4 159 187

762x267x134 133.9 750 264.4 12 15.5 16.5 686 8.53 57.2 150700 4788 29.7 5.3 4018 362 4644 570 0.854 49.8 6.46 119 171

686x254x170 170.2 692.9 255.8 14.5 23.7 15.2 615.1 5.4 42.4 170300 6630 28 5.53 4916 518 5631 811 0.872 31.8 7.42 308 217

686x254x152 152.4 687.5 254.5 13.2 21 15.2 615.1 6.06 46.6 150400 5784 27.8 5.46 4374 455 5000 710 0.871 35.5 6.42 220 194

686x254x140 140.1 683.5 253.7 12.4 19 15.2 615.1 6.68 49.6 136300 5183 27.6 5.39 3987 409 4558 638 0.868 38.7 5.72 169 178

686x254x125 125.2 677.9 253 11.7 16.2 15.2 615.1 7.81 52.6 118000 4383 27.2 5.24 3481 346 3994 542 0.862 43.9 4.8 116 159

610x305x238 238.1 635.8 311.4 18.4 31.4 16.5 540 4.96 29.3 209500 15840 26.3 7.23 6589 1017 7486 1574 0.886 21.3 14.5 785 303

610x305x179 179 620.2 307.1 14.1 23.6 16.5 540 6.51 38.3 153000 11410 25.9 7.07 4935 743 5547 1144 0.886 27.7 10.2 340 228

610x305x149 149.2 612.4 304.8 11.8 19.7 16.5 540 7.74 45.8 125900 9308 25.7 7 4111 611 4594 937 0.886 32.7 8.17 200 190

610x229x140 139.9 617.2 230.2 13.1 22.1 12.7 547.6 5.21 41.8 111800 4505 25 5.03 3622 391 4142 611 0.875 30.6 3.99 216 178

610x229x125 125.1 612.2 229 11.9 19.6 12.7 547.6 5.84 46 98610 3932 24.9 4.97 3221 343 3676 535 0.873 34.1 3.45 154 159

610x229x113 113 607.6 228.2 11.1 17.3 12.7 547.6 6.6 49.3 87320 3434 24.6 4.88 2874 301 3281 469 0.87 38 2.99 111 144

610x229x101 101.2 602.6 227.6 10.5 14.8 12.7 547.6 7.69 52.2 75780 2915 24.2 4.75 2515 256 2881 400 0.864 43.1 2.52 77 129

533x210x122 122 544.5 211.9 12.7 21.3 12.7 476.5 4.97 37.5 76040 3388 22.1 4.67 2793 320 3196 500 0.877 27.6 2.32 178 155

533x210x109 109 539.5 210.8 11.6 18.8 12.7 476.5 5.61 41.1 66820 2943 21.9 4.6 2477 279 2828 436 0.875 30.9 1.99 126 139

533x210x101 101 536.7 210 10.8 17.4 12.7 476.5 6.03 44.1 61520 2692 21.9 4.57 2292 256 2612 399 0.874 33.2 1.81 101 129

533x210x92 92.14 533.1 209.3 10.1 15.6 12.7 476.5 6.71 47.2 55230 2389 21.7 4.51 2072 228 2360 356 0.872 36.5 1.6 75.7 117

533x210x82 82.2 528.3 208.8 9.6 13.2 12.7 476.5 7.91 49.6 47540 2007 21.3 4.38 1800 192 2059 300 0.864 41.6 1.33 51.5 105

457x191x98 98.3 467.2 192.8 11.4 19.6 10.2 407.6 4.92 35.8 45730 2347 19.1 4.33 1957 243 2232 379 0.881 25.7 1.18 121 125

457x191x89 89.3 463.4 191.9 10.5 17.7 10.2 407.6 5.42 38.8 41020 2089 19 4.29 1770 218 2014 338 0.88 28.3 1.04 90.7 114

457x191x82 82 460 191.3 9.9 16 10.2 407.6 5.98 41.2 37050 1871 18.8 4.23 1611 196 1831 304 0.877 30.9 0.922 69.2 104

457x191x74 74.3 457 190.4 9 14.5 10.2 407.6 6.57 45.3 33320 1671 18.8 4.2 1458 176 1653 272 0.877 33.9 0.818 51.8 94.6

457x191x67 67.1 453.4 189.9 8.5 12.7 10.2 407.6 7.48 48 29380 1452 18.5 4.12 1296 153 1471 237 0.872 37.9 0.705 37.1 85.5

457x152x82 82.1 465.8 155.3 10.5 18.9 10.2 407.6 4.11 38.8 36590 1185 18.7 3.37 1571 153 1811 240 0.873 27.4 0.591 89.2 105

457x152x74 74.2 462 154.4 9.6 17 10.2 407.6 4.54 42.5 32670 1047 18.6 3.33 1414 136 1627 213 0.873 30.1 0.518 65.9 94.5

457x152x67 67.2 458 153.8 9 15 10.2 407.6 5.13 45.3 28930 913 18.4 3.27 1263 119 1453 187 0.869 33.6 0.448 47.7 85.6

457x152x60 59.8 454.6 152.9 8.1 13.3 10.2 407.6 5.75 50.3 25500 795 18.3 3.23 1122 104 1287 163 0.868 37.5 0.387 33.8 76.2

457x152x52 52.3 449.8 152.4 7.6 10.9 10.2 407.6 6.99 53.6 21370 645 17.9 3.11 950 84.6 1096 133 0.859 43.9 0.311 21.4 66.6

Torsional Constant

Area of section

Radius of Gyration Elastic Modulus Plastic ModulusBuckling

ParameterTorsional

IndexWarping Constant

Universal Beams to BS4 Part1 1993 - Dimensions & Properties

Designation

Mass Per metre

Depth of section

Width of section

ThicknessRoot radius

Depth betw een

f illets

Ratios for Local Buckling Second Moment of Area

Section table for some universal beams

5454



(4) Cross-section classification.

(5) Check bending resistance of cross-section.

(6) Check shear resistance of cross-section.

(7) Check shear buckling.

(8) Check bending and shear.

(9) Check deflection: using design bending moment under serviceability limit state.

lecture-6

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