IS800-8Beam

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Dr S R Satish Kumar, IIT Madras 1

IS 800:2007 Section 8Design of members

subjected to bending

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SECTION 8 DESIGN OF MEMBERS SUBJECTED TO BENDING8.1 General8.2 Design Strength in Bending (Flexure)

8.2.1 Laterally Supported Beam

8.2.2 Laterally Unsupported Beams8.3 Effective Length of Compression Flanges8.4 Shear

-------------------------------------------------------------------------------------------------8.5 Stiffened Web Panels

8.5.1 End Panels design8.5.2 End Panels designed using Tension field action

8.5.3 Anchor forces8.6 Design of Beams and Plate Girders with Solid Webs

8.6.1 Minimum Web Thickness8.6.2 Sectional Properties8.6.3 Flanges Cont...

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SECTION 8 DESIGN OF MEMBERS SUBJECTED TO BENDING8.7 Stiffener Design

8.7.1 General8.7.2 Design of Intermediate Transverse Web Stiffeners8.7.3 Load carrying stiffeners8.7.4 Bearing Stiffeners8.7.5 Design of Load Carrying Stiffeners8.7.6 Design of Bearing Stiffeners8.7.7 Design of Diagonal Stiffeners8.7.8 Design of Tension Stiffeners8.7.9 Torsional Stiffeners8.7.10 Connection to Web of Load Carrying and Bearing Stiffeners

8.7.11 Connection to Flanges8.7.12 Hollow Sections

8.8 Box Girders8.9 Purlins and sheeting rails (girts)

8.10 Bending in a Non-Principal Plane

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Plastic hinge formation Lateral deflection and twist Local buckling of

i) Flange in compressionii) Web due to sheariii) Web in compression due to

concentrated loads Local failure by

i) Yield of web by shearii) Crushing of webiii) Buckling of thin flanges

RESPONSE OF BEAMS TO VERTICAL LOADING

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LOCAL BUCKLING AND SECTION CLASSIFICATION

OPEN AND CLOSED SECTIONS

Strength of compression members depends on slenderness ratio

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(b)(a)

Local buckling of Compression Members

LOCAL BUCKLING

Beams compression flange buckles locallyFabricated and cold-formed sections prone to local bucklingLocal buckling gives distortion of c/s but need not lead to collapse

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L

Bending Moment Diagram

Plastic hinges

M p

Collapse mechanism

Plastic hinges

M p

Formation of a Collapse Mechanism in a Fixed Beam

w

Bending Moment Diagram

BASIC CONCEPTS OF PLASTIC THEORY

First yield moment MyPlastic moment MpShape factor S = Mp/MyRotation Capacity (a) at M y (b) M y < M

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SECTION CLASSIFICATION

Mp

Rotation

My

y u

Slender

Semi-compact

Compact

Plastic

Section Classification based on Moment-Rotation Characteristics

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Moment Capacities of Sections

My

Mp

1 2 3 =b/t

Semi-Compact SlenderPlastic Compact

SECTION CLASSIFICATION BASED ONWIDTH -THICKNESS RATIO

For Compression members use compact or plastic sections

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Type of Element Type ofSection

Class of Section

Plastic ( 1) Compact( 2)Semi-compact ( 3)

Outstand element ofcompression flange

Rolled b/t 9.4 b/t 10.5 b/t 15.7

Welded b/t 8.4 b/t 9.4 b/t 13.6

Internal element ofcompression flange

bending b/t 29.3 b/t 33.5 b/t 42

Axialcomp.

not applicable b/t 42

Web NA at middepth

d/t 84.0 d/t 105 d/t 126

Angles bending

Axialcomp.

Circular tube withouter diameter D

D/t 44 2 D/t 63 2 D/t 88 2

Table 2 Limits on Width to Thickness Ratio of Plate Elements

y f 250

b/t 9.4 b/t 10.5 b/t 15.7

not applicable b/t 15.7 (b+d)/t 25

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Dr S R Satish Kumar, IIT Madras11

Condition for Beam Lateral Stability

1 Laterally Supported Beam The design bending strength of beams, adequatelysupported against lateral torsional buckling (laterallysupported beam) is governed by the yield stress

2 Laterally Unsupported Beams When a beam is not adequately supported against lateral

buckling (laterally un-supported beams) the design bending strength may be governed by lateral torsional buckling strength

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Design Strength in Bending (Flexure)

The factored design moment, M at any section, in a beam due to

external actions shall satisfy


Type 1 Sections with stocky websd / t w 67

The design bending strength as governed by plastic strength, M d ,shall be found without Shear Interaction for low shear case

represented byV

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V exceeds 0.6 V d

M d = M dv M dv= design bending strength under high

shear as defined in section 9.2

8.2.1.3 Design Bending Strength under High Shear

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Definition of Yield and Plastic Moment Capacities

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8.2 Design Strength in Bending (Flexure)

The factored design moment, M at any section, in a beam

due toexternal actions shall satisfy


The design bending strength as governed by plasticstrength, M d , shall be taken as

M d = b Z p f y / m0 1.2 Z e f y / m0

8.2.1.4 Holes in the tension zone

( Anf / Agf ) (f y /f u) ( m1 / m0 ) / 0.9

d M M

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Laterally Stability of Beams

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BEHAVIOUR OF MEMBERS SUBJECTED TOBENDING

Plastic Range

InelasticRange

Elastic Range

Mp

My

Mcr

Unbraced Length, L

Mo Mo

L

Beam Buckling Behaviour

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LATERAL BUCKLING OF BEAMS

FACTORS TO BE CONSIDERED Distance between lateral supports to the compressionflange.Restraints at the ends and at intermediate supportlocations (boundary conditions).Type and position of the loads.Moment gradient along the unsupported length.Type of cross-section.Non-prismatic nature of the member.Material properties.

Magnitude and distribution of residual stresses.Initial imperfections of geometry and eccentricity ofloading.

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SIMILARITY BETWEEN COLUMN BUCKLINGAND LATERAL BUCKLING OF BEAMS

Column Beam

Short span Axial compression & attainment

of squash load

Bending in the plane of loads and attaining plastic capacity

Long span Initial shortening and lateral buckling

Initial vertical deflection and lateral torsional buckling

Pure flexural mode Function of slenderness

Coupled lateral deflection and twist

function of slenderness

Both have tendency to fail by buckling in their weaker plane

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Beam buckli ngEI x >E I y EI x >GJ

SIMILARITY OF COLUMN BUCKLING AND BEAM BUCKLING -1

M

u

M

Section B-B

uP

P

Section B-B

B

B B

B

Y

X Z

Column buckling

3l

y EI

l

EA

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LATERAL TORSIONAL BUCKLING OFSYMMETRIC SECTIONS

Assumptions for the ideal (basic) case Beam undistorted Elastic behaviour Loading by equal and opposite moments in the

plane of the web No residual stresses Ends are simply supported vertically and laterally

The bending moment at which a beam fails bylateral buckling when subjected to uniform endmoment is called its elastic critical moment (M cr )

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(a) ORIGINAL BEAM (b) LATERALLY BUCKLED BEAM

M

Plan

Elevationl

M

Section

(a)

Lateral

Deflection

y

z

(b)

Twisting

x

A

A

Section A-A

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Mcr = [ (Torsional resistance ) 2 + (Warping resistance ) 2 ]1/2

21

2 y

2

ycr L

I E J G I E

L

M

2

1

2

2

21

ycr J G L

E 1 J G I E

L

M

or

EIy = flexural rigidityGJ = torsional rigidityE = warping rigidity

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FACTORS AFFECTING LATERAL STABILITY

Support Conditions effective (unsupported) length

Level of load application stabilizing or destabilizing ?

Type of loading Uniform or moment gradient ?

Shape of cross-section open or closed section ?

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EQUIVALENT UNIFORM MOMENT FACTOR (m)

Elastic instability at M = m Mmax

(m 1)m = 0.57+ 0.33+ 0.1 2 > 0.43 = M min / Mmax (-1.0 1.0)

M m i nM max

M m i n

Posit ive

M max M m i n

M m i nNegative

M max

M max

also check M max Mp

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8.2.2 Laterally Unsupported Beams

The design bending strength of laterally unsupported beamis given by:

M d = b Z p f bdf bd = design stress in bending, obtained as , f bd = LT f y / m 0

LT = reduction factor to account for lateral torsionalbuckling given by:

LT = 0.21 for rolled section,

LT = 0.49 for welded sectionCont

0.1][ 1 5.022 LT LT LT LT

22.015.0 LT LT LT LT

cr y pb LT M f Z /

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8.2.2.1 Elastic Lateral Torsional Buckling Moment

2

2

2

2

KL

EI

GI KL

EI

M w

t

y

cr

5.02

2

2

/

/

20

11

)(2 f y y LT

cr

t h

r KL

KL

h EI M

APPENDIX F ELASTIC LATERAL TORSIONAL BUCKLING

F.1 Elastic Critical Moment

F.1.1 BasicF.1.2 Elastic Critical Moment of a Section Symmetrical aboutMinor Axis

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EFFECTIVE LATERAL RESTRAINT

Provision of proper lateral bracing improves lateral stability

Discrete and continuous bracingCross sectional distortion in the hogging moment regionDiscrete bracing Level of attachment to the beam

Level of application of the transverse load Type of connectionProperties of the beams Bracing should be of sufficient stiffness to produce

buckling between braces Sufficient strength to withstand force transformed by

beam before connecting

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Effective bracing if they can resist not less than

1) 1% of the maximum force in the compression flange

2) Couple with lever arm distance between the flangecentroid and force not less than 1% of compression

flange force.

Temporary bracing

BRACING REQUIREMENTS

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Other Failure Modes

Shear yielding near support

Web buckling Web crippling

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Web Buckling

45 0

d / 2

d / 2 b1 n1

Effect ive width for w eb buckl ing

c f t )1n1b( wb P

t d

5.2t

32d 7 .0

yr E L

32t

t 123t

A y I

yr

yr d 7 .0

yr E L

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Web Crippling

b1 n 2 1:2.5 slope

Rootradius

Stif f bearing length

yw f t )2n1b( crip P

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Dr S R Satish Kumar IIT Madras 33

SUMMARY

Unrestrained beams , loaded in their stiffer planes may undergolateral torsional buckling

The prime factors that influence the buckling strength of beams

are unbraced span, Cross sectional shape, Type of end restraintand Distribution of moment

A simplified design approach has been presented Behaviour of real beams, cantilever and continuous beams

was described. Cases of mono symmetric beams , non uniform beams and

beams with unsymmetric sections were also discussed.

Documents

IS800-8Beam