3 Restrained Beams - 2012

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Restrained Beams

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Introduction

ShearResistancePlasticShearResistance

ShearArea

ShearBucklingResistance

MomentResistanceMomentResistancewithHighShear

ServiceabilityBeamDeflections

Examples

ExampleRB

1(Section

resistance

and

deflection

of

UB)

Outline

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Beams are structural members which transfer transverse loads on the

member to the supports through bending and shear.

Beams which are unable to deflect laterally are termed restrained .

Restrained beams are often designed on the basis of bending momentresistance which is dependent on section classification.

Deflection is normally significant and has to be checked at serviceabilitylimit state.

Introduction

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Full lateral restraint may be assumed to exist if the frictional orpositive connection of a floor (or other)

construction to the compression flange of the member is capable of resisting a lateral force ofmore than

2.5% of the maximum force in the compression flange of the member. This load should be considered as

distributed uniformly along the flange. Examples of full lateral restraint are:

1) insitu or precast concrete slab which is supported directly on the top flange or cast around it

2) steel plate floor which is welded or bolted to the flange at closely spaced intervals

3) provision of closely spaced bracing elements so that the minor axis slenderness is low ( )

tw

Friction force

(h tf)

L

FullyRestrainedBeam

Min. friction or connection resistance reqd=2.5% * max. moment in member

(h tf) *L

C =M/(h-tf)

T

M =Applied Moment

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Shear Resistance

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Shear Resistance

EN 1993-1-1 (Cl 6.2.6)

The design shear force, VEd, should satisfy:

Vc,Rdis the design shear resistance, which may be calculated based on a plastic or an

elastic distribution of shear stress. The usual approach is to use the plastic shearresistance, Vpl,Rd.

The design plastic shear resistance is given by:

PlasticShearResistance

whereAv is the shear area.

ShearCheck8/14/2012

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ShearArea

tf

b

tw

rRolledIandHsections,loadparalleltoweb

tf

b

tw

rRolledIandHsections,loadparalleltoflange

tw

hw

WeldedI,H&boxsections,loadparalleltoweb

twhw

hw

WeldedI,H&boxsections,loadparalleltoflange

hw

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ShearArea

tf

b

tw

rRolledchannelsections,loadparalleltoweb

b

tfRolledTsections,loadparalleltoweb

Rectangularhollowsections,loadparalleltodepth

Rectangularhollowsections,loadparalleltowidth

Circularhollowsections

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The shear buckling resistance for webs should be checked if

Shear buckling is unlikely to affect rolled sections.

ShearBucklingEN 1993-1-5 (Cl 6.2.6(6))

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Moment Resistance

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Moment Resistance

EN 1993-1-1 (Cl 6.2.6)

The design bending moment,MEd, should satisfy the following cross-section check:

The bending moment resistance,Mc,Rdabout a principal axis depends on the class of

the section:

MomentCheck

Class 1 and 2 sections

Class 3 sections

Class 4 sections

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The following sections are class 3 (semi-compact), all other UB andUC sections are either class 1 (plastic) or class 2 (compact):

Grade S275 steel Grade S355 steel152 152 23 UC 152 152 23 UC

305 305 97 UC356 368 129 UC

Non of the UB and UC under bending is class 4.

Notes

The Corus Advance range of sections includes UB and UCs thatare not in BS446, these are included in the above.

Dimensions of all sections in the Advance range are given in SCIpublication No P-363.

Section classification for bending only


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EN 1993-1-1 (Cl 6.2.8)

When the design value of the shear force is less than 50% of the design plastic shear

resistance, i.e. VEd 0.5 Vpl,Rd, its effect on the moment resistance may be neglected.

MomentResistancewithHighShear

When the design value of the shear force exceeds 50% of the design plastic shear

resistance i.e. VEd> 0.5 Vpl,Rd, the yield strengthfy should be reduced by (1 ) in the

determination of the moment resistance,Mc,Rd.

where

Class1&2IsectionswithequalflangesandbendingaboutmajoraxisAn alternative approach is available to determine the reduced design plastic resistance moment

for class 1 and 2 I sections.

but

where

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Serviceability

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Deflection Check

Maximum Deflection due to unfactored imposed load

Cantilevers Length/180

Internal beams carrying plaster or other brittle finish Span/360 or 40mm

Other beams (except purlins and sheeting rails) Span/200 or 40mm

Edge beam Span/300 to span/500 or

20mm

Vertical deflection due to stat ic vertical wheel loads from overhead

traveling cranes Span/600

Horizontal deflection (calculated on the top flange properties alone)

due to horizontal crane loads Span/500

EN 1993-1-1 (Cl 7.2)

Excessive deflection at service load may impair the function of a structure.

Deflection check should be carried using the unfactored variable actions Qk.

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Examples of simple beam and cantilever forcesBeamDeflections

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Examples

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Eurocode3:DesignofSteelStructures RLiew&SDPang

Example RB-1: Section resistance and deflection of UBA beam of span 10 m is simply supported at its ends and fully restrained along its length. It

supports a uniformly distributed load across the entire span and a point load at its mid-span.

Check and verify if section UB 533210101 in S355 steel is suitable for this beam. Assume

that the beam carried plaster finish.

Unfactoredload values:

Dead Load UDL 5 kN/m Imposed Load UDL 10 kN/m

Point load 50 kN Point load 100 kN

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5m 5m

50 kN + 100 kN5 kN/m + 10 kN/m


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Ultimate Limit State

Design Loads

Dead Load Distributed load 5 1.35 = 6.75 kN/m

Point load 50

1.35 = 67.5 kNImposed Load Distributed load 10 1.5 = 15 kN/m

Point load 100 1.5 = 150 kN

5m 5m

67.5 kN + 150 kN

6.75 kN/m + 15 kN/m

217.5 kN 217.5 kN

Design Moment

Maximum bending moment at mid-span:MEd= (6.75+15)*102

/8 + (67.5+150)*10/4 =816 kNm.

Design Shear

Maximum shearforce at the supports: VEd= 217.5 kN.

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Yield Strengthtw = 10.8mm, tf= 17.4mm.

Maximum thickness = 17.4mm


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Shear Resistance

Shear Area

hwtw =(h2tf)tw = 1.0*(536.7 2*17.4)*10.8 =5421 mm2.

Av =A2btf+ (tw + 2r)tf= 12900 2*210.0*17.4 + (10.8 + 2*12.7)*17.4 = 6222 mm2.

Plastic Shear Resistance

SinceVEd= 217.5 kN


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Serviceability L imit State

Check for Deflection

The deflection of the beam under unfactored imposed load is

Since the beam carries plaster finish,

the maximum deflection of the beam is within limit.

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Using Design Table

UB 533210101 in S355 under pure bending

Page D-66:

Section is class 1

Moment Resistance about major axisMcy,Rd= 901kNm

(hand calculation 900 kNm)

Page D-103

Design shear resistanceVc,Rd= 1240kN

(hand calculation 1239 kN)

Note that the moment capacity given in the table is for low shear.

The moment needs to be reduced for high shear case.

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Page D-66

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Page D-103

Design shear resistance


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Homework

Consider a simply supported beam 914 x 419 x 388 UB, S275 steel subjected to a

factored shear force of 2500kN and moment of 4000kNm. Check the shear andbending resistance of the beam if it is fully restrained against lateral-torsional buckling.

3 Restrained Beams - 2012

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