PLATE GIRDERS II

INTRODUCTIONThis chapter describes design of plate girders adopting meaningful simplifications as per provisions of BS 5950: Part 1 for buildings

Bending moments are assumed to be carried by flanges by developing compressive and tensile forces

To effect economy, web depth is chosen to be large enough to result in low flange forces

INTRODUCTION - 1

Span to depth ratiosRecommended span / depth (/d) ratios for a plate girder in a building:

Simply-supported girders 12 < /d < 20

Continuous girders 15 < /d < 25

Simply-supported crane girders10 < /d < 15

Recommended proportions for webd/t 66.2 - web plate will not buckle and design is similar to rolled steel beams

d/t > 66.2. - shear buckling should be considered

Web thicknesses recommended are:

For un-stiffened webt d/250For stiffened web with a/d > 1t d/250 with a/d 1t (d/250)(a/d)1/2

a is horizontal spacing between the transverse stiffeners in a web of depth d and thickness t

Recommended proportions for web - 1To avoid flange buckling into web, BS 5950: Part - 1, specifies

For un-stiffened webt (d/294)(pyf /250)1/2

For stiffened web with a/d > 1.5t (d/294)(pyf /250)1/2with a/d 1.5t (d/337)(pyf /250) 1/2

Recommended proportions for web - 2

Recommended proportion of flangesThickness of flange plates is not varied along spans for plate girders used in buildings

For non-composite plate girder the width of flange plate is chosen to be about 0.3 times depth of section as a thumb rule

b/T 8.9 - This is to avoid local buckling before reaching yield stress

For preliminary sizing, overall flange width-to-thickness ratio may be limited to 24. For tension flanges width can be increased by 30%

Stiffener spacingVertical stiffeners are provided close to supports to increase bearing resistance and shear capacity

When vertical stiffeners are provided, panel aspect ratio a/d is chosen in range of 1.2 to 1.6

Where end panel near support is designed without using tension field action a smaller spacing of a/d = 0.6 -1.0 is adopted

Sometimes double stiffeners are adopted near bearing and in such cases the overhangs beyond supports are limited to 1/8 of depth of the girder

Stiffener spacing - 1

MOMENT AND SHEAR CAPACITY AS PER BS 5950-PART 1Design may be based on any one of following assumptions:

Moment is resisted by flanges and shear is resisted by web onlyMoment is resisted by entire section while web is designed to resist shear and longitudinal stresses due to bendingA combination of (1) and (2) above by approximating a percentage of the shear to the web and remaining to the entire section (rarely used)

Assumptions made in method (1) is followed here

Moment CapacityMoment capacity Mc is computed from plastic capacity of the flanges Mc = pyf Zpf

pyf = design stress of the flange steel ( = fyf /m)Zpf = Plastic section modulus of flanges about the transverse axis of the section.m = Material safety factor for steel (= 1.15)

Shear Capacity - Webs without intermediate stiffenersShear capacity is limited to its shear buckling resistanceVcr = qcr d t

qcr values depend on the slenderness parameter w defined as w = (0.6 pyw / qe)

Elastic critical shear strength function of a/d and d/t

Shear Capacity - Webs with intermediate stiffenersShear resistance is improved in following two ways:

Increase in buckling resistance due to reduced a/d ratioWeb develops tension field action

Stiffeners act as struts and tension field act as ties, thus plate girder behaves similar to an N-truss

Full shear buckling resistance is calculated as,

Vb = [ qb + qf (kf)1/2 ] d t but 0.6 py dt

Shear Capacity - Webs with intermediate stiffeners - 1Contribution of flange to shear resistance will be reduced by longitudinal stress f induced because of overall bending moment, by the factor (1 f/pyf)

When f approaches pyf at maximum moment region, factor nearly becomes zero and hence the contribution of flanges to shear resistance will become negligible

Shear Capacity - Webs with intermediate stiffeners - 2

END PANELSFor tension field action to develop in end panels, adequate anchorage should be provided all around end panel

Anchor force Hq required to anchor tension field force is

End panel, when designed for tension field will impose additional loads on end post and hence it will become stout

END PANELS - 1For a simple design, capacity of end panel is restricted to Vcr. In this case, end panel acts as a beam spanning between flanges to resist shear and moment caused by Hq and tension field of penultimate panel [CONSERVATIVE]

When end panel is designed using tension field action, then bearing stiffener and end post are designed for stresses resulting from compression due to bearing and a moment equal to 2/3 caused due to tension in flanges

STIFFENERSLoad bearing stiffenersProvided to transfer transverse concentrated compressive force on the flange into the web

Normally a web width of 20 t on both sides is assumed to act along with stiffener as an equivalent cruciform shaped strut of effective length 0.7 times its actual length between top and bottom flanges

Bearing stress in stiffener is checked using area of that portion of stiffener in contact with flange through which compressive force is transmitted

STIFFENERS - 1

STIFFENERS - 2

STIFFENERS - 3

STIFFENERS - 4Intermediate stiffenersProvided to prevent out of plane buckling of web

Buckling resistance Pq of stiffener acting as a strut should be not less than (Vt -Vs)

Vt- maximum shear force in panel Vs-buckling resistance of web without considering tension field action

STIFFENERS - 5 Longitudinal stiffenersHardly used in building plate girders, but sometimes they are used in highway bridge girders For design of longitudinal stiffeners there are two requirements:

A moment of inertia to ensure adequate stiffness to create a nodal line along stiffenerAn area adequate to carry axial compression stress while acting integrally with web

CURTAILMENT OF FLANGE PLATESFor a plate girder subjected to external loading, maximum bending moment occurs at one section usually

Flange area designed to resist maximum bending moment is not required at other sections

Therefore flange plates may be curtailed where plate is no longer required as bending moment decreases

At least one flange plate should be run for entire length of girder

SPLICESWeb splicesA joint in web plate provided to increase its length

Generally, web splices are not used in buildings. They are mainly used in bridges

Splices in web of plate girder are designed to resist shear and moment at spliced section

Splice plates are provided on each side of web

SPLICES - 1Flange splices

A joint in the flange element provided to increase length of flange plate

Flange splices should be avoided as far as possible

Flange joints should not be located at points of maximum bending moment

CONCLUSIONSOutlines procedure for design of plate girders as per BS 5950: Part - I

Shows how reserve strength due to post buckling behaviour can be advantageously used by designer without performing mathematically involved calculations