Lecture -13 Plate Girders

N.W.F.P. University of Engineering and T h l P hTechnology Peshawar

Lecture 13: Plate Girder

By: Prof Dr. Akhtar Naeem Khan

1

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Plate GirdersA girder is a flexural member which is required to carr hea loads on relati el long spansto carry heavy loads on relatively long spans

CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 2

Plate Girder


Plate Girder

Plate girders are typically used as long-span g yp y g pfloor girders in buildings, as bridge girders, and as crane girders in industrial structures.g

Commonly term girder refers to a flexural x-section made up of a number of elementssection made up of a number of elements.

They are generally considerably deeper than the y g y y pdeepest rolled sections and usually have webs thinner than rolled sections.


Plate GirderModern plate girders are normally fabricated by welding together two flanges and a web plate.p


Plate GirderPlate girders are at their most impressive in

d b id t ti h i fmodern bridge construction where main spans of well over 200m are feasible, with corresponding

ti d th h h d thcross-section depths, haunched over the supports, in the range of 5-10m.


Plate Girder

Because plate girders are fabricated separately, each may be designed p y, y gindividually to resist the applied actions using proportions that ensureactions using proportions that ensure low self-weight and high load resistanceresistance.


Plate GirderChanges in X-Section

There is also considerable scope for variation of cross-section in the longitudinal direction. A d i h t d th flA designer may choose to reduce the flange thickness (or breadth) in a zone of low applied momentapplied moment.

Equally, in a zone of high shear, the designer might choose to thicken the web plate.


Plate GirderChanges in Material

Alternatively, higher grade steel might be y g g gemployed for zones of high applied moment and shear, while standard grade would be

d l h S ll d "h b id" i dused elsewhere. So-called "hybrid" girders with different strength material in the flanges and the web offer another possible means ofand the web offer another possible means of more closely matching resistance to requirementsrequirements.


Plate Girder


Plate GirderAny cross-section of a plate girder is normally subjected to a combination of shear force and bending moment.

The primary function of the top and bottom flange plates of the girder is to resist the axialflange plates of the girder is to resist the axial compressive and tensile forces arising from the applied bending momentthe applied bending moment.

The primary function of the web plate is to resist the applied shear force.


Plate GirderPlate girders are normally designed to support heavy loads over long spans in situations where itheavy loads over long spans in situations where it is necessary to produce an efficient design by providing girders of high strength to weight ratio.

To produce the lowest axial flange force for a given bending moment, the web depth (d) must be made as large as possible. To reduce the self weight, the web thickness (tw) must be reduced to a minimuma minimum.

As a consequence, in many instances the web l t i f l d ti d i th fplate is of slender proportions and is therefore

prone to buckling at relatively low values of applied shear


applied shear.

Plate GirderFor efficient design it is usual to choose a relatively deep girder, thus minimizing the required area of flanges for a given applied

t Mmoment, Msd.

This obviously entails a deep web whose y parea will be minimized by reducing its thickness to the minimum required to carry h li d h Vthe applied shear, Vsd.

Such a web may be quite slender (i.e. a high y q ( gd/tw ratio) and may be prone to local buckling and shear buckling.


Plate GirderWeb buckling does not determine the lti t t th f l t i dultimate strength of a plate girder.

Plate elements do not collapse when they p ybuckle; they can possess a substantial post-buckling reserve of resistance.

For an efficient design, any calculation relating to the ultimate limit state should take gthe post-buckling action into account.


Design Criteria

Criteria for design of plate girder may beCriteria for design of plate girder may be based on

Elastic bend-buckling strength

El ti h b kli t thElastic shear-buckling strength

Post bend buckling strengthPost-bend-buckling strength

Post-shear-buckling(Tension field)strengthPost shear buckling(Tension field)strength


Design Criteria

The designer has the choice of following four combinationscombinations

1. Elastic bend buckling + Elastic shear buckling g g(conventional flexural behavior)

2 Elastic bend buckling + Post shear buckling2. Elastic bend buckling + Post shear buckling

3. Post bend buckling + Elastic shear bucklingg g

4. Post bend buckling + Post shear buckling


Elastic Bend Buckling Strength

fThe extreme fiber bending stress at which a perfectly flat web buckles is given by



Using a FOS of 1.25 w.r.t service load bending stress fb gives an eqnuation which is AASHTO bslenderness limit for plat girders webs

Using AASHTO allowable stress fb=0.55Fy

“ h/t 165 f A36 t l “CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 19

“ h/t=165 for A36 steel “


The bend buckling resistance of beam webs can beThe bend buckling resistance of beam webs can be increased considerably by reinforcing the slender webs with Longitudinal stiffeners.with Longitudinal stiffeners.

Means webs thinner than those given by the equation can be usedused.


A typical longitudinally stiffened girder is shown after failure

Web Stiffeners

They usually consists of rectangular bars to welded to web.bars to welded to web.

Transverse stiffeners may be in pairs, one on each side of web, or they may placed on one side of web.placed on one side of web.

Longitudinal stiffeners are usually placed on one side of web.


Web Stiffeners


Web Stiffeners

The main function of the longitudinal stiffeners isThe main function of the longitudinal stiffeners is to increase the buckling resistance of the web with respect of both shear and bending loads. An t espect o bot s ea a d be d g oadseffective stiffener will remain straight, thereby sub-dividing the web panel and limiting the g p gbuckling to the smaller sub-panels. The resulting increase in the ultimate resistance of the girder gcan be significant.


Web Stiffeners Efficiency of stiffener is a function of its location in the compression zonein the compression zone

The optimum location for a longitudinal stiffener has been determined to be at least h/5 fromhas been determined to be at least h/5 from compression edge.In this case k=129. The corresponding allowable webIn this case k 129. The corresponding allowable webslenderness is h/t=330 as compare to 165


Web Stiffeners Stiffener acts as a beam supported at the ends where a vertical stiffener holds the web in linewhere a vertical stiffener holds the web in line.

Stiffener acts as a beam column and hence must b ti d i t f ti l dbe proportioned in terms of x-sectional area and moment of inertia.

AASHTO specifies Is as

Stiffener acts as a beam supported at the ends where a vertical stiffener holds the web in line.


Web Stiffeners The stiffeners must also be proportioned to resist local bucklingresist local buckling.

For plates supported on one longitudinal p pp gedge AASHTO require b/t<1625/√fbMultiple longitudinal stiffeners are used forMultiple longitudinal stiffeners are used for large depth webs.

As longitudinal stiffener is also acting as a column so it must be satisfied for critical stress (Fcrs>0.6Fcrf)


Post buckling bending strength

If bending strain increases after Fcr, the upper g , ppedge of panels shortens and bottom edge lengthens.

If web were to remain flat there will be increase in stress.stress.

Because the web has buckled, the increase in stress is non linearstress is non-linear.



A i ti i t b kl d t t i t kAs variation in post-buckled state is not known, simplify assumptions are made.

Non-linear compression is replaced with linear distribution acting on effective depth be.



Point A gives point that enables a girder to reach its fullPoint A gives point that enables a girder to reach its fullyield moment(925 /√Fy=154).

If stiffeners at h/5 is provided gives point BIf stiffeners at h/5 is provided gives point B.

Considering theA B

0 820.94

Considering the post buckling strength, the

M/My

0 180.4

0.82point where reduction in web effectiveness

154 360315

0.18effectiveness begins s taken to be 980/√Fy=170.


h/tbe 980/√Fy 170.


Equation connecting the revised point A ith i t di t h/t 360 iwith points corresponding to h/t=360 is



LRFD

Where


Compression Flange Vertical buckling



If plate girder web is too slender the compressionIf plate-girder web is too slender, the compression flange may buckle in vertical plane at stress less than yield stressthan yield stress.

The compression flange is a beam-column p gcontinuous over vertical stiffener as supports

Its stability depends on stiffener spacing andIts stability depends on stiffener spacing and relative stiffness of the flange and the web. Fcr is



Slenderness of webs with vertical stiffeners is taken conservativelySlenderness of webs with vertical stiffeners is taken conservatively

AISC ASD/LRFD li it th h/t b th i ti ithAISC ASD/LRFD limits the h/t by the given equation with Aw/Af =0.5


Shear buckling of beam websShear buckling is seldom a determining f t i d i f ll d ti b tfactor in design of rolled section but plate girders have much larger h/t so it

t b id dmust be considered.


Shear buckling of beam websTransverse stiffeners are used to i th b kli t th bincrease the buckling strength by increasing factor k through a reduction in aspect ratio a/h.


Transverse StiffenersTransverse stiffeners play an important role in allowing the full ultimate load resistance of aallowing the full ultimate load resistance of a plate girder to be achieved.

In the first place they increase the buckling resistance of the web;

Secondly they must continue to remain effective after the web buckles, to provide anchorage for p gthe tension field;

finally they must prevent any tendency for thefinally they must prevent any tendency for the flanges to move towards one another.


Transverse StiffenersThe satisfactory performance of a transverse stiffener can best be illustrated by comparing the girders shown afterby comparing the girders shown, after testing.

Fi 1Figure 2


Figure 1g

Transverse Stiffeners

In Figure 1 the stiffeners have remained straight.g g

In Figure 2 the stiffener has failed and has been unable to limit the buckling to the adjacent sub-unable to limit the buckling to the adjacent subpanels of the girder; instead, the buckle has run through the stiffener position extending over g p gboth panels. Consequently, significant reduction in the failure load of the girder occurred.

In Figure 1 One can also see the effect of aspect ratio,i.e greater a/h less k and small Fcr.at o, e g eate a/ ess a d s a c


Transverse StiffenersThe stiffener must be of adequate i idit i th di ti di l trigidity in the direction perpendicular to

the plane of the web to prevent web buckling. This condition is satisfied provided the stiffener has a second pmoment of area Is that satisfies the following empirical formulae:following empirical formulae:



AISC/LRFD Moment of Inertia of tiff istiffener is:

where



Transverse stiffeners spacing can beTransverse stiffeners spacing can be determined from the following


Tension Field ActionThe resulting shear stresses on an l t f b i l t telement of a web are equivalent to

principal stresses, one Tensile and one Compressive, at 45 to the shear stress.


Tension Field Action

Once a web panel has buckled in shear, it p ,loses its resistance to carry additional compressive stressescompressive stresses.

On the other hand tensile principal stress p pcontinues to increase in strain in the diagonal directiondiagonal direction.

Such a panel has a considerable post buckling strength, p p g g ,since increase in tension is limited only by yield stress.



In this post b ckling range a ne load carr ingIn this post-buckling range, a new load-carrying mechanism is developed, whereby any additional shear load is carried by an inclined tensileshear load is carried by an inclined tensile membrane stress field. This tension field anchors against the top and bottom flanges and against the transverse stiffeners on either side of the web panel. The load-carrying action of the plate girder than becomes similar to that of the N-trussthan becomes similar to that of the N-truss

In the post-buckling range, the resistance offered by the web plates is analogous to that of the diagonalthe web plates is analogous to that of the diagonal tie bars in the truss.


Tension Field ActionPhases of behavior up to collapse of a typical panel in shear

Prior to Buckling Post Buckling Collapse



The load carrying action of the plate girderThe load-carrying action of the plate girder than becomes similar to that of the N-truss

In the post-buckling range, the resistance offered by the web plates is analogous tooffered by the web plates is analogous to that of the diagonal tie bars in the truss.



ftV V

Vt=Tsinφ

T=ft ht cosφ

φ

Vt = ft ht cosφ sinφ

Vt = (1/2)ft ht sin2φ φVt (1/2)ft ht sin2φ

Vt =(1/2) ft ht φ=45


Vty=(1/2) Fy ht………….(1)


Vty =(1/2) Fy ht = Fy

Vy Fvy ht 2Fvy

Vty = √3 Vy = 0.87 Vy

2



The angle φ for which Vt is max



Where



(1)

Taking inelastic and strain hardening range

(2)

(3)



Codal equations are derived from eqn;(1),(2),(3)



AISC/LRFDAISC/LRFD

k

a/ha/h


Combined Bending & Shear of Webs

Interaction diagram is based on Tension-fi ld f bfield of webs

If the web is completely yielded inIf the web is completely yielded in shear,any accompanying moment must b i t d ti l b flbe resisted entirely by flanges.


Combined Bending & Shear Bending & shear Interaction Curve

V

BB C D

V/(F

vy A

E 1/√3

Aw

)

E 1/√3

CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan 590.75 0.83 1.0 1.07 1.12 M/My

Combined Bending & Shear 1.0

0.8

Mu/φMn

0.6

LRFD I t ti C

0.4

LRFD Interaction Curve

0.2


0.4 0.6 1.0 Vu/φVn0.2 0.8

Web Proportioning Notations


Web Proportioning

Depth of girder is influenced by many factors:

HeadroomHeadroom

Clearance for high water in deck bridges

Traffic passing beneath the bridge


Web Proportioning

Depth: Overall girder depth, h, willDepth: Overall girder depth, h, will usually be in the range

L /12 ≤ h ≤ L /8Lo/12 ≤ h ≤ Lo/8,

occasionally lighter loads may be accommodated with L /20accommodated with Lo/20.

Flange:g

The breadth, b, will usually be in the range

h/5 ≤ b ≤ h/3,


Design Procedure1. Maximum Moment & Shear for Factored Load

2 W b D i2. Web Design

1. Assume depth of girder L/12 ≤ h ≤ L/8p g

2. Depth of Web hw=h-2tf3. Web slenderness

1. For a/h <5 …………….

2. and for a/h > 5 ……………………

3 h /t = 970/√Fy3. hw/tw= 970/√Fy

4. Select optimum tw


Design Procedure

4. Flange Design1. Find Af

2. Select suitable tf and bf

3 Flange slenderness3. Flange slenderness1. bf/ 2tf < 65/√Fy …………….Compact


Design Procedure5 Check trial girder section5. Check trial girder section

1. Web local buckling limit state1. hw/tw< 640/√Fy…………………..Compact

2. 640/√Fy< hw/tw < 970/√Fy……Non-Compact

3. hw/tw > 970/√Fy…………………..Slender

2. Flange local buckling limit state1. bf/ 2tf < 65/√Fy …………….Compact

3. Lateral Torsional Bucklingg1. Calculate Iy2. A=Af+Aw/6f w

3. ry= √Iy/A

4. Find Lb/ry


b y

5. λp= 300/√Fy ………….. λ< λp ______Compact

Design Procedure 6. Bending strength

C l l t I1. Calculate Ix2. Calculate Sxtxt

3. .

44. .

5. φMn≥ Mu


Procedure for Design

6. Bending strength1. Calculate Ix2 Calculate S2. Calculate Sxt

3. .

4. .

CE-409: Lecture 13 Prof. Dr Akhtar Naeem Khan5. φMn≥ Mu

Lecture -13 Plate Girders

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