N.W.F.P. University of Engineering and
Technology Peshawar
Lecture 13: Plate Girder
By: Prof Dr. Akhtar Naeem Khan
chairciv@nwfpuet.edu.pk
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Plate Girders
A girder is a flexural member which is required
to carry heavy loads on relatively long spans
CE-409: Lecture 13
Prof. Dr Akhtar Naeem Khan
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Plate Girder
CE-409: Lecture 13
Prof. Dr Akhtar Naeem Khan
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Plate Girder
 Plate girders are typically used as long-span
floor girders in buildings, as bridge girders, and
as crane girders in industrial structures.
 Commonly term girder refers to a flexural xsection made up of a number of elements.
 They are generally considerably deeper than the
deepest rolled sections and usually have webs
thinner than rolled sections.
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Prof. Dr Akhtar Naeem Khan
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Plate Girder
 Modern plate girders are normally fabricated
by welding together two flanges and a web
plate.
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Prof. Dr Akhtar Naeem Khan
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Plate Girder

Plate girders are at their most impressive in
modern bridge construction where main spans of
well over 200m are feasible, with corresponding
cross-section depths, haunched over the
supports, in the range of 5-10m.
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Plate Girder
 Because plate girders are fabricated
separately, each may be designed
individually to resist the applied
actions using proportions that ensure
low self-weight and high load
resistance.
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Plate Girder
Changes in X-Section
 There is also considerable scope for variation
of cross-section in the longitudinal direction.
A designer may choose to reduce the flange
thickness (or breadth) in a zone of low
applied moment.
 Equally, in a zone of high shear, the designer
might choose to thicken the web plate.
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Plate Girder
Changes in Material
 Alternatively, higher grade steel might be
employed for zones of high applied moment
and shear, while standard grade would be
used elsewhere. So-called "hybrid" girders
with different strength material in the flanges
and the web offer another possible means of
more closely matching resistance to
requirements.
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Prof. Dr Akhtar Naeem Khan
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Plate Girder
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Plate Girder
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Prof. Dr Akhtar Naeem Khan
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Plate Girder
 Any 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 axial
compressive and tensile forces arising from
the applied bending moment.
 The primary function of the web plate is to
resist the applied shear force.
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Prof. Dr Akhtar Naeem Khan
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Plate Girder
 Plate girders are normally designed to support
heavy 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 minimum.
 As a consequence, in many instances the web
plate is of slender proportions and is therefore
prone to buckling at relatively low values of
applied shear.
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Prof. Dr Akhtar Naeem Khan
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Plate Girder

For efficient design it is usual to choose a
relatively deep girder, thus minimizing the
required area of flanges for a given applied
moment, Msd.

This obviously entails a deep web whose
area will be minimized by reducing its
thickness to the minimum required to carry
the applied shear, Vsd.

Such a web may be quite slender (i.e. a high
d/tw ratio) and may be prone to local buckling
and shear buckling.
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Prof. Dr Akhtar Naeem Khan
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Plate Girder

Web buckling does not determine the
ultimate strength of a plate girder.

Plate elements do not collapse when they
buckle; they can possess a substantial postbuckling reserve of resistance.

For an efficient design, any calculation
relating to the ultimate limit state should take
the post-buckling action into account.
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Design Criteria
Criteria for design of plate girder may be
based on
 Elastic bend-buckling strength
 Elastic shear-buckling strength
 Post-bend-buckling strength
 Post-shear-buckling(Tension field)strength
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Design Criteria

The designer has the choice of following four
combinations
1. Elastic bend buckling + Elastic shear buckling
(conventional flexural behavior)
2. Elastic bend buckling + Post shear buckling
3. Post bend buckling + Elastic shear buckling
4. Post bend buckling + Post shear buckling
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Elastic Bend Buckling
Strength
 The extreme fiber bending stress at which a
perfectly flat web buckles is given by
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Elastic Bend Buckling
Strength
Using a FOS of 1.25 w.r.t service load bending
stress fb gives an eqnuation which is AASHTO
slenderness limit for plat girders webs
 Using AASHTO allowable stress fb=0.55Fy
“ h/t=165 for A36 steel “
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Prof. Dr Akhtar Naeem Khan
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Elastic Bend Buckling
Strength
 The bend buckling resistance of beam webs can be
increased considerably by reinforcing the slender webs
with Longitudinal stiffeners.
 Means webs thinner than those given by the equation can be
used.
A typical longitudinally stiffened girder is shown after failure
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Web Stiffeners
 They usually consists of rectangular
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.
 Longitudinal stiffeners are usually
placed on one side of web.
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Web Stiffeners
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Web Stiffeners
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Web Stiffeners
 The main function of the longitudinal stiffeners is
to increase the buckling resistance of the web
with respect of both shear and bending loads. An
effective stiffener will remain straight, thereby
sub-dividing the web panel and limiting the
buckling to the smaller sub-panels. The resulting
increase in the ultimate resistance of the girder
can be significant.
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Web Stiffeners
 Efficiency of stiffener is a function of its location
in the compression zone
 The optimum location for a longitudinal stiffener
has been determined to be at least h/5 from
compression edge.
In this case k=129. The corresponding allowable web
slenderness is h/t=330 as compare to 165
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Web Stiffeners
 Stiffener acts as a beam supported at the ends
where a vertical stiffener holds the web in line.
 Stiffener acts as a beam column and hence must
be 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.
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Web Stiffeners
 The stiffeners must also be proportioned to
resist local buckling.
 For plates supported on one longitudinal
edge AASHTO require b/t<1625/fb
 Multiple 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)
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Post buckling bending
strength
 If bending strain increases after Fcr, the upper
edge of panels shortens and bottom edge
lengthens.
 If web were to remain flat there will be increase in
stress.
 Because the web has buckled, the increase in
stress is non-linear.
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Post buckling bending
strength
 As 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.
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Post buckling bending
strength
 Point A gives point that enables a girder to reach its full
yield moment(925 /Fy=154).
 If stiffeners at h/5 is provided gives point B.
Considering the
post buckling
strength, the
point where
reduction in web
effectiveness
begins s taken to
be 980/Fy=170.
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B
A
0.94
0.82
M/My
0.4
0.18
154
315
360
h/t
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Post buckling bending
strength
 Equation connecting the revised point A
with points corresponding to h/t=360 is
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Post buckling bending
strength
LRFD
Where
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Compression Flange Vertical
buckling
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Compression Flange Vertical
buckling
 If plate-girder web is too slender, the compression
flange may buckle in vertical plane at stress less
than yield stress.
 The compression flange is a beam-column
continuous over vertical stiffener as supports
 Its stability depends on stiffener spacing and
relative stiffness of the flange and the web. Fcr is
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Compression Flange Vertical
buckling
Slenderness of webs with vertical stiffeners is taken conservatively
AISC ASD/LRFD limits the h/t by the given equation with
Aw/Af =0.5
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Shear buckling of beam webs
 Shear buckling is seldom a determining
factor in design of rolled section but
plate girders have much larger h/t so it
must be considered.
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Shear buckling of beam webs
 Transverse stiffeners are used to
increase the buckling strength by
increasing factor k through a reduction
in aspect ratio a/h.
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Transverse Stiffeners
 Transverse stiffeners play an important role in
allowing 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
the tension field;
 finally they must prevent any tendency for the
flanges to move towards one another.
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Transverse Stiffeners
 The satisfactory performance of a
transverse stiffener can best be illustrated
by comparing the girders shown, after
testing.
Figure 2
Figure 1
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Transverse Stiffeners
 In Figure 1 the stiffeners have remained straight.
 In Figure 2 the stiffener has failed and has been
unable to limit the buckling to the adjacent subpanels of the girder; instead, the buckle has run
through the stiffener position extending over
both 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.
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Transverse Stiffeners
 The stiffener must be of adequate
rigidity in the direction perpendicular to
the plane of the web to prevent web
buckling. This condition is satisfied
provided the stiffener has a second
moment of area Is that satisfies the
following empirical formulae:
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Transverse Stiffeners
 AISC/LRFD Moment of Inertia of
stiffener is:
where
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Transverse Stiffeners
 Transverse stiffeners spacing can be
determined from the following
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Tension Field Action
 The resulting shear stresses on an
element of a web are equivalent to
principal stresses, one Tensile and one
Compressive, at 45 to the shear stress.
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Tension Field Action
 Once a web panel has buckled in shear, it
loses its resistance to carry additional
compressive stresses.
 On the other hand tensile principal stress
continues to increase in strain in the
diagonal direction.
Such a panel has a considerable post buckling strength,
since increase in tension is limited only by yield stress.
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Tension Field Action
 In this post-buckling range, a new load-carrying
mechanism is developed, whereby any additional
shear 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-truss
 In the post-buckling range, the resistance offered by
the web plates is analogous to that of the diagonal
tie bars in the truss.
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Tension Field Action
Phases of behavior up to collapse of a typical panel in shear
Prior to Buckling
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Post Buckling
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Collapse
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Tension Field Action
 The 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 to
that of the diagonal tie bars in the truss.
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Tension Field Action
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Tension Field Action
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Tension Field Action
V
ft
V
Vt=Tsin
Vt = ft ht cos sin
T=ft ht cos
Vt = (1/2)ft ht sin2

Vt =(1/2) ft ht
=45
Vty=(1/2) Fy ht………….(1)
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Tension Field Action
Vty
=(1/2) Fy ht
Vy
Fvy ht
= Fy
2Fvy
Vty = 3 Vy = 0.87 Vy
2
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Tension Field Action
The angle  for which Vt is max
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Tension Field Action
Where
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Tension Field Action
(1)
Taking inelastic and strain hardening range
(2)
(3)
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Tension Field Action
 Codal equations are derived from
eqn;(1),(2),(3)
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Tension Field Action
 AISC/LRFD
k
a/h
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Combined Bending & Shear
of Webs
 Interaction diagram is based on Tensionfield of webs
 If the web is completely yielded in
shear,any accompanying moment must
be resisted entirely by flanges.
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Combined Bending & Shear
Bending & shear Interaction Curve
B
B C
V/(FvyAw)
E 1/3
0.75 0.83
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D
1.0 1.07 1.12
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M/My
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Combined Bending & Shear
1.0
Mu/Mn
0.8
0.6
LRFD Interaction Curve
0.4
0.2
0.2
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0.4
0.6
0.8
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1.0
Vu/Vn
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Web Proportioning
Notations
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Web Proportioning
 Depth of girder is influenced by many
factors:

Headroom

Clearance for high water in deck bridges

Traffic passing beneath the bridge
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Web Proportioning
 Depth: Overall girder depth, h, will
usually be in the range


Lo/12  h  Lo/8,
occasionally lighter loads may be
accommodated with Lo/20.
 Flange:

The breadth, b, will usually be in the range
h/5  b  h/3,
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Design Procedure
1. Maximum Moment & Shear for Factored Load
2. Web Design
1.
Assume depth of girder L/12  h  L/8
2.
Depth of Web hw=h-2tf
3.
Web slenderness
1.
For a/h <5 …………….
2.
and for a/h > 5 ……………………
3.
hw/tw= 970/Fy
4.
Select optimum tw
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Design Procedure
4. Flange Design
1.
Find Af
2.
Select suitable tf and bf
3.
Flange slenderness
1.
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bf/ 2tf < 65/Fy …………….Compact
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Design Procedure
5. Check trial girder section
1.
Web local buckling limit state
1.
2.
2.
640/Fy< hw/tw < 970/Fy……Non-Compact
3.
hw/tw > 970/Fy…………………..Slender
Flange local buckling limit state
1.
3.
hw/tw< 640/Fy…………………..Compact
bf/ 2tf < 65/Fy …………….Compact
Lateral Torsional Buckling
1.
Calculate Iy
2.
A=Af+Aw/6
3.
ry= Iy/A
4.
Find Lb/ry
5.
p= 300/Fy ………….. < p ______Compact
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Design Procedure
6. Bending strength
1.
Calculate Ix
2.
Calculate Sxt
3.
.
4.
.
5.
Mn Mu
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Procedure for Design
6. Bending strength
1.
Calculate Ix
2.
Calculate Sxt
3.
.
4.
.
5.
Mn Mu
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Prof. Dr Akhtar Naeem Khan