Plate Girder P.1

PLATE GIRDER Plate girders are custom fabricated beam members used to carry large loads over long spans. They are used in buildings and industrial structures for long-span floor girders, for heavy crane girders and in bridges. Typical plate girders:

Plate Girder P.2

Web Stiffeners are generally required either to prevent buckling due to compression from bending and shear or to promote tension filed action to increase shear strength. Stiffeners are also required at load points and supports to prevent local failure (bearing, local flexural buckling of web). Types of beam cross-section

Plate Girder P.3

Typical usage of different forms of beam

Plate Girder P.4

Initial Section Dimensions

Depth (D) – may be limited by headroom requirement or typically taken as 1/10 to 1/20 span length.

Breadth (B) – usually about 0.3 to 0.5 D with 0.4D typical. The deeper the girder, the smaller the flanges, but thicker web and additional stiffeners may be necessary. However, a shallow girder can be very much heavier and more expensive than a deeper girder.

• Component Dimensions

Generally, a plate girder may be assumed to consist of semi-compact flange plates (which alone resist the applied moment) and a slender web (which carries the applied shear).

Flanges: at least semi-compact with yfp

27513Tb

≤

Webs: often slender with local web buckling in shear - Min web thickness for serviceability (to prevent damage in

handling)

Cl.4.4.2.2 (a) without stiffeners

250dt ≥

(b) with stiffeners

if a > d , 250dt ≥

a < d , da

250dt ≥

Plate Girder P.5

- Min web thickness to avoid flange buckling into web

Cl.4.4.2.3 (a) without stiffeners

≥

345p

250dt yf

(b) with stiffeners

if a > 1.5 d ,

≥

345p

250dt yf

a < 1.5 d , 455p

250dt yf≥

Typical web thickness:

10t ≈ mm as d = 1200mm ; 20t ≈ mm as d = 2500mm

Typical web stiffeners spacing: 6.12.1da

−≈

end panel spacing: 0.16.0da

−≈

• Moment Capacity of Plate Girder

Where the flanges are plastic, compact or semi-compact, but the

web is thin (i.e. ε> 63td ) or slender, the Mc can be calculated

by:

Plate Girder P.6

(a) Simplified Method Assume that flanges resist the moment and axial load, and the web designed for shear only.

(b) Detailed Method (not applicable where ε> 63td )

Assume that the whole section resists the moment and axial load and the web designed for combined shear and longitudinal stresses.

(c) Hybrid Method

Combination of method (a) and (b)

Pyf Af

do Mc = Pyf Af do

Plate Girder P.7

Buckling and Post buckling Behaviour of Web At buckling:

- For pure beam shear action, principal stresses occur at 45° inclinations

- Web buckling occurs when the 45° principal compressive

stress reaches it critical limit Post-buckling tension field action:

dt

- After web buckling, a tensile membrane stress σt develops at an inclination θt to the horizontal

- This tension field action gives the shear panel

considerable post-buckling strength since the increase in tension is limited only by the yield stress

- Truss analogy

Plate Girder P.8

- Total stress state at the inclination of the tension field (θt)

ttcr 2sinqt

σ+θ=σθ

tcr 2sinq90t

θ−=σ+

θ

tcr 2cosqt

θ=τθ - Apply the von Misses-Hencky yield criterion

2 2 2 290 90 3

t t tt tywpθ θθ θ θσ σ σ σ τ

+ ++ − + =

⇒ [ ] tcr21

t22

cr2

cr2

ywt 2sinq5.1 2sinq25.2q3p θ−θ+−=σ

- Maximum shear gained by tension field action using web anchorage

alone occurs approximately when

2t1

t

da1

12sinadtan2

+

=θ⇒

=θ −

Plate Girder P.9

- So the basic tension field strength, yb, is obtained as

[ ] t21

2t

2cr

2ywtb q3py φ−φ+−=σ= , where

2cr

t

da1

q5.1

+

=φ

- Determine the web shear resistance due to tension field action Resultant of tension field action:

( )thttbt sinCsinacosdtyF θ+θ−θ= Shear resistance of web due to Ft:

( )htt2

b

ttt

Cacotdsinty

sinFV

+−θθ=

θ=

Note that Ch represents the distance of the flange which acts an anchorage for developing the tension field action.

Plate Girder P.10

At collapse: - Once the web has yielded, final failure occurs when plastic hinges

have formed in the flanges at points W, X, Y and Z. - Note that the plastic hinge at point W is developed at the position

where the moment is maximum such that the corresponding shear value is zero.

Determination of the distance Ch

Take moment at X,

2sinCsintCyM2 th

thbpfθ

⋅θ=

⇒ ty

Msin

2Cb

pf

th θ

=

Take moment at W, additional flange dependent shear resistance upon collapse,

h

pff C

M4V =

Plate Girder P.11

Ultimate Shear Resistance (Vult) Vult = Vcr + Vt + Vf

( )h

pfhtt

2bcr C

M4Cacotdsintydtq ++−θθ+=

h

pfht

2btt

2bcr C

M4Csintydt

dacotsinydtq +θ+

−θθ+=

Divide Vult by dt to obtain the ultimate shear strength,

fdbult

ult qqdt

Vq +==

where strengthshear basicqb =

−θθ+=

dacotsinyq tt

2bcr

strengthshear dependent flangeqfd =

dt1

CM4

Csinty h

pfht

2b ⋅

+θ=

Plate Girder P.12