In this article we will discuss about:- 1. Meaning of Plate Girders 2. Plate Girder Connections and Splices 3. Components 4. Design.
Meaning of Plate Girder:
A plate girder is a deep built-up beam consisting of plates (or plates and angles) meant for carrying heavy loads on large spans. For heavily loaded girders of large spans single I-sections even with cover plates do not provide the necessary moment of resistance and shear resistance. A rolled steel beam may be suitable for spans not exceeding 15 m. For spans from 15 m to 20 m I-section with cover plates may be workable.
For greater spans such arrangements will be inadequate and a plate girder is the most practicable solution. Present day plate girders are made by building an I-section with three plates-two flange plates and one web welded suitably. (However in the past plate girders were fabricated by riveting or bolting thus needing the use of angles to provide web to flange joints).
Plate girders provide an economical arrangement for large span beams (over 20 m). A plate girder has enormous flexural strength. The resistance to bending and shear can be increased by increasing the distance between the flanges. The web plate which is thin is liable to buckle and to protect the thin web from buckling stiffeners are provided at supports and load points.
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Variations in Girder Sections:
Based on the variation of the bending moment the girder section can be suitably varied. Such variation can be done by curtailment of cover plate or alternatively single flange plates can be reduced in thickness where the reduction in bending moment permits.
In the case of simply supported girders in which the maximum bending moment occurs at the centre the depth can be varied as shown in Fig. 10.4.
This type of girders has become obsolete in modern times.
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In rigid frame constructions and continuous beams large moments occurs at the supports. The girders may be haunched near the support to provide greater flexural strength.
Present day plate girders are made of plate elements only. This has been possible due to the vast development of welding technique. Before using the welding technique connections were all made by rivets/bolts. In such an arrangement a plate girder would mainly consist of flange plates and web connected to each other with flange angles. A few cover plates were used which could be riveted/bolted to the flange angles. The plates could be curtailed in regions of lesser bending moments.
It is now well known that welded plate girders are very efficient besides being simple in fabrication.
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To realize economy, plate girders are made with depth- span ratios of 1 in 10 to 1 in 12. By such proportioning besides an increase in the flexural capacity, there is considerable increase in moment of inertia due to which there is a great reduction in deflection. No doubt, a plate girder has a higher cost of fabrication than a rolled section, but provides its own advantages.
Following are the advantages:
(i) The section of the girder is designed specifically for the needed purpose.
(ii) Strength to weight ratio of a plate girder is very high.
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(iii) Following a decrease in moment along the span, there is scope to reduce the flange plate size.
Plate girders may be loaded in many ways. They may be loaded through floor slabs, floor beams which frame into the girder. They may be loaded through columns supported by them. Loads may also be suspended from a plate girder through hangers. Fig. 10.6 shows some examples of load application to plate girders.
Plate Girder Connections and Splices:
Fig. 10.6 shows typical connections of beams and columns to plate girders. Splices become necessary in the case of long girders. Bolted as well as welded splices are shown in the figure. The figure also shows support connections.
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The designer has a good amount of freedom in proportioning a plate girder. While exercising such freedom, the designer has to consider some structural problems which are not encountered when rolled sections are used. Very important considerations are local buckling of the compression flange and shear buckling of the web.
Since to reach efficiency of the cross-section to resist bending requires placing of the material as far as possible from the neutral axis a minimum amount of material will be needed for the web. This means for high efficiency planning a very thin web is to be used. In such a case to prevent web buckling, the web has to be stiffened by vertical stiffeners and horizontal stiffeners.
In practice, whether a thin web stiffened by stiffeners is to be used or a thick web without needing stiffeners is to be used in the judicious decision of the designer. (In the latter case the fabrication costs are minimized). In most cases plate girders may not need compression stiffeners while the thin slender web will need stiffeners to resist vertical buckling and/or local crushing.
Components of a Plate Girder:
A welded plate girder consists of following components:
(i) The web plate.
(ii) Flange plates – There may also be cover plates which may be curtailed at an appropriate section.
(iii) Stiffeners – Bearing stiffeners, intermediate stiffeners, and longitudinal stiffeners.
(iv) Splices for web and flange plate
(v) End connections.
The web plate is a vertical plate 8 mm to 15 mm in thickness. The depth of the web plate depends on various factors. Though the web size depends on loading, other factors like head room clearances, difficulties in transporting the fabricated girder to the site may also limit the depth. The depth may vary from 1/8 to 1/12 of the span. It may vary from 1000 mm for small spans to 3000 mm for large spans.
The web plate may be unstiffened or stiffened. The web may be unstiffened if the ratio of the depth to the thickness of the web does not exceed 85. If this ratio exceeds 85 the web is stiffened with stiffeners. The depth of the web plate may also be determined for the condition of minimum weight of the girder. The depth determined from such consideration is called economic depth.
Design of Plate Girder:
Providing Stability against Web Buckling:
Rolled sections are so proportioned that normally there is no fear of web buckling under usually loaded conditions and hence local stability will not be a worthy consideration. But, in a plate girder the web being deep and thin is liable to buckle. Buckling can be avoided by providing stiffeners.
In general the three modes of failure of a plate girder are:
(i) Tension flange yielding
(ii) Compression flange buckling which can occur like buckling into the web or local buckling or torsional buckling, and
(iii) Web buckling.
Near the supports due to high shear in the web severe diagonal tensile and compressive stresses may be developed. The thin web, though can resist the diagonal tensile stresses, may not be strong enough to resist the diagonal compressive stresses and as such is liable to buckle.
Such buckling of the web by diagonal compression can be prevented by any of the following methods:
(i) The depth to thickness ratio of web can be decreased
(ii) Web stiffeners may be provided forming panels to increase the shear resistance of the web
(iii) Web stiffeners may be provided forming panels in such a way as to create tension field action in the web to resist diagonal compression.
Concept of Tension Field Creation in the Web:
Suppose the diagonal compressive force in the web is high enough to cause its buckling. Neglecting the ability of the web to resist this diagonal compression we provide vertical stiffeners, so that the vertical component of the diagonal compression is taken by the stiffeners, while the horizontal component of the diagonal compression is transmitted to the flanges.
The vertical stiffeners and the top and bottom flanges, along with the web are taken to provide a truss action. A truss whose top and bottom chords are the top and bottom flanges, vertical stiffeners act as the compression members while the thin web providing a tension field acting as a diagonal tension member is formed.
Compression Buckling of the Web Plate:
The web plate below the compression flange may be subjected to such flexural compressive stress, that it can buckle. At greater distances from the compression flange such buckling does not take place due to reduced bending stress.
In order to prevent such compression buckling of the web near the compression flange, longitudinal stiffeners are provided.
Shear Resistance of the Web before the Onset of Buckling:
For the sake of analysis let us consider a square web plate of side c subjected to shear stresses and complement shear stress of intensity τ. As a consequence of these shear stresses, diagonal compressive stresses and diagonal tensile stresses of intensity τ are induced along the diagonals of the square plate.
For the plate ABCD in a state of simple shear with shear stresses t as shown compressive stresses of intensity τ are induced along the diagonal BD and tensile stresses of intensity τ are induced along the diagonal AC. As the shear stresses are increased a stage is reached, when the thin plate will buckle due to the diagonal compressive stress. The shear at which the plate buckles due to the diagonal compressive stress is called the elastic critical shear stress τcr,e which is given by-
Kv is a coefficient depending on the supporting conditions of the plate.
End Panel Design:
The diagonal tensile stresses in the web create tension fields in the web panels. So far as the interior panels 2, 3, 4… are concerned each panel is balanced by the tension field of the neighbouring panels. But in the case of the end panel (Fig. 10.12), it is clear that the panel is not balanced and it needs a support or anchorage at its left end. To maintain this panel in balanced condition, the support is provided by the end stiffener. (Besides axial force the end stiffener should also be designed for bending moment produced by the tension field)
We may design the end panel by post critical method. While adopting this method it is also necessary to check for beam action the end panel together with the stiffeners spanning vertically between the top and bottom flanges. The vertical beam so considered should be checked to resist a bending moment Mtƒ and a longitudinal shear Rtƒ given by the following equations – 
If the actual factored shear force, V in the panel designed using tension field approach is less than the shear strength Vtf as found earlier then the values of Hq may be reduced by the ratio (V – Vcr) / (Vtf – Vcr). As an alternate arrangement the end panel may be provided with a double stiffener.
In this arrangement the panels 1 and 2 are designed considering Tension field action. The end post consists of two stiffeners and the part of the web projecting after the end support to act as a rigid end post providing the anchorage needed against the tension field of the end panel. The end post should be checked as a beam spanning between the flanges of the girder to resist a shear force Rtƒ and a bending moment Mtƒ given above.
Where bearing stiffeners are required to provide torsional restraint at the supports of the girder, they should meet the following criteria.
Second moment of area of the stiffener section about the centre line of the web Is should be such that-
D = Overall depth of the girder at support
Tcƒ = Maximum thickness of compression flange in the span under consideration
KL = Laterally supported effective length of the compression flange of the girder
ry = Radius of gyration of the girder about the minor axis.
In a plate girder, where concentrated loads act and also at supports exerting large reactions stiffeners are provided to transfer the load to the full depth of the web. These stiffeners become necessary when the strength of the web from any limit states like web buckling, web crippling or web yielding is insufficient. When the stiffener is designed to carry the whole concentrated load then there is no need to check the strength of web against the above mentioned limit states.
Connection of Stiffeners to the Web:
(i) Connection of Intermediate Stiffeners to the Web:
Intermediate transverse stiffeners not subject to external loading should be connected to the web so as to withstand a shear between each component of the stiffener and the web of not less than-
where,
tw = Web thickness in mm and
bs = Outstand width of the stiffener in mm
For stiffeners subject to external loading, the shear between the web and the stiffener due to such loading has to be added to the above value.
Stiffeners not subject to external loads or moments may terminate clear of the tension flange and in such a situation, the distance cut short from the line of the weld should not be more than 4 tw.
(ii) Connection of Load Carrying and Bearing Stiffeners to the Web:
Stiffeners, which resist loads or reactions applied through a flange, should be connected to the web by sufficient welds or fasteners to transmit a design force equal to the lesser of
(a) Tension capacity of the stiffener
(b) Sum of the forces applied at the two ends of the stiffener when they act in the same direction or the larger of the forces when they act in opposite directions.