behviour of box girder bridges
TRANSCRIPT
BEHAVIOUR OF BOX GIRDER BRIDGES
PRESENTED BYR.CHANDRAKUMAR
B.TECH-CIVIL FINAL YEAR
GIRDER
BOX GIRDER
TYPES OF BOX GIRDER BRIDGES
BEHAVIOUR OF BOX GIRDER BRIDGES
CONCLUSIONS
CONTENTS:
A girder is a support beam used in construction
Girders often have an I beam cross section for strength, but may also have a box shape, Z shape or other forms
Girder is the term used to denote the main horizontal support of a structure which supports smaller beams
A girder is commonly used many times in the building of bridges
GIRDER:
A girder that forms an enclosed tube with multiple walls, rather than an I or H beam.
It can also be known as a tubular girder.
Originally constructed of riveted wrought iron.
They are now found in rolled or welded steel, aluminium extrusions or pre-stressed concrete.
BOX GIRDER
Concrete box girder
Steel box girder
Both type of box girders are available in trapezoidal and rectangular shape.
TYPES OF BOX GIRDER
STEEL BOX GIRDER:
RECTANGULAR TRAPEZOIDAL
CONCRETE BOX GIRDER
RECTANGULARTRAPEZOIDAL
It is a bridge in which the main beams comprise girders in the shape of a hollow box.
The box is typically rectangular or trapezoidal in cross-section.
The box girder is an efficient form of construction for bridges because it minimizes weight, while maximizing flexural stiffness and capacity.
Commonly used for highway flyovers.
BOX GIRDER BRIDGES:
It may be of the following types:
1. Concrete
2. Structural steel
3. Composite (steel and RCC)
TYPES OF BOX GIRDER BRIDGES:
CONCRETE BOX GIRDERSCANADA
BOX GIRDER BRIDGE
STEEL BOX GIRDER BRIDGES San Francisco – Oakland Bay Bridge
BEHVIOUR OF BOX GIRDER BRIDGES: A general loading on a box girder, such as shown in fig 1 for single cell box, has
components which bend, twist, and deform the cross section.
Thin walled closed section girders are so stiff and strong in torsion that the designer might assume, after computations based on the elemental torsional theory, that the torsional component of loading in fig 1(c). has negligible influence on box girder response.
If the torsional component of the loading is applied as shears on the plate elements that are in proportion to St. Venant torsion shear flows, fig 1 (e), the section is twisted without deformation of the cross section.
The resulting longitudinal warping stresses are small, and no transverse flexural distortion stresses are induced. However, if the torsional loading is applied as shown in fig 1 (c), there are also forces acting on the plate elements fig 1 (f), which tend to deform the cross section.
The movements of the plate elements of the cross section cause distortion stresses in the transverse direction and warping stresses in the longitudinal direction.
FIGURE 1
FIGURE 2FIGURE 3
FLEXURE A vehicle load is transferred transversely by flexure of
deck to the web of box girder.
Initially consider that the webs of box girder are not allowed to deflect .The structure resembles a portal frame for understanding the various stresses generated.
The flexure of the deck induce transverse bending stresses in the webs and, consequently in the bottom flanges of the girder. Any vehicle load can thus be replaced by the forces at the intersections of deck and web as shown in fig 4.
FIGURE 4
The high torsional strength of the box section makes it very suitable for long span bridges.
The box girders subjected to torsion undergo deformation or distortion of the section, giving rise to transverse as well as longitudinal stresses.
For a single cell box, the torque is resisted by a shear flow which acts around the wall of the box and is given by
q=T/2A, Where T is the torque and A is the area enclosed by the box. (contd…)
TORSION
The pure torsion of the thin walled section will produce warping of cross section.
Consider four panels of a rectangular box subjected to pure torsion.
Consider, Box width=B, depth=D, flange thickness=tf, Web thickness=tw.
(contd…)
Under the torque T, the shear flow is given by q=T/2BD.
The shear stresses in the flanges is Tf=q/tf=T/2BDtf.
Viewing from above each flange is sheared into a parallelogram, with a shear angle Φ =Tf/G.
If the end sections were to remain plane, the relative horizontal displacement between top and bottom corners would be ΦL at each end.
There would be a twist between the two ends of 2ΦL/D=2TfL/DG=TL/BD²Gtf.
(contd…)
Viewing the box from side and considering the displacements of the webs, if the end sections were to remain plane the twist of the section would be TL/B²DGtw.
The end sections remain plane if TL/BD²Gtf=TL/B²DGtw, i.e. Dtf=Btw.
If this condition not met the end sections cannot remain plane, there will be a slight counter-rotation in their planes of the two flanges and of the two webs, and a consequent warping of the section.
(contd…)
When torsion is applied directly around the perimeter of a box section, by a force exactly equal to the shear flow in each of the sides of the box, there is no tendency for the cross section to change its shape.
The distortional forces are tending to increase the length of one diagonal and shorten the other.
To illustrate how distorsion occurs and is carried between effective restraints, consider a simply supported box with diaphragms only at the supports and which is subject to a point load over one web at midspan.
(contd…)
DISTORSION
If there is no transverse moment continuity at the corners(a pinned connection between web and flange) the cross section will distort as shown below
(contd…)
The in-plan bending of each side gives rise to longitudinal stresses and strains which, because they are in the opposite sense in the opposite faces of the box, produces warping of the cross section.
The longitudinal stresses therefore known as distorsional warping stresses and associated shear stresses are known as distorsional shear stresses.
If a flexible intermediate cross-frame is introduced at the point of application of the load, it tends to resist the distorsion of the cross section by ‘ sway bending’ of the form shown in figure
(contd…)
(contd…)
Warping is an out of plane on the points of cross section, arising due to torsional loading.
concrete box beams with no intermediate diaphragms when subjected to torsional loading, undergo warping displacements composing of two components viz, torsional and distortional warping displacements.
Both these give rise to longitudinal normal stresses i.e. warping stresses whenever warping is constrained.
Distortion of cross section is the main source of warping stresses in concrete box girders, when distortion is mainly resisted by transverse bending strength of the walls and not by diaphragms.
WARPING OF CROSS SECTION
In a box girder a large shear flow is normally transmitted from vertical webs to horizontal flanges, causes in plane shear deformation of flange plates, the consequence of which is that the longitudinal displacements in central portion of flange plate lag behind those behind those near the web, where as the bending theory predicts equal displacements which thus produces out of plane warping of an initially planar cross section resulting in the “SHEAR LAG".
SHEAR LAG
Shear lag can also arise in torsion when one end of box beam is restrained against warping and a torsional load is applied from the other end.
(contd…)
The shear lag that causes increase of bending stresses near the web in a wide flange of girder is known as positive shear lag.
Whereas the shear lag, that results in reduction of bending stresses near the web and increases away from flange is called negative shear lag.
When a cantilever box girder is subjected to uniform load, positive as well as negative shear lag is produced.
However it should be pointed out that positive shear lag is differed from negative shear lag in shear deformations at various points across the girder.
(contd…)
STEEL CONSTRUCTION INSTITUTE, Design Guide for Composite Box Girder Bridges-second edition, march 2007.
Sherif El-Tawil and Ayman M. Okeil, Behaviour And Design OF Curved Composite Box Girder Bridges, October 2002.
Zakia Begum, Analysis And Behaviour Investigations of Box Girder Bridges,2010.
REFERENCES