All about design of plate Girders

All about the design of plate Girders 

In this article, I discussed all-important points related to the design of plate girders and also explain with the help of video lectures.

What is a plate girder ?

A plate girder is a type of structural member designed to resist bending moments and is used when I-sections or other standard rolled sections are not sufficient to support the anticipated loads. Plate girders consist of plates and/or rolled sections welded together to form the desired shape, providing the necessary strength and stiffness to carry the applied loads effectively. They are commonly used in bridge construction, buildings, and other structures where large spans and heavy loads need to be supported.

Elements of plate girder 

1. Web plate 
2. Flange angles with or without flange cover plate 

   

   Design of plate girder 

   
   
3. Stiffeners 
4. Splices

Watch the video on the design of plate girders

• Plate girders are an effective alternative to built-up beams when it comes to withstanding applied loads.
• A plate girder consists of flange plates, flange angles, and a web plate.
• The compression flange comprises a flange plate, flange angle, and a web equivalent (a portion of the web embedded between the flange angles). 
• The web equivalent is calculated as 1/6 of the total area of the web, denoted as Aw.
• The tension flange is made up of flange plates, flange angle, and a web equivalent. 
• The web equivalent is determined as 1/8 of the total area of the web, denoted as Aw.
• In the analysis, it is assumed that bending moments are resisted by the compression and tension flanges, while the shear force is carried by the web.
• To ensure that the shear force is solely taken by the web, a 5 mm gap is provided between the flange plate and the web plate, preventing direct bearing action between them. 
• Load transfer from the flange angle to the web plate occurs through rivets only.
• The flange angles should be designed in a way that they account for at least 1/3 of the total flange area, be it the compression flange or tension flange.
• The width of the outstand in the compression zone is limited as follows: 

1.    b ≤ 16t_f
2.    b ≤ 256t_f/√fy

• The width of the outstand in the tension zone is restricted to: b ≤ 20t_f
• For resisting shear, only the depth of the web is considered, not the overall depth of the plate girder. 
• The shear stress (_{τwva 1 cal.}) is calculated as: τwva 1 cal  = V / (d_wt_w)  ≤  0.4fy[WSM]  ≤ fy/1.1 [LSM]
• The economical depth of the plate girder is given by: teconomical = 1.1√(M / (σ_bc * t_w)) 
• Note: Economical depth refers to the depth of the plate girder that corresponds to the minimum weight but not necessarily the minimum cost.
• The self-weight of the plate girder is given by: Self-weight = Live load / 300
• The maximum permissible bending compressive stress in the plate girder is given by:
•  σ_bc = 0.66fy = 0.66(fcbn + fy/√n), whichever is minimum.
• If d1/tw < 85, no vertical stiffeners are provided as there is no possibility of web buckling due to shear.
• If d1/t_w  > 85, vertical stiffeners are added to prevent web buckling due to diagonal compression.
• Angle (ISA) or flats (ISF) are used as horizontal and vertical stiffeners.
• Unequal angle sections are used as flange angles to increase the bearing area, where the longer leg is connected to flange plates.
• If d1/t_w > 200, horizontal stiffeners are provided above the neutral axis to prevent web buckling due to bending compressive stresses.
• Under concentrated loads, load-bearing stiffeners are provided to prevent web crippling due to excessive bearing stresses. d1 refers to the clear depth of the web between flange angles.
• If d1/t_w  > 250, additional horizontal stiffeners are added at the neutral axis to prevent web buckling between vertical stiffeners due to higher shear forces.
• If d1/t_w  > 400, the section must be redesigned, or truss girders should be used instead of plate girders.
• After adding all the stiffeners, the minimum clear panel dimension should not exceed 180t_w, and the greater clear panel dimension should not exceed 270t_w.

Design of end-bearing stiffeners:

1. End bearing stiffeners are designed as columns with both ends fixed, and the effective length is taken as 0.7 times the length of the bearing stiffener (l₁).
2. The cross-sectional area of the imaginary column is considered to be equal to the cross-sectional area of the web plate and angles whose length is 40 times the thickness of the web (40t_w).
3. Bearing stiffeners should be purely vertical and not bent (joggled) to touch the web plate. To fill the gap between the bearing stiffener and the web plate, a filler plate is used.
4. The filler plate serves the purpose of filling the gap but does not carry any load.
5. If the bearing stiffeners are the only means of providing torsional restraint, the moment of inertia of the bearing stiffeners about the neutral axis should not be less than                 D^3TR / (250 x W), where R is the reaction, T is the maximum thickness of the flange, D is the overall depth of plate girder and W is the total load including the self-weight of the plate girder.

Design of vertical stiffeners:

1. Vertical stiffeners are used to prevent buckling of the web due to shear, specifically diagonal compression.
2. Unlike bearing stiffeners, vertical stiffeners are not designed as columns; hence, they can be joggled, i.e., bent to touch the web plate.
3. A filler is not required for vertical stiffeners.
4. The minimum spacing of vertical stiffeners is taken as 0.3 times d₁, where d₁ is the clear depth of the web between flange angles.
5. The maximum spacing of vertical stiffeners is limited to 1.5 times d₁.