Initial Sizing of Steel Beam Section

The first step of preliminary / detailed design of structure is initial sizing of main structural members. This blog gives quick method of selecting steel section for Beam/Girder. The design of beam requires to satisfy the strength and serviceability provisions of codes. 

The Minimum Second Moment of Inertia of Beam Section I ( in cm^4) required is 

I = 0.5 x Ratio x K x L x M

Here,

M is Mid Span Beam Bending Moment is kNm

L is Span of Beam in m

K is constant based on loading and end supports, it is based on Bending moment diagram of span The value of K is taken from Table 1. ( Reference Table 3.1 of BS 8110-2:1985)

Ratio is Span / Allowable Deflection. It means Allowable Deflection = Span/Ratio

The value of "Ratio"  can be 250,360,400,500  or 600 based on what is going to be put on Beam/Girder

Table 1 Values of K for various Bending Moment Diagram
for allowable deflection = Span/400, The I required for Beam=0.5x400xK L M

I= 200K L M

I is in cm^4 unit. 

Bridge Superstructure

Bridge Superstructure

The loads coming over bridge superstructure are taken by following actions in individual members

• Bending ( Flexure and Shear in Member)
• Axial elongation or axial shortening ( Tension or Compression in Member)
• Combination of Bending and Axial Deformation (Flexure, Shear and Tension/Compression)

Girder Bridges

In this structural form the loads are taken fully by bending of superstructure. In this type of superstructure the loads are taken by members as flexure and shear. The design of superstructure is governed by flexure, shear and deflection criteria. Girder bridges can be anyone of following type

• Solid Slab ( Span 4m – 12m)
• Voided Slab ( Span 8m-16m)
• T Girder ( Girder and Slab) ( Span 12m-25m)
• Box Girder ( Single or Multi Cell) (25m – 60m)

The girder can be simply supported between two adjacent piers or continuous over more than one pier. The Continuous girder provide following advantage over simply supported girder

· Shallower depth superstructure compared to simply supported girders

· Reduce number of expansion joints

· Reduce number of Bearing required to support superstructure

· The continuous girders have redundancy

The continuous girders are not used under weak soil foundation. The settlement of support (Un-even settlement) will generate additional moments and shear in superstructure in case of continuous girder.

In Girder only extreme fibres are only stressed to maximum limit.

Truss Bridges

In this structural form the loads are taken by axial deformation of individual members. In truss bridges the loads are taken by members as axial tension or axial compression. Under axial tension/compression action all fibre of section are stressed to same limit. Hence truss bridges are best structural form for long spans. The truss bridge can be through type or deck type based on traffic movement.

The truss bridges are of following type

• Pratt Truss
• Warren Truss
• Modified Warren Truss
• K Bracing Truss

Bridge Classification

Bridges are broadly classified based on following three criteria

1. Material of Construction
2. Structural Form
3. Construction Technology

Bridge Classsifcation based on Material of Construction

• Reinforced Concrete
• Prestressed Concrete ( Post-Tenions / Pre - Tension)
• Composite
• Steel
• Masonary

Bridge Classification based on Structural Form

• Girder Bridges ( Slab / Girder and Slab ( T Beam) / Box Girder (Single Cell/Multi Cell))
• Truss ( Through Type / Deck Type)
• Cable Supported Bridges ( Cable Stayed / Suspension / Extradosed Bridges)
• Arch Bridges ( Arch Bridges / Bow String Arch Bridges)

Bridge Classification based on Construction Methodology

• Balanced Cantilever Bridges
• Incremental Launched Bridges

Bridge Bearing Layout

The bearing has following main two functions

• Transfer superstructure load ( Vertical / Transverse ) to substructure
• Allow thermal movement

For bridge span more than 40m POT bearings/ POT PTFE bearings are used.

Figure 1 shows bridge bearing layout for simply supported span

Figure 2 shows bridge bearing layout for two span continuous bridge

Figure 3 shows bridge bearing layout for four span continuous bridge

Economical Span of Bridge

Fixing length of typical span in design of bridges across river/elevated road/metro project is very important structural design decision. The cost of building one typical span can be broadly divided into following two components

1. Cost of Substructure
2. Cost of Superstructure

The cost of substructure is covers cost of bridge bearing, pier cap/pier head, pier and foundation (Open/Pile/Cassion). To take decision on most economical length of typical span, initial design and cost estimate is done for four to five different span lengths.

A graph is plotted with span length as abscissa and cost as ordinate. The graph is completed using cost of superstructure and substructure for all different spans. Figure 1 shows typical graph of Span versus cost. Point A on this graph correspondence to the economical span for the bridge project.

Figure 1 Span Versus Cost for Superstructure/Substructure

Continuous Beam / Bridge Span Arrangement

In case of continuous beam /girder bridges the end span is kept 80% of internal span. This span arrangement leads to uniform sagging momnet in mid span compared to sagging momment obtained in all equal span arrangement. Figure 1 shows bending moment diagram for two span arrangement, a) Last span equal to 0.8 times internal span b) All spans equal under uniformly distributed load.

One of bridge designed in Middle East had span arrangement of 40m - 50m - 50m -40m and this arrangement lead to uniform depth of box girder with least consumption of post-tenisoned tendon.

Figure 1 Bending Moment Diagram for uniformly distributed load on all four spans