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Pedestrian bridge stress analysis

Pedestrian bridge stress analysis

Danish Azam2017-ME-66 Mechanical Engg. Department, University of Engineering and Technology LahoreLahore, Pakistandanish.azam33@gmail.com

Abstract—In this document we will do stress analysis of a given pedestrian bridge. We will get knowledge about truss, its types, applications, bridges, their types and different ways and procedures to analyze strength of a given material.

Keywords—complete analysis of bridge, also of truss, stress, static analysis and strength of materials.

Introduction

T

he structural designer of bridge doesn’t know that how much load will be bearing by bridge on daily basis. He wants the bridge not to collapse even on larger loads. He also doesn’t know about the uncertainty by fabricators. So, he makes different assumptions and performs stress analysis of the bridge and apply a factor of safety. For doing such kind of stress analysis a structural engineer needs to know the terms given below

Truss

A truss is a structure that “consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object”. CITATION Ple13 l 1033 [1]Two Force member

Two force member is a structural member on which forces are applied on two points usually on ends, these are axial forces. These are applied on axis direction n either one or both ends which causes compression pr tension.

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Characteristics

Simple Truss

234950488315Figure SEQ Figure * ARABIC 1: A simple truss in a bicycle

00Figure SEQ Figure * ARABIC 1: A simple truss in a bicycle

A single triangle can be considered as a simplest truss. Simple truss has applications in mechanical structures such as bicycles and aircrafts.

Planer Truss

64770084328000Single plane truss is called planar truss. They are used in parallel to construct trussed bridges. It is recognized that a truss bridge will be more strengthened than a concrete bridge and would be cheap and bearing less weight. That is why trusses are more useful in bridges.

Figure SEQ Figure * ARABIC 3: Simple tetrahedron CITATION htt l 1033 [3]Space frame truss

Figure SEQ Figure * ARABIC 2: Space truss is used in electric poles CITATION htt1 l 1033 [2]Three dimensional truss is called space truss. Simplest space frame truss is consisting of six members having tetrahedron shape. They meet at four joints. Other planer trusses are slanted on one another.

Three dimensional trusses are used in house roofs and in the big electrical poles.

Types

On the basis of shape and strength, trusses are of many types

Based on their deck location truss have three categories.

Through truss— When deck locates at bottom cord then the bridge is called as through truss.

Pony truss— It is similar to a through truss, but it is not so high having no lateral bracing in between top cords.

Deck truss— On the level of top chord “,the bridge is called deck truss.

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Figure SEQ Figure * ARABIC 4: Types of truss bridges CITATION htt4 l 1033 [4]On the basis of their geometric arrangement of their chords, trusses are classified as vertical and diagonal trusses. Figures below shows us fifteen different types of truss designs. Most of them were named after the 19th century when engineers created then for the first time. In these diagram, members and supplementary members are represented by solid and dotted lines respectively. Diagonal members are used to carry the weight of moving vehicles. The design of a bridge is not affected by the occurrence or nonappearance of supplemental members.

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Figure SEQ Figure * ARABIC 5 : Different types of trusses

Pratt truss

This is one of the early designs in truss history. Pratt design was famous due to its beautiful design and its popularity remained un affected after evolution from wood to iron. The only tension produced in it divides in its diagonal members and tension is better than compression because of buckling effect in compression causing bending of members.

Figure SEQ Figure * ARABIC 6 : Pratt truss in Railway bridge CITATION htt3 l 1033 [5] That is the reason Pratt truss is the cheapest way for static loading. That is why Pratt truss is used in railway bridges.

Figure SEQ Figure * ARABIC 7: Pratt truss in PUBG Mobile Game

K truss

We can understand the shape of this truss by its name K, it consists of many K shape members in forward direction up to its center then in reverse direction till its end.

Figure SEQ Figure * ARABIC 8: K-deck truss bridge over the Monongahela River on the Wheeling & Lake Erie Railway between Belle Vernon and Speers CITATION htt5 l 1033 [6]Fink truss

Figure SEQ Figure * ARABIC 9: Fink truss bridge

These type of trusses are usually used for pedestrian bridges and roof trusses in building construction and in an inverted form where the lower chord is present and a central upward projecting vertical member and attached diagonals provide the bases for roofing.

Warren Truss

Warren Truss is identified by equilateral triangular structure present in its design. It is a simple design in which load is equally divided among all members. It is little bit expensive because of extra members. It shows poor performance under concentrated loads. It shows best performance when load is uniformly distributed.

Figure SEQ Figure * ARABIC 10: Montana Rail Link Bridge No. 207 America CITATION htt7 l 1033 [7]Howe truss

Its structure is opposite to Pratt truss. In Howe truss vertical members shows tension and horizontal members shows compression. Its way of use is same as that of Pratt truss.

Figure SEQ Figure * ARABIC 11: Howe truss at Old Adam’s Coal Mine in Alberta, CA CITATION htt8 l 1033 [8]Force

A Force an influence on a system, making or tends to make a change in motion or shape or other effects. It is symbolized as alphabet F. If a force is applied on a body it produces acceleration in the body or sometimes elastic deformation and other effects. These Forces can be contact forces or actions at distant forces.

Contact forces includes frictional forces, tension forces, applied forces, normal forces etc.

Action at distance forces includes gravitational forces, electrical forces and magnetically forces.

Load

A load is a kind of weight or a quantity which creates influence on a body.

Types of Loads

Concentrated Load

Concentrated Load is defined as the load which acts on a single point. In small areas load is always concentrated on a single point..

Uniformly Distributed Load

Uniformly Distributed Load is defined as the load that is uniformly distributed over an entire length. It is often abbreviated as UDL. UDL has units N/m.

Triangular Load

Triangular load is a type of load in which force is applied in an ascending order. This makes a direct slope.

Effects

Effect of Temperature on Truss

In wood trusses, effect of temperature is not significant. But in case of metal the temperature effect is very much significant. Metal expands when subjected to heat that is why there is a capacity in their structures to expand up to some extent.

Components of bridge

Abutment

The end points of a bridge are called Abutment. They are subjected to withstand lateral pressure.

Pile

It is a reinforced leg support which is driven into the ground. It gives a proper structural support. There in between distance is calculated. it allows strength to rest of the structure that laid on top of them.

Cap

right50736500Cap is located on the upper side of the pile beam. It provides extra support and distributes the load to the piles. Cap along with pile is collectively called Bent.

Figure SEQ Figure * ARABIC 14: Components of truss bridge CITATION htt11 l 1033 [11]Girder/span

All piles are connected with the help of girders. It is among main components of a bridge. It consists of simple numerous spans that is a single continuous span supported by many beams. They are mostly made up of metal/reinforced concrete or could be seen in the form of haunches girded which are able to carry more load.

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Deck

They are simple, continuous and are made up of metal/reinforced concrete. They consist of sub-components for example approach slab, expansion joint, drainage scupper, curb, running surface, footpath.

Floor beam

It is a beam which provides direct support to the floor loading of a structure and transfers it to the adjacent girders or columns. They are usually made up of steel, reinforced concrete, or wood.

Stringers

These beams are a secondary structure which carries load from slab to cross beams founded at truss nodes. This works as a converter of distributive load to the point load.

Sway bracing:

It is a sway frame which extends in between trusses. Its main purpose is to transfer the reactions from a lateral bracing truss to the ending sides of trusses. So, it depends on the ability of a frame to oppose transverse forces.

Struts

When load is applied on a truss some members bear compressive forces on them these members are called struts. Their length becomes shortened.

Portal bracing

It acts as a combination of struts and ties that lies in a plane of inclined braces. It serves as a medium to transfer wind pressure from upper parts of the structure to pier of the bridge.

Zero force member

421036023469900Zero member is a member in truss. This is the member which is at rest, this member neither goes in tension nor in compression. In a truss a zero force member is often found at pins where no external load is applied and three or fewer truss members meet. Recognizing basic zero force members can be accomplished by analyzing the forces acting on an individual pin in a physical system. If two non collinear points meet in unloaded joint they both are considered as zero member of truss.

Zero member provides stability to the system.

These members can carry loads.

Methods of Static Analysis

Method of joints

The process which is used to for solving unknown forces acting on members of a truss is known as method of joints. The method relies on the joints or connecting points between the members, and it is probably the fastest and easiest method for solving all the unknown forces in a truss structure.

left22441900The process of this method is described below:

Figure SEQ Figure * ARABIC 15: Method of joints CITATION htt12 l 1033 [12]Firstly, label all members and joints. Usually, members are labeled with letters and joints are labeled with numbers

Draw a free body diagram and treat the whole truss structure as a rigid body. Write all necessary information e.g. equilibrium equations, and then solve it for external reacting forces bearded by the truss structure. This analysis should be same as analysis of a single rigid body.

Assume that the connecting material between the members is a pin or some other small amount of material. Then draw a free body diagram of every connection point.

Now write down the equilibrium equations for every joint. Here we want only force equations not moment equations so we will treat joints as particles. Then solve the equilibrium equations.

Figure SEQ Figure * ARABIC 16: Method of joints CITATION htt12 l 1033 [12]Method of sections

right70259100The process of solving unknown forces on members of truss by breaking down all members into different sections and analyze every section separately. It is easiest way of determining of forces.

Figure SEQ Figure * ARABIC 17: Method of sections CITATION htt13 l 1033 [13]Following steps are included in this method:

Firstly, label all members and joints. Usually, members are labeled with letters and joints are labeled with numbers.

Draw a free body diagram and treat the whole truss structure as a rigid body. Write all necessary information e.g. equilibrium equations, and then solve it for external reacting forces bearded by the truss structure. This analysis should be same as analysis of a single rigid body.

Now imagine your truss cut into two different sections. The cutting line should pass through the member you are trying to solve in.

Draw a free body diagram of one or both sections you want to solve for.

right43370500For each section you made, draw equilibrium equations and solve it for unknown forces.

Figure SEQ Figure * ARABIC 18:Method of sections CITATION htt13 l 1033 [13]Graphical Method

Method of joints served as basis for graphical analysis of a structure. It was developed by the force polygons which were drawn to scale for each joint, and after that, forces in each member were measured from one of these force polygons.

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Following steps should be followed for this procedure:

Solve the equations of equilibrium for the entire truss to find reactions on it.

Moving clockwise outside of the truss; draw the force polygon for scaling of entire truss

Take each joint in turn, then by treating successive joints acted upon by only two unknown forces, draw a force polygon

Calculate the magnitude of the force in every member from its diagram

right56131000At last, note work done from one end to another of the truss, as it is used for checking of balance and connection to the other end.

Figure SEQ Figure * ARABIC 19: Graphical Method

Experiment

Problem statement

For a specific pedestrian bridge analyze the stresses produced and find the highly stressed element.

Figure SEQ Figure * ARABIC 20:3-D rendered image of the given bridge

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Aknowledgement

Thanks to N. Ahmed (Assistant Professor Mechanical Engineering Department UET Lahore).

References

BIBLIOGRAPHY

[1] M. E. Plesha, G. L. Gray and F. Costanzo, Engineering Mechanics: Statics, 2nd ed., New York: McGraw-Hill Companies Inc. , 2013, p. 364–407.

[2] http://readtiger.com/img/wkp/en/BSTROM1.jpg.

[3] http://upload.wikimedia.org/wikipedia/commons/e/e7/Tetrahedron-4-3D-balls.png.

[4] https://image.slidesharecdn.com/footbridge-140131082351-phpapp01/95/foot-bridge-presentation-11-638.jpg?cb=1391156699.

[5] http://www.morgan-nj.org/blog/contentdir/uploads/2013/10/Rt-35-Pratt-Truss-Bridge-01-v3.jpg.

[6] https://bridgehunter.com/pa/westmoreland/belle-vernon-rr/.

[7] https://www.kljeng.com/featured-projects/montana-rail-link-bridge.

[8] http://www.pbase.com/martinbunting/images_of_alberta.

[9] https://ourpastimes.com/characteristics-suspension-bridge-5942062.html.

[10] http://www.kansastravel.org/clementsbridge.htm.

[11] https://en.wikipedia.org/wiki/Truss_bridge.

[12] http://adaptivemap.ma.psu.edu/websites/structures/method_of_joints/methodofjoints.html.

[13] http://adaptivemap.ma.psu.edu/websites/structures/method_of_sections/methodofsections.html.

[14] http://www.technologytom.com/assets/images/common_20truss_20bridges_1_.gif.

[15] https://structurae.net/structures/bridges-and-viaducts/fink-type-truss-bridges.

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