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Sunday, 1 December 2019

TRUSSES IN ENGINEERING MECHANICS

We have started a new topic in our previous post i.e. engineering mechanics. We have seen there the basic concept of force system with the help of our recent post. 

Now, we will be interested here to understand the basic concept of truss in engineering mechanics with the help of this post. 

Basic concept of truss 

First of all, we must know that what is the origin of the word truss. Truss word comes from the French word trousse and its means collection of things bound together or we can say that collection of two force members bound together. 

Trusses are basically defined as the collection of two force members subjected with axial loads. 

Trusses are basically used in order to support the transverse loads. Members of truss will be subjected with axial loads even the external loading on truss will be in the transverse direction. Members of the truss might be subjected with the tensile load or the compressive load. 

Let us see here a very basic truss as displayed here in following figure. We can see here that external loading on the given truss is in the transverse direction, while members of the given truss are subjected with axial loads. 


There will be some members in the truss which will not transfer any load and those members of the truss will be termed as zero force members. We must note it here that zero force members are very important part of the truss. 

Just because of it is a zero force member, we can not remove it. If we will remove the zero force member then truss will be collapsed. 

You might be thinking that if a member of truss is not transferring any load then why we should keep such member in the truss. Zero force members are very important part of the truss. 

We must know that with the application of the concept of truss, we can save quite enough cost in providing the solution for a given problem. 

Let us see here few examples of structure made with following the principle of truss. You can see that quite enough materials are saved with the application of truss. Therefore, we can say that truss provides the economical solutions for the specific problems. 


If we analyse the various examples of trusses, we will be able to say that most structures are made of several trusses joined together to form a space framework. 

Each truss will be designed to carry those loads which acts in its plane and therefore each truss could be treated as two-dimensional structure and could be considered as a plane truss for the purpose of analysis. 

We have used here one term i.e. plane truss. What is the meaning of the plane truss? When the truss members lie in a single plane, the truss will be termed as plane truss. Plane trusses will be usually supported at its two ends. 

Now we will see here the joint in a truss. 

Joint in a truss 

Let us see here how the members of a truss are joined together to form a space frame work and to support the transverse loads. 

Members of truss could be joined together by welding, bolting, pin joints, riveting etc. 

Bolted and riveted connections or joints permit small amount of rotation while welded connections are more rigid and do not permit the rotation at the joints. 

Welded connections in truss will be used where we need to build less critical structure. It will cost less and its manufacturing process will be relatively less time consuming and easy. 

Riveted connections in truss will be used where we need to build critical structure. Riveted connections in truss will be quite costly and it will take relatively more time as riveted connections need to have drilling and reaming action. In case riveted connections, there must be very small clearance between the drilled holes and rivet pins. 

The cross-section of truss members could be channels, angles, seamless pipes, ERW pipes, I-section or circular rods as displayed here in following figure. 


Let us see the following truss joint as displayed here in following figure. Ends of the members of the truss are joined together with the help of rivets with the foundation plate. The foundation plate over which ends of truss members are fixed by riveting will be called as gusset plate. 

Centroidal axis of the truss members must meet with each other as displayed in the figure. 


In a truss, no member of the truss should be continuous through a joint.  If any member of a truss will be continuous through a joint then it will behave as a beam not as the truss member and there will be high probability that it will be bent. 

When we will solve the truss problems and we will draw the truss, we will have to mark the joints as small circles in order to display that no truss member is continuous through the joint and we will also mention the co-ordinate axis as displayed here in following figure. 


How to construct a truss?

Let us see the following structure ABCD made of four members those are joined with the help of pin joints. Once we will apply the load at point C, this structure will be collapsed and we tried here to display the condition of structure after application of external load at point C by AC’D’B. 

Do you have any idea that why structure will be collapsed after application of external loading at point C.? 

As we know very well that in case of pin joint, translation motion will be arrested but there will be some rotational motion. Once we apply the load at point C, structure will have the rotation as displayed in the figure by AC’D’B. 


So, how we will make this structure stable? 

We will simply add a diagonal member AD and structure will become strong and stable. 


Now we must know that when we need to accept the given truss, there are few check points that we need to check in order to accept the truss for the given specific problems. So what are the check points? 

Check points for accepting the given truss for a specific problem

We need to check the following points in the given truss as mentioned below. 

There must not be any member continuous through the joint. If any member of a truss will be continuous through a joint, then it will behave as a beam not as the truss member. 

Truss members must be properly aligned on the gusset plate so that their centroidal axis meet with each other at a common point. 

External loads must be applied only at the joints in order to avoid the moment reaction at the joints. 

Provision for thermal expansion or thermal contraction and deformation due to the application of eternal loads must be there in the design of truss. For example, if a truss is supported at its one end by pin joints then it should be supported at its other end with the help of roller support. 

Types of trusses 

There are following basic types of trusses as mentioned below 

Simple truss 

Simple truss could be considered as a single triangular truss. Roof trusses are one of the best example of simple truss. 

Planar truss

When the truss members lie in a single plane, the truss will be termed as plane truss or planar truss. Planar trusses will be usually supported at its two ends. 

Space frame truss 

In case of space frame truss, the truss members and nodes will be located in three dimensional space. Electrical and telecommunication towers are one of the best example of space frame truss. 

There are some basic forms of trusses as displayed in following figure. 


Classification of truss

Let us see here now very important point that is the classification of truss on the basis of the relation between the number of members, number of joints and the reaction forces. 

We will have following equations that will provide the relation between the number of members, number of joints and the reaction forces as mentioned below. 

Statically determinate truss 

m + r = 2j 

Statically determinate, we can determine the forces in the members and reaction forces with the help of the statics principle alone. 

We must note it here that above equation is necessary but not sufficient to classify a structure. 

Statically indeterminate truss 

m + r > 2j 

Statically indeterminate, we will not be able to determine the forces in the members and reaction forces with the help of the statics principle alone. 

Mechanism 

m + r < 2j 

The framework will have rigid body motion. 

Therefore, we have seen here the meaning and basics of truss, the manufacturing methods and joints for truss, the importance of supports in the truss, the consideration of thermal expansion and contraction during the construction of truss, some check points for a given truss, types and forms of the truss and finally we have also looked here classification of the truss with the help of this post. 

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Now, we will be interested here to understand the basic concept of truss in engineering mechanicsmethod of joints and method of sections to determine the internal forces in the members of the given truss with the help of this post. 

Reference:  

Engineering Mechanics, By Prof K. Ramesh 
Image courtesy: Google  

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