# Truss: What is Truss, Types, Components, Truss in Civil Engineering

By Aina Parasher|Updated : August 3rd, 2022

Truss allows us to create strong and durable structures while using materials efficiently and cost-effectively. A truss is a structure that consists of members assembled into connected triangles so that the overall assembly behaves as a single object. Trusses are most commonly used in bridges, roofs, and towers.

When the truss members lie essentially in a single plane, that type of truss is called a plane truss. When the members of the truss lie three-dimension, the truss is called a space truss. Trusses are made of triangular units constructed with straight members. The ends of these members are connected at joints. They can carry significant loads, transferring them to supporting structures.

## What is a Truss?

A truss is a structure that consists of straight members arranged into connected triangles so that the whole assembly forms a stable structure. In a truss, the straight members are connected at joints called nodes, and all the forces and reactions are assumed to act only at these nodes. Consequently, the truss members are subjected to axial loads (tensile and compressive) without bending.

A truss is statically determinate when all its member forces can be calculated using only equilibrium equations. Otherwise, it is statically indeterminate.

## Types of Truss

There are various types of trusses. Different designs carry loads in different ways. The members of these trusses are located in the same plane, these are called Planar Trusses, and we can analyze them as Two - Dimensional structures. Following are the various types of trusses:-

• Fink Roof Truss
• Fan Roof Truss
• King Post Truss
• Howe Roof Truss
• Pratt Roof Truss
• Modified Queen Roof Truss
• Howe Bridge Truss
• Pratt Bridge Truss
• Warren Bridge Truss
• Parker Bridge Truss
• Baltimore Bridge Truss
• K Bridge Truss

## What is a Perfect, Imperfect, and Redundant Truss?

### Efficient or Perfect Truss

If the number of members in the truss is just sufficient to prevent distortion of its shape when loaded externally, it is called a perfect truss. A perfect truss satisfies the equation m = 2j-3, where j is the number of joints and m is the number of members.

### Deficient or Collapsible or Imperfect Truss

When the number of members is less than 2j - 3, it is a deficient truss. It is an imperfect truss. It is also known as a collapsible truss, as under the action of collapsible forces, the truss tends to collapse.

### Redundant Truss

An imperfect truss in which the number of members is more than 2j-3 is called the redundant truss.
2 force members- A member of the truss is a two-force member. Here, the forces are collinear; therefore, a truss member would be in tension or compression. ## Types of Truss Based on Determinacy

If the number of unknown forces (reactions and internal forces) of a given structure is equal to equilibrium equations, the structure is known as a determinate structure. Determinacy is of two types; one is Internal Indeterminacy other is External Indeterminacy.

• Statically Determinate Truss
• Statically Indeterminate Truss

## Statically Determinate Truss

If it is possible to determine the reactions, forces, and internal forces in members of a truss by applying an equilibrium equation, that truss is known as a Statically Determinate Truss. To design or analyze a truss, it is essential to determine the force in each member. The main purpose is to check whether the members can carry the applied loads without failing.A truss is considered statically determinate if all of its support reactions and member forces can be found using only the equilibrium equations. For a planar truss to be statically determinate, the number of members added to the number of support reactions must not exceed the number of joints multiplied by 2. This condition is the same as that used previously as a stability criterion.

### Assumptions:

While solving problems on Statically Determinate Trusses, we consider some assumptions like, Members are subjected to axial forces only (Compression or Tension), Shear Force and Bending Moment are neglected, Self Weight of the members is ignored, Members are assumed to be linear, All joints are smooth, frictionless hinges, Loads and Reactions will act directly or indirectly at joints only.

#### Degree of Static Indeterminacy

1. DS = m+re – 2j
where, DS = Degree of static indeterminacy m = Number of members, re = Total external reactions, j = Total number of joints
2. DS = 0 ⇒ Truss is determinate
If Dse = + 1 Dsi = –1 then DS = 0 at specified point.
3. DS > 0 ⇒ Truss is indeterminate.

## Statically Indeterminate Truss

If it is impossible to determine the truss members' reaction forces and internal forces by applying equilibrium equations, it is known as a Statically Indeterminate Structure. It is defined as structures that can't be statically analyzed using only equilibrium equations (statics). These structures indicate that there's at least one more unknown force than there are equations of equilibrium, meaning that the sum of forces and moments in each direction is equal to zero.

In 2D structures, there are three equations of equilibrium. Statically Indeterminate Structures are analyzed by Force method or Displacement method. In the Force method, redundant forces are treated as unknowns. In the Displacement method, displacements are treated as unknown.

## Zero Force Members

Some members don't carry any load. They are known as Zero Force Members. There are different ways to find these zero-force members. The purpose of Zero Force Members is to provide stability to the structure and to avoid failure because of unexpected loads. Some of the ways are:

1. In a pin joint, if the number of members is three and two of the members are in the same line, the force in the third member is zero. ( No load, No reaction at the joint )
2. At the pin joint, if the number of members is 2 and they are in different lines, then the force on both members is zero. ( No load, No reaction shall be present at that joint)

#### Truss Member Carrying Zero forces

(i) M1, M2, M3 meet at a joint

M1M2 are collinear

M3 carries zero force

where M1, M2, M3

represents member.

(ii) M1 M2 are non collinear and Fext = 0

M1 M2 carry zero force.

## Assumptions in Truss Analysis

Analysis of a Truss is generally a complex process. We need to simplify such a process. It is physically impossible for all these conditions to be satisfied exactly in an actual truss. Therefore, an ideal truss in which these idealized conditions are assumed is called an ideal one.

We make some assumptions in the truss analysis that significantly simplify the process. Some assumptions are as follows:

• Members are inter-connected only at their ends.
• Members are connected at joints by frictionless pin.
• Loads must only be applied at joints.
• Self-weight of the member may be neglected.
• Members must be straight.
• A pin connection can represent all the joints in the structure, i.e., those members are free to rotate at the joints.
• The members of a truss are rigidly connected using a gusset plate.
• Loads are only applied at the joints of the truss. Loads are never applied in the middle of the member as all joints are pinned, and members cannot carry Bending Moment; they can carry only Axial Loads.
• Each member has to be in equilibrium. Therefore, the forces acting at each end of the member must be equal and opposite.

## Sign Convention and Graphical Representation of Internal Forces

In the analysis of trusses, we will use the positive sign for tensile force and the negative sign for compressive force. In addition to this, the graphical representation of the direction of internal forces is described as follows –

• If the direction of force is away from the joint, then it means that the force in the member is tensile. • If the direction of force is towards the joint, then it means that the force in the member is compressive. ## Method of Truss Analysis

Truss analysis can be done via various methods. While designing trusses, it is essential to know the forces acting on each element of the truss to design it according to the safety factor. The two commonly used methods for truss analysis are:

• Method of joint
• Method of section

## Methods of Joints

Method of Joints is used to find the unknown forces acting on members of a truss. Method of Joints is usually the fastest and most convenient way to discover the unknown forces in truss structure. The equilibrium of a joint is considered in the Method of Joints. Following are the steps that need to be followed to use this method.

1. Draw a Free Body Diagram of the truss and solve for reaction forces. Use equilibrium equations to calculate the reaction force.
• 2. Draw FBD of each joint and solve the internal forces. (Unknown forces are found using equilibrium equations.) The force will act away from the joint for members in tension, and for members in compression, the force will act towards the joint. FBD Example:

Taking equilibrium of the horizontal forces.

∑Fx = 0, HA= 0

Equilibrium of Vertical Forces

∑Fy = 0

FA+ FE= 20kN

MC= 0

dFA= dFE

FA= 10kN

FE= 10 kN

To find force in each joint.

E.g. – Joint A FAB = -10/Sin 60 = –11.5kN

FAC = FAB Cos 60 = – 5.75 kN

Like this, we can find out forces in each joint.

### Disadvantages of Method of Joints

To find out the forces in any internal member, we must find the forces in prior members. Hence, the Method of Joints is a lengthy method. Hence, it is a time taking method. Another disadvantage of this method is that if the number of members is greater than two, then this method is not suitable.

## Method of Section

The equilibrium of a structure is considered in the Method of Sections. In this method, we need to pass a section through the member which we have chosen. A section may divide the entire structure into two separate parts. It is preferred that the section must pass through three members. It is a time-effective method as there is no need to find the force in a prior member to find the force in any chosen internal member. A section may be horizontal, inclined, or vertical. Following are the steps that need to be followed to use this method.

1. Draw a Free Body Diagram of the truss and solve for reaction forces. Use equilibrium equations to calculate the reaction force.
2. Cut the truss through the members of interest.
3. Apply the equilibrium equations to solve the internal forces.
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## FAQs on Truss

• A framework is made up of straight members joined at their ends, forming a structure known as a truss. Truss supports moving or stationary load. Roof supports, bridges, and other such structures are some of the common examples of trusses.

• To find the force in any internal chosen member, we have to find the forces in prior members. Therefore, this method is suitable when there is a need to find forces in all the members of the structure. So, the best-suited method is the Method of Joints.

• To find or analyze a few specific members. Method of Section is the best suitable method as there is no need to find the forces in prior members. The equilibrium of a structure is considered in the Method of Sections. In this method, we need to pass a section through the member which we have chosen. The section may divide the entire structure into two separate parts.

• Roof covering in a truss prevents rain, sun, snow, etc. Various types of roof coverings used in a truss are:

• A.C. sheets,
• G.I. sheets,
• Tiles,
• Slabs
• Wooden shingles
• In the method of joint, the equilibrium of isolated joints is considered to calculate internal forces in members. On the other hand, in the method of the section, the truss is divided into 2 parts by an imaginary section, and the equilibrium of either part is considered to calculate the unknown internal forces in the members. Computations are very convenient in the case of the method of joints but can become cumbersome if forces in only some members are required, and the truss is large. When internal forces in only some members are required, then analysis by the method of the section is a better choice.

• In the analysis of the truss, we assume that all members are connected at joints by frictionless pins, and external forces only act at joints and never at the middle of the member. Combining these assumptions ensures that the members are only subjected to axial force, and no bending moment is generated.

• In the method of joint, we isolate individual joints and, using two equilibrium equations (∑Fx = 0 and ∑Fy = 0), determine the unknown forces in the members. The method of the joint is the simplest and most convenient method for the analysis of trusses. However, for a larger structure, we'd have to work our way from the support nodes to the area of interest, evaluating the forces at each node along the way, which may be tiresome. In addition, we can only analyze the joints having two unknown forces acting on them.

In the method of the section, we can quickly get the force in any individual member for a determinate truss without having to work through the entire truss. In this method, we draw a convenient section that cuts through the members for which internal forces must be calculated and, using equilibrium equations, determine those forces. Unlike method of joint, in method of section we can also utilize 3 equilibrium equations (∑Fx = 0, ∑Fy = 0, ∑M = 0)

• Analysis of a truss can be a complex process. To simplify the process, we make certain assumptions to make our analysis work more convenient. The main assumptions for the analysis of the truss are as follows -

• Truss members are interconnected only at their ends.
• Truss are connected together by frictionless pins.
• The truss system is loaded only at the joints.
• The weights of the members may be neglected.
• All trusses can be called pin-jointed plane frames, but all pin-jointed plane frames can not be called a truss. This is due to the assumption made in the analysis of truss that the loads on a truss only act at the joints, which may not be true for all pin-jointed frames.

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