## Trusses and Frames

A structure is a system of connected parts necessary to support a load. Some of the important examples include towers, buildings, ships, tanks, pressure vessels, mechanical systems and electrical supporting structures.

**TRUSSES**- A framework made up of straight members joined at their ends forming a structure is 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.

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 in three-dimension, the truss is called a space truss.

## CLASSIFICATION OF TRUSS

**EFFICIENT OR PERFECT TRUS-**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 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 and therefore a member of the truss would either be in tension or compression.

**ASSUMPTIONS OF TRUSS ANALYSIS**

- Members are linked by their ends by smooth frictionless pins. The weight of members is negligible.
- Loads and reactions are applied to the truss at joints only.
- The line connecting the joint centres present at the end of the member coincides with the centroidal axis of each member.
- All members function as two-force members ie, they are subjected to either tension or compression.

It is physically impossible for all these conditions to be satisfied exactly in an actual truss, and therefore a truss in which these idealized conditions are assumed is called an ideal truss.

**EQUATION OF EQUILIBRIUM- **When a balance of force and moment is maintained, a structure or one of its members are in equilibrium. The force and moment equation of equilibrium must be satisfied for this.

ΣF_{X}= 0 ΣF_{Y} = 0 and ΣM = 0

Whenever these equations are applied, it is first necessary to draw a free body diagram of the truss or its members. For the selected member, only its outlined shapes must be drawn free from its supports and surroundings.

**ANALYTICAL METHOD OF TRUSS ANALYSIS**

**METHOD OF JOINTS-**For analyzing or designing a truss, the force in each of its members must be obtained. If we were to consider a free body diagram of the entire truss, then the forces in the members would be internal forces, and they could not be obtained from an equilibrium analysis. Instead, if we consider the equilibrium of a joint of the truss then member force becomes an external force on the joints free body diagram, and the equations of equilibrium can be applied to obtain its magnitude. Hence, the method of joints is based upon this.

At each joint, the forces in the members meet at the joint and these forces at the joint, if any, constitute a system of concurrent forces. Two independent equations of equilibrium can therefore be formed at each joint i.e. ΣF_{H} = 0 And ΣF_{V} = 0

When three members are meeting at a joint where no load acts and out of these three, two are collinear, then the force in the third member will be zero, as shown below.

**METHOD OF SECTIONS-**When few members of the truss are to be analyzed for forces, we can do it by the method of sections. If a body is in equilibrium then any part is also in equilibrium, and this forms the basis of the method of sections.

In the method of sections, a section is of the truss is cut, such that not more than three unknown forces are required to be computed. A free-body diagram is drawn for either of its two parts.

Three equilibrium equations i.e. ΣF_{X} = 0 ,ΣF_{Y} = 0 and ΣM = 0 for a plane are used to find out three unknown forces. The force in almost any desired member may be found directly from an analysis of a section that has cut that member is a basic advantage of the method of sections method. Firstly, the reactions are needed to be found.

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