TRUSS :

Truss is a kind of framed structure made of entirely by rigid metallic rods joined by pin. The rods are called as Links or Linkages and the pins are called as joints. Their primary goal is to support the applied loads or we can say they are primarily load bearing structures. We often encounter trusses in our daily life as trusses are used to support roofs of various kinds of industrial sheds. Trusses are used as poles carrying high tension electricity.

LINK/ LINKAGES :

A link is a rigid rod which can bear any external load applied on it. A link can bear two types of forces.

COMPRESSIVE FORCES :

When the external forces applied on the link or rod tries to decrease the length of the rod, then they are called as External Compressive Forces. A truss in equilibrium counters this compressive force by inducing an internal force, equal and opposite the externally applied force. The internal force thus induced balancing the external compressive force is named as Internal Compressive Forces. Generally Compressive Forces are considered as negative in truss analysis.

TENSILE FORCES :

When external loads applied on a link try to increase the length of the link, we call them External Tensile Loads. To neutral the tensile load applied on a link, an equal but opposite internal force is generated named as Internal Tensile forces. Tensile forces are generally considered as positive internal forces.

THE SIMPLEST TRUSS:

A triangular shaped truss made of three linkages and three joints is the simplest type of truss. As it is the simplest geometric shape where there is no change in shape with the application of forces at the joints if the length of rods/ linkages remain unchanged / constant.

MAXWELL'S TRUSS EQUATION:

To distinguish between "statically determinate structure" and "statically indeterminate structure" Maxwell formulated an equation involving the number of linkages (m) and number of joints (j).

The trusses which satisfies the equation,

m = 2j - 3

are statically determinate structures and named as "Perfect Trusses".

If m > 2j - 3, then the number of linkages are more than required, hence, called as "Redundant Trusses".

Where as if m < 2j - 3 for any truss, then the number of linkages are less than that of a perfect truss. These kinds of trusses are called as "Deficient Trusses".

ASSUMPTIONS CONSIDERED WHILE ANALYZING TRUSSES :

While analyzing trusses, to simplify the analysis we often consider certain assumptions. The purpose of these assumptions are the simplification of a complex problems. The assumptions are

(i) The links are perfectly rigid bodies, ie there occurs no change in the dimensions of the links.

(ii) The pin joints are perfectly smooth, ie there is no friction in the each and every joints.

(iii) The mass and weights of the links are so small compare to the magnitudes of the applied forces, that for truss analysis we shall neglect them. It means the links are massless as well as weightless.

(iv) The cross-sections and material of the links are uniform by nature.

(v) The external loads are only applied on a joint in the truss, whenever we shall place any external load, we must place it one of the joints in the truss.

METHODS OF TRUSS ANALYSIS :

There are two different methods to analyze a truss. The analysis of Truss actually is the procedure to find the internal forces induced in the each and every linkages or may be in a specified linkage.

When we shall have to find internal forces induced in each and every links of the Truss, we employ the (i) Methods of Joints to analyze the truss.

Here we shall treat each and every joints as objects in equilibrium and apply the conditions of equilibrium for coplanar concurrent force system.

TRUSS ANALYSIS: METHOD OF JOINTS

The first to analyze a truss by assuming all members are in tension reaction.

(i) TENSILE FORCE IN A LINKAGE:

A tension or tensile force is induced in a member when the member experiences pull forces at both ends of the bar and usually denoted as positive (+ve) sign.

(ii) COMPRESSION FORCE IN A LINKAGE:

When a member experiencing a push force at both ends, then the bar was said to be in compression mode and designated as negative (-ve) sign.

PROCEDURES IN JOINT METHOD:

In the joints method, a virtual cut is made around a joint and the cut portion is isolated as a Free Body Diagram (FBD).

Using the equilibrium equations of ∑ Fx = 0 and ∑ Fy = 0, the unknown member forces could be solve.

It is assumed that all members are joined together in the form of an ideal pin, and that all forces are in tension (+ve) of reactions.

ISOLATION OF A JOINT & ITS FBD:

An imaginary section may be completely passed around a joint in the truss. The joint has become a free body in equilibrium under the forces applied to it. The equations ∑ H = 0 and ∑ V = 0 may be applied to the joint to determine the unknown forces in members meeting there. It is evident that no more than two unknowns can be determined at a joint with these two equations.

STEPS TO ANALYSE A TRUSS USING THE METHODS OF JOINTS:

(i) Draw the Free Body Diagram (FBD),

(ii) Solve the REACTIONS of the given structure,

(iii) Select a joint with a minimum number of unknown (not more than 2) and analyze it with ∑ Fx = 0 and ∑ Fy = 0,

(iv) Proceed to the rest of the joints and again concentrating on joints that have very minimal of unknowns,

(v) Check member forces at unused joints with ∑ Fx = 0 and ∑ Fy = 0,

(vi) Tabulate the member forces whether it is in tension (+ve) or compression (-ve) reaction.

TRUSS ANALYSIS: METHOD OF SECTION

The section method is an effective method when the forces in specific members of a truss have to be determined.

Often we need to know the force in just one member with greatest force in it, and the method of section will yield the force in that particular member without the labor of working out the rest of the forces within the truss analysis.

If only a few member forces of a truss are needed, the quickest way to find these forces is by the method of sections.

In this method, an imaginary cutting line called a section is drawn through a stable and determinate truss.

Thus, a section subdivides the truss into two separate parts. Since the entire truss is in equilibrium, any part of it must also be in equilibrium.

Either of the two parts of the truss can be considered and the three equations of equilibrium ∑ Fx = 0, ∑ Fy = 0, and ∑ M = 0 can be applied to solve for member forces.

STEPS TO ANALYSE A TRUSS USING THE METHODS OF JSECTION:

(i) Pass a section through a maximum of 3 members of the truss, 1 of which is the desired member where it is dividing the truss into 2 completely separate parts.

(ii) At 1 part of the truss, take moments about the point (at a joint) where the 2 members intersect and solve for the member force, using ∑ M = 0.

(iii) Solve the other 2 unknowns by using the equilibrium equation for forces, using ∑ Fx = 0 and ∑ Fy = 0.

Note: The 3 forces cannot be concurrent, or else it cannot be solved.