Engineering Mechanics - Analysis of Structures (I)

Analysis of Structures (I)

• Trusses

A framework composed of members joined at their ends to form a structure is called a truss. Truss is used for supporting moving or stationary load. Bridges, roof supports, derricks, and other such structures are common example of trusses. When the members of the truss lie essentially in a single plane, the truss is called a plane truss.

Fig. 3.1 shows most basic triangular truss. Members are connected by pin-joints, which arrest translation but not rotation. Each member has three degrees of freedom in a plane, two translations and one rotation. Total degrees of freedom are 9. Each pin joint arrests two degree of freedom. Hence, degrees of freedom of pin-joint connected structure is 3. For keeping the structure stationary, these three degrees of freedom should be arrested. In the figure, left fixed support arrests two degrees of freedom, whereas in the right, the roller support arrests one degree of freedom. Thus the structure cannot move and the structure is called stable. This type of structure is also called rigid structure.

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Fig 3.1: A 3-member truss

• Frames

A structure is called a frame if at least one of its individual members is a multiforce member. A multiforce member is defined as one with three or more forces acting on it, or one with two or more forces and one or more couples acting on it. Frames are structures which are designed to support applied loads and are usually fixed in position.

Frames:

1. Support loads.

2. Usually stationary.

3. Fully constrained.

Not all forces are directed along the members as in a truss. In a member of truss, forces are directed along the member only. For example, in the following illustration, truss is subjected to compressive forces.

• Machines

Frames and machines are built-up structural and mechanical systems consisting of multiple parts assembled together in a number of possible ways. For example, the parts could be pin-connected or welded together. The primary difference between frames and machines is that there are moving parts in machines and not in frames. The method of analysis is the same. Although machines involve moving parts, we analyze the system at one instant in time when the positions of individual parts and the applied loads are clearly defined. The solution to these systems usually requires the drawing of the free-body diagrams of individual parts, and the application of the equilibrium equations.

When a frame or machine is broken up into multiple parts, the forces and/or moments present at the points of separation must be shown on the free-body diagrams of the separated parts in a manner consistent with the third law of Newton. That is the forces and moments are shown as equal and opposite on the two parts that have been separated.

Some important definitions

Load: This is the resistance to be overcome by the machine.

Effort : This is the force required to overcome the resistance to get the work done by the machine.

Mechanical advantage: This is the ratio of load lifted to effort applied. Thus, if W is the load and P is the corresponding effort, then

Mechanical Advantage =