ME 101: Engineering Mechanics

A. Narayana Reddy

Department of Mechanical Engineering,Indian Institute of Technology Guwahati,

Guwahati - 781039, India.

Sample free-body diagrams

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Sample free-body diagrams

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Complete the following free-body diagrams

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Complete the following free-body diagrams

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Complete the following free-body diagrams

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Complete the following free-body diagrams

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Draw the free-body diagrams

(a) (b)

(c) (d)

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Engineering structures

Engineering structures are made of several connectedmemebrs. The members are assumed to be rigid bodies inthis discussion.

There is force applied by one member on another and viceversa if the two members are interconnected.

Newtons third law states that forces of action andreaction between two connecting bodies must have samemagnitude, line of action, and opposite in direction.Engineering structures are classified into three categories.

Trusses - Contain all two-force members.Frames - Contain at least one multi-force member.Machines - Strcure contain moving parts and used fortransmit the motion and also to modify forces.

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Definition of a truss

A truss consists of straight members connected atjoints. No member is continuous through a joint.

Bolted, riveted, or welded connections areassumed to be pinned together. Force acting atthe member reduce to a single force and nocouple. Only two-force members are considered.

The forces are applied only at the joints.

When forces tend to pull the member apart, it isin tension. When the forces tend to compress themember, it is in compression.

Plane truss - Members lie in a single plane.

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Definition of a truss

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Applications of trusses

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Simple trusses

A rigid truss will not collapse under the application of a load.Basic element of plane truss is the triangle.The polygon formed by four or more bars is a nonrigid frame.Nonrigid frame can be made as a stable structure by adding extramemebrs.A simple truss is constructed by successively adding two members andone connection to the basic triangular truss.

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Analysis of Trusses

If the truss is in equilibrium then the forces are in balance at every point onthe truss and in particular at every joint.

Method of jointsSatisfying the equilibrium equations at every joint of truss.

If the truss is in equilibrium then every part or segment is also in equilibrium.

Method of sectionsThe equilibrium is used for the part of truss. This is useful for getting force ina member of interest without solving all joints.

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Method of joints

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Example

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Example

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Example

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Example

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Example

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Joints under special loading conditions

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Statically indeterminate truss

Statically indeterminate trussExternal redudancy

Internal redundancy

External redundancy:

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Internal redundancy

Internal redundancyThe members in a truss is more than that are required to maintain theequilibrium. This is also known as degree of internal indeterminacy.

Let n be number of joints in a given truss.Let m be number of members in a given truss.

Therefore, we can form 2n equations as force is balanced at every joint alongx and y direction. On the other hand, we have m+ 3 unknowns as axial forcein m members along with three reaction forces.Thus, the necessary condition for internal static determinacy is given by

m+ 3 = 2n.

The Maxwells rule:m+ 3 = 2n. statically determinate internallym+ 3 > 2n. statically indeterminate internallym+ 3 < 2n. unstable

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Internal redundancy

The criterion m+ 3 = 2n is necessary condition but not sufficient condition.In other words, if the truss is statically determinate internally then that mustsatisfy the criterion m+ 3 = 2n. But all the structures that satisfy thecondition m+ 3 = 2n is not necessarily statically determinate internally.

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Necessity of redundancy

Why to provide redundant members?

To maintain allignment of two members during construction.

To increase stability during construction.

To prevent buckling of compressive members.

To provide support if the direction of loding is changed.

Redundant members can act as backup members if some members arefailed during loading.

Analysis of truss with redundant members is difficult but possible.

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Example

Determine the force in members FH, GH and GI.

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Method of sections

CautionThe section of truss must be consider such that there are only three unknownforce members are on the section as we have three equilibrium equations.

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Example

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Example

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Example

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Example

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Example

Calculate the forces induced in members KL, CL, and CB by the 200 kN load on cantilever truss.

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Space trusses

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Space trusses

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Example

Determine the forces acting in members of the space trussSolution:At joint A:

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Example

At joint B:

At joint C and D:

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