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ME F211 - MF F211 - ES C 221Mechanics of Solids

Jitendra S Rathore, LecturerDepartment of Mechanical Engineering

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Fundamental principles of mechanics

Chapter - 1

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A 7 m long ladder rests against a vertical wall (with which it

makes an angle of 45o) and floor. If a man, whose weight is one

half of that of the ladder, climbs on it, at what distance (l) along

the ladder will he be, when the ladder is about to slip?

The coefficient of friction between the ladder & wall is 1/3, and

between the ladder & floor is 1/2.

Q1: Friction

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Q2 (Problem 1.37, Crandall)

A circular cylinder A rests on top of two half-cylinders B and C, all

having the same radius r. The weight of A is W and that of B and

C is ½W each. Assume that the coefficient of friction between the

flat surfaces of the half-cylinders and the horizontal table top is f.

Draw FBD of A, B & C.

Prove that distance d between the centers of the half-cylinders

to maintain equilibrium is d = 4 r sin(tan-12f).

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Space Trusses

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Plane Trusses

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Plane Trusses: Method of Joints

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Truss

Load carrying structure made of straight

members joined in form of one or more

triangles.

Transmits the load largely through axial forces

in its members, i.e. truss members are designed

to carry tension or compression.

Rigid/Stable truss: minimum 3 members

m = (2j - 3)

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Truss

Under-rigid/Unstable truss: m < (2j – 3)

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Truss

Over-rigid truss: contains more members than

required to be stable m > (2j – 3)

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assumptions

All real time trusses are statically

indeterminate.

Truss supportsA roller or some kind of slip joint is used at other

end.

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assumptions

Truss Joints:

In general, all

truss joints are

riveted or bolted

or welded.

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assumptions

All the members are straight and have

negligible weight in compare to the load applied

externally.

Load is applied only at the joints.

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Plane truss problem

If you don’t want the

members of the truss

to be subjected to an

axial load (T or C)

greater than 20 kN,

what is the largest

acceptable magnitude

of downward force F?

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Plane truss problem

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Special Conditions:

To identify zero force members.

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Method of sections