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The test specimen AB is placed in the grip of a tension-testing machine and secured with a wedge. The coefficient of static friction at both surfaces of the specimen is µs. If the wedge angle is θ = 18◦, determine the smallest µs for which the grip is self-locking (no slipping takes place regardless of the magnitude of the force P). Neglect the weight of the wedge.

Question

The test specimen AB is placed in the grip of a tension-testing machine and secured with a wedge. The coefficient of static friction at both surfaces of the specimen is µs. If the wedge angle is θ = 18◦, determine the smallest µs for which the grip is self-locking (no slipping takes place regardless of the magnitude of the force P). Neglect the weight of the wedge.

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Step 1

Following is the given information

The coefficient of static friction at both surfaces of the specimen is µS .

The wedge angle is θ = 18◦.

To be found: The smallest coefficient of static friction ( µS ) at both surfaces of the specimen for which the grip is self-locking (no slipping takes place regardless of the magnitude of the force P).

ΟΟΟ
P
В
θ
Α
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ΟΟΟ P В θ Α

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Step 2

Neglecting the weight of the wedge.

The given wedge is a two-force member which implies that it has forces and no moments which act on the member at two positions. The net force acting on each position must be equal, opposite and collinear as shown in the diagram below.

And let the two forces be represented by R on both sides of the wedge.

R
A
R
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R A R

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Step 3

 The following condition should prevail

...

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