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A horizontal force of P = 56kN is applied to joint C. Each pin has a diameter of 25 mm and is subjected to double she...

A horizontal force of P = 56kN is applied to joint C. Each pin has a diameter of 25 mm and is subjected to double shear.


Determine the average shear stress developed in pin Aof the truss.

A horizontal force of P = 56kN is applied to joint

A horizontal force of P = 56kN is applied to joint C. Each pin has a diameter of 25 mm and is subjected to double shear. Determine the average shear stress developed in pin Aof the truss.

Solutions

Expert Solution

Concepts and reason

Newton’s third law:

Newton’s third law states that “For every action, there is an equal and opposite reaction”.

When two objects interact, the force magnitude on each body is equal and the force directions are opposite.

Equilibrium of a rigid body:

An object is said to be in equilibrium when the sum of external forces and couples are zero.

For a rigid body to be in equilibrium in three dimensions, the sum of external forces acting along , and directions have to zero.

For a rigid body to be in equilibrium in three dimensions, the sum of external couples about any point should be zero.

Shear force:

When force acting on a body pushes two parts of the body in opposite direction then the force is referred as shear force. Shear force on an object acts normal to its cross section.

Shear stress:

The stress developed as a result of shear force is referred as shear stress.

Fundamentals

Write the equilibrium of forces along the -axis.

Write the equilibrium of forces along the -axis.

Write the equilibrium of moments about pin joint A.

The formula to calculate the resultant force is as follows:

Here, the horizontal and vertical components of reaction force are and respectively.

The formula to calculate the cross section area :

Here, diameter of pin is d.

The formula to calculate the shear force acting on the pin that undergoes double shear is as follows:

Here, reaction force acting on the pin is .

The formula to calculate the shear stress is as follows:

Draw the free body diagram of the truss as shown in Figure (1).

Calculate the sum of forces along the x-axis.

Here, the force acting at point C is and the horizontal component of reaction force at point A is .

Substitute for .

Calculate the sum of moments about point A.

Here, the vertical component of reaction force at point B is .

Substitute for .

Calculate the sum of forces along the y-axis.

Here, the vertical component of reaction force at point A is .

Substitute for .

Calculate the resultant reaction force at point A .

Substitute for and for .

Calculate the shear force at point A .

Substitute for .

Calculate the cross section area of pin.

Substitute 25 mm for .

Calculate the shear stress at point A .

Substitute for and for .

Ans:

The average shear stress acting at pin A is .

Amanda K answered 2 years ago
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