#102 Forces are applied at points A and B of the solid cast-iron

Forces are applied at points A and B of the solid cast-iron - Mechanical Engineering 

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Free Chegg Question

Forces are applied at points A and B of the solid cast-iron bracket shown. Knowing that the bracket has a diameter of 0.8 in., determine the principal stresses and the maximum shearing stress at (a) point H, (b) point K.

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Free Chegg Answer

Draw the free-body diagram of the solid cast iron:

Forces Couples

Find the force in Z-direction from the diagram

Find the force in y-direction from the diagram

Find the moment in x-direction from the diagram

Find the moment in y-direction from the diagram

Find the moment in z-direction from the diagram

Find the radius of a bracket by using geometric properties of the section

Here, the diameter of the bracket is d
Find the area bracket by using the equation

Substitute  in the above equation

Find the moment of inertia by using the equation

Substitute  in the above equation

Find the polar moment of inertia by using the equation

Substitute  in the above equation

Determine the first moment Q by using the equation

Here, the centroid of the semicircle
Substitute  in the above equation

Substitute  in the above equation

Find the thickness by using the equation

Substitute  in the above equation

(a)
Find the bending stresses at point H by using the equation

Substitute  and in the above equation


Find the maximum shearing stress at point H by using the equation

Substitute  and  in the above equation


Find the average stress by using the equation

Substitute  in the above equation

Find the radius of the circle by using the equation

Substitute  and  in the above equation

Find the maximum principle stress by using the equation at point H

Substitute  and 

Therefore, the maximum principal stress at point H is 
Find the minimum principle stress by using the equation at point H

Substitute  and 

Therefore, the minimum principal stress at point H is 
Find the maximum shear stress at point H

Substitute in the above equation

Therefore, the maximum shear stress at point H is

(b)
Find the stress at point K by using the equation

Substitute  and  in the above equation

Find the shear stress at point K by using the equation

Substitute     and  in the above equation

Find the average stress by using the equation at point K

Substitute  in the above equation

Find the radius of the circle by using the equation at point K

Substitute  and  in the above equation

Find the maximum stress by using the equation at point K

Substitute  and  in the above equation

Therefore, the maximum principal stress at point K is 
Find the minimum stress by using the equation at point K

Substitute  and  in the above equation

Therefore, the minimum principal stress at point K is
Find the maximum shear stress by using the equation at point K

Substitute  and  in the above equation

Therefore, the maximum shear stress at point K is