Total moment of shear stress about the center line of a cylinder

In summary, the total moment of shear stress about the center line of a cylinder is the sum of all the moments of shear stress acting on the cylinder. It can be calculated by multiplying the shear stress at a particular point on the cylinder by the area of that point and integrating over the entire surface. The magnitude and direction of shear stress, as well as the shape and size of the cylinder, affect the total moment of shear stress. This value is important in cylinder design as it impacts structural integrity and stability. To reduce the total moment of shear stress, engineers can use stronger and stiffer materials, increase cylinder thickness, or change the shape to distribute stress more evenly. Proper design and maintenance can also help minimize the total moment of shear stress.
  • #1
eterna
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http://postimg.org/image/onxjqc26l/

I have found the shear stress of the inner cylinder to be 405 Pa like in the solution
but I am having trouble visualizing the total moment of this stress about the center line.
I was wondering if someone could explain where that d(theta) in the moment expression comes from, possibly with a diagramthanks
 
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  • #2
The d(theta) comes in because you have to integrate around the circumference of the cylinder. The force on a differential area of the cylinder is ##dF=\tau (L r_id\theta)##.
 

Related to Total moment of shear stress about the center line of a cylinder

What is the total moment of shear stress about the center line of a cylinder?

The total moment of shear stress about the center line of a cylinder is the sum of all the moments of shear stress acting on the cylinder. It is a measure of the rotational force or torque experienced by the cylinder due to shear stress.

How is the total moment of shear stress calculated for a cylinder?

The total moment of shear stress can be calculated by multiplying the shear stress at a particular point on the cylinder by the area of that point, and then integrating over the entire surface of the cylinder. This gives the total torque acting on the cylinder due to shear stress.

What factors affect the total moment of shear stress about the center line of a cylinder?

The total moment of shear stress is affected by the magnitude and direction of the shear stress, as well as the shape and size of the cylinder. It also depends on the material properties of the cylinder, such as its elasticity and strength.

What is the significance of the total moment of shear stress in cylinder design?

The total moment of shear stress is an important factor in the design of cylinders, as it affects the structural integrity and stability of the cylinder. Engineers use this value to determine the appropriate material and dimensions for a cylinder to ensure it can withstand the forces acting on it.

How can the total moment of shear stress be reduced in a cylinder?

The total moment of shear stress can be reduced by using materials with higher strength and stiffness, increasing the thickness of the cylinder, or changing the shape of the cylinder to distribute the stress more evenly. Proper design and maintenance can also help reduce the total moment of shear stress on a cylinder.

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