Shear Stress Problems: Calculating Lateral Movement

In summary, the problem involves a rectangular block of cheese being grated with a lateral force of 20 N. The shear modulus, G, of the cheese is 3.7 kPa and the thickness of the block is 3 cm. To calculate the lateral movement of the upper surface in relation to the lower surface, one can use the equation tan(shear strain) multiplied by the thickness of the block. However, for small strains, the difference between using sine and tangent is negligible.
  • #1
aeroengine123321
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Homework Statement


The bottom surface (8 cm x 12 cm) of a rectangular block of cheese (3 cm thick) is clamped in a cheese grater. The grating mechanism moving across the top surface of the cheese, applies a lateral force of 20 N. The shear modulus, G, of the cheese is 3.7 kPa. Assuming the grater applies the force uniformly to the upper surface, estimate the lateral movement of the upper surface with respect to lower surface?

Homework Equations


How would I calculate the lateral movement of the upper surface in relation to the lower surface?

The Attempt at a Solution

 
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  • #2
aeroengine123321 said:
How would I calculate the lateral movement of the upper surface in relation to the lower surface?
What standard equations can you quote regarding shear modulus, shear stress and shear strain?
 
  • #3
I've worked out the shear strain but I'm not sure how to get the lateral movement from there
 
  • #4
aeroengine123321 said:
I've worked out the shear strain but I'm not sure how to get the lateral movement from there
The shear strain is an angle, right? From there it is just geometry. You know the thickness of the block. Draw a diagram of it in its strained (parallelogram) shape.
 
  • #5
Right, so I can just do sin(shear strain) and then multiply it by the height of the block?
 
  • #6
aeroengine123321 said:
Right, so I can just do sin(shear strain) and then multiply it by the height of the block?
Yes.
 
  • #7
Thank you
 
  • #8
Would it not be tan(shear strain) then multiplied by the thickness? Because when I draw a diagram of it, the thickness (3cm) is the adjacent while the length I'm looking for is the opposite. Is this correct or am I going wrong with these geometries?
 
  • #9
aeroengine123321 said:
Would it not be tan(shear strain) then multiplied by the thickness? Because when I draw a diagram of it, the thickness (3cm) is the adjacent while the length I'm looking for is the opposite. Is this correct or am I going wrong with these geometries?
I'm sure these things are only valid for small strains anyway, so sine versus tan versus angle in radians makes no difference.
If you treat the block as constant volume then the height doesn't change, so tan would be right. If you treat it as a framework of rigid rods initially at right angles embedded in a compressible matrix then the rods have fixed length, so sine would be right.
 
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FAQ: Shear Stress Problems: Calculating Lateral Movement

1. What is shear stress and how does it cause lateral movement?

Shear stress is a type of force that acts parallel to a surface. In the context of lateral movement, shear stress can occur when there is a difference in forces acting on a structure, causing it to slide or tilt in a sideways direction.

2. How is shear stress calculated?

Shear stress can be calculated by dividing the force acting parallel to a surface by the surface area over which it acts. This is expressed as force per unit area, or in units of pressure such as Pascal or pounds per square inch.

3. What are some common causes of shear stress problems?

Shear stress problems can be caused by a variety of factors such as uneven loading, seismic activity, soil movement, or inadequate support or reinforcement of a structure. They can also be exacerbated by natural forces like wind or water.

4. How can shear stress problems be prevented?

To prevent shear stress problems, it is important to carefully consider the forces acting on a structure and ensure that it is designed and built to withstand them. This may involve using appropriate materials, reinforcement techniques, and accounting for potential sources of stress in the design process.

5. How are shear stress problems typically addressed?

If shear stress problems do occur, they can be addressed through various measures such as reinforcing the structure, redistributing the load, or implementing structural modifications. In some cases, it may also be necessary to monitor and regularly assess the structure for signs of ongoing stress.

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