Solving Shear Strain Problem: Find Vertical Displacement

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SUMMARY

The discussion focuses on calculating the vertical displacement of plate A due to shear strains in rubber pads when a vertical force of 5 N is applied. The rubber pads have cross-sectional dimensions of 30 mm by 20 mm, and the shear modulus (Gr) is 0.20 MPa. The solution involves using the equation d = 40(0.02083) = 0.833 mm, where 40 mm represents the horizontal length of the padding. The approximation of the tangent function is justified due to the small angle of 0.02083 Rad.

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Homework Statement


The support consists of three rigid plates, which
are connected together using two symmetrically placed
rubber pads. If a vertical force of 5 N is applied to plate
A, determine the approximate vertical displacement of
this plate due to shear strains in the rubber. Each pad
has cross-sectional dimensions of 30 mm and 20 mm.
Gr = 0.20 MPa.

Homework Equations



The Attempt at a Solution


http://www.academia.edu/6204124/Chapter_03
It is problem #3-33. I need help understanding the last part,
d =40(0.02083) =0.833 mm
Why do they use 40mm, the horizontal length of the padding. Also, where is this equation coming from?
 
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The last line is just trigonometry. Note that 0.02083 Rad is a very small angle so you can make a suitable approximation for Tan rather than use Tan itself.
 
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