Does Fastener Member Stiffness Need to be Multiplied by 2 in Calculations?

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The discussion centers on the calculation of fastener member stiffness in mechanical design, specifically referencing Shigley's Mechanical Design book. It is established that when calculating the spring rate for components like a cylinder head and cylinder, the individual spring rates are multiplied by 2 before summation to obtain the total stiffness (Km). This multiplication accounts for the radial expansion and contraction of the components in two directions, as opposed to a single axial direction when fixed at one end.

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djdoug99
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I am going through Shigley's Mechanical Design book and have a quick question on fasteners. Sometimes when calculating the spring rate for a member, you have to multiply the rate by 2, why is this? For instance in this problem
http://imgur.com/2ug9AaR

When the spring rate is calculated for both the cylinder head and cylinder, both spring rates are multiplied by 2 and then added together to get the total Km. (This is not a homework problem)

Thanks.
 
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I'm not familiar with the precise context, but could it be because the objects can expand/contract radially in two directions (whereas if fixed at one end could only expand/contract axially in one)?
 

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