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

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In calculating the spring rate for fasteners, it is sometimes necessary to multiply the rate by 2 to account for the behavior of the components under load. This adjustment is often made when both ends of a member can move, allowing for radial expansion or contraction in two directions. The total spring rate is then derived by adding the adjusted rates of each component, such as in the case of a cylinder head and cylinder. This method ensures a more accurate representation of the system's stiffness. Understanding this principle is crucial for precise mechanical design calculations.
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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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