Wow hard to believe people having mechanical issues when torquing ring cap screws to 15 in-lbs! Seekins recommends 20 in-lbs for their scope cap screws and I never had any issues with a few different scopes. Now I am using ARC rings that are torqued to 55 in-lbs (but just 1 screw per ring).
We can determine the clamping force of a single ring on the scope tube by summing the tension in each of the screws that holds the ring cap against the scope tube. Let's use the Seekins recommended 20 in-lbs of torque and assume 4 screws per cap. Let's assume the use of some Molykote P-37 thread lubricant so the coefficient of friction of the screw threads can be approximated as 0.15. I believe the ring cap screws are #8-32 which have a nominal diameter of 0.164".
The general relation between torque and tension is given as Torque (T, in-lbf) = Tension (F, lbf) * Screw Dia (d, in) * Thread Coeff. (K, unitless).
To solve for the tension in each screw, the equation is re-written: F = T / (d * K)
Plugging in the variables, and solving for F -----> F = 813 lbf
Therefor with 4 screws, the total clamping force of a single scope ring cap on the tube body is approximately 4 * 813 lbf = 3252 lbf
This seems like a lot, but when we are talking about single piece scope tubes that I believe are usually constructed of 7075-T6 aluminum, it really isn't much at all.
We can now apply this clamping load over the "clamping area" of the scope ring to determine the stress it exerts on the scope body. I will make some more assumptions here to make the math easier. I will assume a ring width or thickness of 1" and I will assume the top and bottom halves of the rings perfectly make contact with the entire circumference of a 34mm scope body.
The area is determined by calculated the surface area of a 34mm diameter cylinder with a length of 1". The radius (r) is equal to 17mm or .67 in, and the length (h) is 1"
Area = 2 * pi * r * h = 4.2 in^2
The stress felt by the scope body is just the total clamping force divided by the area, or 3252 lbf / 4.2 in^2 = 774 psi
Obviously some assumptions were made to make this calculation simple, but you can see that by tightening 4 screws on a ring clamp to 20 in-lbs, the scope body will see somewhere on the order of ~775 psi, which is almost nothing given its construction.
Per the link below, 7075-T6 aluminum has an ultimate tensile strength of over 80,000 psi and a yield strength over 70,000 psi. Also note that these values are for tensile stress, and the stress that I calculated here is more of a compressive (or bearing) stress, which typical materials like this tend to handle better.
http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=ma7075t6 Obviously if you have some junk-ass rings and they are "point-loading" your scope tube, the stress experienced by the tube could spike significantly, but even if the actual stress exerted on the scope tube is double or triple what I have calculated, it is still next to nothing for a quality scope tube. Hope this helps shed some light on scope cap torque vs tension and how it applies to a scope tube.
