Monday, December 3, 2007

Shear Stress of Bolts

Shear Stress of Bolts

Big Bertha's rebuild will be mounted on what is called a dovetail plate, which slides into the saddle of the Losmandy mount. There are then two large screws (on the CI-700 mount) that tighten down against the dovetail plate, preventing motion.

How does the dovetail plate attach to the telescope? Usually, this is done with some screws that go up through the bottom of the dovetail plate, and screw into the telescope tube, or a ring that holds the telescope tube. For Big Bertha 2.0, this is going to be screwed into a tapped hole in the square aluminum tubing that holds the components in place.

But these are typically 1/4"-20 screws that hold telescopes to the dovetail. Will that be strong enough? I have become intoxicated with the power of computing this stuff, like a mechanical engineer would do, and so I decided to try and compute it.

The definition of shear stress is the force per unit area that will cause a material to fail and that "act over an area which is in line with the forces." To compute the force that will cause a bolt or screw to fail, you compute its area, and then compare the force applied across that screw to the shear strength.

For a 1/4" bolt, that's roughly (.00635^2) square meters. The shear strength of stainless steel is approximately 186 MPa (megapascals). This means that to shear a stainless steel bolt of that size would require about 7500 Newtons. (A Newton is one kilogram accelerating at 1 m/sec^2. Use 9.8 m/sec^2 as the force of gravity to compute the force on this planet.) For weight alone to shear the bolt would therefore require a bit more than 765 kilograms (or about 1684 pounds).

There are two bolts that will hold Big Bertha 2.0 to the dovetail plate, and from what I have read, the stress is divided by the number of bolts (although I can see how in some positions, one bolt might get all the load).

Big Bertha 2.0 is only going to weigh about 60 pounds. I think I'm safe using two 1/4"-20 bolts!

UPDATE: A reader whose signature line indicates that he is a mechanical engineer working on commercial jetliner landing struts points out that:

1. A fully thread bolt's shear cross section is a smaller than the nominal diameter. I presume that this is because the minor diameter of the thread (the bottom of the threads) is a good bit smaller than the major diameter of the thread (which is about the nominal diameter).

2. He thought the numbers above for the shear strength of stainless bolts was a bit low--although he also pointed out that most of the bolts that you actually buy at a hardware store are less than perfect chunks of steel.

3. Apparently it is considered good rule of thumb to assume that only half the bolts holding an assembly in place actually are carrying the load. This is not surprising; as I pointed out above, depending on position and angle, the load may be disproportionately on one bolt, instead of evenly distributed.

He still thinks that two 1/4"-20 bolts will more than do the job.

UPDATE 2: Another reader points to these two pages for finding strength of various bolts, one of which shows strengths for various grades of bolts, and the other shows minor diameter of various threads, and area. The weakest grade of bolt (ASTM A320 Grade 8) in 1/4"-20 shows a yield strength of 954 pounds. It might be tempting when the time comes to buy two of the higher grades of bolts, which will take the yield strength in that size up into the 2000 pound range.

UPDATE 3: The shear strength of bolts is typically about 55% of the yield strength.

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