Bending moment and Shear stress limits on bolts 1

[helpee]

My problem is this: I have a flat plate and Object A (Object A: roughly 3 ft. x 2 ft. x 1ft. and 270 lbs.; flat plate: 1 ft. x 1 ft. x 1 in.). Obejct A is to be bolted to the flat plate so that it sits above the flat plate. Three bolts will be used in a configuration that fits within a 2 inch by 10 inch area (forming an isocoles triangle). However, I must leave about a 2.5-inch clearance in between the two components. Object A is now fixed in relation to the flat plate at a distance of about 2.5 inches, but the flat plate will be able to rotate freely about its X and Y axes. As the flat plate rotates, the connecting bolts will experience shear stress and a bending moment. I believe shear would be maximum at a 45 deg angle and the bending moment would max out at 90 deg. How can I fiugre out what bolts can withstand these loads? And I know there've been variations of the same type of problem previously posted, but I also would like to see or be directed to some calculations that could solve the problem. What is the material property of the bolts that determines the strength to withstand circumstances such as this? Thanks.

 

[CoryPad]

For a problem such as this, I recommend using fastened joint software. An excellent program is SR1, available at:

http://www.hexagon.de

 

[vonlueke]

helpee: I don't understand how object A is standing off of flat plate unless the isosceles right triangular plate is 2.5 inches thick. Also we don't know if the three bolts have nuts or are in tapped holes. Localized bending on the individual bolts themselves can probably be neglected if plates are thick (stiff), have adequate edge distances, and bolt pattern or plates have sizable footprint.

Distribute applied moment at bolt pattern centroid about x and y axes to convert to equivalent bolt tensile and compressive loads based on moment of inertia of bolt shank cross sectional areas about x and y axes w.r.t. bolt pattern centroid (conservative). Zero the bolt compressive loads, as these are plate contact.

Once individual bolt loads are obtained, you can check bolt equivalent combined tensile and shear stress for steel bolts as follows (conservative). This only checks fastener, not thread shear (stripping) stress if you have tapped holes. sigma_vm = {[max(U P_i + FS C P_t, FS P_t)/A_ts]^2 + 2.78(FS V/A_s)^2}^0.5, where U = torque uncertainty (1.25 to 1.30), FS = rupture or yield factor of safety for your project, C = bolt stiffness relative to joint total stiffness (0.35 for steel plates or 0.45 for aluminum plates is usually a conservative guess), A_ts = bolt tensile stress area, A_s = bolt transverse shear area = 0.25 pi D^2 if shear plane in solid shank, or equals A_ts if shear plane in threads, V = bolt applied shear force, P_t = bolt applied tensile force, P_i = bolt installation preload = T/(K D), T = bolt installation torque, K = torque coefficient (sometimes assumed 0.20 for dry installation or 0.15 for greased, for steel on steel), D = bolt shank nominal diameter. Once sigma_vm is obtained for each bolt, compute bolt stress level R = sigma_vm/S_t, where S_t = S_tu if FS was for rupture (the usual analysis), or S_t = S_ty if FS was for yield, S_tu = bolt material tensile ultimate strength, S_ty = bolt tensile yield strength. If bolt stress level R > 100%, the analysis indicates bolt is overstressed.

The reason no bolt material shear strength is listed above is because S_s = 0.60 S_t is built into 2.78 coefficient in above paragraph.

Bolt shear force should be maximum at 90 deg flat plate tilt if I understand your configuration.

 

[helpee]

vonlueke: This is all still a design problem I am working on so some of the names are not specific. However, There needs to be 2.5 inches of space between Object A and the flat plate because of different obstructions. So there will be spacers or hardened metal sleeves of some sort that the bolts will fit through. The bolts will be fitted into tapped holes. And it is the bolt pattern itself that forms the isocoles triangle. You'll have to give me a little time to digest the information you posted. Thanks for the effort, though.

 

[helpee]

vonleuke: and you are correct - the shear force will be max at 90 deg. my mistake.

 

[vonlueke]

I forgot to discuss P_t and V mentioned in my previous post, so I'll finish mentioning that first. Bolt applied tensile force P_t = max(0, P_z/n + P_m), and bolt applied shear force could perhaps be assumed V = [(V_x^2 + V_y^2)^0.5]/n, where P_z = bolt pattern uniform applied tensile load, V_x and V_y = bolt pattern shear loads, n = number of bolts in bolt pattern, and P_m = bolt tensile force component induced by joint applied moments described in second paragraph of my previous post. The above assumes there is no applied moment about the z axis and assumes all bolts have same cross-sectional area and material.

Now moving on to your second post, because you're using standoffs (spacers, sleeves), bending stress on the bolt threads is not at all negligible unless you use very wide, stiff spacers and a relatively high preload, and plenty of thread engagement length in tapped hole. You'll need to figure out the moment, tension, and shear at the base or head of each bolt. You can then figure out the bending stress component on the bolt threads and add a bending stress term sigma_b to the bolt combined stress equation mentioned in my previous post. Namely, sigma_vm = {[max(U P_i + FS C P_t, FS P_t)/A_ts + FS sigma_b]^2 + 2.78(FS V/A_s)^2}^0.5.

If feasible, consider using a solid steel or aluminum isosceles triangular plate, or rectangular plate, of sizable footprint instead of the standoffs if you want to reduce some of your analysis difficulty. It could even be hogged out in the center to reduce weight. Otherwise, size your standoffs large to try to reduce the bolt bending stress component. Good luck.