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Being a fan of stackoverflow, I thought I could try this question here, hope its not too off topic.

I'm wanting to build a free standing climbing wall in my garden and dont know where to start working out its strength and so construction.

It will be made from interlocking (using bolts) 50cmx50cmx50cm mild steel cubes stacked 3m tall with a base of 1mx1m. The 4 base cubes will then be bolted to a concrete foundation.

If I then bolt other cubes to the side of the main stack to create an overhang how can I work out the stress put onto the joints between the overhang and the main stack and between the stack and the foundations?

The bolts between the cubes will be 3cm long and 2cm diameter.

I havent decided what fixings to use between the stack and concrete as I believe this is where the problem will lie.

Thanks for any help its much appreciated!

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"" 50cmx50cm mild steel cubes "" A 50 x 50 cm Cube is rather flat! –  Georg Jun 15 '11 at 13:03

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up vote 4 down vote accepted

Dave, to answer your question, we need to know the wall thickness and weight of each cube. BUT I can tell you that if you give any reasonable answer (like wall thickness = 1/8 of an inch = about 3.2mm), and choose steel bolts with right-sized steel washers, that it will be pretty hard to fail. Also, assuming your bolts are 60ksi tensile strength steel (which is not a very high quality bolt), they will hold about 29K pounds each (tensile strength). That is over 13 metric tons PER BOLT : Certainly not the weak link in your design.

the major sress-strain "weak point" for the interface between the overhanging cubes and the rest of the structure will be shear stress on the bolts converting into tearing forces in the cube wall (think of sticking a nail into aluminum foil, and then pulling it towards you, tearing the foil). If you used 2cm diameter bolts and 3.2mm thick steel wall in the cubes, each cube would be about 38.4 kg. (84.5 lbs.). If we assume 60ksi steel for the cubes as well as the bolts, each bolt would support about (0.099 inch^2)(60ksi) = 5950 lbs. = 26500N of shear before irreversibly deforming the hole. One bolt in each corner gives 4 x 5950 lbs. = about 24000 pounds. Enough to support well over 100 large men hanging off the wall.

For the other cube-to-cube interfaces, assuming the bolt holes are near the cube edges, the weak point will be tension in the bolt converting into a force which tends to pull the nut or bolt out of the cube, thereby ripping the cube wall (think of a nail inserted into foil, and then pulled through so that the head of the nail rips through the foil). Good choices for washers will greatly strengthen these weak points. Assuming you get the right washers (say, 25-30mm thick steel, ID = 2.1cm and OD = 4cm) and attach the cubes very near the corners, then the cube wall would be expected to support (2/3)(3.1416)(0.04m)(0.0032m)((39.36in/1m)^2)(60ksi) = 24920 lbs = 111kN PER BOLT. (The 2/3 is a fudge factor, since the steel opposite the bolt from the cube corner will not aid as much in resisting pull-through.) Four bolts --> about 100K lbs or 444kN. That is roughly the same force as needed to support 500 large men.

The metal to concrete connection does not need to be the weak point of your structure, but it does require a little thought for structural integrity over time (rust prevention). Chooing the right size, shape and material for the bolts and embedding them deeply enough into rebar-reinforced concrete during the pour will ensure that the mode of failure is NOT having the bolt rip out of the concrete. Certainly four 2-cm diameter bolts total, one at each of the four corners of the 1m x 1m structure, would do the trick.

The resistance of the structure to leaving the ground would be the weight of the structure, including the concrete. The resistance to tipping would be about (2)(111kN)(0.9m) = about 200kNm, or ((width of concrete foundation)/2)(weight of concrete + structure), whichever is less. It is almost guaranteed that the least of these will be governed by the weight of your concrete. You can greatly increase resistance to tipping (from, say, a hurricane or tornado) by digging post holes at the four corners of your foundation, widen them at the very bottom, and fill the holes with rebar-reinforced concrete as part of the monolithic pour of your foundation.

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