I am building a stair from aluminium to go to my basement, the stair sides-plates are made from 10mm thick aluminium AWS 5454.

I am planning to tap M10 thread into this plate. To avoid the step slipping against the stair sides a tension of 715N is required. The bolt material is A2-70.

But will this aluminium thread be able to hold this load? How do you calculate this? • It's not usually recommended to use Stainless Steel Fasteners in direct contact with Aluminium, due to the risk of Galvanic Corrosion - you might be OK since it's indoors in a dry environment, but I would still take precautions to add a boundary layer between the two materials – Jonathan R Swift Nov 28 '18 at 10:00
• What Thread Depth/Engagement do you have? Is your step supported from both sides? Can you provide a diagram showing how the step will actually be loaded/supported? "I will need to load my bolt with 715N" is a bit vague for me... – Jonathan R Swift Nov 28 '18 at 10:10
• My step is supported on both side, I determinated a maximum step load, divided it by 4 bolts (no of bolts to hold the step) and used a friction coefficient of 0.75. this is the force required on the bolt to avoid shear. The thread depth is 10mm minus the small chamfer so lets say 9mm. – Mech_Engineer Nov 28 '18 at 10:14
• Don't divide it by 4 bolts. That would work only if the load is centered, so the most optimistic scenario. If the load is placed above one of the bolts it will carry almost the entire load. – SF. Nov 28 '18 at 10:25
• @Mech_Engineer: Your weight standing still, not taking a heavy step from some 5 inches above? Also, when I walk, I place my left leg left of center, right leg right of center. If there's an obstacle, say, some box on the step, I step to the other side. And when I lose my balance, I place my feet wherever they could help me prevent falling, and as hard as necessary to prevent me from falling. You do NOT calculate structure durability for the 'best case' scenario. You do it for worst case and add a safety margin on top of that! – SF. Nov 28 '18 at 10:36

As a first estimate, assuming the stair is straight and runners are equally spaced:

We assume each step is populated with one person going down and multiply the 200kg by 3 which is not too conservative a factor of safety, 600kg per step.

say we have a ratio of 18cm riser to 31cm runner of each step we get an angle of

$$\ alpha = arctan 18/31 = 30\ degree$$

We do a first attempt at designing the stringer as a uniformly loaded horizontal beam and then multiply the depth by cos(30) = 0.86

Assuming the horizontal projection of the length of the flight of stairs as L we have this moment,

$$M = \frac {1980\times l^2} {8} \ \$$ for a simply supported beam.

Assuming allowable tensile strength of alum 2000kg-cm^2

$$M = \sigma\times S \ and \ S= bh^2/6$$

$$M = 2000\times 1\times h^2/6$$

All you need is plug L , the length and you have the h of your aluminum beam.

Later you check with your local code and refine the loads, dynamic safety factor of potential several people running down the stairs scaping a fire, etc.

This is just to give a sense of rough idea, otherwise this member has to be checked for longitudinal forces like column, local buckling, torsion, etc.

• The question is about the holding power of a tapped 10mm Al plate. Can it hold M10 bolts torqued to give 715 N of tension? – Phil Sweet Apr 28 '19 at 13:52