Bolt Tension Brain Teaser!
Bolt Tension Brain Teaser!
(OP)
This is a hypothetical question which my colleagues and I have been discussing all afternoon - please help!
A bracket is fixed to the underside of a steel beam with a nut and bolt. The bolt is torqued up to provide a tension in the bolt of 10 Tonnes. An additional weight of 5 tonnes is then suspended from the bracket.
Question: What is the tension in the bolt?
A bracket is fixed to the underside of a steel beam with a nut and bolt. The bolt is torqued up to provide a tension in the bolt of 10 Tonnes. An additional weight of 5 tonnes is then suspended from the bracket.
Question: What is the tension in the bolt?





RE: Bolt Tension Brain Teaser!
RE: Bolt Tension Brain Teaser!
Check out the site above. I have found its information usefull.
RE: Bolt Tension Brain Teaser!
Pretty straight forward, unless you're mis-stating the scenario.
RE: Bolt Tension Brain Teaser!
Where:
Fb = Force on bolt
Fi = Preload on bolt
Kb = Spring Constant for bolt
Fa = Applied Force on bolt
Kp = Spring Constant for clamped parts
RE: Bolt Tension Brain Teaser!
RE: Bolt Tension Brain Teaser!
RE: Bolt Tension Brain Teaser!
RE: Bolt Tension Brain Teaser!
For starters, a tonne (as opposed to the various tons) is a unit of mass. You cannot have a tension force or a weight of 10_tonnes or 5_tonnes or 3.14159265897_tonnes. The SI unit for force is the Newton.
If you clamp an infinitely rigid bracket with a force of 100kN (g=10m/s2approx), you generate a contact force between the bracket and the steel beam of 100kN.
If you hang a 50kN weight from the bracket, you subtract 50kN from the contact force. The bolt tension is not affected, unless the weight exceeds the original bolt tension.
Remember Hooke's Law. If your model does not change the strain on the bolt, it does not change the stress.
RE: Bolt Tension Brain Teaser!
Israelkk has the best explanation. It is because of the elasticity of the beam and bracket sandwiched between the nut face and bolt head. The bracket and beam are not infinitely stiff. If they were infinitely stiff, then additional load would be added directly to the preload, where 5T on top of 10T would be 15T. However, since as israelkk stated, you are dealing with a system that is NOT theoretical, it is real-world where the clamped members are elastic and about 5 - 10 times stiffer than the bolt, you have to consider that as you add a load to the bracket, and the bolt is elongating a small amount, the very stiff clamped members are losing their preload until there is a gap between the two. At the point where there is a gap between the two sandwiched members, they are no longer applying the 10T load that was found in the preload. So when you put a few percent over 10T on the bolt, the clamped members are no longer able to apply any load, so the bolt is only experiencing a bit over 10T.
And drawoh is correct about the units.
Engineering is not the science behind building. It is the science behind not building.
RE: Bolt Tension Brain Teaser!
RE: Bolt Tension Brain Teaser!
But I think that we all agree that in the real world, it still wouldn't be simply additive.
Engineering is not the science behind building. It is the science behind not building.
RE: Bolt Tension Brain Teaser!
Thanks for the formula GregTirevold, that will be useful in solving the actual problem that started our debate!
Tmoose - no we weren't considering any leverage, just a simple case where the load is suspended directly below the bolt.
Thanks again,
Tom
RE: Bolt Tension Brain Teaser!
Something I think that is worth considering is that for a full metallic joint of generous proportions the fastener stiffness is relatively quite low, so the variation in fastener load up to the point preload is overcome is a pretty small. Hence even Holokrome has made statements like this -
"Suppose a joint has been tightened to a preload Pi and additional load, Pe, tending to separate the members is applied. In general in rigid assemblies, as long as the external load is less then Pt it primarily decompresses the joint and has little effect on the tension in the screw.
Thus even if such a load is repeatedly applied, the fastener will not fail in fatigue."
Being able to ignore fatigue reduces having to calculate, test and worry about sundries like rounded thread root profiles, proof load vs yield strength, bolt thread engagement and stripping, and exotic materials, and instead waste time on the internet instead.
Dan T
RE: Bolt Tension Brain Teaser!
Here is a good summary of the phenomena:
http://
RE: Bolt Tension Brain Teaser!
If the stiffness of the plate is k1 and the stiffness of the bolt is k2, then any external force separating the bolt would cause an equal increment on the plate separation as well as the bolt. So
If the external force is F, then
F/k1=delta bolt tension/k2
and
delta bolt tension=F*k2/k1
valid as long as the plate remains under compression
confirming Isaelkk
RE: Bolt Tension Brain Teaser!
Put an elastic band around a ruler lengthways. The elastic band is the nut and bolt, the beam/bracket is the ruler. When adding an initial load to the elastic band at the end of the ruler, the length and therefore the tension the elastic band does not change until the initial preload is exceeded.
But from the discussion above, we have realised that the tension in the elastic band is actually changing with the added load, although it is much too small to see, and it is essentially the case of an infinitely stiff beam/bracket.
RE: Bolt Tension Brain Teaser!
The answer should be
x=increment tension=K2*F/(K1+K2)
The reasoning is
if you call the decrease in plate force against bolt head, y
and the increase in tension x for an external force F
you get 2 equations
x=y=F
y/k1=x/k2
solution:
x=k2*F/(k1+k2)
k1 plate stiffness
k2 bolt stiffness
Tomosmith,
Your colleague demonstrated for
k1>>k2
x goes toward 0
RE: Bolt Tension Brain Teaser!
eq should read
x+y=F
y/k1=x/k2
RE: Bolt Tension Brain Teaser!