# Additional jacking force to overcome stiction/dry friction

It is common to lift bridges to replace bearings, etc.

In an ideal world the lifting capacity required of the jacks would be the self-weight of the bridge divided by the number of jacks (+ allowances for wind/snow, etc.).

From my (limited) experience, however, bridges begin to 'stick' to their bearings, and an additional allowance for over-coming this has to be provided.

Does anyone have any guidance about how to determine this figure?

• I think the "stick" you are referring to is commonly called stiction or dry friction. Searching some references for these terms might help with your specific problem? – welf Jan 21 '15 at 11:22

So there's an incorrect assumption underlying your question.

In an ideal world the lifting capacity required of the jacks would be the self-weight of the bridge divided by the number of jacks (+ allowances for wind/snow, etc.).

And the assumption there is that the lifting capacity is equivalent only to the weight of the bridge. The problem is that if anything goes wrong, you're likely to see a catastrophic failure of some sort which could lead to irreparable damage.

Real world lifts don't operate in that "ideal" manner, and instead rely upon a safety factor in order to make sure that the lifted weight is well within the limitations of the equipment. And in some cases, the safe working limit (SWL) may be derated further from the working lift limit (WLL) if there are any extenuating circumstances such as worn equipment or hazardous weather.

So the ideal lift capacity is one that is significantly larger than load to be lifted. The actual lift capacity used is tempered by the fact that you generally pay for that lift capacity whether you need it or not.

According to the Wikipedia article on safety factors, a factor of 2 is common with building materials and 3 is common for automobiles. You need to weigh the risk to human health or safety within the lift you're considering and use an appropriate safety factor. A conservative approach would be to use a higher safety factor of 3, so you need at least 3 times the bridge weight for the lifting capacity.

Assuming you're staying within the SWL and WLL of the lift equipment you're using, that still doesn't necessarily account for the binding forces caused by corrosion between the bridge and the bearings supporting it. Static friction can also come into play if the bridge itself has to be slid out of the supporting structure.

Unfortunately, it's hard to determine what that binding force is going to add up to without a lot more detail. At a minimum, you would need to know the materials involved and the cross sectional area of contact between them. You would also want to approximate how long they've been exposed to the elements and what sort of conditions the elements have brought - such as salt water exposure vs mountain air.
This is where I'm going to wave my hands in an airy fashion and not attempt to swag the binding force created by corrosion.

Static frictional force can be guessed at a little more easily than the corrosion binding. $\mu_{static}$ ranges from 0.6 to 0.8 for various materials in contact with steel. And while the general formula for calculating the Force from friction is $F_{static} = \mu_{static} * F_{normal}$, that equation also assumes horizontal movement. As you're likely lifting vertically, not sliding horizontally, the static frictional forces will be less since the equivalent $F_{normal}$ for vertical motion will be less.

Based upon that, I'd use a conservative guess of $\frac 23$ or $\frac 34$ of the weight of the bridge to estimate the static friction forces involved in the lift. Experience and the particulars of the lift will guide you in adjusting that guess up or down.

So depending upon your safety factor, it could very well be that the SWL of the equipment will provide sufficient lift to overcome any static friction or binding caused by corrosion. Or it could be that you need to increase the lift capacity requirements to overcome that effect. And it's worth pointing out that equipment can exceed those limits, so a lower safety factor may be "good enough" to get past the effects of static friction at the start of the lift.