Help solving garden gate statics problem

[ckerr83]

TL;DR Summary

how to calculate the force required to counteract the sag in a garden gate due to deformation of joints etc.

I am installing a garden gate at the back of my house.

The length (L) of the gate is 1.7m and the mass is 62.6kg, there are 2 hinges positioned 1.3m apart.

The gate has an inherent sag, such that, the bottom corner on the unhinged side is 5cm lower than the corner on the hinged side.

What upward force(to be provided by a spring loaded wheel) is required at the unhinged side to ensure the gate is horizontal?

 

[Baluncore]

Welcome to PF.
The simple answer is 62.6 / 2 = 31.3 kg.
That assumes the weight is carried equally on both sides of the gate.
But the compressive diagonal on the gate is there to transfer that force to the hinge post.
Is the hinge post leaning, or is the gate sagging due to poor joints?
Poor joints will fail sooner with a wheel under the gate as it will encourage vibration when the gate is moved.

 

[ckerr83]

the post is not leaning, we can assume this is vertical, the sag will be due to joint strength etc.

Would the weight be carried equally on both sides? I was thinking that since the hinged side is fixed, this would then become a question of torque and the resultant vertical component?

 

[Lnewqban]

I would remove the deformation of the gate by installing a wire-rope with a turnbuckle, running it between anywhere close to the point of anchoring to the top hinge and the opposite bottom corner of the gate.

You will basically have a triangle shape which weight will be pulling from the top hinge (anchorage to gate and post needs to be robust) and pushing against the bottom one.

The main problem with wheels are a non-flat=level surface along its trajectory, as well as a twisting effect on the gate each time it is pushed by hand to open or close.

If you still install the wheel, you could loose the anchors of the bottom hinge some and see by the formed gap how much height you can use for wheel with spring before it starts overstressing the bottom hinge (pulling it out from the post).

 

[Rive]

As @Lnewqban already pointed out, the problem is the misplaced diagonal brace of the gate. This way that brace has compression and it will easily deform together with the gate. It's better to have tension/strain. Preferably with adjustable length. The wire rope (or a thin metal bar) across the other diagonal is actually a very good idea. You can add a turnbuckle strainer.

 

[256bits]

There also could be some slack in the hinges which should be checked.
The bottom hinge will push in, and the top will stretch out.

First, check if the gate is square by measuring both diagonals. If these are equal then its not a problem with the gate per se.
Then see how much wiggle there is in the hinges by just lifting up the far end.
If that is the cause of the problem, then perhaps a shim added to the bottom hinge to extend it out, and subsequently raise the far end. That could solve the whole problem.

We had a wheel gate, 20 feet or so in length, and it was no problem opening or closing, except for the annoying twisting that was mentioned. With time, gates do tend to sag.

 

[AZFIREBALL]

Place a car jack (or blocks) under the sagging end to make it just above level.
Then run a heavy-gauge double strand, twisted wire from the upper hinge location diagonally across the gate down to the bottom of the drooping end. Fasten very tightly and securely. This should hold it up.

 

[anorlunda]

Often, a picture is worth a thousand words.

 

[berkeman]

Place a car jack (or blocks) under the sagging end to make it just above level.
Then run a heavy-gauge double strand, twisted wire from the upper hinge location diagonally across the gate down to the bottom of the drooping end. Fasten very tightly and securely. This should hold it up.

Often, a picture is worth a thousand words.

Yes! I was just about to suggest adding a turnbuckle to the suggestion by @AZFIREBALL

 

[anorlunda]

One more tip for DIY. This video shows a simple way to eye splice wire rope, that is much better than clamps. On thin wire ropes, it's easy.