Force on the top hinge of an open door

In summary: Thanks for the response, does anyone know how to calculate the shear force on a hinge when the weight is distributed on both hinges?The shear force on a hinge when the weight is distributed on both hinges is just W.Mg/H.
  • #1
LeeH
5
0
Please can one of you bright people help me, I am not very good at maths and would appreciate a line by line answer so I can copy it onto a spread sheet and use it in the future.

What I am trying to work out is what force will be excerted on a partition when a door is open at 90 degrees. If by calculating what the force on the top hinge is gives me this then that would be great, it doesn't have to be too accurate, just so I can get some rough idea of what the force will be.

Door leaf: 1.2M wide x 2.4M high = total 2.88M2
Weight: 20kg / M2, so 57.6kg in total

I have been trying to upload a photo of a typical door, but it keeps saing its too big so will try to add something after this first post.

Many thanks
 

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  • #2
How many hinges does the door have?

If more than two, then you have a statically indeterminate problem, which is much more difficult to solve. Then you would never be completely sure of the answer because of uncertainties in your input data.

If I were designing the door, I’d make a simplifying assumption that would be a bit conservative—but reasonable in the worst case not knowing how the hinges were installed and accounting for wear over time. I’d model the hinges as a pin connection on the top, and a sliding connection on the bottom. The vertical component of the load would be simply the weight of the door. To find the horizontal component, I’d sum the moments about the top pin and solve.

Then I’d be concerned about dynamic loads if someone slams the door or hangs something from it. So I’d put a safety factor of maybe three onto the result, and select hinges from a catalog of the next larger size.
 
  • #3
Thanks for the response, to try to keep this simple, if the hinge was a continuous one then what be the force at the top acting on the partition, it's just like a sign sticking out of the wall then.
 
  • #4
LeeH said:
if the hinge was a continuous one then what be the force at the top acting on the partition, it's just like a sign sticking out of the wall then.

Treating the hinge as uniform, straight and elastic, the door will hang at some small angle to the vertical. Let the tangent of this be T. The horizontal force per unit length at height X will be proportional to T.X. The moment of this about the bottom of the hinge is K.T.X2. The total moment integrates this to get K.T.H3/3, where H is the height of the door.
If the door has width 2W, weight Mg, we have:
W.Mg = K.T.H3/3.
K.T = 3W.Mg/H3
The horizontal force per unit length near the top of the door is K.T.H = 3W.Mg/H2
There will also be a vertical force to balance the weight of the door. This will be a shear force on the hinge.

It's rather simpler with just one hinge at the top and one at the bottom. The horizontal force at the top is then W.Mg/H. The vertical force is hard to determine because it will depend on the precise positioning of the fittings. If the screw holes are slightly too close together on the doorway, most of the load will be on the lower hinge. If too far apart then on the upper.
 
  • #5


The force on the top hinge of an open door can be calculated using the following formula:

Force (F) = Weight (W) x Distance from Hinge (d)

In this case, the weight of the door is 57.6kg and the distance from the top hinge to the center of the door is 1.2m (half of the door's width). Therefore, the force on the top hinge can be calculated as:

F = 57.6kg x 1.2m = 69.12 kgm/s²

This means that the force on the top hinge of the door is approximately 69.12 Newtons (N). Keep in mind that this is just an estimate and the actual force may vary depending on the weight distribution of the door.

To put this into perspective, the average force that a person can exert on an object is about 500N, so the force on the top hinge of the door is relatively small. However, it is still important to ensure that the hinges are strong enough to support this force to prevent any damage to the door or surrounding structures.

I hope this helps and please let me know if you need any further clarification. Good luck with your spreadsheet!
 

1. What is the force on the top hinge of an open door?

The force on the top hinge of an open door is the amount of pressure or weight exerted on the hinge due to the weight of the door and any additional external forces acting on it.

2. How is the force on the top hinge of an open door calculated?

The force on the top hinge of an open door can be calculated using the equation F = m x a, where F is the force, m is the mass of the door, and a is the acceleration due to gravity (9.8 m/s^2).

3. What factors affect the force on the top hinge of an open door?

The force on the top hinge of an open door can be affected by the weight and size of the door, the angle at which it is opened, and any external forces such as wind or pressure.

4. How can the force on the top hinge of an open door be reduced?

The force on the top hinge of an open door can be reduced by using lighter materials for the door, installing a doorstop to limit the angle at which the door can be opened, and ensuring proper maintenance of the hinges.

5. Can the force on the top hinge of an open door cause damage?

Yes, if the force on the top hinge of an open door exceeds its weight-bearing capacity, it can cause damage to the door, hinges, or surrounding structure. It is important to consider this force when designing and installing doors to prevent any potential damage.

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