Hinge reactions from wind loading on gate

[gy122]

Homework Statement

Determine the forces at the 3 hinges of closed gate with a wind pressure of 700Pa on the gate.

Mass of gate = 236kg
wind pressure = 700Pa (apllied perpendicularly to the gate)
gate dimensions: 4.1m high, 2.45m wide
Distacnce from bottom of door to centre of hinges: h1=0.375m, h2=1.975, h3=3.375

Homework Equations

sumFx = 0, sumFy = 0, sumFz = 0, sumM = 0
F = PA

The Attempt at a Solution

I can calculate the hinge reactions due to weight but um unsure of how to account for the wind force acting on the door which I have approximated with a 7100N force acting through the centre of gravity.

Will there be a moment in both the y and z axis due to the wind? How would I calculate this?

 

[SteamKing]

Homework Statement

Determine the forces at the 3 hinges of closed gate with a wind pressure of 700Pa on the gate.

Mass of gate = 236kg
wind pressure = 700Pa (apllied perpendicularly to the gate)
gate dimensions: 4.1m high, 2.45m wide
Distacnce from bottom of door to centre of hinges: h1=0.375m, h2=1.975, h3=3.375

Homework Equations

sumFx = 0, sumFy = 0, sumFz = 0, sumM = 0
F = PA

The Attempt at a Solution

I can calculate the hinge reactions due to weight but um unsure of how to account for the wind force acting on the door which I have approximated with a 7100N force acting through the centre of gravity.

Will there be a moment in both the y and z axis due to the wind? How would I calculate this?

A sketch of the gate would be helpful, as would drawing a free body diagram of the situation.

 

[gy122]

how can I upload an image of the free body diagram

 

[gy122]

https://www.physicsforums.com/attachments/105037

 

[gy122]

https://www.physicsforums.com/attachments/105037

 

[gy122]

View attachment 105038

 

[Nidum]

You will have to make some assumption as to how the outboard end of the gate is fixed .

 

[gy122]

Yes it is assumed to be fixed ie closed and locked

 

[Nidum]

I doubt whether the person setting the question thought about this very much but the arrangement of the fixings on the outboard end of the gate has an effect on the distribution of loading on the gate hinges .

So what arrangement of fixings do we assume ?

 

[gy122]

The three hinges are dimensioned from the bottom of the door. The bottom hinge is 0.375m from the bottom of the door the middle hinge is 1.975m and the top hinge is 3.375m from the bottom of the door

 

[Nidum]

Pedantic possibly but these are the sort of questions I would ask if I was dealing with this problem in reality :

Do fixings carry any of the weight of the gate ?

Does arrangement of fixings allow or prevent gate twisting out of plane under wind load ?

 

[gy122]

Those dimensions are to the center of the hinge

 

[gy122]

Well the hinges are the only thing supporting the gate so yes they take the load. The hinges also resist any rotation, however as the hinges are not evenly or symmetrically spaced on the door there must be a rotational force in the system that is resisted by the hinges that i am not accounting for

 

[Nidum]

Ok . We'll have to pass on the finer details of the problem . Assume a simple latch at the half height of the gate .

What forces are acting on this latch ? Answer in words if this is easier for you pro tem .

 

[gy122]

There are no details on the latch so yes your assumptions are valid a simple latch. There will be a reaction force preventing rotation in the zy plane and act perpendicularly to the door. Is this correct

 

[Nidum]

I think that's the best we can do .

So now draw the free body diagram(s)for the gate . Easiest is to do two diagrams - one broadside on and one looking vertically downwards - but you can use a combination 3D version if you prefer .

 

[gy122]

Yeah I've just added it to my original and free body diagram. At which point would i cslculate the moment?

 

[SteamKing]

For the time being, ignoring how the gate is latched, having 3 hinges holding up the gate implies that you won't be able to calculate the forces in the hinges due to a wind load using only the equations of statics and equilibrium. You can write only 2 equations using statics, but you have three hinges with unknown forces to find.

IMO, this is analogous to analyzing a beam which is simply supported at two locations (and the beam is statically determinant) to find the reactions at the supports.

When a third simple support is added between the two original supports (making the beam statically indeterminant), the third reaction can be calculated only if an additional equation can be developed from the behavior of the beam under loading, to use with the equations of statics.

This is a deceptively simple-looking problem, but much lurks in the details of finding a solution.

 

[Tom.G]

Since no latch is specified, the gate will swing open in the wind. Then being parallel to the wind, there will be no wind pressure on it.

 

[Nidum]

@gy122 : Are you still with us ?