# Forces at freely-jointed and freely-hinged

1. May 16, 2014

### 124anne

Could someone please explain to me what it means (in terms of forces acting) 'freely jointed' and 'freely hinged'? Or is it the same thing? I'm really confused, I have my mechanics exam coming up soon ( A levels mechanics) and not sure how to deal with these questions. I understand that if there's a hinge, there are also two reactions (at 90 degrees to each other) but what happens when two beams are 'freely jointed' to each other? e.g a horizontal beam (made from part A and art B) is hinged to the wall and is in equilibrium. Part B of the beam is freely jointed at the end of part A. so what does this mean in terms of forces acting at this point?? would be very grateful for any response and explanation :)

2. May 16, 2014

### bhillyard

Freely jointed means there will be no friction at the joint so the only forces acting would be the normal reaction at the wall and the turning effect of the weight of the beam and any forces at the other end.
The hinge means the wall end can neither move up nor down the wall. Freely hinged and freely jointed are effectively the same thing - jointed when the joint itself could move (i.e. attached to another beam that could move), hinged when attached to something that cannot itself move (the wall).

3. May 16, 2014

### 124anne

thank you so much!!! :) it makes much more sense now :)

4. May 16, 2014

### abitslow

Seems to me that another meaning is that a joint is not (necessarily) restricted to motions in 2D, while a hinge is.
Not sure why anyone would belabor the point about what "free" means. I think bh make a generally correct assertion that usually hinges are connected to stationary structures. A hinge is one type of join.
Joints and hinges are both bearings. I would add that DEPENDING ON CONTEXT a joint might be rigid (non-moving) or compound (consisting of more than two bearing surfaces), while the only question about a hinge's movement is the range of angle allowed. I really don't know the sophistication of A level students, could it be that shear forces, lateral forces, transverse forces aren't part of your vocabulary? That is, a hinge allows motion in a plane while a joint allows motion in some part of a spherical space. If the problem is restricted to 2D, then they are equivalent...I guess you'd assume that the hinge only allows motion in that plane. I don't understand your comment about 90°, at all. You SEEM to be implying that the components of a force are the force...The components of a force are CHOSEN to aid in analysis and computation. In some problems we may choose an orthonormal basis, while for others polar or spherical coordinates vastly simplify the solution. The components of a force depend on the bases (frame of reference, aka coordinates), while the force does NOT. As long as a bases (basis vectors) spans the space of vectors it is a valid choice. 90° doesn't necessarily have anything to do with it.
I should add that there is often a "natural" choice for coordinate system. For instance, for structures that are small relative to the radius of the body they are built on (say a building on Earth) it is natural to think that the best coordinates for a horizontal beam are Euclidean, but if you consider such a beam having a length of 2000 km, a moment's thought might suggest that polar coordinates will probably be much better. Same type of consideration must be made for height - is there any significant difference between the mass of 1kg 3 km below sea level compared to at the top of the Burj Khalifa?

Last edited: May 16, 2014
5. May 16, 2014

### bhillyard

As a retired teacher of 'A' level applied maths (this is a UK qualification, usually age 17-18, on the basis of which University places are determined), the problems involving hinges/free joints would be 2D only.