3
$\begingroup$

Triangle

If we imagine the load being placed at the top of the below triangle, I realise that the downwards force is transferred into one which goes in a 'south east' and 'south west' direction down to the end of the triangle.

What I am trying to understand however, is how we get the sideways movement from a straight down movement. Is this simply a product of the force needing to travel along a beam which can only transfer compression, therefore even though there is no 'input' sideways force, one comes from the downwards force only. Or is the sideways force created by the reaction force from the opposing 'leg' of the triangle?

Thank you!

$\endgroup$
0
5
$\begingroup$

The direction of Forces isn't necessarily along the connecting element. If that happens depends a lot on the constraints between the different elements. For example see the following image:

enter image description here

In the left column is a "welded" structure, while on the right column is a pin jointed structure (a basic truss) if you like.

On the top there are the shapes before deflection, while at the bottom are $\color{red}{\text{the shapes after deflection with red}}$ (superimposed on the original structure). (NOTE: on the no joints there is another case with the opposite curvature, but I left it for simplicity sake's).

AS you can see the behavior is totally different (at least initially). Eventually the jointed structure will also have a similar shape due to buckling. However, on the no-joint structure the curves will start to appear immediately.

structure with joints

I will focus on the structure with joints and why the forces indeed travel towards one direction. The direction of the force is parallel to the member.

enter image description here

If I take a member - let;s say no 1 - then the only way that this element will be in equilibrium of moments and forces is when the forces are in the direction of the beam.

enter image description here

IF there are any forces perpendicular to the element axis then there is no equilibrium of moments of forces. Try it for any combination of forces (any of the yellow, green, red, purple that don't sum up to zero).

enter image description here

As a result, the structure divides the force in a way that new forces are generated that cancel each other (horizontal forces on the top sides of 1 and 2. Those forces are such that the resultant force combined with the fraction of the vertical force that travels downwards is in the direction of the beam.

A word of caution about (Fluid) Pressure

One final note, is that pressure from fluids is not the same thing. Although there are a lot of similarities with fluid pressure and material stress (similar units, definition), pressure does not have a direction (its a state quantity/function). Pressure is always normal to a surface. Therefore, although the result is the same (diversion of the flow, diversion of forces), the mechanism that happens is different.

$\endgroup$
1
$\begingroup$

Strickly to say, this can only occur for fluid materials or airflow. For which you shouldn't have any problem in understanding how the diverging occurs.

Diagrams below show how the force flow in a hollow triangle (left), a rigid body (middle), and the random flow of the fluid force. Note there is no surface pressure/force in the first and second cases.

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.