3D Physics - Frameworks

Concurrent, Coplanar Forces

Concurrent, coplanar forces are forces which act through one point and are in one plane.

Triangle Of Forces

For three co-planar forces to be in equilibrium they must be concurrent. A triangle of forces can then represent the forces in magnitude and direction.

framework jib crane

Jib Crane

triangle of forces for a crane

Triangle of Forces

Polygon Of Forces

If more than three forces act on a body they may be represented in magnitude and direction by the sides of a polygon:

forces at a joint

Forces at a joint

polygon of forces

Polygon of forces

If a closed polygon results, then the forces are in equilibrium. If an open polygon results, then aa' is the resultant (opposes flow of arrows) aa' is known as the equilibrant (follows flow of arrows).

Resolution of Forces

Any single force can be replaced by two others at right angles to each other, known as horizontal and vertical components.

forces on joint

resolution of forces

Example

force resolution example

The following forces act at a point:

Determine the magnitude and direction of the resultant of these forces when they are pulling away from the point

a) by drawing the polygon of forces
b) by resolving the forces

Frameworks

For frameworks we can combine the polygon of forces for each joint in the framework to give a combined force diagram.

For each instance of a framework we can draw two complimentary diagrams:

In the space diagram we can denote struts and ties as follows:

strut and tie

The two diagrams are complementary, the lines in the space diagram correspond to the points in the force diagram and the points in the space diagram correspond to the lines in the force diagram. The lines (struts or ties) in the space diagram are marked by upper case letters, there are corresponding lower case letters shown for the points in the force diagram.

Example

space diagram

Space Diagram

force diagram

Force Diagram

The forces are:

Member Force (N) Nature
AF 9000 tie
BF 10000 strut
FG 4000 strut
CG   strut
GH   tie
DH   strut
HJ   strut
JA   tie
EJ 10000 strut

metadata block
see also:
Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

 

cover 3d Games: Physics -

 

cover Casio WV-300DE-7AER Tough Solar Wave Ceptor Watch.

Commercial Software Shop

Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them.

 

cover Dark Basic Professional Edition - It is better to get this professional edition

cover This is a version of basic designed for building games, for example to rotate a cube you might do the following:
make object cube 1,100
for x=1 to 360
rotate object 1,x,x,0
next x

cover Game Programming with Darkbasic - book for above software

This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2017 Martin John Baker - All rights reserved - privacy policy.