Find all the angles and lengths of the truss members using the Law of Cosines.© BrainMass Inc. brainmass.com September 21, 2018, 12:34 am ad1c9bdddf - https://brainmass.com/engineering/structural-engineering/analyze-truss-for-member-lengths-and-angles-in-frame-133362
When two (2) letters are together without any spaces or symbols it is referring to the distance between the two points labeled by the letters. When there are three (3) letters together without any spaces or symbols between them it is referring to the smallest angle that is between the two lines formed by the first two letters and the last two letters. For example, AB is the length of the line connecting points A and B. ABC is the smallest angle between the lines AB and BC.
To use the Law of Cosines, it is most useful to use this law in both forms.
The approach is to find all the lengths so that the Law of Cosines can be used almost exclusively.
1. Look at triangle AoF:
Know already: oF, AC, CE, Eo, oG, pI, qK, Mr, op, pq, qM, MN, Kr, IK, GI
Ao = 1.8 + 1.8 + 0.6
By the Pythagorean theorem, AF = sqrt( (2.1m)^2 + (x1)^2), where x1 = 1.8 + 1.8 + ...
By starting at one point in the truss, or frame, one can find the angles among the truss members by first finding the lengths of each truss member and then using the Law of Cosines.