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Truss problem : Timoshenko

Truss problem : Timoshenko

(OP)
Hello everyone,
i am new to the forum and this is my first message, please go easy on me if i break any rules/make mistakes

i recently started reading Strength of Material by Timoshenko and in the first chapter encountered a problem in one of the solved examples (attached screenshot)

The problem is of a truss with point load,
i dont understand the second figure(b) particularly how it was calculated, i tried using method of joints, but i am getting different results.

RE: Truss problem : Timoshenko

Figure (b) is calculated using triangle law of forces where three force (vectors) acting at a point are represented by triangle sides.

RE: Truss problem : Timoshenko

(OP)
@NRP99 Thanks for replying to my post

if you mean the trignometric approach and i think you do, then i know it
i just dont understand how 18000 and 9000 came to be why not 27000 how come it got assigned like that

RE: Truss problem : Timoshenko

(OP)
I got the answer, thanks to @NRP99 for their help

solution i found: using the triangle law of forces as suggested by @NRP99

Now that i think on it, i was too concerned about why it was that 18000 and 9000 were written seperately and if they had any physics significance turns out it was just a mathematical by-product of solving the problem and doesn't represent anything

also, i want to end this by giving credit to the author,
while calculating the solution i came across the number 1053
i wouldn't have thought anything of it if i didn't know the answer 9000√13
i wouldn't have thought 13 was a factor of 1053
i know he is a super smart guy, i just thought it was interesting to mention.

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