Revisting the collar tie calc using trig

[keyPitsimplE]

thread507-285010

BAretired,
In referencing the "tie-force" .pdf you attached to the original referenced thread, I have a question.

When I look at it using trig, method of joints I think it is, I get a different value for T, which was my original "mistake" of twice the force you calculated. Knowing R = 1066 lb and the angle at A = 18.5 deg, I get T = 3185 lb. This comes from ABx = AB cos 18.5 = T, ABy = 1066 = AB sin 18.5, AB = 1066 / sin 18.5 = 3359, ABx = T = 3359 cos 18.5 = 3185.

The numbers above correspond with using L = 13.33 and h = 2.25 in your pdf, which gives T = 1579. I'm wondering where the error is.

 

[keyPitsimplE]

Sorry, I just re-read the original post and noticed that hokie66 did the same thing I did, by neglecting the bending of the top chord member. So I guess the method of joints does not work for this triangle with a uniform load. HOWEVER, lets assume there is a strut from B to the middle of the bottom chord and the entire W is hanging from that. Or even with no strut, but applied as a point load at the ridge. The method of joints now works, right? If it only works when all loads are applied directly to the joints, and not when the exact same load is being applied uniformly, as I typically find in residential wood trusses, I guess I should avoid the method of joints. This is a good exercise for me.

 

[keyPitsimplE]

...of course also noting that BAretired's formulas that he derived in the .pdf will ONLY work with uniform loads.

 

[hokie66]

The method of joints always works, but you just have to use it correctly. You and I both erred in the previous thread, and our friends corrected us. We used the wrong vertical force at the support in calculating the member forces.