ceilinlg joist as collar tie

[keyPitsimplE]

refer to thread507-105386

Similar situation, but simpler. 13'-4" between rafter supports. 27" vertical dimension (based on 4:12 roof pitch) from ceiling joist to ridge. 40 psf total S+D loads. Rafters @ 4' o.c.

Rafter reaction = 1066 lb.

Summing moments about the ridge I get the tension in the collar tie to be 3158 lb. Sounds really high. Anyone see my error, or maybe it is just because it is such a low roof pitch.

Thanks.

 

[msquared48]

The moment is wl^2/8 = 3.58 Kip feet and with the 27" dimension, assuming that it is a difference in centerlines dimension rafters to joists, the tension would be 3.58k'/2.25' = 1.59K, or half what you calculated.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[BAretired]

R = 1066#
W = 2*R = 2132#
M = WL/8 = 3553'#
h = 27" = 2.25'

T = M/h = 1579# (tension in ceiling joist)

You are out by a factor of 2.0

BA

 

[keyPitsimplE]

You both clearly agree, but I'm missing something.

I was looking at a free body diagram, summing moments about the ridge, solving for T = (1066 x (13.33'/2))/(27/12) = 3158. What moment are you calculating with WL^2/8? That is for a "uniformly loaded beam".

W = 2xR ?

 

[msquared48]

The truss, collar tie is still a beam, subject to a uniform loading - ie, wl^2/8, and the couple in the truss to resist that moment, - ie, the distance between the T and C forces is the 27". Hence the 1.59K T/C force. It's just that simple.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[hokie66]

With a reaction of 1066 lb, the axial force on the horizontal would be 3198 lb. Just 1066 x 12/4.

 

[keyPitsimplE]

Msquared48, that certainly is simple. I see your logic.

Hokie66, that is almost exactly what i got originally by my method. Do you not agree with the simple logic of the 2 gentlemen above?

Is one of our methods just simplified too much?

 

[BAretired]

It is not simplified too much. It is just plain wrong!

BA

 

[hokie66]

keyPitsimple,

The value calculated by Mike and BA for the bottom chord force is correct. These guys are rarely wrong, at least both at the same time. You and I both made different errors and got the same wrong answer.

I think you neglected the uniform load on half the truss when summing moments about the ridge. When you deduct that moment from the reaction x L/2, you get the correct answer.

In my case, in using the method of joints, I neglected the fact that half of the 1066 reaction goes directly into the support through top chord bending, thus does not affect the axial forces. For axial force at the joint, the bottom chord force is 1066/2 x 12/4.

 

[msquared48]

I agree BA. See attached calc and freebody.

It all hinges on equating the moments (uniform and point force applications) and the force freebody.

Sorry for the quick sketches. I am obviously not an art major.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[BAretired]

The attached diagram indicates the equilibrium of the tied rafters. Mike, you are absolutely right but your artwork needs a little upgrading.

BA

 

[csd72]

Good old method of sections, works in almost any structure.

 

[keyPitsimplE]

I see my error. My FBD skills have obviously gotten a bit rusty.

I greatly appreciate the guidance, gentlemen.