Idealizing connections 3

[LeonhardEuler]

I have been doing some thinking on idealized vs. real connections and I'm looking for a good reference, or explanation that helps me understand when it is really safe to assume pin connection and full moment connection.

My train of thought started today thinking of two trusses spaced 15' apart with purlins running between them and the purlins nailed to the top of the truss. Now I picture a load in the center of the purlins and think surely that would create a moment on the trusses and a great enough load would pull the tops of the trusses in and collapse them. To me it seems like the nail through the top of the purlins create some moment resistance and makes the trusses unstable with only a nail into a top plate supporting them. Is this correct and the only way the trusses stay upright is due to sheathing, Or is the connection with the purlin truly a pinned connection and flexes enough to not allow lateral deflection of the truss?

Again any reference material on the idealization of connections and how we can make these assumptions would be appreciated, so I can feel safe that one day I will not have trusses that topple

 

[jayrod12]

The connection you describe is most definitely a pinned connection.

I don't have any documentation that would give you guidance.

Unless you are providing significant connection of both purlin flanges to the supporting material then the connection can usually be idealized as pinned.

 

[LeonhardEuler]

Yea and I understand that it should be pinned and all, but thinking of the actual physical reaction it seems to me that the nails/screws by resisting pull out would have some moment resistance and pull the trusses in.

 

[jayrod12]

Even with a fairly large purlin length. The actual lateral movement would be minor.

 

[LeonhardEuler]

So is it just a thing where we are ignoring the moment resistance because it is relatively small?

 

[LeonhardEuler]

How does the nail not rip out if it's not able to resist moment? Is the material "flexing" around it without pulling up on the nail considerably?

 

[LeonhardEuler]

Does the idealization of the pinned connection have to do with the way the connected members are allowed to deflect/rotate. The nails/screws just "go along for the ride" as the top of the truss and purlin flex and the nails/screws don't arrest this movement and thus don't pull out or break?

 

[BAretired]

That last comment by LeonhardEuler hits the nail on the head if you'll pardon the expression. If the purlins are designed in accordance with code, they should not deflect more than L/360 under live load. A simple span purlin would rotate approximately 1/100 radians at the truss under full snow load which could easily be accommodated by localized squashing of the chord member and purlin, not to mention strain and pullout of the screw or nail.

To state that the connection is not a perfect pin is absolutely correct. Some moment will be transferred, but not nearly enough to cause the trusses to collapse.

BA

 

[LeonhardEuler]

Ok I think I'm starting to understand. So perhaps if the purlin were allowed to deflect to extreme amounts it would cause extreme deflection at the truss, but the nature of the design of the purlin limits potential problems at the truss. Would you think this squashing would occur in a similar way in a far stiffer material.

Do you know of any references that covers this and maybe similar theory? I'm very interested in knowing "why" for many of our assumptions and theories

 

[12345abc6ttyui67]

The load will always follow the stiffest path. In your example, the lateral stiffness of the truss is probably less then the compressive stiffness of the purlin and shear stiffness roof diaphragm. Therefore, if / when the purlin applies an end moment to the truss, the truss deflects first (e.g. the end moment is relaxed) and instead resisted by compression of the purlin and shear across the roof diaphragm.

 

[MrHershey]

I'd start with the stability bracing requirements of AISC 360 and commentary for digging into the "why". It's Appendix 4 in AISC 360-10 (red book). You can calculate out what the required brace strength and stiffness is in order to keep a beam under a given moment from rotating or LTB.

You'll find it often doesn't take much.

 

[dhengr]

LeonhardEuler:
Think of it this way...., you have a structurally sufficient purlin spanning 15' and supported by two trusses. If the purlin meets ultimate strength requirements and serviceability criterial, BA’s L/360 or L/240 deflection criteria, etc., it will deflect a bit, but not change the chord length btwn. the two trusses/supports very much, but that is also why we usually say one end of a beam/purlin is pinned and the other is pinned and on rollers, so you aren’t inducing an axial load in the beam, or a thrust on the supports, due to the beam’s curvature during deflection. Nails or screws have some lateral cap’y. so they will impart some small lateral load to the tops of the trusses, but the truss lateral movement is limited to the chord length change, and limited by some axial strength in the purlin, or by adjacent purlin spans and roof sheathing. The nails have almost no withdrawal cap’y. so they won’t impart a fixed end moment to the top of the truss, due to the slight end rotation/curvature of the purlin. In fact the purlin might pull the nails out a bit over several loadings. Screws have a bit more withdrawal cap’y. than nails, so to that extent, whatever rotation in the end of the purlin, times a lever arm from the edge of the truss top chord to the screw, that might impart some small fixed end moment to the truss. But, as already mentioned crushing/compression perpendicular to the grain, and some small rotation/rolling of the top truss chord will cause all that activity to be compatible with a small (negligible) end moment. On the other hand, if you had a cable in place of the purlin, the only way it can support the load is by imparting no moment, but a significant deflection and a very large lateral load to the tops of the trusses. Undoubtedly, we could design an end connection which would impart an end moment to the top chord of the truss, but that would probably just roll the top chord a bit.