Thursday, July 21, 2011

Roof Diaphragms

When I started working as a structural engineer, one of the principals of the firm grabbed me and asked me to take a look at a "new" part of the building code. Until that time, except for certain conditions, roof diaphragm strength and behavior was ignored by the majority of structural engineers working in our region. I found the topic fascinating. The play between the stiffness of the roof, the stiffness of the building frames and walls, and the effect of seismic loads stretched my understanding of mechanics.
A little background, a roof's first job is to support itself against gravity. Following that it needs to provide shelter from sun, rain, snow, etc. These are generally considered gravity loads (except for sun, light doesn't weigh very much). Anybody who has heard of tornadoes, hurricanes and the like, knows that roofs also resist the forces due to wind; up, down, around, any way about town, wind does what it wants, when it wants and will do whatever it wants to any roof structure it can find.
A nice steady wind travelling across the Great Plains will push on a building, like my toddler son crawling across my floor to put his hands against the sides of his green painted wooden toy box. A building is an essence in itself, but it is generally made up of discrete parts. Wind pushing on the walls of the building makes the walls push back. They only have two places to hold themselves up against the constant, straining pressure of the winds of the Plains. First is the ground. The Earth is massive and considers the buffeting of stormy winds as a mere exfoliating cleanse at the spa. So lets ignore that for now. Second is the roof. The walls reach up like a desperate man grabbing for a tree branch to halt his imminent fall. If he gets the branch it will bend, and maybe snap, or flex out of the way like a sapling. A roof will behave in similar ways. When the walls push on the roof, it will bend, it might tear, it might move too far, this is the study of roof diaphragms. They push, and pull, and snap, and stretch like a ship's sail in a stiff breeze.
When I look at most roof diaphragms, the easiest analogy for me is that of a great beam, turned on its side and spanning the distance between the walls of the building. As such, it experiences both shear and moment. A shear failure would consist of tearing of the roof structure near the walls. A moment failure would be the rupture of the roof due to the great bending force in the building. Or if we look at the falling man example, shear failure would be his feet slip or his grip on the branch gives way, and moment failure would be his body bending too far at the waist and injuring him. ouch.
I am fascinated with the interaction between shear and moment. Shear is a state of instantaneous stress acting in all directions in the plane of the force. Not only is it acting all directions, it has the same value in all directions. Integrating the distribution of this shear in a beam produces the moment in the beam. Stress in no direction, integrated yields bending with a direction. Awesome. Check out Beer and Johnston for the true description of this.
At our firm, when we put all this into real engineering practice, we design the roof deck, and the beams (chords and struts) for all of these loads, but that is not nearly as interesting as a fifteen story toddler crawling and drooling all over Kansas.

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