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RE: Ridge beam/joist analysis

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I had to think about this one a while (in between doing real work) before I
figured out the problem.

In the board-on-roller model, the horizontal "force" results from the fact
that the support reactions aren't vertical - they're normal to the sloped
board.  Since the load (gravity) is vertical and the reactions have vertical
AND horizontal components, you have unbalanced horizontal forces and a
moving board.

In the original problem, the beam was modeled flat, the reactions were
vertical, and the load was applied at an angle with horizontal and vertical
components.  This requires a horizontal component in one reaction to
compensate, with a resulting axial force in the beam.  

Back to the real world -- vertical load on a sloped joist supported by a
ridge beam and wall.  If you cut notches in the joist so that a horizontal
surface rests on top of the ridge beam and wall, you have no horizontal
force.  This is the model that Nels is talking about.  If you support the
joist on a hanger with a sloped seat the reaction is no longer perfectly
vertical and you introduce a horizontal component.  This is the horizontal
force that must be resisted by the hanger, by a strap, or by nailing. 

Jason Kilgore
Leigh & O'Kane, LLC
Kansas City, Missouri

> -----Original Message-----
> From: Rand Holtham, P.E. [mailto:rand(--nospam--at)]
> Sent: Monday, June 28, 2004 3:57 PM
> To: seaint(--nospam--at)
> Subject: Re: Ridge beam/joist analysis
> Good point. I've often struggled with this concept. The system you
> described
> (board on roller) is inherently unstable and so cannot be analyzed using
> statics. By virtue of assuming (and providing) a joint  that has the
> ability
> to resist lateral loading (pinned), the net effect becomes zero lateral
> load
> for the inclined board and the supporting member. Where did the load go in
> theory? We know there is a force there otherwise the roof would slide off.
> For the wood framed house obviously the diaphragm is the only way the top
> of
> the wall can resist the lateral load so that you can assume that the
> sloped
> rafter is pinned at one end. But according to statics no load is in the
> diaphragm.Where did that intuitive load go? Perhaps we should add dead
> load
> of the rafters and sheathing to the diaphragm forces to be resisted?
> Rand
> ----- Original Message -----
> From: "Jordan Truesdell, PE" <seaint(--nospam--at)>
> To: <seaint(--nospam--at)>
> Sent: Monday, June 28, 2004 1:48 PM
> Subject: Re: Ridge beam/joist analysis
> > Nels - It's a poor assumption, as shown by placing a board on two
> rollers
> > (the kind used to support the free end of a woodworking project).  If
> the
> > two rollers are at different elevations, the board WILL roll towards the
> > lower roller (and off the setup) if not restrained, even through the
> only
> > force on the board is gravity.
> >
> > I agree that there will be no NET force on a balanced rafter system (one
> > rafter on each side), but there will be a horizontal reaction force at
> the
> > rafter ends in a FBD.
> >
> > One part of the equation we're ignoring is that the roof sheathing will
> act
> > as a diaphragm, transmitting the horizontal loads to exterior walls.
> Part
> > of the "luck" (along with glue, drywall, interface friction, etc.) that
> > keeps houses from falling down all the time.
> >
> >
> > At 11:24 AM 6/28/2004 -0700, you wrote:
> > >Craig,
> > >
> > >The ridge beam allows you to assume that the wall and the ridge support
> the
> > >gravity-loaded rafter with reactions that are vertical only.  If W is a
> > >gravity load, it acts vertically -- no matter how you analyze the
> rafter,
> > >whether analyzing it with strictly vertical loads, or resolving the
> vertical
> > >gravity load into components perpendicular and parallel to the plane of
> the
> > >rafters, the result will be vertical reactions onto the ridge and the
> wall.
> > >If that is not the answer you get, brush up on statics and keep trying.
> > >
> > >If W is a wind load, the analysis becomes a little more complicated and
> will
> > >involve the two sloping planes of the roof as a two diaphragm planes.
> In
> > >determining how the joist reactions are resolved, base your analysis
> model
> > >on the assumption that the wall and ridge resist only vertical loads
> and
> the
> > >each of the diaphragm planes resist loads only in its plane.
> > >
> > >Nels Roselund
> > >Structural Engineer
> > >South San Gabriel, CA
> > >njineer(--nospam--at)
> >
> > Jordan Truesdell, PE

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