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Timber roof fabricated of trusses and common rafters, load transferred to canted purlin.

Timber roof fabricated of trusses and common rafters, load transferred to canted purlin.

Timber roof fabricated of trusses and common rafters, load transferred to canted purlin.

(OP)
Hi, I am having some trouble visualising the load transfer in the following scenario, and would be grateful for any insight. My questions are:

(1) What proportion of the load is transferred from the common rafter into the purlin and therefore into the truss (i.e. what proportion of the 5/8 of the perpendicular component of the total UDL is transferred).
(2) What angle is this force to the horizontal.

The roof is composed entirely of timber members. Lightweight trusses are spaced at 1.8 metre centres. Load is 700N/m run. Common rafters, 3 in No., and same dimensions as the truss rafters, are spaced equidistantly between the trusses (i.e. at 450mm centres). (The arrangement of trusses/common rafters is set out below).

TRUSS Commn Commn Commn TRUSS Commn Commn Commn TRUSS Commn Commn Commn TRUSS Commn Commn Commn TRUSS

Each pair of common rafters is tied together via a ceiling joist. All rafters, whether truss or common, span continuously from eaves to the ridge board (perhaps I should stress ridge board NOT ridge beam). I am treating all nodes as pinned. The common rafters are supported at their mid point by a single purlin. The purlin is canted i.e. depthwise, it sits perpendicular to roof slope, so it can take only the perp. reaction. Roof is symmetrical duo pitch – one purlin each slope. Slope is 35 degrees. Trusses support the purlin (purlin not supported by gable wall or struts).

Thanks in advance for any comments/ insight.

RE: Timber roof fabricated of trusses and common rafters, load transferred to canted purlin.

If I'm understanding your system correctly,
Here are some thoughts.....

1. "...The purlin is canted i.e. depthwise, it sits perpendicular to roof slope, so it can take only the perp. reaction.... " I think you're correct on this but for perhaps an incorrect, but also ultimately perhaps an inconsequential reason. It seems to me that a) your purlin will only feel any force as your rafter deflects and b) your common rafter will deflect into an arc shape under uniform loads, whether they be vertical gravity loads or perpendicular wind loads and c) your purlin is coincidentally at midspan where the tangent to the deflected shape is parallel to the original roof line and therefore perpendicular to your canted purlin.
2. It seems to me like you essentially have a truss composed of two common rafters and a ceiling joist and that the purlin does basically the same duty that a vertical web does in a modified warren truss, ie, reduce the span of the compression chord. So the reaction at your purlin is middle reaction at a two span beam.
3. In practical wood design for a members like this, it seems to me that these mathematical refinements can easily be negated by the natural vagaries in mother nature's lumber. The cost difference between the next larger and next smaller milled sizes is minimal but the section property difference can be quite significant. Be conservative.

RE: Timber roof fabricated of trusses and common rafters, load transferred to canted purlin.

1) As I understand your framing scheme, the purlin is a beam which distributes the load from the rafters to the trusses at centre span. Therfore, the full 5/8 reaction will be carried by the truss, as the truss will be much stiffer than the rafters.

2) Normal to the roof plane.

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