Introduction

Simple doubly pitched roof. Two structural members and three joints, with two of the joints as supports. The basic connection options for joints is pinned that is having no moment restraint, or fully fixed in which case has moment restraint. If have moment restraint then joint can resist forces which tend to cause rotation at the joints. If two members are joined using only one bolt then the two members can rotate about the shaft of the bolt. If use more than one bolt then have some restraint against such rotation.

However a connection in which a member is connected to a simple cleat plate is typically considered a pinned connection, as its resistance to rotation is low. A bolted moment connection typically involves member end plates, or multiple bolt gusset plates. The preferred connection type is pinned, as the connections are easier to design and fabricate, and the structures are also easier to analyse. A properly triangulated pinned structure is typically much stiffer than a structure with rigid joints. However when it comes to buildings the bracing of a structure can interfere with the usability of the internal building space, and therefore for certain structures rigid frames are preferred.

Timber Framed House Construction

In Australia our timber framed housing is based on the residential timber framing code AS1684, this is an engineered solution based on the loading code AS1170 and the timber structures code AS1720, and structural model presented in AS1684.1 and simplified wind classification system presented in AS4055. For South Australia the main code used is AS1684.2, and the supplementary span tables. There are other parts to AS1684 for cyclonic regions.

The timber framing code is based on the structural form of a pinned and braced structure. The building should have a rectangular plan, or such that it can be broken up into segments with each segment being a single rectangle and having a prismatic section. It covers L-shaped, T-shaped, and U-shaped plans.

A building shape however comprised of several overlapping rectangles, producing a building perimeter which steps in and out, and which has a roof shape comprising of broken hips and valleys, is not strictly within the scope of the code (AS1684).  At the very minimum such structure raises questions about the structural adequacy of the ceiling diaphragm which props the top of the walls. It should also raise questions about the stability of the roof structure, and the proper determination of loads on the structural members.

None the less AS1684 is a good starting point for studying structures and their basic behaviour. The primary roof structure considered for a doubly pitched roof, is traditionally and more completely and properly called a closed coupled roof. The requirements of this roof structure causes problems, when it comes to using the timber framing code for canopy structures without a ceiling, and when it comes to assessing cold-formed steel sheds having rigid frames.

In a house the ceiling joists and plasterboard lining, form a nominal diaphragm, or deep horizontal beam which spans between braced walls. This diaphragm is typically restricted to a span of 9m, and it supports the top edge of the walls. The ceiling joist is also an essential part of the roof structure, and helps tie the rafters together and stop them from spreading apart. When it comes to canopies the ceiling is not wanted and therefore builders wish to leave the ceiling joists out: doing so renders the proposed structure unstable.

The other issue that arises from the use of the timber framing code is a lack of familiarity with rigid moment frames. The typical cold-formed steel shed has frames with rigid knee and ridge connections. The columns and rafter behave as a single structural entity. The removal of a column, creates a different frame, and cripples the structure. The structure doesn’t have braced walls or a ceiling diaphragm. The more columns that are removed the less resistance the structure has to the horizontal push of the wind. With such structural form, it is necessary to do more than simply provide a lintel to support the roof over the opening created.

With stick frame house structures, the studs and rafters transfer loads to one another in a manner such that they can be considered in isolation, as simple beams and columns. With the rigid frame of the shed, the column and rafter interact with one another. Horizontal load applied to the shed wall produces bending in the rafter, this doesn’t occur with the stick frame house construction. Therefore with stick frame house construction can simply remove wall studs and provide a lintel to support the rafters.

The following discussion uses bending moment diagrams printed from Multiframe structural analysis program, to help illustrate the difference between having pinned joints and rigid/fixed joints. In each case the loads applied are unit loads. Therefore in situations where a linear elastic analysis is suitable, the values in the diagrams can be multiplied by the actual loads. The spans are typically 3m, and eaves height 2.4m where posts are included.

A Coupled Roof

Moment Diagram for Coupled Roof

Moment Diagram for Coupled Roof

A coupled roof comprises of two rafters, one propped against the other. The two rafters are thus coupled because one depends on the other. In the timber framing code, the ridge board is simply provided for convenience in connecting the rafters, and provides some restraint against lateral buckling. As can be seen from the diagram, at the roof supports the reactions are both vertical and horizontal. The horizontal thrusts, generated by gravity load, can kick the house wall over. The large buttresses and fling buttresses seen in old stone buildings, are there to resist such thrusts. The horizontal forces generated by wind uplift can pull the top of the walls inward. The rafters can be considered in isolation as simply supported beams, spanning between the wall support and the ridge. Since abutments or buttresses, are constructed from heavy stonework, and occupy a lot of space and use a lot of material, some more economical solution was sought for roof construction. That solution was and is the closed coupled roof.

A Closed Coupled Roof

In a closed coupled roof the base of the triangle formed by the rafters is closed by an horizontal element. This horizontal element is typically called a tie, as traditionally the only loading really considered was the weight of the roof, and downward gravity loads put tension in the element, and hence a rope was a suitable element. Wind uplift on the other hand imposes a compressive force on the element, making it a strut. So sometimes the element is a tie and others it is a strut depending on the current loading condition. However generally speaking it ties the rafters together, irrespective of the sense of the force in the element.

Moment Diagram for Close Coupled Roof

Moment Diagram for Close Coupled Roof

Now with a coupled roof the two supports are considered pinned supports, and are able to resist both horizontal and vertical forces. With a closed coupled roof, only one support is considered pinned the other support is considered to be a roller. A roller can only resist vertical loading, it is free to slide horizontally. In practice a structure may be supported on a sliding bearing, some actual roller, or the roller simply represents the fact that the support is free to move. A roof is typically constructed on top of flexible walls or flexible posts. The tops of these walls and posts are free to move, so for all intents and purposes they can be replaced by rollers when considering the roof structure in isolation. The rafters can also be further isolated and considered as simply supported beams.

The problem with a closed coupled roof is that the span is limited by the maximum length of material available for the tie. If a long enough piece of material is available then the next issue is its compressive buckling capacity.

Varying The Supports And Connections

The basic roof form has two to three elements and three nodes, with two nodes being supports. The basic types for supports are fixed, pinned and roller, whilst the basic types for joints are fixed and pinned. For any point or node there are 6 to 12 degrees of freedom depending on how an author chooses to count them. There are three axes of rotation, and three axes of translation, and two directions of movement for each of these axes. Typical structural analysis software restrains or releases movement in both directions for an axis.

So just by changing the nature of the connections and supports, a variety of different structures can be formed.

Pin/Pin/Pin

Axial Forces Showing how the Tie has Become Redundant

Axial Forces Showing how the Tie has Become Redundant

If the roller is removed from the closed coupled roof and replaced by a pinned support, then the tie becomes redundant. The tie is redundant because the supports are taken as able to resist the horizontal forces.

In stick frame house construction the ceiling joist typically forms the tie. The ceiling joist can either be considered as restraining the top of the walls, and the vertical and horizontal forces from the coupled roof are applied to the wall structure. Or the ceiling joist ties the rafters, and the vertical forces from the closed coupled roof are applied to the walls. The ceiling joist therefore has to be there for reasons other than supporting the ceiling.

Pin/Fixed/Roller

Moment Diagram for Fixed Ridge, with pinned and roller supports

Moment Diagram for Fixed Ridge, with pinned and roller supports

Another option is to create a rigid moment connection at the ridge. In timber construction such connection can be formed by using large plywood gusset plates. This effectively makes the roof structure a single span simply supported cranked beam. The rafters are now a single continuous frame, and span a greater distance and therefore would need to have larger sections than for the coupled roof.

Pin/Fixed/Pin

Moment Diagram with Fixed Ridge and Pinned Supports

Moment Diagram with Fixed Ridge and Pinned Supports

With both supports pinned and the ridge fixed, the rafters are now effectively propped cantilevers with the prop at the eaves level. The bending moments are reduced so smaller section rafters are possible. But have the support thrust forces to deal with.

Fixed/Fixed/Fixed

Moment Diagram with Fixed Ridge, and Fixed Supports

Moment Diagram with Fixed Ridge, and Fixed Supports

With supports and ridge fixed, the rafters are effectively fixed beams or encastre beams spanning between wall and ridge. The bending moments in the rafters are reduced, but have the thrusts to deal with at the supports as well as moments. Fixed ended beams are traditionally constructed by building the ends of the beam into heavy masonry construction. An alternative is a timber portal frame, in which case the columns and rafters would form a continuous frame. Large plywood gusset plates can be used to form the moment connection at the eaves or knee of the frame.

Changing the nature of the supports can make the tie-beam redundant. Therefore the stresses in the rafters, and support reactions are similar to the case when the tie-beam is missing.

Canopies: Carports, Pergolas and Verandahs

 

Moment Diagram for Collar-Tied Roof

Moment Diagram for Collar-Tied Roof

For doubly pitched timber canopies, since there is typically no ceiling, there is also no desire for a ceiling joist. The solution has been the use of a collar tied roof truss. The collar tie is typically placed at one third the height of the roof. The bottoms of the rafters are fastened to fascia beams. The supports for the isolated roof frame are taken as pinned one side and roller the other.

However the gable ends of these canopies are typically formed from two rafters and a fascia: in other words it is the equivalent of a closed coupled roof. This is not a problem until come to the issue of attaching the canopy by its gable end to the eaves of an existing house.

Typically the canopy is attached by cranked steel brackets to the rafters of the house. If the eaves of the canopy is attached to the house, then the canopy rafters can be at a spacing different than the rafters in the house. As the reactions from the canopy roof frame are transferred to the fascia beam, and the fascia beam is attached by the cranked brackets to the house rafters. The forces on the fascia beam can be assumed uniformly distributed, and from there can be equally distributed to the rafters in the house.

Attaching the Canopy Gable End to House

Canopy Gable End Frame - showing no reactions at interior supports

Canopy Gable End Frame – showing no reactions at interior supports

For the gable end frame however this is not true. Attaching the end fascia by brackets at 1200mm centres as is typically the case is of little value. As should be apparent from the force diagrams so far, the rafter tie doesn’t carry any of the roof load. The load on the rafters is carried down to the supports on either side of the roof. Placing supports along the fascia does not distribute any of the roof load into these supports.

To get the roof load into the fascia, the rafters and fascia need to be trussed, by the addition of internal webbing. The simplest approach is to bring some diagonal members down from the ridge to the fascia. This will then distribute some of the roof load into the interior supports.

Simple Trussed End Frame for Canopy

Simple Trussed End Frame for Canopy

Further internal webbing can result in more roof load being distributed to the interior supports than to the side supports. The objective therefore is to get an appropriate balance, to minimise the strengthening requirements for the house structure.

There is however another issue for the gable end, and that is the supports at the house have to carry the load from more than just the canopy gable end frame. The side fascia beams which provide the support for multiple roof frames are being supported by the house structure. Effectively half the length of the canopy between the house and the first canopy post is being supported. These forces are concentrated at the ends of the side fascia beams, and will not be shared by additional supports on the end gable fascia. The forces will be concentrated into the end brackets.

More Complex Trussed End Frame for Canopy

More Complex Trussed End Frame for Canopy

The situation is more complicated if the canopy is built into the corner of a L-shaped house, and connected along two adjacent sides to the house. So that both the eaves and gable end of the canopy roof are attached to the house. In such situation there is some triangular area, on plan, which is distributed to the gable end supports. The outer most support carrying the greater concentration of force.

Providing additional tie-down against wind uplift for the existing house structure is mostly impractical, and therefore it is preferable to by pass the house structure all together and provide additional columns adjacent to the house. This is typically done with steel construction by cranking columns under the eaves of the house and bring them down the face of the wall.

Alternatively if really don’t want columns near the house, a cantilevered canopy roof can be constructed. Though with such roof, heavy construction would be preferable to avoid vibration in strong winds.

Moment Diagram for Cantilevered Roof

Moment Diagram for Cantilevered Roof

Moment Diagram for Umbrella Roof

Moment Diagram for Umbrella Roof

Summary

If there appears to be inconsistency in what gets approved and what you are told is possible it is largely due to differences in the way the same assembly of structural elements is modelled and where the maximum forces are consequently distributed.

Additional diagrams of structural roof forms, with and without columns, along with  bending moment, axial forces and shear forces can be found in the following pdf download:

NotesOnRoofStructures


Revisions:

  1. [16/04/16] : Original {Associative Freewriting: or otherwise mindless ramblings and brain leak}