Gable roof rafter system: calculation of rafters for various coatings

Recommendation points

• Types of gable roof truss systems
• Coating composition
• Roof
• Lathing
• Rafters
• Calculation of the layered rafter leg
• Example No. 1
• Example No. 2

The pitched roof has a system of inclined planes (slopes). The design of the rafter system is selected and calculated, taking into account the availability of supports for it, the type of coverage, the size and shape of the building to be covered. A special calculation will help you choose the required size of the rafter leg and ensure the strength of the roof.

Types of gable roof truss systems

The scheme of the rafter system is selected based on the conditions of the number of supports for it and the distance between them.

Inclined rafters are supported on the external load-bearing walls of buildings and on additional internal supports if the distance between the main supports exceeds 4.5 m. The rafter leg rests from below on a support bar (Mauerlat), which transfers weight from the roof to the building wall. The upper end connects to the ridge girder and the other rafter leg.

1, 2 – hanging rafter system. 3, 4 – layered rafter system. a – rafters, b – tightening, c – crossbar, d – purlin, e – Mauerlat, f – brace, g – rack.

The hanging view of the truss systems is tightened at or above the lower support nodes and does not imply intermediate supports. The distance between the external bearing supports should not exceed 6.5 m. This version of the truss structure can be attributed to triangular trusses. The horizontal distance between them is taken as 1.3-1.8 m.

Coating composition

Roof

Eternite roofs are flat or corrugated sheets of asbestos cement. This is a cheap type of roofing that is quite easy to install. Recently, studies have shown its harmful effects on human health..

Slate roofs also include slate roofs. They are constructed from natural material of the layered structure of shale. Euroslate, ondulin are descendants of ordinary slate. They are pressed fiberglass or cellulose impregnated with bitumen.

Metallic cladding is often used in the construction of residential buildings. It reliably protects the house from atmospheric influences, has a low weight and is not time consuming to install. This type of roofing includes corrugated board, galvanized steel, aluzinc.

Rolls are soft types of roofs. They are waterproof, resistant to environmental influences and easy to install. These include the following types:

• roofing felt (rubemast, glass-mat, euroruberoid, roofing felt, etc.);
• bitumen-polymer (glass-insulated, glass-ceramic, linokrom, etc.);
• membrane roofs (PVC, thermoplastic membranes, synthetic rubber films, etc.).

If earlier tiled roofs were only ceramic, today there are: cement-sand, bituminous and metal tiles..

Wooden roofs are rarely used due to the difficulty of the device. They are shingle, pancake, shindable, ploughshare, plank.

Light-transmitting roofs are made of polymeric materials and glass. These include cellular polycarbonate, corrugated polyvinyl chloride, triplex, polyester, etc..

Lathing

Roof decking or sheathing is the basis for the roof. It is made from planks or blocks. When installing a metal, wooden or tile roof, the lathing bar is taken with a cross section:

• 50×50 mm with a distance between the rafters – 1.0-1.1 m;
• 50×60 (h) mm with a rafter pitch – 1.2–1.3 m;
• 60×60 mm with a step of 1.4–1.5 m.

For other types, you can use boards 2.5 cm thick. A double plank decking is arranged under the roll roof. The working bottom layer is laid perpendicular to the direction of the rafters with openings. The upper one is laid at an angle of 45 ° to the underlying layer. The width of the boards for it is taken no more than 8 cm, and the thickness is 2 cm.

Rafters

Wooden rafters are used log, sawn to one edge, from sawn wood (timber, board laid on the edge). For layered rafters, a round section of the log is better suited. Their diameter is 12–20 cm. The advantages of using a log in comparison with a board or timber are as follows:

• saving wood (to withstand the same loads for a circular section, a smaller diameter of the source material is needed);
• higher fire resistance limit;
• less consumption of metal fasteners;
• higher indicators of rigidity and durability.

Calculation of the layered rafter leg

Between the rafter legs, a step of 1.0–1.5 m is allowed. Their section is determined by calculation, based on the strength, as well as the rigidity of the structure. To do this, the calculated constant load on the rafter is determined, which includes the calculation of constant loads per one running meter of the roof and snow load.

Diagram of load distribution along the rafter leg:? – the angle of inclination of the roof, q – total constant loads, qⁿ – normal load

The initial data for the calculation are accepted:

• step of installing rafter legs;
• roof slope;
• roof width and height.

The choice of parameters, as well as the selection of most of the coefficients depends on the material of the roofing covering and the detailed composition of the roofing cake.

For sloped roofs, permanent loads are calculated using the formula:

The rafter leg is also calculated for stiffness (deflection). The normative load is used here:

• ? – the angle of inclination of the roof;
• n, n_c – safety factors for snow loads – 1.4, roof loads – 1.1;
• g – weight 1 m² , which the rafter leg perceives (roofing, lathing, rafters);
• S₀ – standard snow load;
• a – the step of the rafter legs (along the axis).

• S_g – snow weight per 1 m², which depends on the climatic region;
• from_e – the coefficient of snow drift due to the influence of wind and other atmospheric influences, depends on the operating mode of the roof;
• c_t – thermal coefficient.

Coefficients with_e and c_t accepted in accordance with the requirements of SP 20.13330.2011 section 10 “Snow loads” in accordance with 10.5 and 10.6. For a private house with a pitched roof with a roof slope of over 20 °, the coefficients with_e and with_t are equal to one, therefore, the formula for snow cover:

µ – coefficient that depends on the angle of inclination of the roof and is determined according to Appendix “D” SP 20.13330.2011:

• for roofs with an angle of inclination less than 30 ° µ = 1;
• for roofs with an angle of inclination over 60 ° µ = 0;
• in other cases for an angle of inclination of 30 °<?<60 ° µ = 0.033 x (60 ° -?).

The weight of snow cover by region can be specified in SP 20.13330.2011 “Loads and Impacts”, where the number of the region is also determined according to the map of Appendix G.

Snow cover weight S_g

District	I	II	III	IV	V
Sg kg / m2	80	120	180	240	320

Since the rafter leg is subjected to bending from the effect of loads on it, it is checked for strength as a bending element, according to the formula:

M < m_andR_andW_nt

• M – bending design moment;
• R_and – calculated resistance to bending of wood;
• m_and – coefficient reflecting the working conditions;
• W_nt – moment of resistance of a given section;
• R_and = 130 kg / cm² – for pine and spruce;
• m_and equal to 1.0 – for sections up to 15 cm high and 1.15 – for sections more than 15 cm high.

The moment of resistance and moment of inertia for the rafter material are calculated individually. Based on the data obtained, the required size of the structural elements of the rafters is selected.

The proposed calculation is approximate and requires an addition in the form of the maximum permissible length of supporting elements, the placement of spacer or retaining beams and racks.

Example No. 1

Consider a tiled ceramic roof on a gable roof in the Moscow region (III climatic region).

Tilt angle 27 °; cos? = 0.89; the pitch of the rafters along the axis is 1.3 m; the estimated span of the rafters is 4.4 m. The lathing is taken from a bar of 50×60 mm.

Roof weight for 1 m²:

• roof weight – 45 kg;
• crate – 0.05 x 0.06 x 100 x 550/25 = 7 kg;
• rafter weight – 10 kg.

Total: g_n = 62 kg / m²

Estimated load per linear meter:

• q = (1.1 x 62 x 0.89 + 1.4 x 126 x 0.89²) x 1.3 = 260 kg / m.

Normal load per running meter:

• q_n = (62 x 0.89 + 126 x 0.89²) x 1.3 = 201 kg / m
• M = 0.125 x q x l² = 0.125 x 2.60 x 440² = 62 920 kg • cm

Moment of resistance:

Moment of inertia (I), which is necessary from the condition of possible deflection f = 1/150 l; E = 100,000 kg / cm²; qн = 201 kg.

According to specially developed tables, you can determine the diameter of the log for the rafters.

Log diameter (cm) depending on W and J (for logs trimmed by one edging).

Legend	13	fourteen	15	sixteen	17	18	nineteen
J	1359	1828	2409	3118	3974	4995	6201
W	211	263	324	393	471	559	658

According to the table below, we determine the diameter of the log – 18 cm.

Example No. 2

Let’s take all the data from the previous example, but for an ondulin roof. It is necessary to calculate the cross-section of the rafter leg from the bar.

Tilt angle 27 °; cos? = 0.89; the pitch of the rafters along the axis is 1.3 m; the estimated span of the rafters is 4.4 m. The lathing is taken from a bar of 50×60 mm.

Roof weight for 1 m²:

• the weight of the roof made of ondulin is 3.4 kg;
• crate – 0.05 x 0.06 x 100 x 550/25 = 7 kg;
• rafter weight – 10 kg.

Total: gн = 20.4 kg / m²

Estimated load per linear meter:

• q = (1.1 x 20.4 x 0.89 + 1.4 x 126 x 0.89²) x 1.3 = 207.6 kg / m.

Normal load per running meter:

• qн = (20.4 x 0.89 + 126 x 0.89²) x 1.3 = 153.3 kg / m
• M = 0.125 x q x l² = 0.125 x 2.08 x 440² = 50 336 kg • cm

Moment of resistance:

Moment of inertia (I), which is necessary from the condition of possible deflection f = 1/150 l; E = 100,000 kg / cm²; qн = 153.3 kg.

We accept timber 15cm high. For a bar with a height of more than 14 cm Ri = 150 kg / cm². Therefore:

According to the table, we determine the size of the section of the timber for the rafters.

Width (b) and height (h) of the timber depending on W and J.

b	Legend	h
8	nine	ten	eleven	12	13	fourteen
fourteen	J	1829	2058	2287	2515	2744	2973	3201
W	261	294	327	359	392	425	457
15	J	2250	2531	2812	3094	3375	3656	3937
W	300	337	375	412	450	487	525

We accept a timber with a section of 10×15 cm for the rafter leg.

The formulas given can be used to calculate other roof coverings. In this case, the load on the rafter leg is calculated based on the selected option. Formulas may change:

• rafter length;
• rafter step;
• roof slope angle;
• snow load, which is selected according to the region of construction;
• crate weight.

The connection of the rafter legs between themselves and the run must be reliable. This ensures that there is no destructive thrust on the walls of the building. Wooden structures must be inspected from time to time, therefore, when constructing layered rafters, the distance from the mark of the top of the attic floor to the lower mark of the Mauerlat is taken at least 400 mm.

Gable roofs are still a tradition of private housing construction today. The correct roof structure is a solid, durable and beautiful home.