Calculation of the cross-section of the rafter leg. Section of rafters and sheathing: optimal sizes for roof types

To draw up a technical design for a house, it is necessary to calculate the rafters. There are several options for rafter structures.

Rafter legs that rest on two supports, but do not have any additional supports, are called rafters without struts. They are used for single-pitched roofs, the span of which is about 4.5 meters, or for gable roofs, the span of which is about 9 meters. The rafter system is used either with the transmission of the thrust load to the Mauerlat, or without transmission.

Layered rafters without spacers

A rafter that bends and does not transfer load to the walls has one support that is firmly fixed and freely rotating. The other support is movable and rotates freely. These conditions can be met by three options for fastening the rafters. Let's look at each in detail.

Upper hem rafter leg or the upper support notch is installed in a horizontal position. It is enough just to change the method of support to the purlin, and the rafter leg will immediately show a spread. This calculation of the rafter leg, due to the rigidity of the conditions for creating the upper node, is usually not used for gable options roofs Most often it is used in construction pitched roofs, since the slightest inaccuracy in the manufacture of the unit will turn the diagram without a spacer into a spacer. In addition, in gable types roofs, if there is no spacer on the Mauerlat, due to the deflection of the rafters under the influence of the load, destruction of the roof ridge assembly may occur.

At first glance this system may seem unrealistic to perform. Since a support is created on the lower part of the rafter in the Mauerlat, in fact, the system must exert pressure on it, that is, a horizontal force. However, it does not show the thrust load.

Thus, in all three options complied with next rule: one edge of the rafter is installed on sliding support, which allows you to turn. The other is on a hinge that allows only rotation. Fastening the rafter legs to the sliders is installed using the most different designs. Most often they are performed using fastening plates. It is also possible to fasten with nails, self-tapping screws, or using overhead bars and boards. You just need to choose the right type of fastener that will prevent the rafter leg from sliding in the support.

How to calculate rafters

In the process of calculation truss structure, as a rule, they accept an “idealized” calculation scheme. Based on the fact that a certain uniform load will press on the roof, that is, an equal and identical force that acts uniformly along the planes of the slopes. In reality, there is no uniform load on all roof slopes. So, the wind sweeps snow onto some slopes and blows it off others, the sun melts from some slopes and does not reach the rest, the same situation with landslides. All this makes the load on the slopes completely uneven, although outwardly this may not be noticeable. However, even with an unevenly distributed load, all three of the above options for rafter fastenings will remain statically stable, but only under one condition - a rigid connection of the ridge girder. In this case, the purlin is either supported by slanted rafter legs, or inserted into the gables of the wall panels hip roofs. That is, the rafter structure will remain stable only if the ridge run is firmly secured against possible horizontal displacement.

In the case of making a gable roof and supporting the purlin only on racks, without support on the front walls, the situation worsens. In options number 2 and 3, when the load on any slope decreases, opposite the calculation on the opposite slope, the roof may move in the direction where the load is greater. The very first option, when the very bottom of the rafter leg is made with a notch with teeth or with a support block hemmed, while the top is laid horizontally on the purlin, will hold well uneven load, however, only under the condition of perfect verticality of the posts that hold the ridge girder.

In order to give the rafters stability, a horizontal brace is included in the system. It is minor, but still increases stability. That is why in those places where the scrum intersects with the racks, it is secured with nails. The statement that a contraction always works only to stretch is fundamentally wrong. Scrum is a multifunctional element. Thus, in a non-thrust truss structure, it does not work in the absence of snow on the roof, or it only works in compression when an insignificant uniform load appears on the slopes. The structure works in tension only during subsidence or when the ridge girder bends under the influence of maximum load. Thus, the scrum is an emergency element of the truss structure, which comes into operation when the roof is filled with a large amount of snow, the ridge run is bent by the maximum calculated amount, or uneven unexpected subsidence of the foundation occurs. The consequence may be uneven settlement of the ridge girder and walls. Thus, the lower the contractions are set, the better. As a rule, they are installed at such a height that they do not create obstacles when walking in the attic, that is, at a height of about 2 meters.

If in options 2 and 3 the lower rafter support unit is replaced with a slider with the edge of the rafter leg moving beyond the wall, this will strengthen the structure and make it statically stable with completely different combinations of the structure.

Also one in a good way To increase the stability of the structure, it is necessary to fairly rigidly fasten the bottom of the racks that will support the run. They are installed using the cutting method and secured to any ceilings accessible ways. Thus, the lower rack support assembly turns from a hinged one into a rigidly pinched assembly.

How to calculate the length of the rafters does not depend on the method of attaching the rafter legs.

The cross section of contractions, due to the development of rather small stresses in them, is not taken into account in the rafters, but is taken quite constructively. In order to reduce the size of the elements that are used in the construction process of the truss structure, the section of the scrum is the same size as the rafter leg, and thinner disks can be used. Contractions are installed either on one or both sides of the rafters and secured with bolts or nails. When calculating the cross-section of a rafter structure, contractions are not taken into account at all, as if they did not exist at all. The only exception is screwing the contractions to the rafter legs with bolts. In that case bearing capacity wood, due to weakening of the bolt holes, is reduced by using a factor of 0.8. Simply put, if holes are drilled in the rafter legs to install bolted joints, then the calculated resistance must be taken in the amount of 0.8. When fastening the contractions to the rafters only with nails, the resistance of the rafter wood does not weaken.

But it is necessary to calculate the number of nails. The calculation is made for shear, that is, bending of nails. The design force is taken to be the thrust that occurs in the emergency position of the truss structure. Simply put, when calculating the connection between the scrum and the rafter leg with nails, a spacer is introduced, which is absent when standard work rafter system.

Static instability of a non-thrust rafter system appears only on those roofs where it is not possible to install a ridge purlin that protects against horizontal displacement.

In buildings with hip roofs and gables made of stone or brick, non-thrust rafter systems are quite stable and there is no need to take measures to ensure greater stability. However, to prevent the breakdown of structures, contractions should still be installed. When installing bolts or studs as fasteners, you should pay attention to the diameter of the holes for them. It should be the same as the diameter of the bolts or slightly smaller. In case emergency situation The grip will not work until the gap between the wall of the hole and the stud is selected.

Please note that in this process the bottoms of the rafter legs will move apart by a distance of several millimeters to several centimeters. This can lead to shifting and scrolling of the Mauerlat and to the destruction of the wall cornice. In the case of spacer rafter systems, when the Mauerlat is firmly fixed, this process can cause the walls to move apart.

Spacer layered rafters

The rafter, which performs bending work and transfers the thrust load to the wall panels, must have at least two fixed supports.

To calculate this type of rafter systems, in the previous diagrams we replace the lower supports with different degrees of freedom with supports with a single degree of freedom - hinged. To do this, where there are none, bars for support are nailed to the edges of the rafter legs. As a rule, a block is used, the length of which is at least a meter, and the cross-section is about 5 by 5 cm, taking into account the nail connection. In another embodiment, you can arrange a support in the form of a tooth. In the first version of the calculation scheme, when the rafters rest horizontally against the purlin, the upper ends of the rafters are sewn together either with nails or a bolt. Thus, a hinged support is obtained.

As a result, the calculation schemes remain virtually unchanged. Internal stresses bending and compression remain unchanged. However, a thrust force appears in the old supports. At the upper nodes of each rafter leg, the oppositely directed thrust, originating from the end of the other rafter leg, disappears. Thus, it does not cause much trouble.

The edges of the rafters that abut each other or across the purlin may need to be checked for material collapse.

In rafter spacer systems, the purpose of the contraction is different - in emergency situations it works for compression. During operation, it reduces the thrust on the walls of the edges of the rafters, but does not completely eliminate it. She can remove it completely if she secures it at the very bottom, between the edges of the rafter legs.

Please note that the use of spacer layered rafter structures requires careful consideration of the impact of the thrust force on the walls. This expansion can be reduced by installing rigid and durable ridge girders. It is necessary to try to increase the rigidity of the girder by installing racks, cantilever beams or struts, or by erecting a construction lift. This is especially true for houses made of timber, chopped logs, and lightweight concrete. Concrete, brick and panel houses withstand the force of thrust on the walls much more easily.

Thus, the truss structure, erected using the spacer option, is statically stable under various combinations of loads; it does not require rigid fastening of the mauerlat to the wall. In order to maintain the thrust, the walls of the building must be massive, equipped with a monolithic reinforced concrete belt around the perimeter of the house. In the event of an emergency, inside a spacer system that works in compression, a contraction will not save the situation, but will only partially reduce the thrust that is transmitted to the walls. It is precisely in order to avoid an emergency situation that it is necessary to take into account all the loads that may act on the roof.

Thus, no matter what shape the roof of the house is chosen, the entire rafter system must be designed in such a way as to satisfy the requirements of reliability and strength. Doing a complete analysis of the truss structure is not an easy task. In consideration wooden rafters must be enabled large number various parameters, including expansion, bending, possible weight loads. For a more reliable arrangement rafter system it is possible to install more suitable fastening methods. At the same time, you should not accept the dimensions of the rafters without making a full analysis of their technical and functional capabilities.

Calculation of rafter cross-section

The cross-section of the rafter beams is selected taking into account their lengths and the load they accept.

Thus, timber up to 3 meters long is selected with a cross-sectional diameter of 10 cm.

Beam, up to 5 meters long, with a cross-sectional diameter of 20 cm.

Beams up to 7 meters long – with a cross-sectional diameter of up to 24 cm.

How to calculate rafters - example

Given a two-story house measuring 8 by 10 meters, the height of each floor is 3 meters. Corrugated asbestos-cement sheets were chosen for the roof. The roof is gable, the support posts of which are located along the central load-bearing wall. The pitch of the rafters is 100 cm. You need to select the length of the rafters.

How to calculate the length of the rafters? As follows: the length of the rafter legs can be selected so that three rows of slate sheets are laid on them. Then required length: 1.65 x3 = 4.95 m. The roof slope in this case will be equal to 27.3°, the height of the formed triangle, that is attic space, 2.26 meters.

1. Calculation of load-bearing elements of the coating

Rafter legs are calculated as freely lying beams on two supports with an inclined axis. The load on the rafter leg is collected from the load area, the width of which is equal to the distance between the rafter legs. The calculated live load q must be located in two components: normal to the axis of the rafter leg and parallel to this axis.

2.1.1. Lathing calculation

We accept sheathing made of boards with a cross-section of 50´50 mm (r = 5.0 kN/m), laid in increments of 250 mm. Wood - pine. The pitch of the rafters is 0.9 m. The roof slope is 35 0.

The calculation of the sheathing for the roof is carried out according to two loading options:

a) Own weight of the roof and snow (calculation of strength and deflection).

b) Own weight of the roof and concentrated load.

Initial data:

1. We accept bars of the 2nd grade with the calculated resistance Ru=13 MPa and elastic modulus E=1´ 10 4 MPa.

2. Operating conditions B2 (in the normal zone), mV=1 ; mn=1,2 for installation load in bending.

3. Reliability factor according to purpose g n=0,95 .

4.Density of wood r =500 kg/m 3.

5. Reliability factor for load from the weight of galvanized steel g f=1,05 ; from the weight of the bars g f=1,1 .

6. Standard weight of snow cover per 1 m 2 horizontal projection of the earth’s surface S 0 =2400 N/m 2.

Lathing design diagram

Table 2.1

Load collection for 1 m.p. battens, kN/m

Where S 0 - standard value of the weight of snow cover per 1 m 2 horizontal

surface of the earth, taken according to the table. 4, for IV snow paradise

she S 0 = 2.4 kPa;

m- coefficient of transition from the weight of the snow cover of the earth to

snow load for coverage, accepted according to clauses 5.3 – 5.6.

When the beam is loaded with a uniformly distributed load from its own weight and snow, the maximum bending moment is equal to:

Kn m

At roof slope angles of a³10°, it is taken into account that the own weight of the roof and sheathing is evenly distributed over the surface (slope) of the roof, and the snow is distributed over its horizontal projection:

M x = M cos a = 0.076 cos 29 0 = 0.066 kN´m

M y = M sin a = 0.076 sin 29 0 = 0.036 kN´m

Moment of resistance:

The strength of the sheathing bars is checked taking into account oblique bending according to the formula:

Where M x And M y- components of the calculated bending moment relative to the main axes X and Y.

Ry=13 MPa

gn=0,95

The moment of inertia of the block is determined by the formula:

cm 4

Deflection in a plane perpendicular to the slope:

Deflection in a plane parallel to the slope:

Where E=10 10 Pa- modulus of elasticity of wood along the grain.

Full deflection:

= m

Deflection check: ,

where = is the maximum permissible relative deflection, determined according to table. 16.

When a beam is loaded with its own weight and a concentrated load, the maximum moment in the span is equal to:

Checking the strength of normal sections:

Where Ry=13 MPa- calculated bending resistance of wood.

gn=0,95 - reliability coefficient for the intended purpose.

The conditions for the first and second combinations are met, therefore we accept the sheathing with a section b´h=0.05´0.05 with a pitch of 250 mm.

2.1.2. Calculation of rafter legs

Let's calculate layered rafters made of beams with a single-row arrangement of intermediate supports for a galvanized roof. cr. iron. The base of the roof is a lathing made of bars with a cross-section of 50-50 mm in increments =0.25 m. Rafter foot step =1.0 m. Material for everyone wooden elements– pine of the 2nd grade. Operating conditions – B2.

Construction area - Vologda.

Calculation diagram of the rafter leg

The sheathing bars are placed along the rafter legs, which are lower

the ends rest on mauerlats (100 100), laid along the inner edge of the outer walls. In the ridge unit, the rafters are fastened with two plank overlays. To compensate for the expansion, the rafter legs are tightened with a crossbar - two paired boards. Roof inclination angle 29 0 .

We collect loads per 1 m2 of inclined surface of the coating, and enter the data in Table 2.2.

Table 2.2
Load collection for 1 m.p. rafter leg, kN/m

Where S 0 - standard value of snow cover weight per 1 m 2 horizontal surface land, taken according to the table. SNiP 4, for IV snow region S 0 = 2.4 kPa;

m- coefficient of transition from the weight of the snow cover of the ground to the snow load on the cover, accepted according to clauses 5.3 - 5.6.

We perform a static calculation of the rafter leg as a two-span beam loaded with a uniformly distributed load. The dangerous section of the rafter leg is the section at the middle support.

Bending moment in this section:

The vertical pressure at point C, equal to the right support reaction of the two-span beam, is:

=0.265 kN

With a symmetrical load on both slopes, the vertical pressure at point C doubles: kN.

By spreading this pressure in the direction of the rafter legs, we find the compressive force in the upper part of the rafter leg:

Collectionloads

First, to determine the loads, we set the cross-section of the rafter leg to 75x225 mm. The constant load on the rafter leg is calculated in table. 3.2.

Table 3.2 Calculated constant load per rafter leg, kPa

	Exploitation-		Limit
Elements and Loads		γ fm	meaning
	meaning		loads
	loads

Rafter leg 0.0750.2255/0.95
	g page e =0.372		g c tr. m = 0.403

Estimated maximum load on the rafter leg (combination of constant plus snow)

Geometric pattern of rafters

Schemes for calculating the rafter leg are shown in Fig. 3.2. With the width of the corridor in axes =3.4 m distance between the longitudinal axes of the outer and inner walls.

The distance between the axes of the power plate and the bed, taking into account the reference to the axis (

=0.2 m)m. We install the brace at an angle β = 45° (slope 2 = 1). The slope of the rafters is equal to the slope of the roof i 1 =i = 1/3 = 0.333.

To determine the dimensions necessary for the calculation, you can draw a geometric diagram of the rafters to scale and measure the distances with a ruler. If the mauerlat and the leg are on the same level, then the spans of the rafter leg can be determined using the formulas

Node heights h 1 =i 1 l 1 =0.333*4.35=1.45 m; h 2: = i 1 l=0.333*5.8=1.933 m. Height mark: take the crossbar 0.35 m below the intersection point of the axes of the rafter leg and the post h = h 2 - 0.35 (m) = 1.933 -0.35 = 1.583 m.

Forces in the rafter leg on the crossbar

The rafter leg acts as a three-span continuous beam. Support settlements can change the supporting moments in continuous beams. If we assume that due to the subsidence of the support, the bending moment on it has become equal to zero, then we can conditionally cut the hinge into the place of zero moment (above the support). To calculate the rafter leg with a certain safety margin, we assume that the subsidence of the strut has reduced the supporting bending moment above it to zero. Then the design diagram of the rafter leg will correspond to Fig. 3.2, c.

Bending moment in rafter leg

To determine the thrust in the crossbar (tightening), we assume that the supports have sagged in such a way that the supporting moment above the strut is equal to M 1 and above the racks - zero. Conventionally, we cut the hinges into places of zero moments and consider the middle part of the rafters as a three-hinged arch with a span l cp = 3.4 m. The space in such an arch is equal to

Vertical component of the strut reaction

Using the diagram in Fig. 3.2.g, we determine the force in the strut

Rice. 3.2. Schemes for calculating rafters

a-cross section of the attic covering; b - diagram for determining the estimated length of the rafter leg; c - design diagram of the rafter leg; d - diagram for determining the thrust in the crossbar; l - also for a scheme with one longitudinal wall; 1 - Mauerlat; 2 - lying down; 3 - run; 4 - rafter leg; 5 - stand; 6 - strut; 7 - crossbar (tightening); 8 - spacer; 9, 10 - thrust bars; 11 - filly; 12 - overlay.

Calculation of rafter legs based on the strength of normalsections

Required moment of resistance of the run

According to adj. M we take the width of the rafter leg b = 5 cm and find the required section height

According to adj. We take a board with a section of 5x20 cm.

There is no need to check the deflections of the rafter leg since it is located in a room with limited access by people.

Calculation of board jointsrafter leg.

Since the length of the rafter leg is more than 6.5 m, it is necessary to make it from two boards with an overlapping joint. We place the center of the joint at the point where it rests on the strut. Then the bending moment at the joint during subsidence of the strut M 1 = 378.4 kN*cm.

We calculate the joint in the same way as the joint of purlins. We accept the overlap length l nahl = 1.5 m = 150 cm, nails diameter d= 4 mm = 0.4 cm long l guards = 100 mm.

Distance between axes of nail connections

150 -3*15*0.4 =132 cm.

Force perceived by a nail connection

Q=M op /Z=378.4/ 132 =3.29 kN.

Estimated nail pinching length taking into account the normalized maximum gap between boards δ W = 2 mm with board thickness δ D = 5.0 cm and nail tip length l.5d

a p = l gv -δ d -δ w -l.5d = 100-50-2-1.5*4 = 47.4 mm = 4; 74 cm.

When calculating a dowel (nail) connection:

– thickness of the thinner element a= a p =4,74 cm;

– thickness of the thicker element c = δ d =5.0 cm.

Finding a relationship a/c = 4,74/5,0 = 0,948

According to adj. T, we find the coefficient k n =0.36 kN/cm 2.

We find the load-bearing capacity of one seam of one nail from the conditions:

– crushing in a thicker element

= 0.35*5*0.4*1*1/0.95 = 0.737 kN

– crumpling in a thinner element

= 0.36*4.74*0.4*1*1/0.95 = 0.718 kN

– nail bending

= (2,5* 0,4 2 + 0,01* 4,74 2)

/0.95=0.674 kN

– but not more than kN

Choose the smallest of the four values T = 0.658 kN.

Finding the required number of nails n guards ≥ Q/ T =2,867/0,674=4,254.

We accept n guards = 5.

We check the possibility of installing five nails in one row. The distance between the nails across the wood fibers is S 2 = 4d = 4 * 0.4 = 1.6 cm. The distance from the outer nail to the longitudinal edge of the board is S 3 = 4d = 4 * 0.4 = 1.6 cm.

According to the height of the rafter leg h = 20 cm should fit

4S 2 +2Sз=4*1.6+2*1.6 = 9.6 cm

Calculation of the connection between the crossbar and the rafter leg

According to the assortment (Appendix M), we accept a crossbar made of two boards with a cross-section bxh = 5x15 cm each. The force at the joint is relatively large (N = 12, kN) and may require the installation of a large number of nails under construction site conditions. To reduce the labor intensity of installation of the covering, we design a bolted connection of the crossbar with the rafter leg. We accept bolts with a diameter d = 12 mm = 1.2 cm.

In the rafter leg, dowels (bolts) crush the wood at an angle to the fibers α = 18.7 0. According to adj. We find the coefficient k α =0.95 corresponding to the angle α =18.7 0.

When calculating a dowel connection, the thickness of the middle element is equal to the width of the rafter c = 5 cm, the thickness of the outer element is the width of the crossbar board a = 5 cm.

We determine the load-bearing capacity of one seam of one dowel from the conditions:

– crushing in the middle element

= 0.5*5* 1.2*0.95* 1 *1/0.95 = 3.00 kN

– crushing in the outermost element

= 0.8*5*1.2*1*1/0.95 = 5.05 kN;

– dowel bend = (l.8* 1.2 2 + 0.02* 5 2)

/0.95=3.17 kN

- but not more than kN

Of the four values, select the smallest T = 3.00 kN.

We determine the required number of dowels (bolts) with the number of seams n w =2

We accept the number of bolts n H =3.

There is no need to check the cross-section of the cross-bar for strength since it has a large margin of safety.

4. ENSURING SPATIAL RIGIDITY AND GEOMETRICAL STABILITY OF THE BUILDING

Collectionloads

First, to determine the loads, we set the cross-section of the rafter leg to 75x225 mm. The constant load on the rafter leg is calculated in table. 3.2.

Table 3.2 Calculated constant load on the rafter leg, kPa

	Exploitation-		Limit
Elements and Loads		γ fm	meaning
	meaning		loads
	loads

Rafter leg 0.0750.2255/0.95
	g page e =0.372		g c tr. m = 0.403

Estimated maximum load on the rafter leg (combination of constant plus snow)

Geometric pattern of rafters

Schemes for calculating the rafter leg are shown in Fig. 3.2. With the width of the corridor in axes =3.4 m distance between the longitudinal axes of the outer and inner walls.

The distance between the axes of the power plate and the bed, taking into account the reference to the axis (
=0.2 m)m. We install the brace at an angle β = 45° (slope 2 = 1). The slope of the rafters is equal to the slope of the roof i 1 =i = 1/3 = 0.333.

Forces in the rafter leg on the crossbar

Bending moment in rafter leg

Vertical component of the strut reaction

Using the diagram in Fig. 3.2.g, we determine the force in the strut

Rice. 3.2. Schemes for calculating rafters

Calculation of rafter legs based on the strength of normalsections

Required moment of resistance of the run

According to adj. M we take the width of the rafter leg b = 5 cm and find the required section height

According to adj. We take a board with a section of 5x20 cm.

There is no need to check the deflections of the rafter leg since it is located in a room with limited access by people.

Calculation of board jointsrafter leg.

We calculate the joint in the same way as the joint of purlins. We accept the overlap length l nahl = 1.5 m = 150 cm, nails diameter d= 4 mm = 0.4 cm long l guards = 100 mm.

Distance between axes of nail connections

150 -3*15*0.4 =132 cm.

Force perceived by a nail connection

Q=M op /Z=378.4/ 132 =3.29 kN.

Estimated nail pinching length taking into account the normalized maximum gap between boards δ W = 2 mm with board thickness δ D = 5.0 cm and nail tip length l.5d

a p = l gv -δ d -δ w -l.5d = 100-50-2-1.5*4 = 47.4 mm = 4; 74 cm.

When calculating a dowel (nail) connection:

– thickness of the thinner element a= a p =4,74 cm;

– thickness of the thicker element c = δ d =5.0 cm.

Finding a relationship a/c = 4,74/5,0 = 0,948

According to adj. T, we find the coefficient k n =0.36 kN/cm 2.

We find the load-bearing capacity of one seam of one nail from the conditions:

– crushing in a thicker element

= 0.35*5*0.4*1*1/0.95 = 0.737 kN

– crumpling in a thinner element

= 0.36*4.74*0.4*1*1/0.95 = 0.718 kN

– nail bending

= (2,5* 0,4 2 + 0,01* 4,74 2)
/0.95=0.674 kN

– but not more than kN

Choose the smallest of the four values T = 0.658 kN.

Finding the required number of nails n guards ≥ Q/ T =2,867/0,674=4,254.

We accept n guards = 5.

According to the height of the rafter leg h = 20 cm should fit

4S 2 +2Sз=4*1.6+2*1.6 = 9.6 cm<20 см. Устанавливаем гвозди в один ряд.

Calculation of the connection between the crossbar and the rafter leg

In the rafter leg, dowels (bolts) crush the wood at an angle to the fibers α = 18.7 0. According to adj. We find the coefficient k α =0.95 corresponding to the angle α =18.7 0.

We determine the load-bearing capacity of one seam of one dowel from the conditions:

– crushing in the middle element
= 0.5*5* 1.2*0.95* 1 *1/0.95 = 3.00 kN

– crushing in the outermost element
= 0.8*5*1.2*1*1/0.95 = 5.05 kN;

– dowel bend = (l.8* 1.2 2 + 0.02* 5 2)
/0.95=3.17 kN

- but not more than kN

Of the four values, select the smallest T = 3.00 kN.

We determine the required number of dowels (bolts) with the number of seams n w =2

We accept the number of bolts n H =3.

There is no need to check the cross-section of the cross-bar for strength since it has a large margin of safety.

4. ENSURING SPATIAL RIGIDITY AND GEOMETRICAL STABILITY OF THE BUILDING

The construction of any house ends with the construction of a roof, for which it is necessary to make a rafter system. Its design includes: Mauerlat, rafter legs, struts, tightening, sprigs, racks, trusses, sheathing and other elements that provide rigidity and strength.

The rafter leg in different roof designs can be called a slant (diagonal) or an ordinary rafter. The dimensions of the rafter leg are selected based on the constant and variable loads that will subsequently affect the roof. This is necessary to ensure that the rafters are strong enough to withstand the impact.

coating weight;
the mass of other elements of the truss structure;
weight of hydro- and vapor barrier materials;
a lot of ceiling finishing if there is an attic room.

Characteristics of rafter legs

Based on the calculation of loads, they choose - the dimensions must be such that they can withstand the planned impact. At the same time, pay attention to the type of roofing covering and the type of roof. Rafters can be layered or hanging; complex roofing systems consist of both types.

In hip roofs, in addition to rafter legs, shortened rafters are also used - rafters, which also have to be calculated. It is necessary to calculate the dimensions of additional elements of the rafter system - tie rods, racks, struts, crossbars, since part of the load from the rafters is transferred to them.

The length of the rafter leg is determined based on the parameters of the building and the roof slope, which depends on the selected type of roof. The size of roof rafters usually does not exceed 6 meters in length, since lumber of longer lengths is not commercially available. But it happens that the dimensions of the house require the use of elements of greater length - in this situation they are increased (read: ""). Long rafter legs are most often found in diagonal parts, during the construction of half-hip or hip roofs.

The selection of the rafter leg section is influenced by various factors:

slope of slopes;
type of coating material;
house dimensions;
roof type;
climatic features of the region;
the quality of the material from which they were made.

Coniferous wood is usually used to create a rafter system. When choosing, you need to pay attention to the fact that there is no blue stain or a large number of knots on the beams or boards.

The humidity of the raw materials should be no more than 20-22%, since an overly wet tree will change in size during drying, and this can cause a violation of the roof’s tightness and other adverse consequences.

It is advisable to entrust all calculations related to the rafter system, including, to a specialist - currently there are enough enterprises that provide this service. You can also find ready-made programs on the Internet that allow you to calculate rafter legs - their length and dimensions. You only need to enter the data necessary for the calculation into the program, and the program will calculate what the section, length and should be.

When constructing roofs of private houses, boards are often used. The size of the rafter boards is such that the cross-section is 50x150 millimeters - they are suitable for roofs of various designs. The pitch of the rafter legs is approximately one meter - this distance depends on the type of roofing material, the slope of the roof and the amount of snow in winter.

If the roof slope exceeds 45 degrees, then the rafter pitch can be 1.2 - 1.4 meters. If the region is characterized by winters with a lot of snow, then the pitch between the rafters will be 0.6 - 0.8 meters.

Much attention should be paid to the type of roofing material. Natural tiles are the heaviest. The greater the length of the legs of the rafters and the step between them, the larger the cross-section will be. The dimensions of the timber for the rafters are usually 150x150 millimeters.

Installation of rafter legs

It is very important to correctly attach the rafter legs to the mauerlat. The strength and reliability of the roof depends on how it is done with the Mauerlat. There are two mounting options - rigid and sliding. Each of them fits certain rafters - hanging or layered.

Rigid fastening makes any turns, movements or bends of the rafters impossible. To do this, make cuts on the rafters and secure the leg with the Mauerlat using wire, metal staples or long nails. You can also use metal corners.

A sliding joint (also called a hinged joint) can have two degrees of freedom. It is usually used when constructing a roof over a wooden house, since it allows the roof to settle over time on the frame, which shrinks over the first few years. In this case, the connection of the rafters to the ridge is not made rigid. With this method, the rafter leg is joined to the mauerlat by sawing and strengthening on both sides with two nails driven diagonally or opposite each other. It is also possible to hammer one nail into the rafter leg from top to bottom, penetrating into the mauerlat (read also: "

To strengthen them, they make struts in the form of vertical posts. More than two racks are rarely installed. To strengthen the slanted rafters, a strut or stand is also installed, which should rest on a wooden lining located directly on the ceiling (in the case of a reinforced concrete slab) or on a tie, which is also a ceiling beam. The struts are supported on a bench and placed at an angle of 45 to 50 degrees. Their main purpose is the ability to take on the maximum load from the rafters.

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The calculation of the rafter system should be done not after the construction of the house frame, but at the stage of preparing the building project. It must be remembered that for very important and prestigious buildings, it is recommended to order such work from professional architects, only they will be able to perform the correct calculations and guarantee the duration and safety of the structure’s operation.

Although this is one of the simplest types of systems for residential buildings, there are several types of design. Diversity allows you to increase the options for using roofs when building houses according to standard or individual exclusive projects.

Type of gable roof truss system	Architectural features and brief description
	The most commonly used option has two completely identical rectangular slopes. Loads between individual elements are distributed evenly regardless of their location. The number of additional stops is not limited; the specific decision is made depending on the plans for using the attic space. Calculations can be done using free programs posted on construction sites.
	The ridge is shifted to one side of the house or slopes with different angles of inclination. The roof truss system is more complex to calculate. If in a simplified version it is possible to calculate one slope and automatically apply the obtained data to the second, then this option cannot be used for an asymmetrical rafter system. Advantages: original appearance. Disadvantages are the complexity of calculations and installation and the reduction in usable attic space.
	Most often used during the construction of attic spaces, it allows you to significantly increase the volume of attic spaces. The calculations are of medium complexity. Rafter system with external bend. Systems with an internal fracture are rarely found; apart from the original appearance, they have no advantages.

Structural elements of the rafter system

We will give a list of all the elements that need to be calculated for each specific case.

The simplest element of the rafter system can be made from timber 150×150mm, 200×200mm or boards 50×150mm and 50×200mm. On small houses it is allowed to use paired boards with a thickness of 25mm or more. The Mauerlat is considered an unimportant element; its task is only to evenly distribute point forces from the rafters along the perimeter of the facade walls of the building. It is fixed to the wall on a reinforcing belt using anchors or large dowels. Some rafter systems have large expansion forces; in these cases, the element is designed for stability. Accordingly, the optimal methods for fixing the Mauerlat to the walls are selected, taking into account the material of their masonry.

Prices for timber

They form the silhouette of the rafter system and absorb all existing loads: from wind and snow, dynamic and static, permanent and temporary.

They are made from boards 50×100 mm or 50×150 mm, and can be solid or extended.

The boards are calculated based on their bending resistance, and taking into account the data obtained, wood species and types, the distance between the legs, and additional elements to increase stability are selected. The two connected legs are called a truss and may have tie-rods at the top.

Tightenings are calculated for tension.

Runs

One of the most important elements of the rafter system of a gable roof. They are designed for maximum bending forces and are made of boards or timber with a section corresponding to the loads. A ridge girder is installed in the highest place; side girders can be mounted on the sides. Run calculations are quite complex and must take into account a large number of factors.

Can be vertical or inclined. Inclined ones work in compression and are attached at right angles to the rafters. The lower part rests against floor beams or concrete slabs; options for resting against horizontal beams are acceptable. Due to the stops, it is possible to use thinner lumber to make rafter legs. Vertical stops work for compression, horizontal stops for bending.

Lezhny

They are laid along the attic space, resting against several load-bearing walls or interior partitions. Purpose - to simplify the manufacture of a complex rafter system, to create new points for transferring loads from various types of stops. For the beds, you can use beams or thick boards; the calculation is made based on the maximum bending moment between the support points.

Lathing

The type of sheathing is selected taking into account the technical parameters of roofing coverings and does not affect the performance of the rafter system.

What type of lathing is needed for corrugated sheeting? When to install wood and when to install metal? How to choose the right lathing pitch and what factors to consider?

Prices for construction boards

Construction boards

Stages of calculating a gable roof

All work consists of several stages, each of which has a great impact on the stability and durability of the structure.

Calculation of parameters of rafter legs

Based on the data obtained, the linear parameters of the lumber and the pitch of the trusses are determined. If the loads on the rafters are very large, then vertical or angular stops are installed to distribute them evenly, and the calculations are repeated taking into account new data. The direction of influence of forces, the magnitude of torque and bending moments change. During calculations, three types of loads must be taken into account.

Permanent. These loads include the weight of roofing materials, sheathing, and insulating layers. If the attic space is in use, then the weight of all finishing materials on the internal surfaces of the walls should be taken into account. Data on roofing materials is taken from their technical characteristics. Metal roofs are the lightest, natural slate materials, ceramic or cement-sand tiles are the heaviest.
Variable loads. The most difficult efforts to calculate, especially now, when the climate is changing dramatically. For calculations, data is still taken from outdated SNiP reference books. For his tables, information from fifty years ago was used; since then, the height of the snow cover, the strength and the prevailing direction of the wind have changed significantly. Snow loads can be several times higher than those in the tables, which has a significant impact on the reliability of calculations.

Moreover, the height of the snow changes not only taking into account the climate zone, but also depending on the location of the house on the cardinal points, the terrain, the specific location of the building, etc. Data on the strength and direction of the wind are also unreliable. Architects have found a way out of this difficult situation: data is taken from outdated tables, but to ensure reliability and stability, a safety factor is used in each formula. For critical rafter systems on residential buildings, the standard is 1.4. This means that all linear parameters of the system elements increase by 1.4 times and due to this, the reliability and safety of the structure’s operation increases.

The actual wind load is equal to the indicator in the region where the structure is located, multiplied by the correction factor. The correction factor characterizes the location of the building. The same formula is used to determine the maximum snow load.
Individual loads. This category includes specific forces that affect the rafter system of a gable roof during an earthquake, tornado and other natural disasters.

The final values are determined taking into account the probability of simultaneous action of all the above loads. The dimensions of each element of the rafter system are calculated using a safety factor. Using the same algorithm, not only rafter legs are designed, but also lintels, stops, braces, purlins and other roof elements.

The construction of the roof frame is carried out according to the developed project, which specifies all the necessary parameters, including the type of structure, rafter spacing, cross-section of elements and method of installation of components.

Principles of system calculation

During the operation of the roof, its frame experiences high loads of various types.:

constant (weight of the rafter system itself and the roofing pie);
periodic (wind and snow load, weight of a person servicing or repairing a roof or chimney).

To correctly calculate and make a reliable roof, you need to decide on its configuration, choose the type of roofing, and calculate the optimal angle of inclination of the slopes. The degree of complexity of the frame and the dimensions of its elements depend to a certain extent on the parameters of the design load, the main part of which falls on the rafters. It is advisable to choose the dimensions of a wooden rafter, such as cross-section, with some margin of safety.

How to determine the length of the rafters? For calculations, you need to apply the Pythagorean theorem (if the length of the end wall and the height of the ridge are known), or the theorem of sines (if, in addition to the length of the end wall, the angle of inclination of the roof slope is known).

To make rafters, you can use boards or timber. Additional elements that give rigidity to the structure will help build a roof frame designed for high loads.

Determining the pitch of the rafters

To calculate the pitch of the rafters, it is necessary to take into account the weight of the roofing, the angle of inclination of the slopes, wind and snow loads. On average, the pitch (the distance between adjacent legs that form the roof slope) ranges from 70 to 120 cm.

To eliminate the risk of deformation of the rafter legs under high loads, it is recommended to use dry lumber when installing the rafter system. Usually this is a beam or board with a thickness of at least 50 mm. The exact dimensions of the wooden rafters and other elements are determined based on the requirements for structural strength.

The pitch of the rafters depends on the degree of roof slope and the length of the rafter legs. To build a strong roof by covering the large span between the ridge and the top of the wall, the pitch of the rafters should be reduced. For example, for a roof with a slope of 45°, the maximum pitch should be no more than 80 cm. The pitch of the rafters should also be reduced when using heavy roofing materials, which include ceramic tiles, cement-sand tiles, and asbestos-cement slate.

Calculation of the cross-section of rafter system elements

If you have to build a roof with your own hands, you need to do this. You should also pay attention to the characteristics of the material from which the rafter legs are made.

Regulatory documents regulate the load-bearing capacity of wood of various species. If the cross-section of rafters made of timber or boards weakened by cuttings and/or holes for bolted connections is considered, the load-bearing capacity of the wood is calculated with a coefficient of 0.8 from the standard value. It is also necessary to pay attention to the type of wood used for manufacturing - defects reduce its resistance to stress. The cross-section of the rafters is selected taking into account the standard dimensions of lumber. A continuous supporting structure should be made from timber or boards no more than 6.5 m long.

Having calculated the system and determined the dimensions of the rafter legs and crossbars, you need to calculate the total weight of these elements and add the resulting value to the design loads:

the total volume of lumber required for the roof frame is multiplied by the volumetric weight of the wood;
the resulting value (the dead weight of the rafters, kg/m2) is added to the calculated load;
the design design diagram is recalculated using the result obtained above.

Treating rafter elements with an antiseptic

In private construction, the construction of a rafter system is most often carried out from lumber, since wood is affordable and allows you to make structures with your own hands without the use of complex tools. Wood material prepared for installation (such as timber, rounded logs) often arrives at the construction site already treated with protective agents under production conditions. But production usually involves boards or timber that are not impregnated with special compounds.

How to treat the rafters before installing the roof frame? Treatment is required to protect the wood from rotting and prevent fire hazards. Treatment with an antiseptic and a fire retardant can be carried out separately. Using a complex fire-bioprotective agent, treatment will take half as much time.

Treatment with an antiseptic or a combined composition should be performed in two steps. It is necessary to saturate the top layer of wood with a special liquid, applying it with a brush or roller. After the first layer has dried, the antiseptic treatment is repeated.

Pitched roof rafters

How to make rafters for a pitched roof? Construction of a rafter system for a single-pitched or gable roof with your own hands requires a careful approach to the manufacture of rafter legs. Dimensions are calculated at the roof design stage. To correctly make these structural elements, it is necessary to use lumber of a section and length regulated by the design.

The degree of complexity of the work largely depends on which structure is chosen for installation. If it is necessary to make layered rafters from boards or timber, each element is adjusted to the installation site when attaching it to the ridge girder and mauerlat. It is important to strictly monitor compliance with the geometry of the entire structure.

It is more convenient to make hanging trusses using a template in order to achieve an exact match of the dimensions of each structure. For this purpose, cutting into boards and assembling trusses is recommended to be done on the ground. Then it is necessary to check the horizontality of the mauerlat or support beams, and the geometric dimensions of the building box. Having eliminated possible shortcomings, you can begin installing roof trusses on the house.

Diagonal rafters

Arranging a hip roof rafter system with your own hands requires the installation of various types of rafters, such as:

sloped (diagonal beams forming a triangular slope);
central hip;
lateral;
shortened (narozhniki).

The side rafter legs are made of boards and installed similarly to the elements of a conventional pitched roof with a hanging or layered structure. The central hip rafters are layered elements. To make sprigs, bars or boards are used, which are attached to diagonal beams and the mauerlat.

How to make rafters for a hip roof? To properly install this type of roofing structure, you need to accurately calculate the cross-section and angle of inclination of the slant beams. The dimensions of the elements depend on the length of the span being covered. It is important to maintain symmetry when installing diagonal rafter beams, otherwise the roof may deform under load.

Manufacturing rafters to a given size

The use of standardized lumber for the manufacture of various elements of the rafter system allows you to optimize construction costs and simplify the calculation and installation of roof components. In particular, if it is necessary to make rafter legs of a certain section and length, a solid beam, its sections or boards can be used.

To make a rigid beam with your own hands, the method of joining the boards is used - they are connected with wide sides and punched in a checkerboard pattern with nails. A long beam of a given section can be made from four or more correctly joined boards - interconnected with a shift of half the length of the board. This beam is highly durable and can be used as a diagonal rafter.

When deciding how to lengthen rafters, you can use the liner method. In this case, a third one is laid between two boards, protruding to a certain length. To connect the boards, nails driven in in a checkerboard pattern are used. It is important not only to carefully align the boards, but also to insert board fragments (inserts) corresponding in thickness to the central board into the empty space between the outer elements. This method allows you to extend the length of standard rafter legs (not hip ones).

Principles of fastening rafters

To ensure the reliability of a rafter system that you build yourself, you need to decide in advance how to attach the rafters to the ridge and to the roof support. If you intend to make a fastening that will prevent deformation of the roof during shrinkage of the building, it is necessary to fasten the rafters together at the top with a bolt with a nut or a hinge plate, and at the bottom to install a special fastening element - a sliding support.