Lecture 5 пдк

1.

LECTURE 5
Enclosing structures
of timber buildings
Roof coverings, decking, purlins and factory-made ribbed panels: in plain language
TIMBER AND PLASTIC
and with real numbers
STRUCTURES
TIMBER STRUCTURES · ENCLOSING STRUCTURES
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OUTLINE
Lecture structure
01
02
03
Types of enclosing structures
Thermal and vapour insulation
Decking and battens
Cold and warm, attic and non-attic roofs
Where the insulation and vapour barrier are placed
The base under roofing felt and corrugated sheets
04
05
06
Purlins
Factory-made ribbed panels
Calculations and real numbers
Five types, joints and key ratios
Frame, sheathing, insulation and joints
Loads, cross-sections, deflection limits
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PART I
Enclosing structures:
types and layers
What roofs are like, how they are protected from heat loss and moisture, and what
materials they are made of
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CLASSIFICATION
Enclosing structures: what types are there?
• By heating. Unheated buildings are designed with cold structures (without insulation), and heated buildings with warm structures (with thermal
insulation).
• By place of manufacture. They can be assembled on site from individual elements or produced at a factory as ready-made slabs and panels.
• Industrialisation. After construction moved to industrial methods, large roof slabs and wall panels with a timber frame, sheathed with plywood,
asbestos-cement sheets and wood-based boards, became widespread.
TERM
Enclosing structure
A structure that separates the building from the external environment (rain, snow, wind, cold): the roof and external walls. It not only carries loads but also retains heat
inside.
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ROOF TYPES
Attic and non-attic roofs
• Attic roof. The roof covering is on top, with a separate attic floor below it.
• Non-attic roof. A single structure performs the functions of both roof and
ceiling.
• Depending on the span. If the distance between walls does not exceed 7 m,
the roof rests on rafters and the attic floor on the walls. For larger spans, the
roof rests on beams and trusses, and the attic floor is suspended from them.
In the figure: а — attic roof, б — non-attic roof; в, г, д — design schemes of decking and wall sheathing (load
and bending moment diagrams). Key: 1 — roof covering, 2 — decking, 3 — rafter system, 4 — attic floor, 5 —
building wall, 6 — roof slabs, 7 — load-bearing structure.
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7m
Up to this span, the roof rests directly on the
rafters
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PROTECTIVE LAYERS
Thermal and vapour insulation
• Thermal insulation. To prevent heat loss, insulation is placed on the external (cold) side of the
structure. Light, non-combustible or low-combustible rigid or semi-rigid boards are
recommended.
• Vapour barrier. It is placed on the internal (warm) side and protects against wetting by
condensation. Roll materials are used: tar paper, roofing paper, synthetic films.
• Depending on air humidity. If the indoor air humidity is up to 60 %, the roof is made without
cavities; if it is higher, vent cavities (through ventilation channels) are provided to remove excess
moisture.
≤ 60 %
Up to this air humidity limit, an unventilated (cavity-free) roof is
used
TERM
Vapour barrier
A thin barrier layer placed on the warm side so that
water vapour from the warm room does not penetrate
the structure, turn into water (condensate) in a cold zone
and wet the timber.
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REAL DATA
Roofing materials and their weight
Roofing material
Application
Weight, kN/m²
Three layers of roofing felt bonded with mastic
Unheated buildings
0.2…0.3
Standard-profile corrugated asbestos-cement sheets
Unheated buildings
0.25…0.4
Three layers of roofing felt on mastic over a levelling layer
Heated, indoor air humidity ≤ 60 %
0.5…0.7
Three layers of roofing felt bonded with mastic
Heated, humidity > 60 %
0.4…0.6
Standard-profile asbestos-cement sheets
Heated, humidity > 60 %
0.4…0.6
Weights are given without thermal insulation. The lightest is uninsulated roofing felt (0.2…0.3 kN/m²); the heaviest is a warm roof with a levelling layer (0.5…0.7
kN/m²).
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8.

PART II
Decking and
purlins
The decking and battens that form the roof base, the transverse beams (purlins) that
support them, and their calculation
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ROOF BASE
Decking and battens: what holds the roof up?
• Under roofing felt. Laid in two layers of boards joined with nails. The upper protective layer of boards no wider than 100 mm is laid at 45° to the lower one.
The lower layer is spaced out for better ventilation.
• Under corrugated sheets, steel or tiles. Battens are made of bars with a cross-section of at least 50×50 mm; their spacing depends on the load and the size of
the roofing material.
• Roof of a heated building. Thermal insulation is laid on continuous board decking or on a solid deck. The boards are butted tightly or joined with tongue and
groove.
16…22 mm
19…32 mm
≥ 50×50 mm
Board thickness of the upper protective layer
Thickness of the lower (spaced) layer or solid deck (by
calculation)
Minimum cross-section of batten bars under corrugated
sheets
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DESIGN PROCEDURE
How is decking calculated? In plain language
• Material. Decking and battens are usually made of grade 3 softwood. Soft hardwoods (poplar, aspen,
alder) are also suitable for battens.
• Design scheme. Decking made of long boards is calculated as a two-span beam.
• Two load cases. 1) dead and snow load: for strength and stiffness; 2) self-weight plus a 1 kN point
1 kN
Design point load on the decking (weight of a person with tools)
load (worker with tools): for strength only. Wall sheathing is designed for wind load.
• Erection factor. For the erection load case, the design bending resistance is taken as 13 × 1.2 = 15.6
MPa.
15.6 MPa
Design bending resistance of timber for the erection case
TERM
Design bending resistance
The limit of bending stress that timber can withstand
without failure, reduced by safety factors. For grade 3
timber it is 13 MPa.
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TRANSVERSE BEAMS
Purlins: types and joints
TERM
Purlin
A transverse beam that transfers the roof load from the decking, battens or
rafters to the load-bearing structures.
In the figure (top to bottom): а — simple (simply supported) purlin; б — with corbels (subbeams); в — with knee braces; г — cantilever (Gerber) purlin; д — continuous, made of
paired boards; е — plan of continuous purlins. On the right: joints А, Б, В, Г. Key: 1 —
load-bearing structure, 2 — purlin, 3 — corbel, 4 — knee brace, 8 — nail, 10 — bolt.
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PURLIN TYPES · 1
Simple purlins, purlins with corbels and with knee braces
а
б
в
Simple (simply supported)
With corbels (sub-beams)
With knee braces
Made of logs or squared timber, jointed
over the supports. Easy to make and erect,
but timber consumption is high, especially
for spans over 4 m.
A short additional beam is placed on the
support to reduce the design span. Its
overhang is a₁ = 0.17 l (l is the distance
between supports). No corbels are placed
on the end supports.
The upper ends of the braces connect at
about one third of the purlin span. Angle
of inclination to the horizontal: 30…45°.
Makes the system stable along its length.
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PURLIN TYPES · 2
Cantilever and continuous purlins
г
д
Cantilever (Gerber)
Continuous (paired boards)
Used in non-attic roofs when the distance between load-bearing structures does
not exceed 4.5 m. Joints are staggered from span to span.
Joints are staggered so that each joint in one board is covered by a continuous
board alongside it. Used on low pitches (under roofing felt): on steep pitches, thin
boards cannot carry the load component along the slope.
x ≈ 0.15 l
x ≈ 0.21 l
500 mm
≤ 4.5 m
Joint at this distance from the support:
span and support moments are equal (M =
ql²/16)
At this distance, the deflections of the span
and the cantilever part are equal
In a continuous purlin, nails are driven in a
staggered pattern at this spacing
Maximum distance between supports of a
cantilever purlin
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WORKED EXAMPLE · 1
Loads on the decking and purlin
Load component
Characteristic
n
Design
Roofing felt
0.1
1.3
0.13
Cement screed, 20 mm
0.4
1.3
0.52
Wood-wool insulation, 100 mm
0.5
1.2
0.6
Vapour barrier
0.02
1.3
0.026
Board decking
0.095
1.1
0.105
Total
1.12
—
1.38
Snow load
0.5
1.4
0.71
TERM
Problem statement
Industrial building 24×35 m, heated, roof pitch 0.1. Loadbearing structures spaced at 4.5 m; purlins placed every
1.25 m along the slope.
• Roof. Three layers of roofing felt, cement screed, 100 mm
wood-wool slab, a single layer of pine board decking.
• Snow. The snow load for the design region is taken as 0.7
kN/m².
Loads in kN/m; n is the load factor (accounts for possible variation of the load).
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WORKED EXAMPLE · 1
Result: which cross-section was chosen?
19 mm
1/327
2 × (50×150) mm
Selected thickness of the board decking (by
calculation, at least 13.5 mm is sufficient)
Deflection of the decking; permissible 1/143 —
requirement met
Cross-section of the continuous purlin: two paired
boards
1/562
4.61 kN·m
6 nails
Deflection of the purlin; permissible 1/190 —
requirement met
Maximum bending moment in the purlin (over the
support)
Number of nails in the purlin joint (4 mm diameter,
120 mm long)
TERM
Deflection
How much a beam bends under load. It must not exceed a certain fraction of the span (e.g. 1/143), otherwise the roof sags visibly.
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PART III
Factory-made ribbed
slabs and panels
Lightweight timber panels manufactured ready-made at a factory: design, materials,
joints and calculation
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KEY CONCEPT
What is a ribbed panel?
TERM
Ribbed slab (panel)
A lightweight element consisting of a timber frame (longitudinal and transverse ribs) and sheathing (flanges) glued or screwed to it, with thermal insulation inside. The frame
carries the load; the flanges form the wall or roof surface.
• Application. In heated buildings with indoor air humidity up to 75 %, and in unheated
buildings without water vapour emission, in regions with a design outdoor temperature
down to –50 °C.
• Roof slabs. Intended for buildings without roof lights and with external drainage. Floor
slabs are no longer than 3 m.
75 %
–50 °C
Limit of indoor air humidity in
heated buildings
Design outdoor temperature for
unheated buildings
3 / 4.5 / 6 m
Typical lengths of roof slabs (9 and 12 m in special cases)
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FROM THE FIGURE
Types of ribbed slabs
• а, б. 6 m plywood slab; two-span slab (3 m each).
• в, г, д. Cross-sections: with board ribs; with bent plywood profile ribs; with glued reinforced
ribs.
• е. Cross-section of a slab with a flat asbestos-cement bottom flange and corrugated sheet
roofing.
• ж, и. Three-rib and two-rib slabs spanning 9…12 m.
• к, л. Slab with steel tie rods (trussed slab); detail of fixing the slab to the load-bearing structure.
Key: 1 — top flange, 2 — longitudinal rib, 6 — transverse rib, 8 — thermal insulation, 9 — bottom flange, 10
— vapour barrier, 16 — steel tie rod, 18 — roofing felt, 20 — elastic gasket and sealant.
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MATERIALS
What is a panel made of?
1
2
3
Frame (ribs)
Sheathing (flanges)
Insulation and vapour barrier
Longitudinal load-bearing ribs: solid
boards, glued elements, plywood profiles
or plywood-web beams. Transverse ribs
are usually made of boards. The spacing of
longitudinal ribs does not exceed 500 mm.
Water-resistant construction plywood, flat
asbestos-cement sheets, hard and extrahard fibreboard, fibreglass. Particleboard
and cement-bonded particleboard are
also suitable for internal flanges. The
external flanges of wall panels must be
moisture-resistant.
Non-combustible or low-combustible:
mineral wool boards, glass fibre. With
asbestos-cement flanges, wood-wool
board and foam plastic are also used. Soft
insulation is held by clamping grids made
of 25×25 mm bars. Vapour barrier: roll
waterproofing material or paint.
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KEY DIMENSIONS
Plywood and asbestos-cement panels: the numbers
≥ 6 mm
≥ 8 mm
≤ 500 mm
10 × thickness
Thickness of the plywood bottom
flange
Thickness of the plywood top flange
Spacing of longitudinal ribs
Length of a scarf joint between
plywood sheets
8…10 mm
≥ 5×60 mm
≥ 55 mm
25×25 mm
Thickness of a flat asbestos-cement
sheet
Size of the galvanised screws fixing the
sheet to the rib
Minimum bearing length of the slab on
its support
Cross-section of the clamping bars
holding soft insulation
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LONG PANELS
How are 9–12 m slabs made?
• Closely ribbed. Rib spacing does not exceed 500 mm.
• Widely ribbed. Three or two ribs across the width. With three ribs, the middle one carries
more load and is made wider than the edge ribs. With two ribs, transverse load-bearing ribs are
placed between them.
• Trussed slab. Under heavy loads, a truss is attached to the slab: its bottom chord is a steel tie
rod and its top chord is the slab itself.
• Fixing. Slabs are fixed to the load-bearing structures with screws or nails and fastening parts.
TERM
Trussing (sprengel)
A system of steel tie rods and struts placed under a long
beam. It “shortens” the beam's span and reduces its
deflection.
500 mm
Maximum rib spacing in a closely ribbed slab
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JOINTS AND PROTECTION
Joints and protecting the roof from moisture
1
2
3
Sealing joints
Elastic gaskets must be
compressed
Roofing felt glued at the factory
Joints between insulated slabs and panels
are sealed with elastic gaskets (Porizol,
Gernit sealant) and mastics (Thiokol, etc.).
The insulation inside the joint is mineral
wool products.
Elastic gaskets in the joint must be kept
compressed: only then do they stop air
and moisture. Slabs are fixed to the loadbearing structures with screws or nails
and fastening parts.
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One layer of roofing felt is glued to the top
flange of the roof slab at the factory
(protection against wetting); the other
layers are laid when the roof is installed.
With corrugated sheet roofing, no top
flange is made, and the slab is temporarily
covered with polyethylene film.
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DESIGN
How is a panel checked?
TERM
Transformed section
Plywood and timber are different materials with different moduli of elasticity. For calculation, the plywood is converted to equivalent timber (using the ratio E/Eф), and the
whole section is treated as one material.
• Effective flange width. Not the whole width of a plywood flange works equally: if the length l > 6a, the width is taken as 0.9 b.
• Five checks. 1) strength of the bottom (tension) flange; 2) stability of the top (compression) flange; 3) shear of the glue line between plywood veneers; 4) local bending of
the top flange under a 1.2 kN load; 5) deflection of the slab.
• Asbestos-cement flanges. The top flange is calculated as a three-span plate 100 cm wide. Because a screwed connection is very flexible, composite action of the flange
and rib is not taken into account.
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WORKED EXAMPLE · 2
Plywood roof slab: results
TERM
Problem statement
Warehouse roof, roofing felt, pitch 0.1. Insulation: 50 mm semi-rigid
mineral wool. Slab size 5980×1470 mm, four longitudinal ribs; top
plywood flange 9 mm, bottom 6 mm.
8.41 kN·m
5.68 kN
Maximum bending moment in the
slab
Maximum shear force
1.92 kN/m
Check
Result
Limit
Bottom flange strength
3.5 MPa
8.8 MPa
Top flange stability
5.7 MPa
12.65 MPa
Local bending of top flange
5.3 MPa
8.2 MPa
Glue line shear
0.13 MPa
0.89 MPa
Slab deflection
1/395
1/237
In every check the result is below the permissible limit: the slab is adequate.
Total design load (characteristic 1.39 kN/m)
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DETAILS
Eaves and plinth details: weak points
• Goal: long service life. In service, timber should be kept in a uniform and, preferably, constant temperature and humidity regime.
• The difficulty. This cannot always be achieved, especially where a structure passes from a heated room to an unheated room or to the outside.
• Weak points. Places where timber meets eaves, plinths, foundations and structures made of other materials are most prone to decay. They must
therefore always be shown on the working drawings.
TERM
Decay
Damage to timber by fungi under the effect of moisture and heat. It develops quickly where the timber's moisture content is constantly high and reduces the strength of the
structure.
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CONCLUSIONS
Key takeaways
• A roof is a layered system. In a warm roof, the insulation is on the outside and the vapour barrier on the inside; if room humidity exceeds 60 %, the roof
needs ventilation cavities.
• Decking and purlins are beams. Decking is calculated as a two-span beam; there are five types of purlins, and the joint position (0.15 l and 0.21 l)
controls moments and deflections.
• A factory panel is a light frame with sheathing. Rib spacing ≤ 500 mm, plywood flanges ≥ 6 and ≥ 8 mm; long (9–12 m) slabs are strengthened with
trussing.
• Deflection is checked in every calculation. In the examples, the deflections of the decking (1/327), purlin (1/562) and panel (1/395) were all below the
permissible limits.
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27.

Thank you for your attention
Questions and discussion
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