CONSTRUCTION BOIS AU CB71 NOTES DE COURS CHAPITRE 1 : PROPRIETES PHYSIQUES ET MECANIQUES DU BOIS CHAPITRE 2 : CALCUL DES STRUCTURES AU CB71 CHAPITRE 3 : CALCUL DES ASSEMBLAGES AU CB71 CHAPITRE 4 : LE LAMELLE COLLE ANNEXES
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PROPRIETES PHYSIQUES ET MECANIQUES DU BOIS 1 Bois et environnement 1.1 Le bois, un matériau biologique Le bois est un tissu végétal qui assure le rôle de conduction de la sève brute des racines jusqu’aux feuilles et le rôle de soutien mécanique de la plante. Les végétaux sont autotrophes : ils sont capables de fabriquer leur propre nourriture à partir de composés minéraux puisés dans le sol ou prélevés dans l’atmosphère. La réaction de photosynthèse permet à la plante de produire, à partir du gaz carbonique atmosphérique et de l’eau puisée dans le sol et grâce à l’énergie solaire, les sucres nécessaires à son métabolisme et notamment à la fabrication du bois. La réaction de photosynthèse produit de l’oxygène gazeux. La fabrication et le recyclage du bois s’inscrivent dans le cycle naturel du carbone.
1.2 Le bois, le cycle du carbone, carbone, l’effet de serre Aujourd’hui, on note des bouleversements rapides du cycle du carbone : l’utilisation des combustibles fossiles et la déforestation ont pour conséquence une augmentation du taux de gaz carbonique atmosphérique qui était de 280 ppm avant la révolution industrielle, en 1750, et atteint en 2000 plus de 360 ppm. Le gaz carbonique est le principal responsable de l’accentuation de l’effet de serre. Dans l’avenir, le choix des matériaux et des technologies ne pourra plus se faire sans une prise en compte des impacts sur l’environnement. L’émission de gaz carbonique généré au cours du cycle de vie d’un produit sera un critère important. La fabrication du bois ne génère pas de gaz carbonique, elle en consomme . Le bois est un matériau de qualité qui se fabrique et se recycle naturellement sur Terre depuis des centaines de millions d’années. Il est d onc amené à jouer un rôle primordial dans l’industrie future, notamment dans le domaine de la construction. Le bois est composé d’environ 50 % de carbone, 43 % d’oxygène, 6 % d’hydrogène et 1 % d’azote. Tout le carbone contenu dans le bois provient du CO 2 atmosphérique utilisé par l’arbre par photosynthèse. Construire en bois, c’est stocker du carbone. Un mètre cube de bois mis en œuvre (700 kg), c’est 350 kg de carbone en moins dans l’atmosphère ou encore plus de 1 200 kg de CO2 . L’utilisation du bois permet ainsi de retarder le moment où le carbone fixé par photosynthèse sera rejeté par décomposition ou combustion. Elle répond à la nécessité actuelle de réagir rapidement, étant donné la longue durée de séjour du gaz carbonique dans l’atmosphère (50 à 200 ans). D’autre part utiliser de préférence du bois, c’est utiliser moins de matières plastiques, moins de métaux, moins de béton, matériaux non renouvelables dont la fabrication dégage du CO2 . Le tableau 1 positionne le bois dans cette approche environnementale. Tableau 1 - Effet environnemental des matériaux de construction
Procédé de fabrication et mise en œuvre Masse volumique
Matériau
(kg/m3 )
Dégagement de CO 2
Fixation de CO2
(kg/m3 )
(kg/m3 )
Acier
7 200
5 000
0
Béton
2 300
375
0
Ciment
1 600
Bois feuillus
700
2 500
0
Prise en compte des procédés industriels ≈ 200
1 000
(1) Le bois est constitué de C = 50 %, O = 43 %, H = 6 %, N = 1 % :
(1)
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La fabrication et l’exploitation du matériau bois, loin d’être polluantes, permettent le stockage du carbone et l’entretien des massifs forestiers. Par ailleurs, le bois, comme toutes les matières organiques naturelles, est biodégradable. Quelle que soit l’essence considérée, le bois sera à plus ou moins long terme réintégré dans le cycle naturel du carbone. C’est là un avantage incontestable du matériau. Pour augmenter la durabilité du bois, on peut avoir recours à des produits de préservation mais, avant tout, il faut essayer de placer le bois en dehors des conditions de biodégradabilité, grâce à des précautions architecturales, le choix d’essences appropriées, l’utilisation de produits de préservation naturels (sel de bore) et une conception réfléchie. L’une des plus anciennes constructions en bois n’est autre que le sanctuaire bouddhiste Horyu-ji du VIIe siècle situé près de Nara au Japon. Au-delà des avantages évidents du bois, il en existe d’autres mis en évidence grâce aux écobilans comparés, appelés également analyse des cycles de vie (LCA : Life Cycle Assessment ou Life Cycle Analysis ). Ceux-ci prennent généralement en com pte l’impact environnemental des étapes suivantes de la vie d’un produit : élaboration et extraction des matériaux bruts, transformation, transport, installation, performances à l’usage, élimination (déconstructi on, recyclage).Le bois apparaît nettement comme le choix c hoix « écologiquement responsable ». Le bois permet donc de stocker une partie du carbone qui a été rejeté par l’activité industrielle passée mais également de participer à la réduction des émissions de gaz carbonique en tant qu’alternative aux matériaux non renouvelables qui induisent des coûts én ergétiques que notre planète ne peut que difficilement s upporter.
2 Equilibre hygroscopique Comme schématisé ci-dessous, la structure cannelée du bois permet une circulation d’eau : Exemple d’un plan ligneux de résineux (pin sylvestre)
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Structure du tronc dans l’arbre. E xemple du chêne, essence à aubier différencié
Le bois est un matériau hygroscopique : il peut fixer ou libérer des molécules d’eau gazeuse en fonction du degré d’hygrométrie de l’air dans lequel il se trouve. La fixation de l’eau se fait sur les groupements chimiques hydroxyles (composés d’un atome hydrogène et d’un atome d’oxygène) qui ont une grande affinité pour l’eau avec laquelle ils établissent établis sent des liaisons faibles : les liaisons hydrogène. La cellulose et les hémicelluloses comportent de nombreux groupements hydroxyles et ont donc de bonnes capacités d’adsorption. Des liaisons hydrogène existent aussi entre les différentes molécules, cellulose et hémicelluloses. Lorsque l’eau vient se fixer sur les chaînes de cellulose, celles-ci sont éloignées les unes des autres. C’est ce qui produit le gonflement du bois, observé lorsque l’humidité de l’air augmente. L’adsorption d’eau augmente la largeur des microfibrilles mais pas leur longueur. Par convention et pour une plus grande facilité de mesure, la quantité d’eau présente dans le bois est exprimée comme un pourcentage de la masse anhydre (après séchage à 103 o C jusqu’à obtention d’une masse constante). Elle s’exprime par:
avec M H H
masse (ou poids) à l’humidité H
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Au moment de l’abattage, l ’abattage, le taux d’humidité du bois peut varier entre 40 et plus de 200 % (dans certains peupliers par exemple). L’eau dans le bois est présente sous deux formes : l’eau « libre » retenue dans les vides, lumens des fibres, trachéides et vaisseaux, et l’eau « liée » présente dans les parois cellulaires. Pour évaporer l’eau libre, il suffit de fournir la chaleur latente d’évaporation normale. Pour évaporer l’eau liée, il faut fournir une énergie additionnelle ou énergie de sorption pour rompre les liaisons avec les constituants chimiques du bois. Lorsque le bois ne contient plus que de l’eau liée, il a atteint « le point de saturation des fibres » (les parois cellulaires sont saturées en eau, toute l’eau libre est évaporée). Ce point de saturation des fibres est de l’ordre de 30 % pour pratiquement toutes les essences. Les qualifications commerciales normalisées des bois en fonction du taux d’humidité sont données c i après : Tableau 2 - Qualifications normalisées des bois en fonction du taux d’humidité (NF B51-002)
Taux d’humidité
Qualification
Au-delà du point de saturation des fibres (30 %)
Bois vert
De 30 à 23 %
Bois mi-sec
De 22 à 18 %
Commercialement sec
De 17 à 13 %
Bois sec à l’air
En dessous de 13 %
Desséché
0%
Anhydre
2 Aspect réglementaire – définition des classes d’humidité 2.1 Courbes d’équilibre hygroscopique En fonction de la température et surtout de l’humidité de l’air ambiant, le bois se stabilise à une humidité d’équilibre, dite équilibre hygroscopique, qui est indépendante de l’essence. Sous les climats tempérés (France) l’équilibre hygroscopique du bois varie d’environ 13 % en été à 19% en hiver.
Toutes les propriétés physiques et mécaniques du bois sont affectées par l’humidité. Un exemple est donné ci après concernant le module d’élasticité longitudinal
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Influence du taux d’humidité du bois sur son module d’élasticité longitudinal
2.2 Eurocode 5 3 classes d’humidité sont définies aux Eurocodes (EC5 2.5.4). Du choix d’une classe d’humidité découle les valeurs caractéristiques de résistances et le calcul des déformations. Classe 1 : Hair ne dépassant 65% (à 20 ± 2°C)que quelques qu elques semaines semai nes par an (H
≈
12% dans les résineux),
Classe 2 : Hair ne dépassant 80% (à 20 ± 2°C)que quelques qu elques semaines semai nes par pa r an (H
≈
18% dans les résineux),
Classe 3 : conditions d’humidité plus élevées. Les valeurs des résistances caractéristiques sont affectées d’un coefficient en fonction de la classe d’humidité. Par exemple : Si σcompression (classe 3) = R alors σcompression (classe 1 ou 2) = 1,2.R
2.2 CB71 Les contraintes admissibles sont définies pour H = 15%. Il conviendra de pondérer ces contraintes par des coefficients correcteurs en fonction de H et du type de sollicitation. Par exemple (3-13), en compression axiale : H%
7,5
10
12,5
15
17,5
20
22,5
25
30
k
1,30
1,20
1,10
1,00
0,90
0,80
0,70
0,60
0,40
3 Caractéristiques physiques 3.1 Masse volumique - densité La densité d’un bois est un paramètre très important. La plupart des propriétés mécaniques et technologiques en dépendent directement. La densité vraie de la matière ligneuse dépend assez peu de l’essence considérée. Elle est toujours voisine de 1,53. Le bois contient toujours de l’eau (eau libre et eau liée), la densité d’un bois sera toujours précisée pour un degré d’humidité donné La densité du bois est donc très variable selon les espèces : de 0,1 à plus de 1, et à l’intérieur d’une même essence.
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Effet de la densité sur les propriétés mécaniques sur l’ensemble des essences
Effet de la densité sur les propriétés mécaniques à l’intérieur d’une même essence
Le Tableau 3 illustre ces résultats sur les caractéristiques de dureté de surface des bois. L’échelle de dureté est exprimée selon la norme NF B 51-013. De manière générale toutes les propriétés mécaniques du bois sont bien corrélées avec la densité .
3.2 Anisotropie - dilatation L’ensemble des caractéristiques et propriétés physico-mécaniques du bois résulte de cette structure de matériau composite alvéolaire multicouche. Cette structure confère au matériau un caractère anisotrope et hétérogène . Dans l’étude ou la reconnaissance d’un bois, les observations doivent se faire selon trois plans parfaitement définis : le plan transversal, perpendiculaire à l’axe de l’arbre (bois de bout) ; le plan radial, parallèle à l’axe et passant par le centre structurel de l’arbre (débit sur quartier) ; le plan tangentiel, tangent aux cernes de croissance (débit sur dosse).
Ces trois plans sont illustrés sur la figure ci après.
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Acier
12
50
Laine minérale
0,035
Bois
H = 12 %
H = 35 %
Chêne (d = 0,65)
3à6
0,3
0,34
Épicéa (d = 0,45)
3à6
0,2
0,25
Panneaux de fibres de bois isolant
0,045
Compte tenu de sa porosité, le bois contient beaucoup d’air lui assurant une faible conductivité thermique, ce qui en fait un isolant naturel. Pour exemple (à H = 15% ) : λ = 0,23 W/m.K (chêne) λ = 0,15 W/m.K (sapin) λ = 0,02 W/m.K (balsa)
4. Caractéristiques mécaniques 4.1 Paramètres d’influence Les paramètres influençant les résistances mécaniques sont :
-
La sollicitation (traction / compression / flexion / cisaillement)
-
L’essence et la qualité du bois
-
H
-
La direction de la sollicitaion par rapport aux fibres
4.2 Comportement en traction - compression La structure tubulaire orientée du composite bois explique la différence de comportement traction/compression pour une sollicitation dans la direction longitudinale. La figure suivante montre le caractère fragile du matériau en traction et son caractère ductile en compression. En compression les éléments tubulaires sont soumis à du microflambement expliquant les différences de résistance traction/compression. Il est à noter que, dans le cas de la compression comme de la traction, le module d’élasticité est le même et est donné en R4.011 en fonction de l’essence du bois et de la sollicitation. E traction = E compression
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Traction perpendiculaire (Radiale ou Tangentielle)
f t ,90, t ,90,k k
0,4
0,5 (0,13)
0,5 (0,2)
0,6 (0,2)
0,6
Compression axiale
f c ,0, c ,0,k k
16
18 (8,5)
21 (9)
23 (10,5)
26
Compression perpendiculaire
f c ,90, c ,90,k k
2
2,2 (2,1)
2,5 (2,3)
2,7 (2,5)
2,9
Cisaillement
f ν , ν ,k
1,7
2 (0,9)
2,5 (1,1)
3 (1,3)
3,8
6 000
7 400
8 000
9 400
E 0,moyen 0,moyen
(9 000)
(11 000)
(12 000)
Module perpendiculaire (R ou T)
E 90,moyen 90,moyen
(300)
(370)
(400)
Module de cisaillement
G moyen moyen
(560)
(680)
(750)
d moyen moyen
0,38
0,42
0,46
Module de déformation au fractile de 5 % (Module moyen) (MPa) 4 700
E 0,05 Module axial (L)
Densité moyenne
Le tableau 6 donne, à titre indicatif, les valeurs des résistances à la rupture des essences les plus courantes en compression et en traction.
4.3 Aspect règlementaire Selon l’EC5, la contrainte admissible est cal culée selon le principe suivant :
f
hd
= k mod
f
hk
γ m
où kmod est un facteur de modification prenant en compte la durée d’application de la charge (parallèle avec θ de fbu en béton armé) et γ m un coefficient de sécurité partiel l ié au matériau. Le CB71 donne les contraintes admissibles en fonction de la sollicitation, contrainte à pondérer en fonction de l’humidité du bois et de la direction principale de la sollicitation.
σ ≤ k ( H ).k ( direction ).σ (type.de.sollicitat ion.et .essence ) Les vérifications se faisant aux contraintes admissibles, il est conseillé d’effectuer le dimensionnement de l’ouvrage à la déformation (4.85 et 4.96). Il est à noter que la déformation due au fluage n’est prise en compte qu’à la flexion et est négligée en traction – compression . Dans le cas de cette dernière sollicitation, le
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Actions de courte durée pi
Actions de longue durée p∞
Flèche fi calculée avec le module conventionnel Ei
Flèche f∞ calculée avec le module différé E∞=Ei/ θ Où θ est le coefficient amplificateur de fluage
Flèche totale f = fi + f ∞ ≤ flèche admissible donnée en 4.962 du CB71 Remarque : Ce calcul est équivalent au calcul de la flèche totale en utilisant les données suivantes : •
E = Ei
•
Charge totale p = pi + θ.p∞
Le coefficient de fluage θ est calculé en fonction de :
σ
f
= contrainte admissible en flexion,
M σ r ∞ = ∞ . I
h
2
= contrainte sous les charges de longue durée, avec M∞ = moment sous les charges p∞,
∆H = différence entre le maximum et le minimum des humidités dans le bois entre la mise en œuvre et la stabilisation des déformations,
H = humidité du bois lors d e sa mise en œuvre.
Si
Si
σ
≤ r ∞
σ
f
5
σ 5
f
alors θ = 1
H + ∆ H
≤ σ r ∞ ≤ σ f
alors θ = 1 +
12 × ∆ H − 5 1+ 20
σ
r ∞
−
σ
σ
f
f
5
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5 Classement, dimensions et appellations commerciales 5.1 Classement En fonctions des défauts (présences de nœuds, de flaches, etc.) et des altérations biologiques (attaque par les champignons), le bois est classé, suivant la NF B 52-001 en trois classes (ST-I pour la meilleure à ST-III) ayant des correspondances dans l’EN 338 selon l e tableau suivant :
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Tableau 7 – Correspondances des class ements NF B 52-001 et EN 338
La classe C18 convient bien aux charpentes traditionnelles, La classe C24 convient bien aux charpentes industrielles (fermettes) et au lamellé-collé, La classe C30 convient mieux au lamellé-collé à hautes performances. On en retirera les propriétés mécaniques suivantes (pour une humidité de 12%) : Tableau 8 – Propriétés mécaniques suivant l e classement
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75 100
n
n
n
n
115
n
n
n
n
n
n
125
n
150
n
200
n
225
n
Pour les bois de structure calibrés : 36 × 72/36 × 97/36 × 112/36 × 122/36 × 147/36 × 172/36 × 197/36 × 222. Les longueurs sont les suivantes : pour le sapin et l’épicéa : de 50 en 50 cm, de 1 à 12 m ;
pour les pins : de 30 en 30 cm, de 2,10 m à 3 m, au-delà, par graduation de 50 cm. (1) 25 mm est une autre dimension possible.
20 % d’humidité) Par ailleurs, il existe un certain nombre d’appellations commerciales pour désigner des sciages en fonction de leurs dimensions :
• • • • • • •
volige : avivé (sciage à vives arêtes) dont le rapport des côtés de la section est égal ou supérieur à 4 et l’épaisseur égale à 12, 15, 18 ou 22 mm ; planche : de même, mais d’épaisseur comprise entre 27 et 4 0 mm ; solivette (ou demi-bastaing) : avivé d’une épaisseur de 32 ou de 38 mm et d’une largeur de 150 à 200 mm ; liteau : avivé d’épaisseur inférieure à 40 mm et de largeur inférieure à 50 mm ; carrelet : avivé de section carrée ou sensiblement carrée, de côté compris entre 15 et 50 mm ; chevron : de même, mais dont le côté est compris entre 40 et 125 mm ; bastaing : avivé dont le rapport des côtés de la section est compris entre 2 et 3, de sections habituelles
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CALCUL DES STRUCTURES AU CB71 1 Actions et sollicitations Les actions sont définies au paragraphe 1.1 du CB71. On distinguera : •
G : actions dues à l a charge permanente,
•
P : actions dues aux surcharges d’exploitation, données dans la NF P 06 001
•
Pc : actions dues aux charges cl imatiques, calculées selon le règlement NV (S et W),
•
SI : actions sismiques.
Les sollicitations sont le résultat d’un calcul de résistance des matériaux en prenant les plus défavorables des combinaisons d’actions suivantes : Combinaisons du 1er genre : S1 = G + 1,2 P S1’ = G + γ p.P p.P + Pc Où γ p prend la valeur 0 ou 1 afin d’obtenir le cas de charge le plus défavorable. Pour simplifier, γ p = 0 dans le cas de soulèvement et γ p = 1 dans le cas de surpression. nd
Les sollicitations du 2
genre sont données par la combinaison d’action suivante :
S2’’ = G + P + SI. Ces combinaisons sont définies dans les règles simplifiées au chapitre 4.9 du CB71.
2 Principe de justification Une fois la géométrie des structures définie par un calcul de déformation ou par des considérations architecturales, la justification se fait aux contraintes admissibles, à savoir : er
Pour les combinaisons du 1 genre :
σ ≤ k ( H ).k ( direction ).σ (type.de.sollicitat ion.et .essence )
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Tableau 1 – Coefficient de réduction en fonction de l’inclinaison des charges en tr action axiale α (°)
0
10
20
CAT 1
1
0.67
0.34
CAT 2
1
0.73
0.41
30
40
50
60
70
80
90
0.20
0.13
0.09
0.07
0.05
0.06
0.06
0.24
0.16
0.12
0.10
0.08
0.08
0.075
3.2 Compression axiale sans risque de flambement (CB71 - 3.24) En compression axiale sans risque de flambement, on vérifie :
σ =
N Ab
≤ σ
où Ab est la section brute sous réserve que la réduction de section due à la présence de boulons ou d’autres assemblages soit inférieure à 15%.
3.3 Compression axiale avec risque de flambement En compression axiale avec risque de flambement, on vérifie :
σ =
1 N ≤ σ . k (λ ) Ab
Où k(λ) est un coefficient de d’amplification de contrainte qui prend les valeurs suivantes, en fonction de l’élancement λ : Si λ ≤ 37,5 alors k(λ) = 1 : pas de risque de flambement, Si 37,5 ≤ λ ≤ 75 alors k(λ) = 1,45 – 1,20 λ / 100, Si 75 ≤ λ alors k(λ) = 3100 / λ².
3.4 Compression transversale ou oblique (CB71 - 3.243) En compression axiale sans risque de flambement, on vérifie :
σ =
N Ab
≤ k (α ).σ
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Si α ≤ 5° 30’ (pente inférieur à 10%), on néglige néglige la composante oblique p1, Si α > 5°30’, on majore les charges par le biais d’un coefficient c : c = cosα + (h/b). sinα et on se ramène à un calcul en flexion simple
p1
α
P2
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CALCUL DES ASSEMBLAGES AU CB71 1 Assemblages traditionnels Ils sont traités au paragraphe 4.61 du CB 71 et consistent à faire transiter les efforts d’une pièce en bois à l’autre sans nécessité de pièces intermédiaires en acier. Les vérifications portent sur la résistance au cisaillement et au matage du bois. Différents types d’assemblages par tenon - mortaise
Assemblage à tenon et mortaise borgne. Le tenon est de même largeur que la traverse. On coupe l'extrémité pour les excès de colle.
Assemblage à épaulement. La largeur du tenon est diminuée d'un tiers. Le renfort d'épaulement peut être un rectangle ou triangle.
Assemblage à tenon et mortaise traversant et renforcement de chevilles qui sont enfoncées sur les côtés du tenon.
Les chevilles sont ici enfoncées dans les fentes ouvertes sur l'about du tenon pour renforcer un assemblage à mortaise
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clou avec tige lisse et pointe biseautée
clou annelé : C'est un type de clou dont la tige est constituée d'anneaux convexes. Il est très résistant à l'arrachement. Le diamètre de ce clou es t mesuré sur la partie lisse de la tige (diamètre avant roulage).
clou annelé
clou torsadé : C'est un type de clou dont la tige est torsadée et carrée. Il est très résistant à l'arrachement. Son diamètre est mesuré sur les arêtes.
clou torsade
clou cranté : C'est un type de clou dont la tige est dentée. Il est très résistant à l'arrachement.
clou cranté
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Cas du simple cisaillement : chaque clou ne traverse qu’un plan de cisaillement
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- cisaillement mixte :
F ≤ 1,3.d . e
- double cisaillement :
F ≤ 2.d . e avec :
F
Effort repris par clou en daN
d
Diamètre du clou en 1/10ème de mm
e
Epaisseur de l’élément le plus mince en cm
Ft
Effort de traction / compression dans l’assemblage en daN
n
Nombre de clous
Pour le chêne : ses valeurs s ont multipliées par 1,3 Il faut également prendre en compte l’effet de groupe, à savoir que plus il y a de pointes et plus l’effort par pointe diminue. Un coefficient correcteur k est à appliquer suivant le nombre de pointes n d e l’assemblage : n < 10 10 ≤ n
20
Ft = n.F
(k = 1)
Ft
(k
0,9.n.F
0,9)
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Assemblages par pointes (clous)
Chaque intervalle e ≥ 5d a ≥ 12d b ≥ 5d c ≥ 10d d = diamètre clou
a ou b c c a ou b On prendra b si la barre oblique est en compression et a dans les autres cas traction traction ou tractio traction-com n-com ression ression alternée alternée
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1,6 2 2,5 3 3,5* 4 5 6 8 10 12
9 10 11 12 13 14 16 18 22 26 30
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- bois sec à l’air (H = 15%) :
F ≤ 400.d . e
- bois commercialement sec (H = 18 à 22%) :
F ≤ 300.d . e
Pour le chêne, ces valeurs admissibles sont à multiplier par 1,3.
3.4 Dispositions constructives (4,62-111 Fig. R-IV-4)
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LE LAMELLE COLLE
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