UNIVERSITE MOHAMMED PREMIER ECOLE NATIONALE DES SCIENCES APPLIQUEES AL HOCEIMA
Rapport du Projet de fin d’études :
« Conception architecturale et dimensionnement en béton armé d’un immeuble R+8 à usage multiple »
Stage d’Ingénieur en Génie Civil Présenté par : Mlle. Jihane ELGHOULALI. Encadré par : M. Issam HANAFI et M. Mohammed SAFAR. Soutenu le 30 Juin 2014 devant la commission d’examen
Jury :
HANAFI Issam, Prof. (ENSAH) : Président
ADDAM Mohammed, Prof. (ENSAH): Rapporteur
DIMANE Fouad, Prof. (ENSAH) : Rapporteur
SAFAR Mohammed, Ing. (GETR) : Examinateur
G.E.T.R
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Projet de fin d’étude
A nos très chers parents, aucun terme et aucune langue ne pourra exprimer notre amour et sentiments envers vous. Dieu seul capable de vous récompenser pour tout ce que vous avez fait pour nous. A mes encadrants, s’il y a vraiment quelqu’un à remerci er, er, ce seront Mr. Mohammed SAFAR Et Mr. Issam HANAFI. Merci pour vos efforts très louable. A mes chers professeurs professeurs pour pour m’avoir m’avoir généreusement généreusement fait profiter fait profiter de leurs connaissances. A ma tante Sanae, pour son soutien, soutien, je lui souhaite le bonheur. bonheur. A tous mes amis, pour tous les instants inoubliables que j’ai passé avec vous, en particulier mes camarades de la promotion du génie civile 2014. A tous ceux qui me sont chers. Je dédie cet humble travail. travail.
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Projet de fin d’étude
Remerciement
Au nom d’Allah le tout miséricordieux, le très miséricordieux. Ce travail, ainsi accompli, n’ aurait aurait point pu arriver à terme, sa ns le soutien et tout le guidage ns l’aide et le univers. d’Allah, louange au tout miséricordieux ; le seigneur de l ’ univers. Nous tenons à remercier et à témoigner toute notre reconnaissance aux personnes suivantes , pour l’expé rience rience enrichissante et pleine d’intérêt qu’ils nous nous ont fait vivre durant toute la période de notre projet de fin d’ét udes: udes: M. Mohammed SAFAR ingénieur d’ état état et notre encadrant externe, qui était très généreux en conseils utiles et en aide précieuse. M. Issam HANAFI, Au long de cette période, pour son soutien et ses conseils constructifs, sans oublier sa participation effective au cheminement de ce rapport. Nous profitons de ces quelques lignes pour dire merci aux membres de jurys, à la direction et à tout le corps professoral de l’ENSAH pour pour l’en seignement seignement de qualité et pour le cadre idéal dont nous avons bénéficié tout au long de notre cursus. Nous remercions également avec dévouement nos familles et nos amis pour leur soutien matériel et moral. Tout mot dit, nous ne les remercierons jamais assez.
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Projet de fin d’étude
Résumé Dans ce projet de fin d’étude, nous nous sommes intéressés à l’étude d’un bâtiment qui se compose d’un un rez-de-chaussée à usage commercial, quatre étage à usage bureautique et quatre étages à usage habitation. Cette étude se déroule sur trois parties : -
La première première partie porte sur une présentation générale générale du projet,
ainsi qu’une
conception architecturale décrivant les éléments constituants le projet.Ensuite le pré dimensionnement et la descente de charge de la structure. st ructure. -
La deuxième partie est destinée
à l’étude des éléments résistants (poteaux, poutres,
semelles). -
La troisième partie est
consacrée à l’étude des éléments secondaires (acrotère,
escaliers, ascenseur, dalles pleine). -
La dernière partie comprend l’étu de sismique de la structure.
Le dimensionnement est fait conformément au BAEL 91, au RPS 2002 et SAP2000.
Mots clés : Bâtiment. BAEL91. RPS 2002. Béton.
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Projet de fin d’étude
Sommaire Dédicace Remerciement Introduction
Chapitre I : Présentation du projet I-1. Présentation du bureau d’étude groupement des études techniques et de réalisations « G.E.T.R »………………………………………………………..............................12 I-2. Présentation du projet………………………………………………………….….....13 I-2-1. Particularité du projet………………………………………………………...........13 I-2-2. Contexte du projet………………………………………………………………....14
Chapitre II : Conception du projet II-1. Conception architecturale……………………………………………………….. ...15 II-1-1. Etapes de conception…………………………………………………………......15 II-1-2. Description du projet……………………………………………………………..16 a. La réalisation du croquis………………………………………………….........16 b. Description par étage…………………………………………………………..16 II-2. Conception parasismique……………………………………………………….......22 II-2-1. Système de portiques…………………… ...……………………………………...23 II-2-2. Système d e refends………………………………………………………. ............23 II-2-3. Système mixte refends- portiques…………………………………………… portiques……………………………………………........23 II-3. Variantes de conception du projet…………………….…………………………….23
Chapitre III : Caractéristiques des matériaux III-1. Béton………………………………………………………………………….......25 III-1-1.Principales caractéristiques et avantages de béton………………………......… .25 a. Résistance mécanique……………………………………………………… ...26 b. Les contraintes limites de compression du béton……………………………. .26 III-2. Aciers……………………………………………………………………………...27 III-3. Combinaisons de calcul…………………………………………………………. .28
Chapitre IV : Pré dimensionnement et descente de charge des éléments porteurs IV-1. Pré dimensionnement et surcharges sur les planchers…………………………… .30 IV-1-1. Pré dime nsionnement des planchers……………………………………………..32 a. Plancher à corps creux………………………………………………….............32 b. Plancher à dalles pleine………………………………………………………...33 IV-1-2. Evaluation des charges et surcharges sur les planchers……………………….. ..34 a. Charges permanentes…………………………………………………........... .34 b. Charges d’exploitation………………………………………………………...35
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Projet de fin d’étude IV-2-2. Descente de charges des poutres ……………………………………………......36 a. Poids propre…………………………………………………………………...36 b. Transmission des charges des planchers aux poutres « Méthodes des surfaces tributaires »…………………………………………………………................37 c. Charges concentrées…………………………………………………………..37 IV-3. Pré dimensionnement et descente de charges des poteaux……………………… ..40 IV-3-1.Descente des charges des poteaux…………………………………….................40 IV-3-2. Pré dimensionnement des poteaux……………………………………………. ...42 IV-4. Pré dimensionnement des semelles…………………………………… ..................44
Chapitre V : Dimensionnement des éléments porteurs V-1. Dimensionnement des poteaux…………………………………………………... ..46 V-1-1. Armatures longitudinales des poteaux………………………………………… ..46 V-1-2. Armatures transversales des poteaux…………………………………………. ...46 V-2. Dimensionnement des poutres……………………………………………………..48 V-2-1. Choix de la méthode de calcul des moments…………………………………... .48 a. La méthode de Caquot- domaine de validité…………………………………...49 b. La méthode forfaitaire-domaine de va lidité…………………………………...49 V-3. Dimensionnement des semelles………………………………………….................65
Chapitre VI : Etude des éléments secondaires VI-1. Introduction………………………………………………. ……............................68 VI-2. Etude de l’acrotère………………………………………………….......................68 a. Calcul des sollicitations………………………………………………………...69 b. Calcul de l’excentricité………………………………………………………....69 c. Détermination du ferraillage…………………………………………………...70 VI-3. Etude des escaliers………………………………………………………………...74 VI-3-1. Introduction……………………………………………………………..............74 VI-3-2. Descente de charge……………………………………………………………...74 VI-3-3. Dimensionnement……………………………………………………….............75 VI-4. Etude de la poutre palière……………………………………………………….....81 VI-4-1. Pré dimensionnement…………………………………………………………....82 VI-4-2. Evaluation des charges…………………………………………………………..82 VI-5. Etude de la dalle machine……………………………………………………….....85 VI-5-1. Introduction……………………………………………………………………...85 VI-5-2. Dimensionnement…………………………………………………………….....85 a. La détermination des charges et surcharges…………………………………..85 b. Calcul des sollicitations…………………………………………………….....86 c. Ferraillage en travée…………………………………………………..............86 d. Ferraillage en appuis………………………………………………………......87 e. Calcul des armatures transversales…………………………………………....87 VI-6. L’ascenseur……………………………………………………………………......89 VI-6-1. Introduction…………………………………………………………………......89
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Projet de fin d’étude d. Evaluation des moments dus aux charges réparties……………………….. ....93 e. Les moments appliqués à la dalle………………………………………….....94 f. Calcul du ferrail lage de la dalle……………………………………………....94 VI-7. Les dalles pleines…………………………………………………………..…......100
Chapitre VII : Etude sismique VII-1. Introduction……………………………………………………………………...104 VII-2. Règlement parasismique marocain…………………………………...………....104 VII-3. Conception parasismique………………………………………………….....….104 VII-4. Méthode de calcul…………………………………………………………..........105 VII-4-1. La méthode sismique équivalente…………………………………………… ..105 a. Principe…………………………………………………………………….105 b. Modélisation……………………………………………………………….106 c. Condition d’application de la méthode statique équivalente………………106 VII-4-2. Méthode modale spectrale…………………………………………………….107 VII-5 : Hypothèses de calcul sismique…………………………………………………108 VII-5-1 : Vérification de la régularité………………………………………………….108 VII-5-2 : Données sismique……………………………………………………………108 VII-5-3 : Résultats de calcul sismique…………………………………………………108 a. Force sismique horizontale équivalente…………………………………....108 b. Force sismique latérale équivalente………………………………………..109 Conclusion générale
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Projet de fin d’étude
Liste des tableaux Chapitre I : Présentation générale du projet Tableau I-1 : Caractéristiques géométriques………………………………………………............16 Chapitre IV : Pré dimensionnement et descente de charge des éléments porteurs Tableau IV-1 : Les types des hourdis……………………………………………………………...34 Tableau IV-2 : Valeurs des charges pour les éléments courants………………………………… ..35 Tableau IV-3 : Revêtement terrasse……………………………………………………………….36 Tableau IV-4 : Revêtement étage courant…………………………………………………………36 Tableau IV-5 : Charge d’exploitation……………………………………………………………..36 Tableau IV-6 : Récapitulatif à l’ELU des charges de la poutre A 1A2A3A4A5A6A7…………….....40 Tableau IV-7 : Récapitulatif à l’ELS de la poutre A 1A2A3A4A5A6A7………………………….....40 Tableau IV-8 : Récapitulatif à l’ELU de la poutreA1A2A3A4A5A6A7………………………….....41 Tableau VI-9 : Récapitulatif à l’ELS de la poutre A1A2A3A4A5A6A7……………………………41 Chapitre V : Dimensionnement des éléments porteurs Tableau V-1 : Récapitulatif des moments sur appuis de la poutre A 1A2A3A4A5A6A7……………55 Tableau V-2 : Récapitulatif des moments en travée de la poutre A1A2A3A4A5A6A7………….....58 Tableau V-3 : Calcul des efforts tranchants sur appuis de la poutre A 1A2A3A4A5A6A7……….....59 Tableau V-4 : Ferraillage en appuis à l’ELU de la poutre axe A du plancher haut Rez de chaussée…………………………………………………………………………………………....61 Tableau V-5 : Ferraillage en travée à l’ELU de la poutre axe A du planchez haut Rez de chaussée…………………………………………………………………………………………....61 Tableau V-6 : Résultats de pré dimensionnement des travées de la poutre A1A2A3A4A5A6A7………………………………………………………………………………....62 Tableau V-7 : Résultats de pré dimensionnement des appuis de la poutre A1A2A3A4A5A6A7………………………………………………………………………………....62 Tableau V-8 : Résultats de dimensionnement des semelles……………………………………… .67 Tableau V-9 : Vérification de la contrainte du sol (σ sol=0,2 Mpa )………………………………..68
Chapitre VI : Etude des éléments secondaires Tableau VI-1 : Ferraillage à l’ELU d’une volée d’escalier au niveau 1 er étage…………………...81 Tableau VI-2 : Récapitulatif pour la v érification à l’ELS………………………………………....82
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Projet de fin d’étude
Liste des figures Chapitre III : Caractéristiques des matériaux Figure III-1 : Diagramme contraintes-Déformation de béton…………………………………….28 Figure III-2 : Diagramme contraintes-Déformation d’acier……………………………………....29 Chapitre IV : Pré dimensionnement et descente de charge des éléments porteurs Figure IV-1 : La surface intervenant au calcul de la descente de charge d’un poteau………….....41 Chapitre V : Dimensionnement des éléments porteurs Figure V-1 : Schéma du ferraillage du poteau P6 …………………………………………………49 Figure V-2 : Cas de chargement pour moment maximal sur appuis……………………………… 51 Figure V-3 : Cas de chargement pour moment maximal en travée ………………………………..51 Figure V-4 : Cas de chargement pour effort tranchant extrême sur appuis……………………….53 Figure V-5 : Ferraillage de la poutre A 1A2A3A4A5A6A7……………………………………….65 Figure V-6 : Schéma du ferraillage de la semelle S6 ……………………………………………...67 Chapitre VI : Etude des éléments secondaires Figure VI-1: Dimensions de l’ acrotère…………………………………………………………....68 Figure VI-2 : Section de calcul d’acrotère………………………………………………………...69 Figure VI-3 : Ferraillage de l’acrotère…………………………………………………………….73 Figure VI-4 : Eléments d’escaliers………………………………………………………………..74 Figure VI-5 : Ferraillage d’un volée d’escalier …………………………………………………...81 … ………………………………………………...81 Figure VI-6 : La poutre palière……………………………………………………………………81 Figure VI-7 : Ferraillage de la poutr e palière……………………………………………………..85 Figure VI-8 : Schéma de la dalle machinerie……………………………………………………..89 machinerie…… ………………………………………………..89 Figure VI-9 : Schéma d’ascenseur mécanique……………………………………………………90 Figure VI-10 : Ferraillage d’ascenseur…………………………………………………………..100 Figure VI-11: Ferraillage de la dalle pleine……………………………………………………...103
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Projet de fin d’étude
Notations G Q
σ bc σs τu σ bc σs τu
f cj cj f tjtj f c28 c28 Ast Ar
γ b γs θ η
µ bu
α
Z d
d’ Br M V
Action permanente
Action d’exploitation Contrainte admissible du béton
Contrainte admissible d’acier
Contrainte ultime du cisaillement Contraintedu béton
Contrainte d’acier
Contraintede cisaillement Résistance à la compression Résistance à la traction Résistance caractéristique à 28 jours
Section d’armature
Armature de répartition Coefficient de sécurité béton
Coefficient de sécurité d’acier Coefficient d’application Facteur de correction d’amortissement Moment ultime réduit Positon relative de la fibre neutre Bras de Levier Distance séparant entre la fibre la plus comprimée et les armatures inférieures Distance entre les armatures et la fibre neutre Section réduite Moment fléchissant Effort tranchant
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Projet de fin d’étude
Introduction Le Génie civil représente l'ensemble des techniques concernant les réalisations et les constructions civiles. Les ingénieurs Les ingénieurs civils ou ingénieurs en génie civil
s’occupent de la conception, de la
réalisation, de l’exploitation et de la réhabilitation des ouvrages de construction et d’infrastructures dont ils assurent la gestion afin de répondre aux besoins de la société, tout en assurant la sécurité du public et la protection de l’environnement. Très variées, leurs réalisations se répartissent principalement dans cinq grands grands domaines
d’intervention : structures, géotechnique, hydraulique, transport et environnement. A ce titre, le projet de fin d’étude a pour but de confronter l’apprentissage théorique avec une application dans la réalité, il sert également à apprendre et maîtriser les ficelles du métier au
sein d’une équipe et se familiariser avec les données des établissements. En outre, il permet d’acquérir les différentes qualités qu’on doit avoir afin de progresser et de pré parer
sa future carrière, aussi il permet d’apprendre l’utilité du travail en groupe et
l’importance des relations humaines concernant le contact de l’ingénieur l’i ngénieur vis-à-vis les techniciens et ses autres collègues.
D’ailleurs, ce rapport traduit les résultats des différentes activités, recherches et études pour la réalisation du projet de fin d’étude dont le thème est : « Conception architecturale et Dimensionnement d’un immeuble R+8 à usage multiple » manuellement. Ce mémoire est composé de six chapitres : Le premier
chapitre entame une présentation générale du projet, du bureau d’étude et des
différentes phases d’élaboration du projet. Le deuxième chapitre présente une conception dét aillée du projet, contenant une conception
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Projet de fin d’étude
Chapitre I : présentation générale du projet. I-1.
Présentation générale du bureau d’études groupement des études
techniques et de réalisations ’’G.E.T.R’’.
Le bureau d’études (Groupement des études techniques et de réalisations) (B.E.T./G.E.T.R S.A.R.L) au capital de 1.000.000 Dhs a été créé en 1989.
C’est un bureau d’études pluridisciplinaire dans le domaine du bâtiment et du génie civil ; ce qui leur a permis de participer à la réalisation d’une centaine de projets différents, diff érents, allant des habitations individuelles ou collectives, passant par des complexes balnéaires et finissant par des établissements publics avec de multiples ministères.
Il faut noter surtout que ces réalisations s’étalent sur tout le territoire national. Ses champs d’activités se présentent dans plusieurs domaines :
Etudes des structures (Béton Armé et charpente métallique) ;
Surveillance et coordination des travaux ;
Expertise des structures en Béton Armé ;
Métré tous corps d’état ;
Etablissement des dossiers d’adjudication et d’appel d’offre ;
Intervention pour réfection, restauration et modification des bâtiments existants.
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Projet de fin d’étude
De nos jours, les grands projets de bâtiment cherchent à maximiser les distances entre poteaux
afin d’aménager le maximum d’espace dans chaque étage tout en essayant de répondre à l’esthétique moderne concernant les légères
retombées de poutres et le passage aisé des canalisations, d’où
l’intérêt des plancher -dalles. -dalles. Aussi, l’essor du domaine du BTP avait mené à des projets partout même sur des terrains qui présentent quelques difficultés comme la faiblesse de leurs caractéristiques
ou la présence d’une
nappe pas assez profonde ou encore remédier aux poussées des terres exercées par le sol au niveau des sous-sols de bâtiments.
Tous ces aspects ont été rencontrés dans ce projet d’envergure englobant 8 étages avec u n Rezde-chaussée et où des solutions ont été proposées et étudiées.
I-2-2. Contexte du projet : Le projet étudié est un immeuble, de 383 m² de surface de plate-forme, il possède une largeur de 18,60m du côté façades avant et arrière et une longueur de 20,60m du côté semi aveugle de
l’immeuble situé à «ABDEL MOMEN » CASABLANCA. L’architecte nous a permis, après avoir réalisé un croquis à la main levé, de saisir à l’échelle la réalisation sur Autocade.
a. Les caractéristiques géométriques :
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Projet de fin d’étude
Chapitre II : Conception du projet La conception de l’ouvrage est la phase la plus importante dans l’étude d’une construction, elle consiste dans le choix de la structure la plus optimale, c’est-à-dire celle qui respecte le plus, les exigences du maitre d’ouvrage, de l’architecte et du bureau de contrôle, tout en gardant une structure bien porteuse, facile à exécuter et moins couteuse sur le plan économique. Aussi, le respect des normes qui réglementent le type de la structure étudiée ét udiée est indispensable.
II-1. Conception architecturale : II-1-1. Etapes de conception : La conception se base sur les plans d’architecte, d’ar chitecte, ces plans sont donnés ou reproduits sur AUTOCAD pour faciliter la manipulation. En général les étapes à suivre dans cette phase sont :
Vérifier la faisabilité du projet ;
S’assurer que les plans respectent les le s fonctions prévues pour la construction ;
Respecter les normes et les règles qui régissent une telle construction ;
Vérifier la conformité entre les niveaux de la structure ;
Chaîner les poteaux ;
S’assurer que les dalles et les poutres sont bien appuyées ;
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Projet de fin d’étude
L’épaisseur des murs extérieurs et des cloisons (séparatives de distributions) est de 20 cm. Les cages d’escaliers et d’ascenseurs sont situées en plein milieu des deux façades, sachant que l’escalier est construit tout autour de l’ascenseur. Exception faite au RDC ou la cage d’escalier n’est située que du côté façade arrière du bâtiment , car la façade avant dispose de deux entrées principales donnant accès au hall hal l d’entrée. Un auvent de 120cm de portée a été mis en place aussi au niveau de l’accès principal, reposant sur 2 poteaux de 25 cm.
Concernant les cotations, l’unité objet utilis ée est le cm.
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Projet de fin d’étude
b. Description par étage : o
Le Rez- de- chaussée :
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Le Rez-de-chaussée est constitué constit ué de 4 espaces magasins identiques deux à deux ; le premier orienté vers la façade avant possédant une surface de 50m² et le deuxième type possédant une surface de 56m².
Il se compose aussi de deux W.C ; un pour homme et l’autre pour femme. La cage d’escalier arrière débute dès le rez-de-chaussée, tandis que la cage d’escalier avant ne commence qu’à partir du premier étage. Deux gaines techniques, à cheval entre les deux types de magasins, se raccordant directement au système externe, pour l’évacuation des eaux
usées.
Le patio, représente normalement un patio dessiné en trait discontinu pour montrer les trémies de
l’étage dessus Nous avons essayé d’être conformes aux réglementations, que constituent les espaces magasins.
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Projet de fin d’étude
o
Du 1er au 4éme étage:
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Projet de fin d’étude
ont été rajoutées dès le premier étage, afin de maximiser les gains de surfaces et r entabiliser, le plus, le coût de la construction. Des locaux de ce genre se vendent au prix du m² de surfa ce. o
Du 5éme au 8éme étage :
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Projet de fin d’étude Les quatre derniers étages sont réservées
pour des locaux de type habitations, L’aménagement L’aménagement du
mobilier, tels que les placards et kitchenettes, à l’intérieur des locaux nous est permis, afin d’attirer les clients à l’achat de ces petites surfaces. Pour simple information, ce type de bâti ment comporte des locaux qui peuvent se vendre à plus de 30 000 dhs/m², s’ils sont placés à des endroits stratégiques à Casablanca.
Les cages d’escaliers et d’ascenseurs sont visibles sur le plan ci -dessus et constituent une continuité entre les étages. o
Façades :
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o
Plans, coupes et détails : Terrasse
Coupe A-A
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Projet de fin d’étude
II-2. Conception parasismique : Toute conception visant le contreventement d’un bâtiment vis -à-vis des efforts sismiques doit appartenir aux trois variantes ci-dessous :
II-2-1. Système de portiques : Les portiques en béton armé, utilisés fréquemment entre les deux guerres mondiales, ont connu un essor remarquable après la découverte de méthodes de calcul simplifiées. Cette structure continue continue à
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II-4. Variantes de conceptions du projet : Il existe toujours plu sieurs variantes dans la conception d’un projet, mais laquelle choisir ? Et quelles sont les paramètres à respecter ?
Vu la taille de notre bâtiment et donc l’importance des charges supportées, on a opté pour un système de contreventement mixte ; ce qui suppose une bonne
réflexion sur l’implantation des
poteaux et surtout des voiles pour assurer un meilleur contreventement de la structure.
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Projet de fin d’étude
Chapitre III : Caractéristiques des matériaux. III-1. Béton : Le béton est un matériau constitué par le mélange du ciment, granulats (sable, gravillons) et d’eau de gâchage, Le béton armé est obtenu en introduisant dans le béton des aciers(Armatures) disposés de manière à équilibrer les efforts de traction.
La composition d’un mètre cube du béton est e st la suivante :
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retrait et le fluage sont souvent des inconvénients dont il est difficile de palier tous les effets.
a- Résistance mécanique :
Résistance caractéristique à la compression :
Le béton est caractérisé par sa bonne résistance à la compression, cette résis tance est mesurée par la
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Projet de fin d’étude
Résultats de dimensionnement des semelles Semelles
A(cm)
B(cm)
d(cm)
H(cm)
As//A
As//B
S1
115
250
40
45
28,72
41,02
S2
150
330
50
55
31,59
58,68
S3
120
340
55
60
20,63
56,4
S4
120
400
60
65
23,37
73,23
S5
150
330
55
60
24,61
50,39
S6
160
530
80
85
35,48
95,64
S7
160
470
70
75
34,79
84,7
S25
140
340
50
55
30,05
63,27
Tableau V-8 : Résultats de dimensionnement des semelles. Semelles/types
Poteaux
Nser(KN) A(cm)
B(cm)
d(cm)
H(cm)
σs
Condition σs< σs
S1
Centrée P1-P11-P15-P23
544,25
1,5
2,5
40
45
0,156
S2
Centrée P2-P12-P14-P24
682,51
1,5
3,3
50
55
0,152 Vérifiée
S3
Centrée P3-P9-P16-P21
749,21
1,2
3,4
55
60
0,199 Vérifiée
S4
Centrée P4-P10-P13-P22
862,15
1,2
4
60
65
0,19
S5
Centrée P5-P8-P17-P20
841,36
1,5
3,3
55
60
0,185 Vérifiée
S6
Centrée
P6-P19
1139,36
1,6
5,3
80
85
0,175 Vérifiée
S7
Centrée
P7-P18
1042,07
1,6
4,7
70
75
0,157 Vérifiée
726,72
1,4
3,4
50
55
0,167 Vérifiée
S25 Centrée P25-P26-P27-P28
Tableau V-9 : Vérification de la contrainte du sol (σsol=0,2MPa).
Vérifiée
Vérifiée
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Projet de fin d’étude
Chapitre VI: Etude des éléments secondaires VI-1. Introduction : Dans toute structure on distingue deux types d’éléments : Les éléments porteurs principaux qui contribuent au contreventement directement. Les éléments secondaires qui ne contribuent pas au contreventement directement.
Ainsi l’escalier et l’acrotère sont considérés comme des éléments secondaires dont l’étude est indépendante de l’action sismique (puisqu’ils ne contribuent pas directement à la reprise de ces efforts), mais ils sont considérés comme dépendant de la géométrie interne de la structure.
VI-2. Etude de l’acrotère : L’acrotère sera calculé comme une console encastrée au niveau du plancher terrasse inaccessible en flexion composée pour une bande de 1,00 m de largeur.
L’acrotère sera calculé en flexion composée sous l’effet d’un effort normal NG dû au poids propre et un moment de flexion à la base dû à la charge de la main courante estimée à : Q=0,7 KN/ml Poids propre de l’acrotère :
- La surface de l’acrotère :
S=(0,5×0,1)+(0,05×0,1)+
,×, = 0,0575m²
- La masse volumique =25 KN/m 3 P = (0,0575×25) = KN/ml Q=0,7 KN/ml
Figure VI-1 : Dimensions de l’acrotère.
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Projet de fin d’étude
a- Calcul des Sollicitations :
Calcul à l’E.L.U :
Poids propre (effort normal) :
G=25×S
S : surface de l’acrotère
S=0,0575 m² G = 25×0,0575 =1,4375 KN/ml Nu=1, 35×G=1,35×1,4375 Nu=1,940KN/ml Surcharge: Q=0,7KN/ml Qu=1, 5×Q=1, 05 KN/ml Le moment: Mu=Qu×h=1,05×0,5 Mu=0,525 KN.m (moment d’ encastrement)
Calcul à l’E.L.S :
Nser = G =1,437KN Mser =
² = ,×,² =0,0875KN.m
b- Calcul de l’excentricité: C’est la distance entre le centre de d e pression et le centre de gravité d’une section. secti on. e=
= ,=0,263m ,
e=0,27m ht =10cm
= =1,66cm e≥ la section est partiellement comprimée parce que le centre de pression est appliquée à e=
l’extérieur du noyau central.
c- Détermination du ferraillage :
Calcul à E.L.U :
Figure VI-2: Section de calcul d’acrotère.
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Projet de fin d’étude - d : la distance séparant la fibre la plus comprimée et les armatures inférieures. - d’ : la distance entre les armatures inférieures et la fibre la plus tendue. Moment de flexion fictif (M A) :
MuNud , M =0,525+1,94 (0,09 MA= A
= 0,6026KN.m=60,26×10 0,6026KN.m=60,26×10 -5 MN.m
Moment réduit (μu) :
μu=²
f bc=0,85× Avec :
γ b=1,50;
=25MPa ,
f c28 c28=
f bc=14,17 MPa Donc ;
μu=×,× ,×, = 0,00520 pivot (pivot A).
0,00520< 0,259
Les armatures comprimées ne sont pas nécessaire c.à .d : Asc=0.
− Ast =1×
σst= Avec : f e = 400MPa et
γs =1,15
d’où : σst =348 MPa α=1,25(1-√(1 − 2μ) = 1,25(1 − √(1 − 2 × 0,00520) = 0,0062 z = d (1- 0,4α)=0,09 (1-0,4×0,0062)=0,087m. (1-0,4×0,0062)=0,087m.
,× −,× − , Ast=1× =1 =0,14cm²
×
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Projet de fin d’étude
Condition de non fragilité :
Ast≥0,23×b×d×
, =1,08cm²
Ast≥0,23×1×0,09×
Donc ; on adopte : A st=1,08cm²
4HA8.
Calcul E.L.S :
Vérification des contraintes
σ bc< σ bc Avec : σ bc=0,6×f c28 c28=15MPa σst< σst
et (σst est choisie en fonction de la fissuration)
Avec :
σ bc=
Z ; σst= Z−
η = 15 ; c’est le coefficient d’équivalence acier – béton. béton. Yser : c’est la distance de l’axe neutre à la fibre la plus comprimée à l’état limite de service. On a: Nser =1,437KN. =1,437KN. Mser = = 0,0875 KN.m e=
= ,=0,061m ,
Yser = z+c Avec : C=
ℎ = , 0,061 = -0,012m
Z : est définie par l’équation du 3éme degré suivante : (−)× −
p=-3c²-
avec Asc=0 ,+,×××,× =0,001m² p= -3(-0,012)² + (−)×× −² q= -2c ,+, ,+,²×××,× q=-20,011 × Δ=q²+ ×, =(0,000141)²+
+pZ+q=0 3
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Projet de fin d’étude
Calcul de (L) : t= 0.5 (
√∆ q = 0,000145 m
L=t1/3
3
L=0,0530m
Calcul de Z : Z=L-
L
= 0,0467m. Donc ;
Yser =Z+C=0,0467+ =Z+C=0,0467+ ( 0,012)=0,0357m Calcul d’inertie (I) : I=
15Astdyser AscYserd′
Avec : Asc=0cm².
,° −0,0090,0357 I= 151,5×10 0,0090,0357 =2,17×105m4
Calcul des contraintes: Z ,××,×,= 0,11Mpa σ bc= = ,× Z− =,××,×,−, = 0,165MPa σst= ,× Fissuration préjudiciable ce qui veut dire:
fe;110√ηft28
σst=min ( Avec :
η= 1,6,
f t28 t28=2,10 MPa
et
σst =201,63 MPa
σst =0,165 MPa < σst Donc ; la section et le nombre d’armature choisie sont acceptables.
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Projet de fin d’étude
Position de l’axe neutre :
²-η.As. (d-y1)=0 50y1²+22,65y1-203,85=0
y1=1,80cm
Moment d’inertie : I=
y1 η. As. dy1 = ×, 15×1,51×91,8² =1368,58cm4
Détermination des contraintes dans le béton comprimé σbc :
σ bc=
y1 = × 1,8 =0,25MPa ,
σ bc= 0,6.f c28 c28=15MPa σ bc= 0,25MPa<σ bc=15MPa………………condition vérifiée Détermination des co ntraintes dans l’acier tendue σst : Fissuration préjudiciable :
σst=min (f e ; 110
√η f
t28 t28)
Avec η : coefficient de fissuration pour HA ϕ≥6mm ; η=1,6 ɸ≥6mm ; η=1,6 σst =min (267MPa; 202MPa) =202MPa σs t=15MPa<σst=202MPa………condition vérifiée Contrainte de cisaillement :
τ
τu= × T=1,5Q=1,05KN
,
τu=,×=11,67KN/m²
τu =min (0,1fc28 ; 4MPa)=2,5MPa τu =11,67×103MPa< τu=2,5MPa……….condition vérifiée
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Projet de fin d’étude
VI-3. Etude des escaliers VI-3-1. Introduction C’est une partie du gros œuvre qui fait communiquer entre eux les différents niveaux d’un immeuble. A la différence d’un incliné (rampe de garage, par exemple), l’escalier est composé de plans horizontale successifs : marches et paliers.
Figure VI-4 : Eléments d’escalier.
VI-3-2. Descente de charge :
Paillasse :
-
Carrelage horizontale (2cm) : 0,44 KN/m²
-
Mortier de pose (H) (2cm) : 0,40 KN/m²
-
Carrelage vertical (2cm) : 0,25 KN/m²
-
Mortier de pose (V) (2cm) : 0,23 KN/m²
-
Les marches : 1,87 KN/m²
-
Paillasse : 4,31 KN/m² Enduit en ciment (2cm) : 0,46 KN/m²
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Projet de fin d’étude
Gtotal = 4,81 KN/m² Q= 2,50 KN/m²
VI-3-3. Dimensionnement: Dimensionner les escaliers revient à déterminer les dimensions du giron ‘’g’’ et contre marches ‘’h’’. En utilisant la formule de BLONDEL on a :
59 ≤2h+g≤ 66cm Avec: h: hauteur de la marcheur g : largeur de la l a marche, On prend généralement 2h+g=60cm H = n×h L=(n-1) ×g Avec : H : hauteur entre les faces supérieurs des deux paliers successifs d’étage n : nombre de contre marches L : la projection horizontale de la longueur total de la volée
L
D’après BLONDEL on a : −
2 × H = m
Et puis : m n 2 – (m+L+2H) (m+L+2H) n +2H=0 Avec : m=60 et H=
=150cm et L=270cm
Donc l’équation devient : 60n 2-630n+300=0 La solution de l’équation est : n=10 contre marches Donc le nombre de marche est n-1=9 marches.
D’où:
H =15cm L g= = =30cm − h= =
On a :
2h+g=2×15+30=60L’inégalité 2h+g=2×15+30=60L’inégalité est vérifiée.
Epaisseur de la paillasse :
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Projet de fin d’étude
On prend une épaisseur e v=15cm.
Epaisseur du palier :
L’épaisseur du palier varie de 10cm à 15cm. Tel que ev=
=13,48cm ,
On prend : ev=15cm
VI-3-3. Etude de type1 d’escalier (à une seule volée) :
Volée (paillasse) : Gv=8,66KN/m² Qv=2,5KN/m² qvu=1,35Gv+1,5Qv=15,44KN/m² qvser =G =Gv+Qv=11,16KN/m² Palier : G p=4,91KN/m² Q p=2,5KN/m²
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Projet de fin d’étude
R A =32,8KN R B = 32,76KN -
Calcul des moments isostatiques et l’effort tranchant à l’E.L.U :
Si 0 ≤x≤1,1m
²
M(x)=R Ax-q p
M(x)=32,8x-5,185x² T(x)= R A-q px =32,8-10,37x M(0) = 0KN.m M(1,1)=34,12KN.m T(0)=R A=32,8KN T(1,1)=21,39N Si 1,1≤x≤3,8
, -qv(−,²
M(x) = R Ax- 1,1q p(x-
M(x)= 32,8x-11,4(x-0,55)-7,72(x-1,1)² 32,8x-11,4(x-0,55)-7,72(x-1,1)² T(x)=R A-1,1q p-qv(x-1,1) T(x)=21,39-15,44(x-1,1) M(1,1)=29,81KN.m
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Projet de fin d’étude
Mmax en travée :
, -qv−,²
M(x) = R Ax-1,1q p(x-
M(x)=32,8x-11,4(x-0,55)-7,72(x-1,1)² T(x)=R A-1,1q p-qv(x-1,1) T(x)=21,39-15,44(x-1,12) Mamax = 0,5 Mmax Mtmax = 0,85 M max -
Mamax = 27, 05 KN.m Mtmax = 45,99 KN.m
Calcul des moments isostatiques et l’effort tranchant à l’E.L.S :
M(x)=R Ax -q p ² M(x)=32,8x-7,41x² T(x)= R A-q px =32,8-7,41x M(0) = 0KN.m M(1,1)=27,11KN.m T(0)=R A=32,8KN T(1,1)=24,64N Si 1,1≤x≤3,8
−,²
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Projet de fin d’étude
M(3,8)= -8,809KN.m M(5)=0KN.m T(3,8)= -5,492KN T(5)= - 14,384KN Mmax en travée : Si 3,8≤x≤5 M(x)=R AX AX-1,1q p(x-
,)-qv−,²
M(x)= 32,8x-8,15(x-0,55)-5,58(x-1,1)² 32,8x-8,15(x-0,55)-5,58(x-1,1)² T(x)=R A-1,1q p-qv(x-1,1) T(x)=24,64-11,16(x-1,1) T(x)=24,64-11,16(x-1,1) Mamax = 0,5 Mmax Mtmax = 0,85 Mmax
Mamax = 29,41KN.m Mtmax = 49,99 KN.m
Calcul des sections d’armatures : -
Calcul à l’E.L.U :
En travée : On a : h=0,15m ;b=1m ;d=0,135m M ut= 45,99KN.m
μ bu=..
,× = 0,1<0,259 = ×,²×,
Pivot A, donc ; les armatures de compression ne sont pas nécessaire
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Projet de fin d’étude Z=d (1-0,4α)=0,130m
= ,× =6,12cm²=6HA12 Z. ,×
Ast=
Condition de non fragilité:
j
, =1,63cm²
Ast=0,23bd. =0,23×1×0,135× Armature de répartition : Ar =
= ,=1,53cm²
On adopte : A r =3,14cm²=4HA10 =3,14cm²=4HA10 Espacement maximal : St ≤ min (3h; 33cm) = min (3×15; 33) cm = 33cm Armatures longitudinales -
En travée: St= 100/10= 10 cm ≤ 33cm
-
Sur appui : St= 100/6= 16,66 cm ≤ 33cm
Armatures de répartition : -En travée: S t= 100/4= 25 cm ≤ 33cm
donc on prend prend S t= 33cm
-Sur appui : S t= 100/4= 25 cm ≤ 33cm donc on prend
S t= 33cm
Position
b(cm)
d(cm)
Mu(KN.m)
μ
Α
Z
As
En travée
100
13,5
45,99
0,1
0,131
0,127
10,4
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Projet de fin d’étude
Détermination de l’axe neutre :
y²+
n .(As+As’).Y-n.(As.d+As’.d’)=0 avec n=15
Moment d’inertie :
I= y3+ n.As’.(Y-d’)² + n.As.(d-Y)²
On a seulement des armatures tendues (pas d’armatures comprimées) donc A s’=0 les résultats obtenus sont dans le tableau : Position
Mser (KN.m) (KN.m) Y(m)
I(m4)
σ b(MPa) σ b≤ σ b
En travée
49,99
0,051
1,54×10
1,65
Vérifiée
En appui
29,41
0,035
1,06×104
0,97
Vérifiée
Tableau VI-2- : Récapitulatif pour la vérification à ELS.
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Projet de fin d’étude
VI-4-1. Pré dimensionnement : La hauteur de la poutre palière doit vérifier la condition suivante : Avec L=4,72m donc
, ≤ h ≤ ,
L ≤ h ≤ L
0,31 ≤ h ≤0,47
Donc on adopte une hauteur h=45 cm
La largeur de la poutre doit être selon le RPS2002 : b ≥200 mm on prend b=25cm
=0,55>0,25 c’est vérifié donc prenant une poutre palière de (25×45). VI-4-2. Evaluation des charges : Le calcul se fait en flexion simple pour une poutre partiellement encastrée à l’extrémité dans les voiles et uniformément chargée, les charges sont : Son poids propre : 0,25×0,45×25=2,81 0,25×0,45×25=2,81 KN/m Poids de mur : 0,5KN/m²×4,72m=2,36KN/m Charge linéaire du palier :
×
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Projet de fin d’étude
D’après l’organigramme de calcul à l’ELU d’une section rectangulaire en flexion simple, les résultats sont : Position
b(cm)
En travée En appuis
25 25
d(cm)
Mu(KN.m)
Μ
Α
Z
As
40,5 32,48 0,0558 0,0719 0,393 1,899 40,5 64,96 0,111 0,1485 0,380 3,929 Tableau VI-3 : Ferraillage à ELU de la poutre palière.
Condition de non fragilité :
= ,××,×,=0,798cm²
Asmin=0,23.b.d.
Armatures utilisées : Ast=max (As ;Asmin) On prend : 2HA12 (2,26cm²) comme armatures tendues en travée
4HA12 (2,26cm²) comme armatures chapeaux en appuis
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Projet de fin d’étude
Position
Mser (KN.m) (KN.m)
Y(m)
I(m4)
σ b(Mpa)
σ b≤ σ b
En travée
23,34
5,84×104
1,15×103
11,81
Vérifiée
En appui
64,96
1,22×103 2,38 ×103
0,97
Vérifiée
écapitulatif pour la vérification à l’ELS. Tableau VI-4 : R écapitulatif La contrainte de compression de béton est vérifiée donc on adopte les armatures calculées à ELU
Calcul des armatures transversales et de l’espacement : Diamètre des armatures transversales :
ɸt≤min( ;ɸlmin ;
ɸt≤min( ;ɸlmin ; ɸt≤8,57mm
on prend ɸt=8mm
Espacement des cours d’armatures dans la zon e courante : On prend A =4T8=2cm²
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Projet de fin d’étude
FigureVI-7 : Ferraillage de la poutre palière. VI-5. Etude de la dalle machinerie : VI-5-1. Introduction :
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Projet de fin d’étude
-
Poids propre de la dalle : 0,25×25=6,25KN/m² G=56,25KN/m²
Charges d’exploitation : Q= 1KN/m² La charge totale : ELU : Nu=1,35G+1,5Q=77,438KN/m² ELS : Ns=G+Q=57,25KN/m²
b- Calcul des sollicitations :
L , =0,8>0,4 L ,
ρ= =
Donc la dalle travaille dans les deux sens x et y. -
Mx=μxqulx²
-
My=μyMx
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Projet de fin d’étude
Espacement : Esp = •
=20cm < Min (3h;33cm)=33cm
Vérifiée
Dans le sens Ly:
Mtx(KN.m)
μbu
A’s(cm²)
α
15,60
0,0646
0
0,0836
Z(cm) Ascal(cm²) choix As adp(cm²) 21,74
2,06
5T10
3,94
Tableau VI-6 : Récapitulatif des résultats de ferraillage en travée (sens Ly) Espacement :
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Projet de fin d’étude
Acier :
dy≤ σ σ =Min ( fe ; 150η)=240MPa
σs=
s
s
Avec :
η=1,6 pour HA ; f e=400MPa
ρ= =0,805 ; q =57,25KN/m
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Projet de fin d’étude
ρ0=0,8% Avec:
L
ρ=L=0,805 Sens Lx-x : Sur appuis : A x=2,5cm²/ml>2,10cm² En travée : Ay=3,94cm²/ml>2,10cm² Vérification de la flèche :
Vérifiée Vérifiée
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Projet de fin d’étude
déplacer la cabine (le moteur électrique; le contre poids; les câbles).
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Projet de fin d’étude
- Hauteur : 2,2 m ; - La largeur de passage libre : 0,8 m ; - La hauteur de la course : 35,11 m ; - L’épaisseur de la dalle qui supporte l’ascenseur : h0=25cm ; - Le poids mort total est : Pm =∑Mi=2342,5 kg ; - Le contre poids : Pp=2342,5+ P p=2342,5+
=2567,5 kg.
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Projet de fin d’étude
M =m×n×L=0,512×2×37,31=3 =m×n×L=0,512×2×37,31=38,20 8,20 kg
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Projet de fin d’étude
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Projet de fin d’étude
,
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Projet de fin d’étude
M =0,75.M =542,88 Kg.m
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Projet de fin d’étude
Le moment réduit μ
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Projet de fin d’étude
Pré dimensionnement de S3 Charge Ns sur P3(KN):
Pré dimensionnement de S4
Grand coté b du poteau P3 (cm) :
749,40 135,00
Grand coté b du poteau P4 (cm) :
Petit coté a du poteau P3 (cm) :
45,00
Petit coté a du poteau P4 (cm) :
Contrainte admissible du sol σ
0,20
Contrainte admissible du sol σ
862,03 165,00 45,00 0,20
(Mpa) :
(Mpa) : surface portante S du semelle (m²): Petit dimension A de S3 (m) Grand dimension B de S3 (m)
Charge Ns sur P4(KN):
3,75
surface portante S du semelle (m²): Petit dimension A de S3 (m)
4,31
1,12 3,35 1,20
Grand dimension B de S3 (m)
1,08 3,98
A addop (m)
1,20
3,40 0,51
B addop (m) Hauteur utile d (m):
4,00 0,59
la hauteur Ht du S3 (m)
0,56
d addop (Cm) Ht addop (Cm)
55,00 60,00
la hauteur Ht du S3 (m) d addop (Cm) Ht addop (Cm)
0,64 60,00 65,00
A addop (m) B addop (m) Hauteur utile d (m):
Pré dimensionnement de S6
Pré dimensionnement de S5 Charge Ns sur P5(KN):
841,36
Charge Ns sur P6(KN):
1139,36
Grand coté b du poteau P5 (cm) :
115,00
220,00
Petit coté a du poteau P5(cm) :
45,00
Contrainte admissible du sol σ
0,20
Grand coté b du poteau P6 (cm) : Petit coté a du poteau P6(cm) : Contrainte admissible du sol σ
(Mpa) :
45,00 0,20
(Mpa) :
surface portante S du semelle (m²):
4,21
Petit dimension A de S5 (m) Grand dimension B de S5 (m) A addop (m) B addop (m) Hauteur utile d (m): la hauteur Ht du S5 (m)
1,28 3,28 1,50 3,30 0,54 0,59
d addop (Cm) Ht addop (Cm)
55,00 60,00
surface portante S du semelle (m²): Petit dimension A de S6 (m) Grand dimension B de S6 (m) A addop (m) B addop (m) Hauteur utile d (m): la hauteur Ht du S6 (m) d addop (Cm) Ht addop (Cm)
5,70 1,08 5,28 1,60 5,30 0,78 0,83 80,00 85,00
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Projet de fin d’étude
Pré dimensionnement de S7 Charge Ns sur P7(KN): Grand coté b du poteau P7 (cm) : Petit coté a du poteau P7(cm) Contrainte admissible du sol σ
Pré dimensionnement de S25 1042,07 190,00 45,00 0,20
Charge Ns sur P25(KN): Grand coté b du poteau P25 (cm) : Petit coté a du poteau P25(cm) : Contrainte admissible du sol σ
(Mpa) :
(Mpa) : surface portante S du semelle (m²): Petit dimension A de S7 (m) Grand dimension B de S7 (m)
5,21
A addop (m) B addop (m)
1,60 4,70
Hauteur utile d (m): la hauteur Ht du S7 (m) d addop (Cm) Ht addop (Cm)
0,70 0,75 70,00 75,00
728,72 140,00 45,00 0,20
1,11 4,69
surface portante S du semelle (m²): Petit dimension A de S25 (m) Grand dimension B de S25 (m) A addop (m) B addop (m) Hauteur utile d (m): la hauteur Ht du S25 (m)
3,64
d addop (Cm) Ht addop (Cm)
50,00 55,00
Vérification de la contrainte du sol Vérification du contrainte de sol pour S1 Aire de la surface portante (m ²) Poids propre de la semelle (MN)
(AxB) ( A x B x Ht x 0.025 )
3,75 0,0422
Charge totale sur le sol (MN) Contrainte de travail sur le sol (Mpa)
( Nser + Pp ) (N/S)
0,59 0,156
Contrôle
( q' < q )
Vérifié
Vérification du contrainte de sol pour S2 Aire de la surface portante (m ²)
(AxB)
Poids propre de la semelle (MN)
( A x B x Ht x 0.025 )
Charge totale sur le sol (MN)
( Nser + Pp )
Contrainte de travail sur le sol (Mpa) Contrôle
(N/S) ( q' < q=0,2 MPa)
4,95 0,0681 0,75 0,152 Vérifié
Vérification du contrainte de sol pour S3 Aire de la surface portante (m ²) Poids propre de la semelle (MN) Charge totale sur le sol (MN) Contrainte de travail sur le sol (Mpa)
(AxB) ( A x B x Ht x 0.025 ) ( Nser+ Pp ) (N/S)
4,08 0,0612 0,81 0,199
Contrôle
( q' < q )
Vérifié
Vérification du contrainte de sol pour S4
1,08 3,37 1,40 3,40 0,50 0,55
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Projet de fin d’étude
Contrôle
( q' < q )
Vérifié
Vérification du contrainte de sol pour S5 Aire de la surface portante (m ²) Poids propre de la semelle (MN)
(AxB) ( A x B x Ht x 0.025 )
4,95 0,0743
Charge totale sur le sol (MN)
( Nser+ Pp )
0,92
Contrainte de travail sur le sol (Mpa)
(N/S)
0,185
Contrôle
( q' < q )
Vérifié
Vérification du contrainte contrainte de sol pour S6 Aire de la surface portante (m²)
(AxB)
7,42
Poids propre de la semelle (MN)
( A x B x Ht x 0.025 )
Charge totale sur le sol (MN) Contrainte de travail sur le sol (Mpa) Contrôle
( Nser+ Pp )
0,1577 1,30
(N/S) ( q' < q )
0,175 Vérifié
Vérification du contrainte de sol pour S7 Aire de la surface portante (m ²) Poids propre de la semelle (MN) Charge totale sur le sol (MN)
(AxB) ( A x B x Ht x 0.025 ) ( Nser+ Pp )
7,52 0,1410 1,18
Contrainte de travail sur le sol (Mpa)
(N/S)
0,157
Contrôle
( q' < q )
Vérifié
Vérification du contrainte de sol pour pour S25 Aire de la surface portante (m ²)
(AxB)
4,76
Poids propre de la semelle (MN) Charge totale sur le sol (MN)
( A x B x Ht x 0.025 ) ( Nser+ Pp )
0,0655 0,79
Contrainte de travail sur le sol (Mpa)
(N/S)
0,167
Contrôle
( q' < q )
vérifié
ANNEXE F : Résultats de dimensionnement des poteaux
Poteaux
Plancher haut 8éme étage
Nu ( KN)
a (m)
b (m)
Br (m²)
λ
α
Ath (cm²)
Amin (cm²)
Amax (cm²)
As (cm²)
barres d'acier
P1-P11-P15-P23
89,40
0,2500
0,25
0,0529
29,10
0,72
-19,68
4
31,25
4,00
4HA12
P2-P12-P14-P24
121,48
0,2500
0,25
0,0529
29,10
0,72
-18,65
4
31,25
4,00
4HA12
P3-P9-P16-P21
125,28
0,2500
0,25
0,0529
29,10
0,72
-18,53
4
31,25
4,00
4HA12
P4-P10-P13-P22
134,87
0,2500
0,25
0,0529
29,10
0,72
-18,22
4
31,25
4,00
4HA12
P5-P8-P17-P20
146,78
0,2500
0,25
0,0529
29,10
0,72
-17,84
4
31,25
4,00
4HA12
P6-P19
177,70
0,2500
0,25
0,0529
29,10
0,72
-16,85
4
31,25
4,00
4HA12
P7-P18
177,62
0,2500
0,25
0,0529
29,10
0,72
-16,86
4
31,25
4,00
4HA12
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Projet de fin d’étude
D i amè am è tr e des des arm ar m a- tur es longitu dinal es D i amè am è tr e des des acier aci erss transversaux E spacement spacement des aciers transv tr ansve er saux Jonctions par r ecou- vrement
4HA12
12
Mm
Øt=
6
Mm
St =
18
Cm
Lr =
36
Cm
Lz = Max(he/6 Max(he/6 ; b ; 45cm)
Lz
50,00
Cm
tcr = Min(15cm ; 8Øl ; 0.25b)
Tcr
6,25
Cm
tc = Min(30cm ; 12Øl ; 0.5b)
Tc
12,50
Cm
Øl = Øt < ( Ølmax / 3 ) avec minimum 6mm St = mini ( a+10 cm ; 15 Øl ; 40 cm) lr = 0.6 ls ( soit 24Øl pour HA 400 ) ( soit 30 Øl pour HA 500 et RL 235 ) RPS
R.P.S longeur du zone cri - tique E space dans dan s l a zon zone e critique E space dans dan s l a zon zone e courant
Choix 1 :
Planchez haut étage courant habitation
Poteaux
Niveau
Nu(Kn)
a (m)
b (m)
Br (m²)
λ
α
P1-P11P15-P23
1,00 2,00 3,00 4,00 1,00 2,00 3,00 4,00 1,00 2,00 3,00 4,00 1,00 2,00 3,00 4,00 1,00 2,00
89,40 164,75 240,11 315,46 121,48 225,44 329,39 433,35 125,28 228,87 332,45 436,04 134,87 269,19 404,38 539,57 146,78 265,62
0,2500 0,2500
0,2500 0,2500 0,2500 0,25 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,3 0,2500 0,2500
0,0529 0,0529 0,0529 0,0529 0,0529 0,0529
29,10 29,10 29,10 29,10 29,10 29,10
0,0529
P2-P12P14-P24
P3-P9-P16P21
P4-P10P13-P22
P5-P8-P17P20
Choix du sec- sec- tion 12mm
0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500
0,72 0,72 0,72 0,72 0,72 0,72
Ath (cm²) -19,68 -17,66 -15,59 -13,53 -18,65 -17,66
Amin (cm²) 4 4 4 4 4 4
Amax (cm²) 31,25 31,25 31,25 31,25 31,25 31,25
As (cm²) 4,00 4,00 4,00 4,00 4,00 4,00
barres d'acier 4HA12 4HA12 4HA12 4HA12 4HA12 4HA12
29,10
0,72
-15,59
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-13,53
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-13,53
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-15,22
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-17,66
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-15,59
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-13,53
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-13,53
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-9,61
4
31,25
4,00
4HA12
0,0644
29,10
0,72
-17,66
4,4
37,5
4,40
4HA14
0,0529
29,10
0,72
-15,59
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-13,53
4
31,25
4,00
4HA12
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Projet de fin d’étude
P7-P18
P25-P26P27-P28
2,00 3,00 4,00 1,00 2,00 3,00 4,00 1,00 2,00 3,00 4,00
355,15 533,29 711,44 177,62 322,94 468,25 613,57 114,04 228,31 342,62 456,93
0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500 0,2500
0,2500 0,3 0,35 0,2500 0,2500 0,25 0,35 0,2500 0,2500 0,25 0,25
0,0529
29,10
0,72
-15,59
4
31,25
4,00
4HA12
0,0644
29,10
0,72
-13,53
4,4
37,5
4,40
4HA14
0,0759
29,10
0,72
-13,53
4,8
43,75
4,80
4HA14
0,0529
29,10
0,72
-16,86
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-17,66
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-15,59
4
31,25
4,00
4HA12
0,0759
29,10
0,72
-13,53
4,8
43,75
4,80
4HA14
0,0529
29,10
0,72
-13,53
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-15,24
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-17,66
4
31,25
4,00
4HA12
0,0529
29,10
0,72
-15,59
4
31,25
4,00
4HA12
Choix du sec- sec- tion 12mm Øl =
D i amètr e des des armat ar matu u r es longitudinales D i amètr e des des aciers aci ers tr ans- Øt < ( Ølmax / 3 ) avec minimum 6mm versaux St = mini ( a+10 cm ; 15 Øl ; 40 cm ) E spacement spacement des d es aciers aci ers transversaux lr = 0.6 ls ( soit 24Øl pour HA 400 ) Jonctions par r ecouvr couvr e- ment ( soit 30 Øl pour HA 500 et RL 235 ) R.P.S RPS Lz = Max(he/6 Max(he/6 ; b ; 45cm) longeur du zone zone cri tique ti que Espace dans la zone cri - tcr = Min(15cm ; 8Øl ; 0.25b) tique Espace dans la l a zone cou- cou- tc = Min(30cm ; 12Øl ; 0.5b) rant
Choix 1 :
4HA12
12 mm
Øt=
6
mm
St =
18
cm
Lr =
36
cm
Lz
50,00
cm
Tcr
6,25
cm
Tc
12,50
cm
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Projet de fin d’étude
D i amètr e des des armatu ar matu r es lon - gitudinales D i amètr e des des acier s trans- tr ans- versaux E spacement pacement des des aci aci ers tr ans- versaux Joncti Jon ctions ons par re r ecouvrement couvrement
Øl =
Choix 1 :
14mm
14 mm
Øt < ( Ølmax / 3 ) avec minimum 6mm St = mini ( a+10 cm ; 15 Øl ; 40 cm ) lr = 0.6 ls ( soit 24Øl pour HA 400 ) ( soit 30 Øl pour HA 500 et RL 235 )
R.P.S
4HA14
Øt=
6
mm
St =
21
cm
Lr =
42
cm
RPS
longe lon geur ur du zone zone cr cr itique it ique Espace Espace dans dans la l a zone zone cri tique ti que E space dans la zone cour ant
Choix du sec- sec- tion
Lz = Max(he/6 Max(he/6 ; b ; 45cm)
Lz
50,00
cm
tcr = Min(15cm ; 8Øl ; 0.25b)
tcr
7,50
cm
tc = Min(30cm ; 12Øl ; 0.5b)
tc
14,40
cm
Plancher haut étage courant bureau
Poteaux
Niveau
Nu(Kn)
a (m)
b (m)
Br (m²)
λ
α
Ath (cm²)
Amin (cm²)
Amax (cm²)
As (cm²)
barres d'acier
P1-P11P15-P23
1,00 2,00 3,00 4,00 1,00 2,00 3,00 4,00 1,00 2,00 3,00 4,00
801,51 882,70 963,89 1045,08 1100,71 1213,25 1325,78 1438,31 1109,57 1221,79 1334,00 1446,22
0,3500 0,3500 0,3500 0,3500 0,3500 0,3500 0,3500 0,3500 0,3500 0,3500 0,3500 0,3500
0,3500 0,3500 0,4 0,45 0,4500 0,5000 0,55 0,55 0,4500 0,5000 0,5 0,55
0,1089 0,1089 0,1254 0,1419 0,1419 0,1584 0,1749 0,1749 0,1419 0,1584 0,1584 0,1749
20,78 20,78 20,78 20,78 20,78 20,78 20,78 20,78 20,78 20,78 20,78 20,78
0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72
-20,78 -17,66 -15,59 -13,53 -25,28 -17,66 -15,59 -13,53 -24,99 -17,66 -15,59 -13,53
5,6 5,6 6 6,4 6,4 6,8 7,2 7,2 6,4 6,8 6,8 7,2
61,25 61,25 70 78,75 78,75 87,5 96,25 96,25 78,75 87,5 87,5 96,25
5,60 5,60 6,00 6,40 6,40 6,80 7,20 7,20 6,40 6,80 6,80 7,20
4HA14
P2-P12P14-P24
P3-P9P16-P21
4HA14 4HA14 4HA14+2HA12 4HA14+2HA12 4HA14+2HA12 4HA14+2HA12 4HA14+2HA12 4HA14+2HA12 4HA14+2HA12 4HA14+2HA12 4HA14+2HA12
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Projet de fin d’étude
P25-P26P27-P28
2,00
1713,75
0,3500
0,6000
3,00
1868,25
0,3500
0,65
4,00
2022,75
0,3500
0,7
1,00
1150,84
0,3500
0,4000
2,00
1274,69
0,3500
0,4500
3,00
1398,53
0,3500
0,5
4,00
1522,37
0,3500
0,55
0,1914 0,2079 0,2244 0,1254 0,1419 0,1584 0,1749
20,78 20,78 20,78 20,78 20,78 20,78 20,78
0,72 0,72 0,72 0,72 0,72 0,72 0,72
-17,66 -15,59 -13,53 -16,65 -17,66 -15,59 -13,53
7,6 8 8,4 6 6,4 6,8 7,2
Choix du section 14mm Øl =
D i amètr e des des armatu arm aturr es longi lon gi- - tudinales Øt < ( Ølmax / 3 ) avec minimum 6mm D i amè am è tr e des des aciers acier s tran tr ansve sverr - saux Espacement Espacement des acie aci er s tran sver ver - St = mini ( a+10 cm ; 15 Øl ; 40 cm ) saux lr = 0.6 ls ( soit 24Øl pour HA 400 ) Jonctions par r ecouvr couvr ement ment ( soit 30 Øl pour HA 500 et RL 235 ) R.P.S RPS Lz = Max(he/6 Max(he/6 ; b ; 45cm) longeur du zone zone cri tique ti que tcr = Min(15cm ; 8Øl ; 0.25b) Espace Espace dans dans l a zone zone cri cr i tique ti que tc = Min(30cm ; 12Øl ; 0.5b) Espace dans la zone cour ant
R.P.S
RPS
7,60 4HA16+2HA12 8,00 4HA16+2HA12 8,40 4HA16+2HA12 4HA14 6,00 6,40 4HA16+2HA12 6,80 4HA14+2HA12 7,20 4HA14+2HA12
Choix 1: 14 mm
4HA14
Øt=
6
Mm
St =
21
Cm
Lr =
42
Cm
Lz tcr tc Choix du section 14mm Øl =
D i amètr e des des armatu arm aturr es longi lon gi- - tudinales Øt < ( Ølmax / 3 ) avec minimum 6mm D i amè am è tr e des des aciers acier s tran tr ansve sverr - saux Espacement Espacement des acie aci er s tran sver ver - St = mini ( a+10 cm ; 15 Øl ; 40 cm ) saux lr = 0.6 ls ( soit 24Øl pour HA 400 ) Jonctions par r ecouvr couvr ement ment ( soit 30 Øl pour HA 500 et RL 235 )
105 113,75 122,5 70 78,75 87,5 96,25
50,00 Cm 8,75 Cm 16,80 Cm Choix 4HA14+2HA12 1: 12mm
Øt=
6
Mm
St =
18
Cm
Lr =
36
Cm
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Projet de fin d’étude
Espacement Espacement des acie aci er s tran sver ver - St = mini ( a+10 cm ; 15 Øl ; 40 cm ) saux lr = 0.6 ls ( soit 24Øl pour HA 400 ) Jonctions par r ecouvr couvr ement ment ( soit 30 Øl pour HA 500 et RL 235 ) R.P.S longeur du zone zone cri tique ti que Espace Espace dans dans l a zone zone cri cr i tique ti que Espace dans la zone cour ant
P1-P11-P15P23 P2-P12-P14P24 3-P9-P16-P21 P4-P10-P13P22 5-P8-P17-P20 P6-P19 P7-P18 25-P26-P27P28
18
cm
Lr =
36
cm
Lz tcr tc
75,00 9,60 14,40
cm cm cm
Plancher haut Rez de chaussée
Nu ( KN) a (m)
Poteaux
RPS Lz = Max(he/6 Max(he/6 ; b ; 45cm) tcr = Min(15cm ; 8Øl ; 0.25b) tc = Min(30cm ; 12Øl ; 0.5b)
St =
b (m)
Br (m²)
λ
α
Ath (cm²)
Amin (cm²)
Amax (cm²)
As (cm²)
barres d'acier
3805,14
0,4500
1
0,4214
21,55
0,79
68,70
11,6
225
11,60
6HA16
5233,56
0,4500
1,35
0,5719
21,55
0,79
-91,22
14,4
303,75
14,40
8HA16
5263,70
0,4500
1,35
0,5719
21,55
0,79
-90,34
14,4
303,75
14,40
8HA16
6503,80
0,4500
1,65
0,7009
21,55
0,79
109,18
16,8
371,25
16,80
8HA16+2HA12
4484,13
0,4500
1,15
0,4859
21,55
0,79
-76,41
12,8
258,75
12,80
6HA16+2HA12
8585,59
0,4500
2,2
0,9374
21,55
0,79
21,2
495
21,20
12HA16
7365,89
0,4500
1,9
0,8084
21,55
0,79
18,8
427,5
18,80
10HA16
5502,78
0,4500
1,4
0,5934
21,55
0,79
149,30 129,87 -92,54
14,8
315
14,80
8HA16
Choix 1 : D i amètr e des des armat ar matu u r es longitudinales D i amètr e des des aciers aci ers tr ans- an s- versaux E spacement spacement des d es aciers aci ers transversaux Jonctions par r ecouvr couvr e-
6HA 16+2H 16+2H A12 Øl =
16mm
12mm
Øt < ( Ølmax / 3 ) avec minimum 6mm
Øt=
6
Mm
St = mini ( a+10 cm ; 15 Øl ; 40 cm )
St =
40
Cm
lr = 0.6 ls ( soit 24Øl pour HA 400 )
Lr =
36
Cm
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Projet de fin d’étude
Choix du section D i amètr e des des armat ar matu u r es longitudinales D i amètr e des des aciers aci ers tr ans- an s- versaux E spacement spacement des d es aciers aci ers transversaux Jonctions par r ecouvr couvr e- ment
Choix 1 : Øl =
8HA 16 16mm
16mm
Øt < ( Ølmax / 3 ) avec minimum 6mm
Øt=
6
mm
St = mini ( a+10 cm ; 15 Øl ; 40 cm )
St =
40
cm
lr = 0.6 ls ( soit 24Øl pour HA 400 )
Lr =
48
cm
Lr =
48
cm
( soit 30 Øl pour HA 500 et RL 235 )
R.P.S longeur du zone zone cri tique ti que Espace dans la zone cri - tique Espace dans la l a zone cou- cou- rant
RPS Lz = Max(he/6 Max(he/6 ; b ; 45cm) tcr = Min(15cm ; 8Øl ; 0.25b)
Lz
150,00
cm
tcr
12,80
cm
tc = Min(30cm ; 12Øl ; 0.5b)
tc
19,20
cm
Choix du section Choix 1 : 8HA 16+2H 16+2H A12 16mm D i amètr e des des armat ar matu u r es Øl = longitudinales Øt= D i amètr e des des aciers aci ers tr ans- Øt < ( Ølmax / 3 ) avec minimum 6mm versaux St = mini ( a+10 cm ; 15 Øl ; 40 cm ) St = E spacement spacement des d es aciers aci ers transversaux lr = 0.6 ls ( soit 24Øl pour HA 400 ) Lr = Jonctions par r ecouvr couvr e- ment ( soit 30 Øl pour HA 500 et Lr = RL 235 ) R.P.S longeur du zone zone cri tique ti que Espace dans la zone cri - tique
RPS Lz = Max(he/6 Max(he/6 ; b ; 45cm) tcr = Min(15cm ; 8Øl ; 0.25b)
12mm 6
mm
40
cm
36
cm
36
cm
Lz
165,00
cm
tcr
9,60
cm
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Projet de fin d’étude
Choix du section D i amètr e des des armatu ar matu r es l ongi tu- tu - dinales D i amètr e des aciers aci ers tran tr ansve sverr saux Espacement Espacement des acie aci er s tran sver ver - saux Joncti ons par re r ecouvre couvr ement
Choix 1 : Øl =
6HA 16+2H 16+2H A12 16mm
Øt < ( Ølmax / 3 ) avec minimum 6mm St = mini ( a+10 cm ; 15 Øl ; 40 cm )
Øt= St =
6 40
mm cm
lr = 0.6 ls ( soit 24Øl pour HA 400 )
Lr =
36
cm
Lr =
36
cm
Lz tcr tc
115,00 9,60 14,40
cm cm cm
12HA 16 16mm
16mm
( soit 30 Øl pour HA 500 et
12mm
RL 235 )
R.P.S longeur du zone zone cri tique ti que Espace Espace dans dans l a zone zone cri cr i tique ti que Espace dans la zone cour ant
RPS Lz = Max(he/6 Max(he/6 ; b ; 45cm) tcr = Min(15cm ; 8Øl ; 0.25b) tc = Min(30cm ; 12Øl ; 0.5b)
Choix du section Choix Choi x 1 : D i amètr e des des armatu ar matu r es l ongi tu- tu - Øl = dinales D i amètr e des aciers aci ers tran tr ansve sverr saux Øt < ( Ølmax / 3 ) avec minimum 6mm Espacement Espacement des acie aci er s tran sver ver - St = mini ( a+10 cm ; 15 Øl ; 40 cm ) saux lr = 0.6 ls ( soit 24Øl pour HA 400 ) Joncti ons par re r ecouvre couvr ement ( soit 30 Øl pour HA 500 et RL 235 ) R.P.S longeur du zone zone cri tique ti que Espace Espace dans dans l a zone zone cri cr i tique ti que Espace dans la zone cour ant
Choix du
ction
RPS Lz = Max(he/6 Max(he/6 ; b ; 45cm) tcr = Min(15cm ; 8Øl ; 0.25b) tc = Min(30cm ; 12Øl ; 0.5b)
Choi 1
Øt= St =
6 40
mm cm
Lr =
48
cm
Lr =
48
cm
220,00 12,80 19,20
cm cm cm
Lz tcr tc
10HA 16
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Projet de fin d’étude
Espace Espace dans dans l a zone zone cri cr i tique ti que Espace dans la zone cour ant
tcr = Min(15cm ; 8Øl ; 0.25b) tc = Min(30cm ; 12Øl ; 0.5b)
Choix 1 : 6HA 16 D i amètr e des des armatu ar matu r es l ongi tu- tu - Øl = dinales D i amètr e des aciers aci ers tr ansversaux ansversau x Øt < ( Ølmax / 3 ) avec minimum 6mm Espacement Espacement des acie aci er s tran sver ver - St = mini ( a+10 cm ; 15 Øl ; 40 cm ) saux lr = 0.6 ls ( soit 24Øl pour HA 400 ) Joncti ons par re r ecouvre couvr ement ( soit 30 Øl pour HA 500 et RL 235 )
Lz Espace Espace dans dans l a zone zone cri cr i tique ti que Espace dans la zone cour ant
100,00 tcr = Min(15cm ; 8Øl ; 0.25b) tc = Min(30cm ; 12Øl ; 0.5b)
tcr tc
12,80 19,20
cm cm
16mm
cm tcr tc
Øt=
6
mm
St =
40
cm
Lr =
48
cm
Lr =
48
cm
9,60 14,40
cm cm
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Projet de fin d’étude
ANNEXE G : Résultats de Ferraillages des poteaux et des semelles
Les Poteaux
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Projet de fin d’étude
Résumé Le présent projet, étudie un bâtiment qui se compose d’un
un rez-de-chaussée à usage
commercial, 4 étage étage à usage bureautique et 4 étage à usage habitation. Cette étude est composée de trois parties : -
la première partie porte sur une présentation générale du projet, ainsi qu’une conception architecturale décrivant les éléments constituants le projet, ensuite le pré dimensionnement et la descente de charge de la structure. st ructure.
-
La deuxième partie a été destinée à l’étude des éléments résistants (poteaux, poutres, semelles).
-
La troisième partie a été consacrée à
l’étude des éléments secondaires (acrotère,
escaliers, ascenseur, dalles pleine). -
La dernière partie comprend l’étude sismique de la structure.
Le dimensionnement a été fait conformément au BAEL 91, au RPS 2002 et SAP2000.
Mots clés : Bâtiment.BAEL91.RPS 2002.Béton.