statique des poutres élastiques

Upload: emmanuel-francis

Post on 07-Apr-2018

222 views

Category:

Documents


0 download

TRANSCRIPT

  • 8/4/2019 statique des poutres lastiques

    1/77

    ! % ( 0

    4 5 7 9 A C D D F A H I P

    R 7 T V V

  • 8/4/2019 statique des poutres lastiques

    2/77

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    3/77

    "% $ & ' ) " 2

    3 4 6 8 4 8 B D F H P H 6 S U F 8 X H 6 `H b 4 6 8 B D F H 6 f H 6 8 F h i 4 6 S 4 X 8 B i F b B H X P H b r `H b 4 6 8 B i B 8 `H i b 4 6 6 B D F H t v h w `H 8 F P B H P H 6

    6 U b B P H 6

    l m

    P U h 8 b 4 U X H H 6 8

    4 6 6 B B b 4 b H 4 F h H b B h H `H S 4 B 6 6 H t z H 8 8 H `H U `H 8 X B H S 4 X 8 B i F b B H X H 4 H h H

    m

    4 F S X B | P H D F H b D F H 6 ~ w S U 8 ~ H 6 H 6

    m

    P H 6 6 B S b B i 4 8 B U h 6 S 4 X X 4 S S U X 8 4 b r `H b 4 6 8 B i B 8 `H 8 X B P B H h 6 B U h h H b b H b H 6 `H D F 4 8 B U h 6 w 6 U h 8 S b F 6 6 B S b H 6 H 8

    b H F X 6 6 U b F 8 B U h 6 6 U F H h 8 4 i i H 6 6 B b H 6 4 h 4 b w 8 B D F H H h 8 t H S b F 6

    m

    P 4 h 6 b 4 B H i U F X 4 h 8 H

    m

    F h X 4 h P h U X H

    P H i U h 6 8 X F i 8 B U h 6 S U h 8 6

    m

    4 8 B H h 8 6

    m

    `H b `H H h 8 6 P H 4 i ~ B h H 6 t t t 6 U h 8 4 6 6 B B b 4 b H 6 4 P H 6 4 6 6 H b 4 H 6

    P H S U F 8 X H 6 t z H 6 P H F | X 4 B 6 U h 6 H | S b B D F H h 8 b H b 4 X H 6 F i i H 6 P H i H U P H b H t

    U F X H 8 8 X H H h S b 4 i H i H U P H b H

    m

    b 4 P `H 4 X i ~ H `H h `H X 4 b H H 6 8 b 4 6 F B 4 h 8 H

    S 4 X 8 B X P r F h i 4 b i F b 8 X B P B H h 6 B U h h H b H h `H b 4 6 8 B i B 8 `H i b 4 6 6 B D F H 6 F X F h 8 X U h i U h P H S U F 8 X H P X U B 8 H b H

    S X U b H H P H 4 B h 8 H h 4 h 8

    m

    U h 8 H h 8 H P H X `H P F B X H 8 U F 6 i H 6 X `H 6 F b 8 4 8 6 4 P H 6 4 b H F X 6 6 F X b 4 b B h H U w H h h H

    P H b 4 S U F 8 X H t

    B h 6 B

    m

    b H 6 X 4 h P H F X 6 4 h B S F b `H H 6 h H 4 X B H h 8 S b F 6 D F r H h U h i 8 B U h P H b r 4 6 i B 6 6 H i F X B b B h H

    6 F X b 4 b B h H U w H h h H t

    v h i U h 6 B P H X H P U h i b H 6 H U X 8 6 i U H 4 S S b B D F `H 6 6 F X b 4 b B h H U w H h h H 4 b U X 6 D F r H h X `H 4 b B 8 `H

    m

    B b 6 6 U h 8

    4 S S b B D F `H 6 6 F X b 4 6 F X 4 i H H | 8 `H X B H F X H P H b 4 S U F 8 X H t H H H

    m

    U h i U h 6 B P H X H D F H b 4 i U h h 4 B 6 6 4 h i H P H 6

    P `H S b 4 i H H h 8 6 P H b 4 b B h H U w H h h H H 6 8 F h H B h U X 4 8 B U h 6 F 6 4 h 8 H

    m

    b H 6 P `H S b 4 i H H h 8 6 P H 6 4 F 8 X H 6 S U B h 8 6

    P H b 4 6 H i 8 B U h P X U B 8 H `H 8 4 h 8 i U h 6 B P `H X `H 6 i U H S H F P B `H X H h 8 6 t

    4 X i U h 8 X H

    m

    b 4 P H 6 i X B S 8 B U h P H 6 i U h 8 X 4 B h 8 H 6 H 8 i H b b H P H 6 P `H U X 4 8 B U h 6 X H 6 8 H h 8 8 X B P B H h 6 B U h h H b b H 6 i 4 X

    b H F X 6 4 X B 4 8 B U h 6 P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H 6 U h 8 B S U X 8 4 h 8 H 6 H 8 B S U 6 6 B b H 6 4 h `H b B H X t

    l

    l

    l

    b H | B 6 8 H F h X 4 h P h U X H P H 8 X 4 B 8 `H 6 6 F X b H 6 S U F 8 X H 6

    m

    P 4 h 6 b H 6 D F H b 6 U h P `H H b U S S H F h X 4 h P h U X H

    P H `H 8 ~ U P H 6 S 4 X 8 B i F b B H X H 6 S U F X X `H 6 U F P X H P H 6 S X U b H H 6 P H S U F 8 X H 6 H 8 P H 6 8 X F i 8 F X H 6 P H S U F 8 X H 6 t

    H 4 F i U F S P r H h 8 X H H b b H 6 6 U h 8 P H H h F H 6 U 6 U b H 8 H 6 H h X 4 B 6 U h P F P `H H b U S S H H h 8 4 i 8 F H b P H 6 i 4 b i F b 4 8 H F X 6

    H 8 P H 6 b U B i B H b 6 t z H i U F X 6 6 H b B B 8 H P U h i 4 F | U h P H H h 8 6 P H b 4 8 ~ `H U X B H P H 6 S U F 8 X H 6 H 8 h H S X `H 8 H h P

    S 4 6 4 b r H | ~ 4 F 6 8 B B 8 `H t b 4 6 H F b H H h 8 S U F X F 8 P r H | S U 6 H X b H 6 h U 8 B U h 6 B h P B 6 S H h 6 4 b H 6 4 i U h h 4 8 X H S U F X

    i U S X H h P X H b H 6 b B B 8 H 6 P H b 4 U P `H b B 6 4 8 B U h

    m

    i U S X H h P X H b H 6 P U h h `H H 6 h `H i H 6 6 4 B X H 6 4 F U P H b H

    m

    H 8 H h h

    B h 8 H X S X `H 8 H X i U X X H i 8 H H h 8 b H 6 X `H 6 F b 8 4 8 6 P r F h i 4 b i F b t

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    4/77

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    5/77

    "

    )

    $

    " &

    2

    ! # ! & ( 03 24 5 & 2 # 7

    U B 8 @ F h H i U F X H

    4 S S H b `H H

    t

    U B 8 B 6 U h S U B h 8 i U F X 4 h 8 H 8 6 U B 8 D 6 U h 4 6 i B 6 6 H i F X B b B h H H 6 F X `H H 4 S 4 X 8 B X P r F h S U B h 8 | H E P H @ t

    U B 8 H h h H I P R P U V b H 8 X B H P X H P H X X H 6 h H 8

    4 6 6 U i B `H 4 b 4 b B h H U w H h h H @ H h B t

    b

    t

    n

    G

    C

    Ligne moyenne

    Section droite

    a b d e

    t g i p

    r

    v h X 4 S S H b b H b H 6 U X F b H 6 P H X X H 6 h H 8 P `H h B 6 6 4 h 8 b H 8 X B H P X H P H X X H 6 h H 8 H 8 b H 6 i 4 X 4 i 8 `H X B 6 8 B D F H 6 `H U `H

    8 X B D F H 6 P H 6 i U F X H 6 P 4 h 6 s t

    I u w x y

    w

    D

    8 4 h H h 8 H F h B 8 4 B X H

    R u w

    I

    w

    D

    h U X 4 b H S X B h i B S 4 b H F h B 8 4 B X H

    U u I R B h U X 4 b H F h B 8 4 B X H

    w

    I

    w

    D

    u

    R

    w

    R

    w

    D

    u

    I

    U

    w

    U

    w

    D

    u

    R

    U F H 6 8 b H

    l

    8 U F U F X 6 H 8 H 6 8 b 4

    f t

    k

    k

    8 9 @ B D D F G I P Q # & ( ) # & 4 m

  • 8/4/2019 statique des poutres lastiques

    6/77

    ! # ( ) ! 1 )

    3 H S b 4 h H RF P U V H 6 8 4 S S H b `H

    B t 4 h 6 i H S b 4 h U h P `H h B 8

    l

    6

    P H b 4

    S U F 8 X H

    m

    P H i U h 8 U F X H | 8 `H X B H F X H X `H 7 H 8 P H i H h 8 X H P H X 4 B 8 `H B 6 F X b 4 b B h H U w H h h H t 3 4 6 H i 8 B U h

    P X U B 8 H S H F 8 4 F 6 6 B 4 U B X P H 6 i U h 8 U F X 6 B h 8 `H X B H F X 6 7 9 A t

    v h 4 S S H b b H S U F 8 X H

    m

    b H U b F H H h H h P X `H S 4 X b H 6 6 H i 8 B U h 6 P X U B 8 H 6 b U X 6 D F H B P `H i X B 8 b 4 b B h H U w H h h H t

    v h 6 F S S U 6 H P H S b F 6 D F H

    i 3 H 6 6 H i 8 B U h 6 P X U B 8 H 6 6 U h 8 i U h 6 8 4 h 8 H 6 U F C C b H h 8 H H h 8 4 X B 4 b H 6 E E b U X 6 D F H B 4 X B H t

    i B U h 4 S S H b b H

    w

    F h H P B H h 6 B U h 8 X 4 h 6 H X 6 4 b H P H b 4 6 H i 8 B U h P X U B 8 H

    m

    U h 4 H h 8 U F 8 S U B h 8 P H b 4

    S U F 8 X H

    w G

    t

    z H 6 P H F | ~ w S U 8 ~ H 6 H 6 6 U h 8 H 6 6 H h 8 B H b b H 6 H b b H 6 S H X H 8 8 X H P r 4 6 6 B B b H X F h 8 X U h i U h P H S U F 8 X H i U F X H P H

    b U h F H F X

    w

    D 4 F h 8 X U h i U h P H S U F 8 X H P X U B 8 H t z H 8 8 H 4 S S X U | B 4 8 B U h H 6 8 4 b 4 4 6 H P H 8 U F 8 i H D F B 6 F B 8 t

    H h h

    m

    U h 6 H S b 4 i H P 4 h 6 b H i 4 P X H P H

    l

    l

    3 H 8 H h 6 H F X P H 6 P `H U X 4 8 B U h 6 F 8 B b B 6 `H H 6 8 P U h i I

    m

    H 8 b H 6 `H D F 4 8 B U h 6 P `H D F B b B X H 6 r `H i X B H h 8

    6 F X b 4 i U h F X 4 8 B U h B h B 8 B 4 b H

    t

    t 3 H 4 8 `H X B 4 F i U h 6 8 B 8 F 4 h 8 b 4 S U F 8 X H 4 P U h i F h H b U B P H i U S U X 8 H H h 8

    D F r U h X 4 S S H b b H B i B

    P

    u

    e Q

    I

    S U

    X V

    y

    6 U B 8 H h i U X H t H h F 8 B b B 6 4 h 8 X H 8 Y

    P

    u

    X

    g

    Y

    a

    I

    Y

    g

    e

    Y U

    X I

    y b

    6 U B 8 H h i U X H

    I u

    g

    Y

    X

    P

    Y

    X

    U

    X

    P

    y

    v h X 4 S S H b b H b H 6 X H b 4 8 B U h 6 H h 8 X H b H 6 i U H i B H h 8 6 P H 3 4 `H H

    Q

    P

    S

    V c H 8 b H 6 i U H i B H h 8 6 F 8 B b B 6 `H 6 H h `H b 4 6 8 B i B 8 `H

    H X P Y V

    X u

    Q

    e Q

    f S

    Q

    S

    H 8 Y u

    S

    e

    Q

    S

    Qu

    X

    e g

    Y

    H 8

    S

    u

    X Y

    g

    Y g e

    Y

    p q

    7

    q s

    #

    7 ! t # ! u 2 t w

    & y

    # 7 ! u 2 t ( t t

    s

    # ! & t ( 7 & ! # t

    v h P `H h B 8 B i B D F H b D F H 6 i 4 X 4 i 8 `H X B 6 8 B D F H 6 `H U `H 8 X B D F H 6 P H 6 H i 8 B U h 6 D F B 6 H X U h 8 F 8 B b H 6 P 4 h 6 b 4 6 F B 8 H t

    H b b H 6 S H X H 8 8 H h 8 P H i 4 X 4 i 8 `H X B 6 H X b 4 X `H S 4 X 8 B 8 B U h P H b 4 4 8 B H X H P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H t

    U B 8

    6

    F h H 6 H i 8 B U h P X U B 8 H

    m

    P H S U B h 8 i U F X 4 h 8 H 8 6 U B 8 F h S U B h 8 | H P F S b 4 h h U X 4 b

    m

    3 H i H h 8 X H

    P H X 4 B 8 `H `H U `H 8 X B D F H H 6 8 P `H h B S 4 X

    y

    u

    g

    j k m

    n

    w

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    7/77

    ) 1 ) ! # 1 ) ( ) ) ! ) ( ! )

    P

    N

    G

    a b d e

    te

    i

    l

    b H 6 8 4 i B b H P H U B X D F H b H i H h 8 X H P H X 4 B 8 `H B H 6 8 B h P `H S H h P 4 h 8 P F i ~ U B | P H H 8 D F r U h 4 b 4 X H b 4 8 B U h

    k m y

    n

    w

    u

    !

    U B 8

    6

    F h H 6 H i 8 B U h P X U B 8 H

    m

    P H S U B h 8 i U F X 4 h 8 H 8 6 U B 8 % F h H P X U B 8 H P F S b 4 h P H b 4 6 H i 8 B U h P X U B 8 H t U B 8

    & b 4 S X U H i 8 B U h P H 6 F X % t 3 H U H h 8 6 8 4 8 B D F H P H

    6

    S 4 X X 4 S S U X 8 4 % H 6 8 P `H h B S 4 X

    '

    6

    P%

    u

    k m )

    n

    w

    G

    NK

    a b d e

    t

    f

    i 0

    l

    2

    ' H 6 8 `H B P H H h 8 F h H i 8 H F X S H X S H h P B i F b 4 B X H 4 % t

    b H 6 8 4 i B b H P H U B X D F H 6 B B 5 %

    m

    4 b U X 6 '

    6

    P % u t 3 H 6 P X U B 8 H 6 % D F B S 4 6 6 H h 8 S 4 X B 6 U h 8 4 S S H b `H H 6

    l

    t

    B U h P `H h B 8 F h X H S H X H i H h 8 X 4 b U X 8 ~ U h U X `H H B P 7

    A

    P 7 t V P 4 h 6 b H S b 4 h h U X 4 b

    m

    U h P `H h B 8 b H 6

    @

    A

    u '

    6

    P 7

    A

    B 7 t u

    k m D

    t

    w

    @t

    u '

    6

    P 7t

    B 7

    A

    u

    km D

    A

    w

    F G

    I

    P G R k T U W X ` a c d e g c g p q s u q e e g ` g w x

    y G k

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    8/77

    ! # ( ) ! 1 )

    D F r U h 4 S S H b b H X H S H i 8 B H H h 8 U H h 8 6 8 4 8 B D F H P H

    6

    S 4 X X 4 S S U X 8 4 7

    A

    H 8 U H h 8 6 8 4 8 B D F H P H

    6

    S 4 X

    X 4 S S U X 8 4 7 t

    !

    H i b H 6 h U 8 4 8 B U h 6 S X `H i `H P H h 8 H 6

    m

    U h P `H h B 8 b H U H h 8 D F 4 P X 4 8 B D F H P H

    6

    S 4 X X 4 S S U X 8 4 %

    6

    P % u

    km )

    n

    A

    w

    z H 8 8 H P `H h B 8 B U h H 6 8 B P H h 8 B D F H 4 i H b b H P H U H h 8 P r B h H X 8 B H P r F h 6 U b B P H 4 F 8 U F X P r F h H P X U B 8 H

    m

    4 B 6

    B i B

    m

    b H 6 U b B P H H 6 8 B P B H h 6 B U h h H b H 8 S b 4 h

    m

    H 8 6 4 4 6 6 H 6 F X 4 i B D F H 4 F 8 g t v h b r 4 S S H b b H 4 B h 6 B 6 U F H h 8

    P H

    6

    S 4 X X 4 S S U X 8 4 % t b H h 4 b H 6 H H 6 S X U S X B `H 8 `H 6 D F r U h X 4 S S H b b H X B H H H h 8 B i B

    B U h P `H h B 8 F h X H S H X H

    l

    H B P 7

    A

    P 7 t V P 4 h 6 b H S b 4 h h U X 4 b

    m

    B b H | B 6 8 H F h 8 H h 6 H F X P F

    6 H i U h P U X P X H 6 w `H 8 X B D F H P `H h B S U 6 B 8 B 4 S S H b `H

    P H

    6

    H h B

    m

    P U h 8 b H 6 i U S U 6 4 h 8 H 6

    6 F X i H 8 8 H 4 6 H 6 U h 8

    u

    !

    A A

    u

    km

    D

    t

    A

    w

    A

    tu

    km D

    A

    D

    t

    w

    t

    A

    u

    k m D

    A

    D

    t

    w

    t t u

    k m

    D

    A

    A

    " #

    %

    8 H b D F H b H U H h 8 D F 4 P X 4 8 B D F H P H

    6

    S 4 X X 4 S S U X 8 4 F h H P X U B 8 H % P H b 4 6 H i 8 B U h P X U B 8 H

    m

    P H P B X H i 8 B U h

    F h B 8 4 B X H &

    m

    H 8 S 4 6 6 4 h 8 S 4 X B H 6 8 P U h h `H S 4 X

    6

    P & u & 1 1 & u 5 7

    A

    7 t 9 A

    A A

    A

    t

    t

    A

    t t C

    A

    7

    A

    7 t C

    b H | B 6 8 H P H F | P B X H i 8 B U h 6 U X 8 ~ U U h 4 b H 6 E F h B 8 4 B X H 6 H G

    A

    P Gt

    V 4 S S H b `H H 6

    l l l

    H 8 P H F | 4 b H F X 6 S X U S X H 6 H

    A

    P t

    V 4 S S H b `H H 6

    l l

    8 H b b H 6

    D F H 1 G

    A

    u

    A

    G

    A

    H 8 1 Gt

    u t

    Gt

    4 h 6 b H X H S H X H U X 8 ~ U h U X `H H B P G

    A

    P Gt

    V

    m

    b H 6 i U S U 6 4 h 8 H 6 P H 6 H X 4 h H h 8 P 4 h 6 F h H 4 8 X B i H

    P B 4 U h 4 b H t

    u

    !

    A

    u

    km

    D

    t

    A

    w

    t t

    u

    k m

    D

    A

    A

    " #

    %

    P 4 h 6 b 4 4 6 H S X B h i B S 4 b H

    T U ! V V V2 a

    z U H U h b H H X X 4 P 4 h 6 b 4 6 F B 8 H

    m

    b 4 U X H b 4 S b F 6 6 B S b H P H 6 `H D F 4 8 B U h 6 P H b 4 8 ~ `H U X B H P H 6 S U F 8 X H

    6 r `H i X B 8 P 4 h 6 b H X H S H X H i H h 8 X 4 b S X B h i B S 4 b P r B h H X 8 B H

    m

    i U S b `H 8 `H S 4 X b 4 8 4 h H h 8 H 4 b 4 b B h H U w H h h H t

    U

    U F 8 H

    `H 8 F P H 6 F X F h H S U F 8 X H i U H h i H S 4 X b 4 P `H h B 8 B U h P H i H X H S H X H t

    4 h 6 i H i U F X 6

    m

    U h F 8 B b B 6 H X 4 b H 6 h U 8 4 8 B U h 6 6 F B 4 h 8 H 6

    i G

    f

    u I 8 4 h H h 8 H F h B 8 4 B X H 4 b 4 b B h H U w H h h H

    i

    D

    f

    u D 4 6 i B 6 6 H i F X B b B h H P r F h H 6 H i 8 B U h P X U B 8 H 6 F X b 4 b B h H U w H h h H b

    c d f y

    h i q r s u s v w G

    x # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    9/77

    ) 1 ) ! # 1 ) ( ) ) ! ) ( ! )

    i G

    A

    S X H B H X H P B X H i 8 B U h S X B h i B S 4 b H P r B h H X 8 B H F h B 8 4 B X H P H b 4 6 H i 8 B U h P X U B 8 H P r 4 6 i B 6 6 H

    D

    f

    i G t 6 H i U h P H P B X H i 8 B U h S X B h i B S 4 b H P r B h H X 8 B H F h B 8 4 B X H P H b 4 6 H i 8 B U h P X U B 8 H P r 4 6 i B 6 6 H

    D

    f

    i

    D

    A

    P

    D

    f

    i U U X P U h h `H H 6 P r F h S U B h 8 P H b 4 S U F 8 X H P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H P r 4 6 i B 6 6 H

    D

    f

    3 H 6 6 H h 6 P H G

    A

    H 8 Gt

    6 U h 8 i ~ U B 6 B 6 8 H b 6 D F H b H X H S H X H U X 8 ~ U h U X `H H B P G

    f

    P G

    A

    P Gt

    V 6 U B 8 P B X H i 8 t

    3

    n

    G

    C

    Ligne moyenne

    b

    1

    2

    a

    b d e

    t i p

    l l

    l

    H h `H h `H X 4 b

    m

    b H X H S H X H H B P G

    A

    P G t V b B `H 4 F | S X U S X B `H 8 `H 6 P H

    6

    H 6 8 P B `H X H h 8 P F 8 X B H P X H P H X X H 6 h H 8 b B `H

    4 F | S X U S X B `H 8 `H 6 P H @ t v h 4 8 U F 8 H U B 6

    G

    f

    u I

    H 8 b H 6 S b 4 h 6 R P U H 8 G

    A

    P G t 6 U h 8 i U h U h P F 6 t

    H B P G

    A

    P G t V

    t

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    10/77

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    11/77

    ' ) "

    ' ) &

    $

    " &

    2

    H H H D F r H h `H b 4 6 8 B i B 8 `H i b 4 6 6 B D F H

    m

    U h 6 H b B B 8 H 4 b r `H 8 F P H P H b 4 6 8 4 8 B D F H t 3 H 6 H U X 8 6 H | H X i `H 6 6 U h 8

    P U h i i U h 6 8 4 h 8 6 U F b H h 8 H H h 8 4 X B 4 b H 6

    m

    i r H 6 8 4 P B X H D F r U h h `H b B H b H 6 H H 8 6 P w h 4 B D F H 6 t H h P 4 h 8

    b H S 4 6 6 4 H P H b r `H 8 4 8 B h B 8 B 4 b 4 b r `H 8 4 8 P `H U X `H

    m

    U h i U h 6 B P H X H D F H b 4 S U F 8 X H S 4 6 6 H S 4 X F h H 6 F i i H 6 6 B U h

    P r `H 8 4 8 6 P r `H D F B b B X H ~ w S U 8 ~ H 6 H D F 4 6 B 6 8 4 8 B D F H t

    H S b F 6

    m

    i U H H h `H b 4 6 8 B i B 8 `H i b 4 6 6 B D F H

    m

    b H 6 P `H S b 4 i H H h 8 6 `H 8 4 h 8 S H 8 B 8 6

    m

    U h S H F 8 `H i X B X H b H 6 `H D F 4 8 B U h 6

    P H b 4 6 8 4 8 B D F H 6 F X b 4 i U h F X 4 8 B U h B h B 8 B 4 b H t

    H h h

    m

    i U H P r ~ 4 B 8 F P H H h `H i 4 h B D F H

    m

    b H 6 4 i 8 B U h 6 `H i 4 h B D F H 6 6 U h 8 X H S X `H 6 H h 8 `H H 6 S 4 X P H 6

    u m

    4 H i F h H i 8 H F X X `H 6 F b 8 4 h 8 H 8 F h H i 8 H F X U H h 8 X `H 6 F b 8 4 h 8 H h F h i H X 8 4 B h S U B h 8 t z U h H h 8 B U h h H b b H

    H h 8

    m

    6 4 F B h P B i 4 8 B U h i U h 8 X 4 B X H

    m

    b H H i 8 H F X U H h 8 H 6 8 P U h h `H 4 F

    l

    P F 8 U X 6 H F X

    m

    i r H 6 8 4 P B X H 4 F S U B h 8 U F B b 6 r 4 S S b B D F H 6 F X b 4 b B h H U w H h h H t

    U

    U F 8 H U B 6

    m

    b r 4 P P B 8 B U h P H P H F | 8 U X 6 H F X 6 h r 4 P H 6 H h 6 D F H 6 B b H F X 6 U H h 8 6 6 U h 8 P `H h B 6 4 F H H S U B h 8 t

    b 4 F 8 P U h i C C 8 X 4 h 6 S U X 8 H X E E b H 6 U H h 8 6 4 F H H S U B h 8 4 4 h 8 P H b H 6 4 P P B 8 B U h h H X t U 8 4 H h 8 U h

    4 P P B 8 B U h h H P H 6 8 U X 6 H F X 6 D F 4 h P U h `H i X B 8 b H 6 `H D F 4 8 B U h 6 P H b 4 6 8 4 8 B D F H

    u

    v h X 4 S S H b b H S U F X `H U B X H b 4 U X F b H P H 8 X 4 h 6 S U X 8 P H 6 U H h 8 6

    u " $& ' )

    '

    u " $& 2

    u

    & '

    4

    $

    )

    2

    6 7 s

    # ! & t y

    s q

    ! u 2 t 8 #

    7 ! 2 7 t

    B U h B 6 U b H F h H S U F 8 X H U F F h 8 X U h i U h P H S U F 8 X H

    m

    U h 4 S S H b b H

    l

    l

    b H 6

    4 i 8 B U h 6 `H i 4 h B D F H 6 4 S S b B D F `H H 6 S 4 X b H B b B H F H | 8 `H X B H F X

    t

    v h P B 6 8 B h F H P H F | 6 U X 8 H 6 P r 4 i 8 B U h 6 `H i 4 h B D F H 6 H | 8 `H X B H F X 6

    i p

    l

    z H 6 U h 8 b H 6 H U X 8 6 4 F D F H b 6 b 4 S U F 8 X H P U B 8 X `H 6 B 6 8 H X t

    i p

    l

    f z H 6 U h 8 b H 6 4 i 8 B U h 6 `H i 4 h B D F H 6 H | H X i `H H 6 S 4 X b H 6 b B 4 B 6 U h 6 D F B 4 B h

    8 B H h h H h 8 b 4 S U F 8 X H H h S b 4 i H t

    H h `H h `H X 4 b

    m

    b H 6 i ~ 4 X H 6 6 U h 8 P H 6 P U h h `H H 6 P F S X U b H H

    m

    H 8 b H 6 4 i 8 B U h 6 P H b B 4 B 6 U h 6 U h 8 P H 6 B h i U h h F H 6 t

    @ R B Dg u pV x q a w s c gC e q u q s a w

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    12/77

    ! ) # 1 ) ( ) ) ! 1 )

    F

    C

    RA

    RB

    A B

    Efforts exterieurs a la poutre isoleeSchema du montage

    F

    A B

    C

    a b d

    f

    t g i

    4 X H | H S b H

    m

    P 4 h 6 b 4 F X H

    f

    t g

    H 6 8 F h H i ~ 4 X H

    m

    $

    H 8

    $

    6 U h 8 P H 6 4 i 8 B U h 6 P H b B 4 B 6 U h t

    U a

    H h 8 ~ `H U X B H P H 6 S U F 8 X H 6 b H 6 i ~ 4 X H 6 6 U h 8 i U h 6 B P `H X `H H 6 i U H `H 8 4 h 8 4 S S b B D F `H H 6 6 F X b 4 b B h H U w H h h H t

    v h P B 6 8 B h F H

    i p

    l l l

    b 6 r 4 B 8 P r F h 8 U X 6 H F X 4 S S b B D F `H H h F h S U B h 8 P H b 4 S U F 8 X H t 4 h 6

    b r H | H S b H S X `H i `H P H h 8

    m

    b 4 i ~ 4 X H 4 S S b B D F `H H H h H 6 8 F h 8 U X 6 H F X P H X `H 6 F b 8 4 h 8 H H 8 P H U H h 8

    H h h F b t

    i p

    l

    z H 6 U h 8 P H 6 P H h 6 B 8 `H 6 b B h `H B D F H 6 P H 8 U X 6 H F X 4 S S b B D F `H H 6 6 F X F h H S U X 8 B U h

    P H b 4 b B h H U w H h h H A t 3 H S b F 6 6 U F H h 8

    m

    b H 6 P H h 6 B 8 `H 6 b B h `H B D F H 6 P H 8 U X 6 H F X 6 H X `H P F B 6 H h 8 4 P H 6

    P H h 6 B 8 `H 6 b B h `H B D F H 6 P H U X i H 6 t 3 H 6 P H h 6 B 8 `H 6 b B h `H B D F H 6 P H U H h 8 6 U h 8 X 4 X H 6 P 4 h 6 b 4 S X 4 8 B D F H t

    U V

    U

    U F 8 H S U F 8 X H U F 6 w 6 8 H H P H S U F 8 X H 6 B 6 U b `H H 8 H h `H D F B b B X H 4 h `H i H 6 6 4 B X H H h 8 P H 6 b B 4 B 6 U h 6 4 H i 6 U h

    B b B H F H | 8 `H X B H F X t 3 H 6 4 i 8 B U h 6 P H i H 6 b B 4 B 6 U h 6 6 F X b H 6 w 6 8 H H B 6 U b `H 6 U h 8 P H 6 8 U X 6 H F X 6 D F r U h P `H h B 8

    i U h H h 8 B U h h H b b H H h 8 4 F S U B h 8 P H b 4 b B 4 B 6 U h

    t

    t 4 h 6 b 4 F X H

    f

    t g

    m

    b H 8 U X 6 H F X 4 i 8 B U h P H b B 4 B 6 U h H h

    @

    H 6 8

    u "$

    )

    H h 8 ~ `H U X B H P H 6 S U F 8 X H 6

    m

    U h h r F 8 B b B 6 H D F H P H F | 8 w S H 6 P H b B 4 B 6 U h 6

    i p

    z H 6 U h 8 P H 6 b B 4 B 6 U h 6 8 H b b H 6 D F H b H 8 X 4 4 B b P H 6 U X i H 6 P H b B 4 B 6 U h P 4 h 6 b H 6

    P `H S b 4 i H H h 8 6 X H b 4 8 B 6 S H X B 6 H 6 8 h F b c t

    B h 6 B

    m

    6 B b 4 b B 4 B 6 U h S H X H 8 F h H U B b B 8 `H P H 8 X 4 h 6 b 4 8 B U h

    P 4 h 6 F h H P B X H i 8 B U h &

    m

    b 4 X `H 6 F b 8 4 h 8 H P F 8 U X 6 H F X P H b B 4 B 6 U h H 6 8 h `H i H 6 6 4 B X H H h 8 S H X S H h P B i F b 4 B X H

    4 & t H H H

    m

    6 B b 4 b B 4 B 6 U h S H X H 8 F h H U B b B 8 `H P H X U 8 4 8 B U h 4 F 8 U F X P H b 4 P B X H i 8 B U h

    m

    b H

    U H h 8 P H b 4 b B 4 B 6 U h H 6 8 h `H i H 6 6 4 B X H H h 8 S H X S H h P B i F b 4 B X H 4 t 3 H b H i 8 H F X H 6 8 B H H h 8 B h B 8 `H

    4 4 h 4 b w 6 H X b H 6 8 U X 6 H F X 6 P H b B 4 B 6 U h P H 6 b B 4 B 6 U h 6 i U F X 4 h 8 H 6 t

    i p

    3 U X 6 D F r B b 6 H b H P B i B b H P H U P `H b B 6 H X F h H b B 4 B 6 U h S 4 X F h H b B 4 B 6 U h

    S 4 X 4 B 8 H

    m

    S 4 X i H D F H b H 6 U F H H h 8 6 6 F S S U 6 `H 6 b U D F `H 6 U h 8 H h X `H 4 b B 8 `H F h H i H X 8 4 B h H 6 U F S b H 6 6 H

    m

    U h U P `H b B 6 H i H 8 8 H X B B P B 8 `H B S 4 X 4 B 8 H S 4 X F h X H 6 6 U X 8 t U F X F h b U i 4 H H h 8 X 4 h 6 b 4 8 B U h B S 4 X 4 B 8

    F i k R T k

    k T k R " T

    y $ & ( 0

    2 4

    I W T y $ T k R

    W 6 R

    T R k

    P 6 T A R

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    13/77

    ! ) # 1 ) 1 )

    P 4 h 6 b 4 P B X H i 8 B U h &

    m

    U h H 8 F h X H 6 6 U X 8 b B h `H 4 B X H P 4 h 6 i H 8 8 H P B X H i 8 B U h

    m

    S U F X F h b U i 4 H H h

    X U 8 4 8 B U h B S 4 X 4 B 8 4 F 8 U F X P H b 4 P B X H i 8 B U h

    m

    U h H 8 F h X H 6 6 U X 8 6 S B X 4 b 4 F 8 U F X P H i H 8 8 H P B X H i 8 B U h t

    3 H 6 X 4 B P H F X 6 P H i H 6 X H 6 6 U X 8 6 H h U F H h

    w

    6 U h 8 H 6 8 B `H H 6 U F X `H 6 F b 8 H h 8 P r F h H H 6 F X H

    6 F X F h H b B 4 B 6 U h H | B 6 8 4 h 8 H t

    p

    l

    t b B h F H P H 4 h B H X H B S U X 8 4 h 8 H 6 F X b H 6 X `H 6 F b 8 4 8 6 t b H 6 8 4 b 4 i ~ 4 X H P H b r B h `H h B H F X P H

    B H h 4 h 4 b w 6 H X b 4 b B 4 B 6 U h X `H H b b H S U F X i ~ U B 6 B X b H U P H b H P H b B 4 B 6 U h 4 P 4 S 8 `H t

    V

    3 H S X B h i B S H U h P 4 H h 8 4 b P H b 4 6 8 4 8 B D F H 4 X H D F H b 4 6 U H P H 6 4 i 8 B U h 6 `H i 4 h B D F H 6 H | 8 `H X B H F X H 6

    i ~ 4 X H 6 H 8 4 i 8 B U h 6 P H b B 4 B 6 U h P r F h 6 w 6 8 H H B 6 U b `H H 8 H h `H D F B b B X H H 6 8 F h 8 U X 6 H F X h F b t

    B U h h U 8 H

    i "

    9

    &

    9

    )

    b H 6 8 U X 6 H F X 6 P H i ~ 4 X H 6 H | 8 `H X B H F X H 6 i U h i H h 8 X `H H 6 4 F | S U B h 8 6

    @9

    m

    i "

    D

    "

    D

    )

    b H 6 8 U X 6 H F X 6 P H i ~ 4 X H 6 H | 8 `H X B H F X H 6 b B h `H B D F H 6 X `H S 4 X 8 B 6 6 F X b 4 b B h H U w H h h H

    m

    i

    "$ #

    %

    #

    )

    &

    b H 6 8 U X 6 H F X 6 P r 4 i 8 B U h 6 P H b B 4 B 6 U h 4 F | S U B h 8 6 4 F | S U B h 8 6 P H b B 4 B 6 U h (

    #

    m

    3 H S X B h i B S H U h P 4 H h 8 4 b P H b 4 6 8 4 8 B D F H 6 H 8 X 4 P F B 8 S 4 X b H 6 P H F | `H D F 4 8 B U h 6 H i 8 U X B H b b H 6

    9

    9

    #

    $ #

    k

    D

    w

    D u

    9

    x

    ' 9 9

    9

    &

    9

    #

    x )

    #

    $ #

    #

    %

    #

    k x

    &

    D

    w

    D

    k

    "

    D

    w

    D u

    B U h i U h 6 B P H X H b H 6 i ~ 4 X H 6 i U H i U h h F H 6

    m

    H 8 b H 6 4 i 8 B U h 6 P H b B 4 B 6 U h h U h h F b b H 6 i U H B h i U h h F H 6E

    m

    U h S H F 8 i b 4 6 6 H X b H 6 S X U b H H 6 H h 8 X U B 6 i 4 8 `H U X B H 6

    i p

    3 H 6 w 6 8 H H P r `H D F 4 8 B U h 6 P H b 4 6 8 4 8 B D F H H 6 8 X `H F b B H X S U F X b H 6 B h i U h

    h F H 6 P H b B 4 B 6 U h t v h S H F 8 P U h i P `H 8 H X B h H X b H 6 B h i U h h F H 6 P H b B 4 B 6 U h H h U h i 8 B U h P H 6 i ~ 4 X H 6

    m

    t

    i p

    3 H 6 w 6 8 H H P r `H D F 4 8 B U h 6 P H b 4 6 8 4 8 B D F H H 6 8 B h 6 F 6 4 h 8 S U F X

    P `H 8 H X B h H X b H 6 B h i U h h F H 6 P H b B 4 B 6 U h t b 4 F P X 4 P H 6 `H D F 4 8 B U h 6 6 F S S b `H H h 8 4 B X H 6 P `H P F B 8 H 6 P H b 4

    8 ~ `H U X B H P H 6 S U F 8 X H 6 S U F X P `H 8 H X B h H X i U S b H 8 H H h 8 b 4 6 U b F 8 B U h t 3 H 6 6 w 6 8 H H 6 ~ w S H X 6 8 4 8 B D F H 6

    6 U h 8 8 X H 6 i U F X 4 h 8 6 P 4 h 6 b 4 X `H 4 b B 8 `H B h P F 6 8 X B H b b H t

    i

    3 H 6 w 6 8 H H P r `H D F 4 8 B U h 6 P H b 4 6 8 4 8 B D F H h r 4 S 4 6 P H 6 U b F 8 B U h t z H b 4

    6 B h B H D F r B b h r w 4 S 4 6 P r `H D F B b B X H S U 6 6 B b H 6 U F 6 b r 4 i 8 B U h P H 6 i ~ 4 X H 6 4 H i P H 8 H b b H 6 b B 4 B 6 U h 6 t

    U B 8 U h H F 8 `H 8 F P B H X b H U F H H h 8 H 8 B b 4 F 8 4 b U X 6 `H i X B X H b H 6 b U B 6 P H b 4 P w h 4 B D F H

    m

    6 U B 8 U h

    H F 8 D F H b H 6 w 6 8 H H S X H h h H F h H S U 6 B 8 B U h P r `H D F B b B X H 6 U F 6 b H 6 i ~ 4 X H 6 H 8 B b 4 F 8 4 U F 8 H X P H 6

    b B 4 B 6 U h 6 S U F X 6 r U S S U 6 H X 4 F U F H H h 8 t

    3 r U H 8 P H i H i U F X 6 `H 8 4 h 8 b 4 6 8 4 8 B D F H P H 6 S U F 8 X H 6

    m

    U h h r H h B 6 4 H X 4 S 4 6 b H 6 S X U b H H 6 ~ w S U 6 8 4 8 B D F H 6 t

    c W G R y 1 1 T

    R R R y

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    14/77

    ! ) # 1 ) ( ) ) ! 1 )

    6

    & 7 # t ! #

    7 ! 2 7 t

    v h P `H h B 8 b H 6 H U X 8 6 B h 8 `H X B H F X 6 4 F h H S U F 8 X H B b B H F i U h 8 B h F i F X B b B h H P H b 4 H H 4 h B H X H D F r H h

    `H i 4 h B D F H P H 6 B b B H F | i U h 8 B h F 6 8 X B P B H h 6 B U h h H b 6 v h B 4 B h H F h H i U F S F X H P F B b B H F D F B X H h P

    H | 8 `H X B H F X 6 b H 6 H U X 8 6 B h 8 `H X B H F X 6 t

    z U h 6 B P `H X U h 6 F h H S U F 8 X H H h `H D F B b B X H 6 U F 6 b r 4 i 8 B U h P r H U X 8 6 H | 8 `H X B H F X 6 i ~ 4 X H 6 H 8 4 i 8 B U h 6 P H b B 4 B 6 U h t

    U B 8 F h H i U F S F X H 4 F S U B h 8 B

    m

    D F B P B B 6 H b H B b B H F H h P H F | S 4 X 8 B H 6 @ H 8 @ t

    G

    C+

    C-

    Partie C- isolee

    G

    C-

    R

    MG

    G

    a b d

    f

    te

    i

    v h 4 S S H b b H

    i

    b 4 S 4 X 8 B H P F 8 U X 6 H F X P H 6 H U X 8 6 H | 8 `H X B H F X 6 D F B 6 r 4 S S b B D F H 6 F X b 4 S 4 X 8 B H @

    m

    i

    b 4 S 4 X 8 B H P F 8 U X 6 H F X P H 6 H U X 8 6 H | 8 `H X B H F X 6 D F B 6 r 4 S S b B D F H 6 F X b 4 S 4 X 8 B H @

    m

    i

    b H 8 U X 6 H F X P r 4 i 8 B U h P H b 4 S 4 X 8 B H @ 6 F X b 4 S 4 X 8 B H @ H h B i r H 6 8 F h H 4 i 8 B U h

    4

    @ t

    H 6 8 4 S S H b `H

    B t

    v h S H F 8 `H i X B X H b H 6 `H 4 b B 8 `H 6

    u

    b 6 F B 4 h 8 H 6

    H D F B b B X H b U 4 b P H b 4 S U F 8 X H

    u

    H D F B b B X H P H b 4 S 4 X 8 B H @

    u

    v h H h P `H P F B 8 P H F | 4 h B H X H 6 P r `H 4 b F H X b H 8 U X 6 H F X B h 8 `H X B H F X

    H h B

    u

    u

    3 H 6 `H b `H H h 8 6 P H X `H P F i 8 B U h

    $

    H 8

    &

    P F 8 U X 6 H F X B h 8 `H X B H F X

    6 U h 8 ~ 4 B 8 F H b b H H h 8 P `H h B 6 H h B t

    b H 6 8 P U h i ~ 4 B 8 F H b P r H | S X B H X

    U F

    H h B S U F X i 4 b i F b H X b H 6 `H b `H H h 8 6 P H X `H P F i 8 B U h

    $

    H 8

    &

    P H

    t

    ! " $

    3 H 6 P B `H X H h 8 H 6 i U S U 6 4 h 8 H 6 P F 8 U X 6 H F X B h 8 `H X B H F X P `H h B H h B 6 F X b 4 4 6 H b U i 4 b H S X B h i B S 4 b H P r B h H X 8 B H

    P H b 4 S U F 8 X H" H B P G

    f

    P G

    A

    P G t V H h B U h 8 P H 6 h U 6 H 8 P H 6 6 w U b H 6 F 6 F H b 6

    i u

    $

    B G

    f

    H U X 8 h U X 4 b

    i B &

    m

    U h P B 8 D F H b 4 S U F 8 X H H 6 8 H h 8 X 4 i 8 B U h 4 F S U B h 8 B

    i B (

    m

    U h P B 8 D F H b 4 S U F 8 X H H 6 8 H h i U S X H 6 6 B U h 4 F S U B h 8 B

    i

    A

    u

    $

    B G

    A

    H U X 8 8 X 4 h i ~ 4 h 8 6 F B 4 h 8 G

    A

    i t u

    $

    B G t H U X 8 8 X 4 h i ~ 4 h 8 6 F B 4 h 8 G t

    i ) u

    A

    G

    A

    t G t H U X 8 8 X 4 h i ~ 4 h 8 H i 8 H F X P 4 h 6 b H S b 4 h P H b 4 6 H i 8 B U h P X U B 8 H t

    i 0

    u

    &

    B G

    f

    1 U H h 8 P H 8 U X 6 B U h

    h i T q

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    15/77

    1 ! ) ( 1 ! ( ) ! 1 )

    i 0

    A

    u

    &

    B G

    A

    1 U H h 8 P H H | B U h 4 F 8 U F X P H G

    A

    i 0 t u

    &

    B G t 1 U H h 8 P H H | B U h 4 F 8 U F X P H G t

    i

    &

    u 0

    A

    G

    A

    0

    tG

    t 1 U H h 8 P H H | B U h H i 8 H F X P 4 h 6 b H S b 4 h P H b 4 6 H i 8 B U h P X U B 8 H t

    "

    "

    !

    "

    ! " $

    U F X X H S X `H 6 H h 8 H X b r `H U b F 8 B U h P H i H 6 P B `H X H h 8 H 6 i U S U 6 4 h 8 H 6 b H b U h P H b 4 S U F 8 X H

    m

    U h 4 b r ~ 4 B 8 F P H

    P H b H 6 S X `H 6 H h 8 H X 6 U F 6 U X H P H i U F X H 6 H h U h i 8 B U h P H b r 4 6 i B 6 6 H i F X B b B h H D t 4 X H | H S b H

    m

    b H

    P B 4 X 4 H P H b r H U X 8 h U X 4 b H 6 8 b 4 i U F X H u $ D

    m

    P H H H U h 8 X 4 i H b H 6 P B 4 X 4 H 6 P H 6 4 F 8 X H 6

    i U S U 6 4 h 8 H 6 t z H 6 X H S X `H 6 H h 8 4 8 B U h 6 X 4 S ~ B D F H 6 6 U h 8 8 X H 6 F 8 B b H 6 S U F X b 4 X H i ~ H X i ~ H P H 6 6 H i 8 B U h 6 P X U B 8 H 6

    b H 6 S b F 6 6 U b b B i B 8 `H H 6 t

    6 6

    u 2

    q

    # ! & t ( 0

    u 2 ! & ! ( 7 & &

    s q

    & ( t 5 & 2 # 7 t

    z U h 6 B P `H X U h 6 F h H S U F 8 X H 6 U F B 6 H 4 F h 8 U X 6 H F X H | 8 `H X B H F X X `H S 4 X 8 B 0 i ~ 4 X H 6 H 8 4 i 8 B U h 6 P H b B 4 B 6 U h

    "

    D

    "

    D

    )

    t z U h 6 B P `H X U h 6 F h 8 X U h i U h D F H b i U h D F H

    @

    ( P H i H 8 8 H S U F 8 X H t

    G B

    A

    a

    b d

    f

    t

    f

    i

    2l

    B U h B 6 U b H b H 8 X U h i U h

    @

    (

    m

    6 H 6 H U X 8 6 H | 8 `H X B H F X 6 6 U h 8

    i b 4 S 4 X 8 B H P H b 4 P H h 6 B 8 `H b B h `H B D F H D F B 6 r 4 S S b B D F H 6 F X b H 8 X U h i U h

    @

    (

    i b r 4 i 8 B U h P F X H 6 8 H P H b 4 S U F 8 X H 6 F X b H S U B h 8 (

    m

    D F B H 6 8 S 4 X P `H h B 8 B U h b H 8 U X 6 H F X B h 8 `H X B H F X H h (

    "

    $

    &

    )

    i b r 4 i 8 B U h P F X H 6 8 H P H b 4 S U F 8 X H 6 F X b H S U B h 8

    @

    m

    D F B H 6 8 S 4 X P `H h B 8 B U h b r U S S U 6 `H P F 8 U X 6 H F X B h 8 `H X B H F X

    H h

    @

    "

    $

    &

    )

    3 H 8 X U h i U h

    @

    ( `H 8 4 h 8 H h `H D F B b B X H

    m

    U h S H F 8 `H i X B X H

    b 4 h F b b B 8 `H P H 6 X `H 6 F b 8 4 h 8 H 6 P H 6 H U X 8 6 H | 8 `H X B H F X 6

    $

    $

    k

    D

    w

    D u

    H 8 b 4 h F b b B 8 `H P H 6 U H h 8 6 H h F h S U B h 8 E D F H b i U h D F H P H 6 H U X 8 6 H | 8 `H X B H F X 6

    &

    x

    '

    $

    &

    x )

    $

    k

    "

    D

    w

    D

    k

    x y

    D

    w

    D u

    3

    W 1

    $ " T k q k G 4

    U 4 w 5 w G T k

    W G

    8 9 @ B D D F G I P Q # & ( ) # & 4 m

  • 8/4/2019 statique des poutres lastiques

    16/77

    ! ) # 1 ) ( ) ) ! 1 )

    v X

    m

    $

    H 8

    &

    `H 8 4 h 8 P H 6 U h i 8 B U h 6 P H D U h S H F 8 `H i X B X H b H 6 `H 4 b B 8 `H 6 6 F B 4 h 8 H 6

    $

    $

    u

    k

    w

    $

    w

    D

    &

    &

    u

    k

    w

    &

    w

    D

    w

    D

    x )

    $

    x

    '

    $

    u

    k

    w

    x y

    $

    w

    D w

    D

    z H D F B S H X H 8 P r `H i X B X H b H 6 `H D F 4 8 B U h 6 P r `H D F B b B X H P H

    @

    ( 6 U F 6 b 4 U X H

    k

    w

    $

    w

    D

    D

    w

    D u

    k

    w

    &

    w

    D

    w

    x y

    $

    w

    D

    "

    D

    x y

    D

    w

    D u

    z H 6 B h 8 `H X 4 b H 6 `H 8 4 h 8 h F b b H 6 S U F X 8 U F 8 8 X U h i U h

    @

    (

    m

    U h U 8 B H h 8

    w

    $

    w

    D

    D u

    w

    &

    w

    D

    w

    x y

    $

    w

    D

    "

    D

    x y

    D u

    H h P `H H b U S S 4 h 8 b 4 P `H X B `H H P F S X U P F B 8 H i 8 U X B H b H 8 H h 6 B S b B 4 h 8 4 H i b 4 S X H B H X H `H D F 4 8 B U h

    m

    U h

    U 8 B H h 8

    l

    w

    $

    w

    D

    D u

    w

    &

    w

    D

    I

    $

    "

    D u

    3 4 X `H 6 U b F 8 B U h P H i H 6 `H D F 4 8 B U h 6 P B `H X H h 8 B H b b H 6 H i 8 U X B H b b H 6 H 6 8 F h H 4 F 8 X H 4 b 8 H X h 4 8 B H S U F X b 4 P `H 8 H X B

    h 4 8 B U h P F 8 U X 6 H F X B h 8 `H X B H F X t

    6

    & 7 t G 2 7 ! #

    7 !' 2 7 #

    s

    & # 7

    q

    ! # t

    v h i U h 6 B P H X H 4 B h 8 H h 4 h 8 b 4 S U F 8 X H i U H F h B b B H F 8 X B P B H h 6 B U h h H b

    m

    b 4 `H i 4 h B D F H P H 6 B b B H F |

    i U h 8 B h F 6 h U F 6 H h 6 H B h H D F r H h 8 U F 8 S U B h 8 0 P H b 4 S U F 8 X H B b H | B 6 8 H F h 8 H h 6 H F X P H 6 i U h 8 X 4 B h 8 H 6 6 w `H

    8 X B D F H

    P

    8 H b D F H b 4 i U h 8 X 4 B h 8 H H h i H S U B h 8 H 8 S U F X F h H 4 i H 8 8 H P H h U X 4 b H F h B 8 4 B X H R H 6 8 P U h h `H

    S 4 X

    u

    P

    1 R

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    17/77

    ! ) 1 1 " & ! )

    T

    1x

    nds

    M

    G

    a b d

    f

    t i

    l

    X H h U h 6 i U H i U F S F X H b 4 6 H i 8 B U h P X U B 8 H

    6

    H h B U B X F X H

    f

    t t U B 8 0 b H S U B h 8 i U F X 4 h 8 P H

    6

    t

    3 4 i U F S F X H P B B 6 H b 4 S U F 8 X H H h P H F | S 4 X 8 B H 6

    H 8

    t

    U

    U F 8 H 6 b H 6 4 i H 8 8 H 6

    w

    P H i H h 8 X H 0 P H

    i H 8 8 H i U F S F X H U h 8 b 4 H H h U X 4 b H R u G

    f

    t

    3 H 8 U X 6 H F X P r 4 i 8 B U h P H b 4 S 4 X 8 B H

    6 F X b 4 S 4 X 8 B H

    H 6 8 b r B h 8 `H X 4 b H P H 6 i U h 8 X 4 B h 8 H 6 6 F X b 4 i U F S F X H

    6

    H 8 i r H 6 8 4 F 6 6 B S 4 X P `H h B 8 B U h b H 8 U X 6 H F X B h 8 `H X B H F X H h B t v h S H F 8 P U h i `H i X B X H b H 6 `H 4 b B 8 `H 6 H i 8 U X B H b b H 6

    $

    u

    km

    w

    u

    km

    P

    1 G

    f

    &

    u

    km

    y

    &

    w

    u

    km

    y

    &

    P

    1 G

    f

    w

    B U h P `H 8 4 B b b H b H 6 i U S U 6 4 h 8 H 6 P F 8 H h 6 H F X P H 6 i U h 8 X 4 B h 8 H 6 H h 0 6 F X b 4 4 6 H b U i 4 b H P H b 4 S U F 8 X H

    H

    y

    P G

    f

    P G

    A

    P Gt

    V

    m

    U h 4

    u

    !

    f f

    f A

    f

    t

    A f

    A A

    A

    t

    t

    f

    t

    A

    t t

    "

    %

    H h S X U H 8 4 h 8 b H 6 `H 4 b B 8 `H 6 H i 8 U X B H b b H 6 6 F X b 4 4 6 H b U i 4 b H P H b 4 S U F 8 X H H h B

    m

    U h U 8 B H h 8

    u

    k m

    f f

    w

    A

    u

    km

    f A

    w

    t u

    k m

    f

    t

    w

    0

    u

    k m D

    A

    f

    t

    D

    t

    f A

    w

    0

    A

    u

    km D

    t

    f f

    w

    0

    tu

    k

    m

    D

    A

    f f

    w

    3 r B h 8 H X S X `H 8 4 8 B U h P H 6 i U S U 6 4 h 8 H 6 P H 6

    P

    H 6 8

    i

    f f

    H 6 8 b 4 i U h 8 X 4 B h 8 H h U X 4 b H S U F X F h H 4 i H 8 8 H P H

    6

    t v h b r 4 S S H b b H

    l

    l

    l

    t

    k

    i G 1 T R y k

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    18/77

    ! ) # 1 ) ( ) ) ! 1 )

    i

    A f

    u

    f A

    H 6 8 b 4 i U S U 6 4 h 8 H 6 F X G

    A

    P H b 4 i U h 8 X 4 B h 8 H 8 4 h H h 8 B H b b H S U F X b 4 P B X H i 8 B U h G

    f

    i

    t

    f

    u

    f

    t H 6 8 b 4 i U S U 6 4 h 8 H 6 F X G t P H b 4 i U h 8 X 4 B h 8 H 8 4 h H h 8 B H b b H S U F X b 4 P B X H i 8 B U h G

    f

    i u

    f A

    G

    A

    f

    t G t H 6 8 b H H i 8 H F X i U h 8 X 4 B h 8 H 8 4 h H h 8 B H b b H S U F X b 4 P B X H i 8 B U h G

    f

    t v h b r 4 S S H b b H

    l

    l

    l

    t

    b H 6 8 X H 4 X D F 4 b H P H i U h 6 8 4 8 H X D F r B b 6 F 8 P H i U h h 4 8 X H b H 6 i ~ 4 S 6

    f f

    m

    f A

    H 8

    f

    tP 4 h 6 b 4 6 H i 8 B U h

    P X U B 8 H i r H 6 8 4 P B X H b H 6 i U h 8 X 4 B h 8 H 6 P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H S U F X b 4 6 H F b H P B X H i 8 B U h G

    f

    S U F X P `H 8 H X B h H X

    i U S b H 8 H H h 8 b H 8 U X 6 H F X B h 8 `H X B H F X t 3 H 6 8 H X H 6

    A

    tH 8

    t th r B h 8 H X B H h h H h 8 S 4 6 f

    t

    H 4 X D F H X 4 F 6 6 B D F H b r H U X 8 h U X 4 b H 8 b H H i 8 H F X U H h 8 P H H | B U h

    &

    h H P `H S H h P H h 8 D F H

    P H 6 i U h 8 X 4 B h 8 H 6 h U X 4 b H 6 P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H

    f f

    m

    4 b U X 6 D F H b H H i 8 H F X H U X 8 8 X 4 h i ~ 4 h 8 ) H 8 b H

    U H h 8 P H 8 U X 6 B U h 0

    h H P `H S H h P H h 8 D F H P H 6 i U h 8 X 4 B h 8 H 6 8 4 h H h 8 B H b b H 6 P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H

    f A

    H 8

    f

    t t

    z H S H h P 4 h 8

    m

    6 B U h 6 H P U h h H b 4 X `H 6 F b 8 4 h 8 H

    $

    H 8 b H U H h 8

    &

    P F 8 U X 6 H F X P H 6 H U X 8 6 B h 8 `H X B H F X 6 H h

    B

    m

    B b H | B 6 8 H F h H B h h B 8 `H P H i ~ 4 S 6 P H i U h 8 X 4 B h 8 H 6 P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H P U h 8 b r B h 8 `H X 4 b H 6 F X

    6

    H 6 8

    `H 4 b H 4 F 8 U X 6 H F X B h 8 `H X B H F X t

    3 4 X H i ~ H X i ~ H P F i ~ 4 S P H 6 i U h 8 X 4 B h 8 H 6 4 6 6 U i B `H 4 F 8 U X 6 H F X B h 8 `H X B H F X H 6 8 b r U H 8 P F i ~ 4 S B 8 X H 6 F B 4 h 8 t

    R 1 y 1 2 G 1 k

    x # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    19/77

    "

    $

    )

    3 H 6 X H 6 8 X B i 8 B U h 6 6 F X b 4 `H U `H 8 X B H P H 6 S U F 8 X H 6 S H X H 8 8 H h 8 P r 4 6 6 B B b H X F h 8 X U h i U h P H S U F 8 X H i U F X H

    P H b U h F H F X

    w

    D 4 F h 8 X U h i U h P H S U F 8 X H P X U B 8 H P H 6 H i 8 B U h i U h 6 8 4 h 8 H t 3 H 6 X `H 6 F b 8 4 8 6 P H b 4 8 ~ `H U X B H P H 6

    S U F 8 X H 6 U h 8 P U h i S U F U B X 6 H P `H P F B X H P H b 4 X `H 6 U b F 8 B U h P r F h S X U b H H P r `H b 4 6 8 B i B 8 `H 8 X B P B H h 6 B U h h H b b H

    6 F X F h 8 X U h i U h P H S U F 8 X H P X U B 8 H P H 6 H i 8 B U h i U h 6 8 4 h 8 H t

    v h H h P `H P F B X 4 b 4 X `H S 4 X 8 B U h P H 6 i U h 8 X 4 B h 8 H 6 h U X 4 b H 6 H 8 8 4 h H h 8 B H b b H 6 P 4 h 6 b H 6 6 H i 8 B U h 6 P X U B 8 H 6

    H h U h i 8 B U h P F 8 U X 6 H F X B h 8 `H X B H F X

    m

    4 B h 6 B D F H P H 6 C C b U B 6 P H i U S U X 8 H H h 8 E E P H 6 S U F 8 X H 6

    m

    i r H 6 8 4 P B X H

    P H 6 X H b 4 8 B U h 6 H h 8 X H b H 8 U X 6 H F X B h 8 `H X B H F X H 8 b H 6 P `H S b 4 i H H h 8 6 H 8 b H 6 X U 8 4 8 B U h 6 P H 6 S U B h 8 6 P H b 4 b B h H

    U w H h h H t

    ! # ! & ( 2 5 7 & ( & y

    !

    U B 8 F h i U X S 6 `H b 4 6 8 B D F H

    m

    B 6 U 8 X U S H

    m

    P H U X H i w b B h P X B D F H

    m

    P H b U h F H F X

    m

    P H 6 H i 8 B U h P X U B 8 H P H U X H

    D F H b i U h D F H

    6

    t v h h U 8 H 7 b H i U h 8 U F X H | 8 `H X B H F X P H

    6

    H 8 7 9 b H 6 `H H h 8 F H b 6 i U h 8 U F X 6 B h 8 `H X B H F X 6 t

    x

    S

    2

    G0

    x3

    G G1

    x1

    a

    b d

    t g i p

    v h i U h 6 B P H X H i H i U X S 6 i U H F h 8 X U h i U h P H S U F 8 X H t v h i ~ U B 6 B 8 b r 4 | H G

    f

    6 F X b 4 b B h H U w H h h H b B h H

    P H 6 i H h 8 X H 6 P H X 4 B 8 `H P H 6 6 H i 8 B U h 6 t 3 H 6 4 | H 6 G

    A

    H 8 Gt

    6 U h 8 i ~ U B 6 B 6 6 F X b H 6 P B X H i 8 B U h 6 S X B h i B S 4 b H 6

    P r B h H X 8 B H P H 6 6 H i 8 B U h 6 P X U B 8 H 6 t

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    20/77

    ! # ( )

    3 4 S U F 8 X H H 6 8 i ~ 4 X `H H 6 F X 6 4 6 H i 8 B U h

    D

    f

    u S 4 X F h 8 U X 6 H F X"

    &

    )

    m

    l l

    l

    l l

    t z H 8 U X 6 H F X X H S X `H 6 H h 8 H b r 4 i 8 B U h P H b 4 S 4 X 8 B H P H S U F 8 X H

    D

    f

    &

    6 F X b H 8 X U h i U h

    m

    i r H 6 8 P U h i H h 4 B 8 b H 8 U X 6 H F X B h 8 `H X B H F X H h B

    f

    t v h h U 8 H

    f

    P

    A

    P t P 0

    f

    P 0

    A

    P 0 t b H 6

    i U S U 6 4 h 8 H 6 P H i H 8 U X 6 H F X 6 F X b 4 4 6 H H G

    f

    P G

    A

    P G t V

    r 4 F 8 X H S 4 X 8

    m

    b 4 6 F X 4 i H b 4 8 `H X 4 b H P F i w b B h P X H h r H 6 8 S 4 6 i ~ 4 X `H H H 8 b H 6 U X i H 6 P H U b F H 6 U h 8 h F b b H 6 f t

    v h H h P `H P F B 8 B `H P B 4 8 H H h 8 D F H b H 8 U X 6 H F X B h 8 `H X B H F X 4 F S U B h 8 B u

    D

    f

    P P H 6 8

    "

    u

    &

    u

    &

    y y

    )

    P U h 8 b H 6 i U S U 6 4 h 8 H 6 6 U h 8

    u

    f

    A

    u

    A

    t

    u t

    0

    u 0

    f

    0

    A

    u 0

    A

    t

    D

    f

    0 t u 0 t

    A

    D

    f

    3 H 8 X U h i U h `H 8 4 h 8 H h `H D F B b B X H

    m

    B b H 6 8 4 i B b H P H U B X

    m

    H h `H i X B 4 h 8 b r `H D F B b B X H P F 8 X U h i U h

    m

    D F H b H 8 U X 6 H F X

    P H 6 4 i 8 B U h 6 H | 8 `H X B H F X H 6 4 F 8 X U h i U h P 4 h 6 b 4 6 H i 8 B U h B

    4 i 8 B U h P H b 4 b 4 S 4 X 8 B H

    D

    f

    ( 6 F X b H 8 X U h i U h

    H 6 8 b H 8 U X 6 H F X

    "

    &

    y y

    )

    u"

    f

    G

    f

    A

    G

    A

    t G t

    0

    f

    G

    f

    0

    A

    t G

    A

    0 t

    A

    G t

    )

    b H 6 8 `H 4 b 4 b r U S S U 6 `H P F 8 U X 6 H F X B h 8 `H X B H F X H h B

    t

    !

    5 & # # t ( %

    q

    ! # ' (

    q

    #

    3 H S X U b H H P r `H b 4 6 8 B i B 8 `H S U 6 `H S X `H i `H P H H h 8 4 S S 4 X 4 8 i U H B h i U S b H 8 H H h 8 P `H h B t H h H H 8

    m

    b H 6

    i U h P B 8 B U h 6 4 F | b B B 8 H 6 6 F X b H 6 6 H i 8 B U h 6 P X U B 8 H 6

    6

    H 8

    6

    f

    6 U h 8 B h i U S b H 8 H 6 i 4 X U h h r 4 S 4 6 P U h h `H

    F h H i U h P B 8 B U h H h i ~ 4 D F H S U B h 8 P H i H 6 6 H i 8 B U h 6

    m

    4 B 6 6 H F b H H h 8 F h H i U h P B 8 B U h 6 F X b r B h 8 `H X 4 b H P H 6

    i U h 8 X 4 B h 8 H 6 6 F X i H 6 6 H i 8 B U h 6 t b w 4 P U h i

    F h H B h h B 8 `H P H 6 U b F 8 B U h 6 t

    p

    i U h 6 B 6 8 H 4 X H i ~ H X i ~ H X F h H 6 U b F 8 B U h 8 H b b H D F H b H 8 H h 6 H F X P H 6 i U h 8 X 4 B h 8 H 6

    6 U B 8 P H b 4 U X H

    u

    !

    f f

    f A

    f

    t

    f A

    f

    t

    "

    %

    v h H X X 4 S b F 6 b U B h D F r 4 H i i H 8 8 H i U h P B 8 B U h 6 F S S b `H H h 8 4 B X H

    m

    U h 8 X U F H B H h F h i ~ 4 S P H 8 H h 6 H F X 6

    P H 6 i U h 8 X 4 B h 8 H 6 F h B D F H t

    k R 0

    1 y T

    4 q 1

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    21/77

    ( )

    6

    7 !

    s

    ! 5 ( %

    q

    ! # ' (

    q

    #

    3 H i ~ 4 S P H 8 H h 6 H F X 6 P H 6 i U h 8 X 4 B h 8 H 6 D F B 6 H X 4 8 X U F `H B S b B D F H P U h i F h H i H X 8 4 B h H X `H S 4 X 8 B 8 B U h P H 6

    i U h 8 X 4 B h 8 H 6 P 4 h 6 b H 6 6 H i 8 B U h 6 P X U B 8 H 6

    6

    H 8

    6

    f

    t 4 X H | H S b H

    m

    H h F h S U B h 8 0 u P

    D

    A

    P

    D

    t P H b 4

    6 H i 8 B U h

    6

    f

    m

    b 4 i U h P B 8 B U h 4 F | b B B 8 H 6 6 r `H i X B 8

    P

    1 G

    f

    u

    U F H 6 8 b r 4 i 8 B U h H | 8 `H X B H F X H 4 F 8 X U h i U h F h H U X i H S 4 X F h B 8 `H P H 6 F X 4 i H 4 F S U B h 8 0 t 3 4 X `H 6 F b 8 4 h 8 H

    H 8 b H U H h 8 X `H 6 F b 8 4 h 8 H h B

    f

    P F i ~ 4 S 6 U h 8 `H 4 F | 4 F 8 U X 6 H F X H P

    &

    V t

    F 8 X H H h 8 P B 8

    m

    b H 8 U X 6 H F X i ~ 4 X H H h 8"

    &

    )

    m

    D F r U h 6 r H 6 8 P U h h `H P U B 8 H 8 X H 4 S S b B D F `H 6 F X b 4

    6 H i 8 B U h P X U B 8 H

    6

    f

    6 F B 4 h 8 b 4 X `H S 4 X 8 B 8 B U h

    m

    6 B h U h B b h r w 4 S 4 6 P H 6 U b F 8 B U h X H 6 S H i 8 4 h 8 b r ~ w S U 8 ~ H 6 H P H

    4 B h 8 H h 4 h 8 t

    p

    l

    i U h 6 B 6 8 H 4 6 F S S U 6 H X D F H 6 B b H 8 U X 6 H F X"

    &

    )

    h r H 6 8 S 4 6 X `H S 4 X 8 B

    i U h H h 4 b H H h 8

    m

    b 4 S H X 8 F X 4 8 B U h P H 6 D F 4 8 X H `H X U 6 h r H 6 8 D F H b U i 4 b H t

    F 8 X H H h 8 P B 8

    p

    l

    l

    l

    v h 4 P H 8 H h S X 4 8 B D F H D F H b 4 6 U b F 8 B U h H 6 8 i U X X H i 8 H 4 F P H b 4 P H D F H b D F H 6 P B 4 H 8 X H 6 A t

    t

    u 2

    q

    #% ! & t ( 2 5 7 & ( & y ( %

    q

    ! # ' (

    q

    #

    U F X X `H 6 U F P X H i H S X U b H H P r `H b 4 6 8 B i B 8 `H

    m

    U h i ~ U B 6 B 8 b 4 U X F b 4 8 B U h H h i U h 8 X 4 B h 8 H 6 t 3 H 6 `H D F 4 8 B U h 6 4

    `H i X B X H 6 U h 8 P U h i b H 6 `H D F 4 8 B U h 6 P r `H D F B b B X H H 8 b H 6 `H D F 4 8 B U h 6 P H H b 8 X 4 B t

    3 H 6 `H D F 4 8 B U h 6 P r `H D F B b B X H 6 U h 8

    P

    u

    D F B P U h h H h 8 6 F X b 4 4 6 H H G

    f

    P G

    A

    P G t V b H 6 8 X U B 6 `H D F 4 8 B U h 6 6 i 4 b 4 B X H 6

    f

    f f

    A

    f A

    t

    f

    tu t g

    f

    f A

    u te

    f

    f

    tu t

    f

    3 H 6 `H D F 4 8 B U h 6 P H H b 8 X 4 B 6 U h 8

    P

    g

    g

    Y

    P

    Y

    g

    Y

    P

    y

    u

    F W 2 R $ 1 ! R k

    R R k 4 R 1 # T

    k R k 6 T

    T % G % # T

    G R $ ( k

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    22/77

    ! # ( )

    D F B P U h h H h 8 6 F X b 4 4 6 H H G

    f

    P G

    A

    P G t V b H 6 6 B | `H D F 4 8 B U h 6 6 i 4 b 4 B X H 6

    f f

    f f

    f f

    u t

    f A

    g

    g

    Y

    f A

    f f

    u t

    f

    t

    g

    g

    Y

    f

    t

    f f

    u t

    A A

    f f

    Y

    f f

    u t

    A

    t

    f f

    u t

    t t

    f f

    Y

    f f

    u t

    t & & 2 # ! & ( t

    s

    & # 7

    q

    ! # t

    !

    f f

    3 H 6 `H D F 4 8 B U h 6 t

    m

    t H 8 t U h 8 X H h 8 D F H b H 6 8 H X H 6

    f f

    f f

    m

    A A

    f f

    H 8

    t t

    f f

    6 U h 8 6 U b F 8 B U h P r F h

    6 w 6 8 H H b B h `H 4 B X H ~ U U H h H H 8 P U h i

    f f

    f f

    u

    A A

    f f

    u

    t t

    f f

    u

    H i b r `H D F 4 8 B U h t

    m

    U h H h P `H P F B 8 D F H b 4 6 U b F 8 B U h `H h `H X 4 b H P H

    f f

    H 6 8

    f f

    u

    f

    D

    f

    f

    D

    f

    D

    A

    f

    D

    f

    D

    t

    3 H 6 i U h 6 8 4 h 8 H 6 P r B h 8 `H X 4 8 B U h P H

    f f

    6 H X U h 8 P `H 8 H X B h `H H 6 S 4 X b H 6 i U h P B 8 B U h 6 4 F | b B B 8 H 6 t

    !

    f A

    f

    t

    3 H 6 `H D F 4 8 B U h 6 te

    H 8 t

    f

    U h 8 X H h 8 D F H

    f A

    H 8

    f

    t h H 6 U h 8 S 4 6 U h i 8 B U h P H

    D

    f

    t

    z U S 8 H 8 H h F P H b 4 6 U b F 8 B U h

    f f

    m

    b r `H D F 4 8 B U h t g P H B H h 8

    f

    f

    D

    A

    f

    D

    t

    A

    f A

    t

    f

    tu

    6 U B 8 H h i U X H

    f

    e

    f

    D

    t

    A

    f A

    u

    f

    e

    f

    D

    A

    t

    f

    t

    H 8 P U h i

    A

    f

    e

    D

    A

    f

    D

    A

    D

    t

    f A

    $

    D

    t " u

    t

    f

    e

    D

    t

    f

    D

    A

    D

    t

    f

    t %

    D

    A

    "

    U F $

    D

    t H 8 %

    D

    A

    6 U h 8 P H 6 U h i 8 B U h 6 i U h 8 B h F H 6 P `H X B 4 b H 6

    t

    b H | B 6 8 H P U h i F h H U h i 8 B U h )

    D

    A

    P

    D

    t 8 H b b H D F H

    A

    ) u

    f

    e

    D

    t

    f

    D

    A

    D

    t

    f

    t %

    D

    A

    t ) u

    f

    e

    D

    A

    f

    D

    A

    D

    t

    f A

    $

    D

    t

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    23/77

    ! ( ! ) 1 # )

    H 8 b H 6 i U h 8 X 4 B h 8 H 6

    f A

    H 8

    f

    t 6 U h 8

    f A

    u

    t)

    f

    e

    D

    A

    f

    D

    A

    D

    t $

    D

    t

    f

    t u

    A

    )

    f

    e

    D

    t

    f

    D

    A

    D

    t %

    D

    A

    b X H 6 8 H b H 6 `H D F 4 8 B U h 6 t H 8 t D F B P U h h H h 8 F h H i U h P B 8 B U h 6 F X )

    t ) u

    g

    g

    Y

    f

    t t$

    A

    ) u

    g

    g

    Y

    f

    A A

    %

    6 U B 8 H h i U X H

    ) u

    g

    g

    Y

    f

    D

    t

    g

    g

    Y

    f

    D

    A

    t$

    A

    %

    @

    $

    D

    t H 8 %

    D

    A

    `H 8 4 h 8 4 X B 8 X 4 B X H 6

    m

    U h i ~ U B 6 B 8

    $

    D

    t u

    g

    g

    Y

    f

    D

    tA

    e

    %

    D

    A

    u

    g

    g

    Y

    f

    D

    A

    A

    e

    )

    D

    A

    P

    D

    t H 6 8 P U h i 6 U b F 8 B U h P H b r `H D F 4 8 B U h

    ) u

    @

    H 8 b H 6 i U h 8 X 4 B h 8 H 6

    f A

    H 8

    f

    t 6 U h 8

    f A

    u

    t)

    f

    e

    D

    A

    f

    D

    A

    D

    t

    g

    g

    Y

    f

    D

    tA

    e

    f

    tu

    A

    )

    f

    e

    D

    t

    f

    D

    A

    D

    t

    g

    g

    Y

    f

    D

    A

    A

    e

    3 H i 4 b i F b P H

    f A

    H 8

    f

    t6 H X 4 H h H P U h i 4 b 4 X H i ~ H X i ~ H P r F h H U h i 8 B U h )

    D

    A

    P

    D

    t 4 b 4 S b 4 i B H h i U h 6 8 4 h 8

    @

    6 F X b 4 6 H i 8 B U h P X U B 8 H t 3 4 6 U b F 8 B U h `H h `H X 4 b H h H S H F 8 H 8 X H P U h h `H H B i B

    m

    S F B 6 D F r H b b H P `H S H h P P H b 4 U X H

    P H b 4 6 H i 8 B U h t

    p

    & ( ! # ! & t

    q

    2 8 & ! y ! # t

    3 H 6 i U h P B 8 B U h 6 4 F | b B B 8 H 6 6 U h 8 4 `H i X B X H 6 F X 8 U F 8 H b 4 X U h 8 B H X H t

    ! " ! 6

    3 4 h U X 4 b H H | 8 `H X B H F X H H 6 8 G

    f

    m

    b H 6 H U X 8 6 H | 8 `H X B H F X 6 6 U h 8 u

    1 G

    f

    m

    3 H F X B h 8 `H X 4 b H 6 F X

    6

    H 8 X H `H D F B 4 b H h 8 H 4 F 8 U X 6 H F X "

    &

    y y

    )

    k m

    P

    1 G

    f

    w

    u

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    24/77

    ! # ( )

    H 8

    k m

    y

    &

    P

    1 G

    f

    w

    u

    &

    y

    y

    i r H 6 8 4 P B X H b H 6 6 B | `H D F 4 8 B U h 6 6 i 4 b 4 B X H 6

    k m

    f f

    w

    u

    f

    t g

    k m

    f A

    w

    u

    A

    t g g

    k m

    f

    t

    w

    u t

    t ge

    k m

    D

    A

    f

    t

    D

    t

    f A

    w

    u 0

    f

    t g

    f

    km

    D

    t

    f f

    w

    u 0

    A

    t t g

    k

    m

    D

    A

    f f

    w

    u 0 t

    A

    t g

    ! " ! 6

    f

    3 4 h U X 4 b H H | 8 `H X B H F X H H 6 8 G

    f

    m

    b H 6 H U X 8 6 H | 8 `H X B H F X 6 6 U h 8 u

    1 G

    f

    m

    3 H F X B h 8 `H X 4 b H 6 F X

    6

    f

    P U B 8

    H 8 X H `H D F B 4 b H h 8 H 4 F 8 U X 6 H F X "

    f

    &

    )

    km

    P

    1 G

    f

    w

    u

    H 8

    km

    y

    &

    P

    1 G

    f

    w

    u

    &

    i r H 6 8 4 P B X H b H 6 6 B | `H D F 4 8 B U h 6 6 i 4 b 4 B X H 6

    k m

    f f

    w

    u

    f

    t g

    k m

    f A

    w

    u

    A

    t g

    k m

    f

    t

    w

    u t

    t g

    k m

    D

    A

    f

    t

    D

    t

    f A

    w

    u 0

    f

    t g

    k m

    D

    t

    f f

    w

    u 0

    A

    t

    e

    k m

    D

    A

    f f

    w

    u 0t

    te

    g

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    25/77

    ! ( ! ) 1 # )

    ! " !

    3 4 h U X 4 b H H | 8 `H X B H F X H H 6 8 R u P

    A

    P t

    m

    b H 6 H U X 8 6 H | 8 `H X B H F X 6 6 U h 8 h F b 6

    1 R u

    f A

    A

    f

    t

    t G

    f

    G

    A

    Gt

    u

    H 8 P U h i

    f A

    A

    f

    t

    t u

    v X

    m

    b H H i 8 H F X u

    f A

    G

    A

    f

    tG

    tH 6 8 b 4 S 4 X 8 B H 8 4 h H h 8 B H b b H P H b 4 i U h 8 X 4 B h 8 H

    l

    i r H 6 8 4 P B X H b 4 S 4 X 8 B H 8 4 h H h 8 B H b b H P H

    P

    1 G

    f

    m

    b 4 i U h P B 8 B U h P H 6 F X 4 i H b 4 8 `H X 4 b H B S b B D F H P U h i D F r B b

    H 6 8 S H X S H h P B i F b 4 B X H 4 R H 8 P U h i 8 4 h H h 8 4 F i U h 8 U F X 7 t

    x

    x

    N

    G 2

    3

    nu

    a b d

    te

    i

    l

    l

    3 4 i U h P B 8 B U h 4 F | b B B 8 H 6 S H F 8 P U h i 4 F 6 6 B 6 r `H i X B X H

    n u

    5 7 t

    e e

    B h 6 B

    m

    6 F X b 4 6 F X 4 i H b 4 8 `H X 4 b H P r F h H S U F 8 X H

    m

    b H H i 8 H F X i U h 8 X 4 B h 8 H 8 4 h H h 8 B H b b H P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H

    H 6 8 8 4 h H h 8 4 F i U h 8 U F X t

    !

    !

    3 H b H i 8 H F X `H X B H X 4 6 4 h 6 P B i F b 8 `H b H 6 X `H 6 F b 8 4 8 6 6 F B 4 h 8 6

    t

    3 H 6 i U h P B 8 B U h 6

    t g H 8

    t g i U h P F B 6 H h 8 4

    u

    f

    j

    u

    f

    u

    3 H 6 i U h P B 8 B U h 6 t g

    m

    t g

    m

    t

    e

    H 8 t

    e

    g i U h P F B 6 H h 8 4

    u

    0t

    A

    t

    u

    0

    A

    t

    A

    f

    u

    A

    t

    f

    u

    t

    A

    3 r H | S X H 6 6 B U h i U S b H 8 H H h 8 P `H 8 H X B h `H H P H

    f f

    H 6 8 P U h i

    f f

    u

    f

    j

    0

    A

    t

    D

    f

    A

    D

    t

    0

    t

    A

    D

    f

    t

    D

    A

    I (

    u

    u

    W

    r # % r # % T R ( 1 r

    # % T

    ( 1

    r

    # % k

    r r # % 1

    8 9 @ B D D F G I P Q # & ( ) # & 4 m

  • 8/4/2019 statique des poutres lastiques

    26/77

    ! # ( )

    6 U B 8 H h i U X H

    m

    H h U h i 8 B U h P H 6 i U S U 6 4 h 8 H 6 P F 8 U X 6 H F X B h 8 `H X B H F X H h B

    f f

    u

    j

    0

    A

    A

    D

    t

    0 t

    t

    D

    A

    3 4 i U h P B 8 B U h t

    e e

    i U h P F B 8 4 F h H i U h P B 8 B U h D F H P U B 8 X H 6 S H i 8 H X )

    D

    A

    P

    D

    t

    l

    7

    w

    ) uA

    A

    tD

    A

    D

    t

    t

    A

    D

    A

    A

    e g

    Y

    C

    wD

    A

    A

    t

    A

    D

    A

    D

    t

    A

    t

    D

    t A

    e g

    Y

    C

    wD

    t

    B h 6 B

    m

    P 4 h 6 F h H 6 H i 8 B U h P X U B 8 H

    m

    b 4 4 b H F X P H )

    D

    A

    P

    D

    t H 6 8 B S U 6 `H H

    l

    4 F h H i U h 6 8 4 h 8 H

    S X H 6 c t

    3 H 6 i U h P B 8 B U h 6 t g g

    m

    t g

    e

    m

    t g H 8 t g 6 U h 8 B P H h 8 B D F H H h 8 `H X B `H H 6 6 B b 4 i U h P B 8 B U h t

    e e

    H 6 8 6 4 8 B 6 4 B 8 H t

    3 4 i U h P B 8 B U h t g i U h P F B 8 4

    0

    u

    k

    D

    A

    A

    )

    D

    t

    t )

    w

    A

    t

    k

    a

    D

    A

    A

    D

    t

    D

    t A

    e

    g

    Y

    b

    w

    t

    A

    k

    a

    D

    A

    D

    t

    A

    D

    A

    A

    e

    g

    Y

    b

    w

    z r H 6 8 i H 8 8 H `H D F 4 8 B U h D F B P `H 8 H X B h H b 4 i U h 6 8 4 h 8 H

    @

    t

    3 H b H i 8 H F X S U F X X 4 `H X B H X H h 8 X 4 h 6 U X 4 h 8 b 4 S X H B H X H B h 8 `H X 4 b H D F r H b b H S H F 8 4 F 6 6 B 6 r `H i X B X H

    0

    ue

    k

    )

    w

    k

    )

    D

    t

    wD

    A

    D

    A

    wD

    t

    A

    t

    k

    a

    D

    A

    A

    D

    t

    D

    tA

    e g

    Y

    b

    w

    t

    A

    k

    a

    D

    A

    D

    t

    A

    D

    A

    A

    e g

    Y

    b

    w

    te

    f

    t 2 y

    ( t 7

    t 2 & #

    q

    # t t 2 7 & t

    s

    & # 7

    q

    ! # t

    4 h 6 F h H 6 H i 8 B U h P X U B 8 H P H S U F 8 X H U F b H 6 i U S U 6 4 h 8 H 6 P F 8 U X 6 H F X B h 8 `H X B H F X 6 F X b H X H S H X H b U i 4 b 6 U h 8

    H P

    A

    P t

    P 0

    P 0

    A

    P 0 t

    V

    m

    U h 4 b H 6 X `H 6 F b 8 4 8 6 6 F B 4 h 8 6

    i 3 H 8 H h 6 H F X P H 6 i U h 8 X 4 B h 8 H 6 P 4 h 6 b 4 4 6 H b U i 4 b H H 6 8 P H b 4 U X H

    u

    !

    f f

    f A

    f

    t

    f A

    f

    t

    "

    %

    3 H 6 i U h 8 X 4 B h 8 H 6 P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H P H h U X 4 b H G

    f

    6 U h 8

    !

    f f

    f A

    f

    t

    f A

    f

    t

    "

    %

    !

    g

    "

    %

    u

    !

    f f

    f A

    f

    t

    "

    %

    3 4 i U h 8 X 4 B h 8 H h U X 4 b H P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H H 6 8

    G

    f

    B

    P

    G

    f

    u

    P

    G

    f

    P G

    f

    u

    f f

    3 H H i 8 H F X i U h 8 X 4 B h 8 H 8 4 h H h 8 B H b b H P 4 h 6 b 4 6 H i 8 B U h P X U B 8 H H 6 8

    u

    f A

    G

    A

    f

    t G t

    P W k k A G T R R k q

    k

    # # % 1 U k R

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    27/77

    ! ) ( 1 # ( ) ! ) )

    i 3 H 6 i U S U 6 4 h 8 H 6 P H

    P

    6 r H | S X B H h 8 H h U h i 8 B U h P F 8 U X 6 H F X B h 8 `H X B H F X

    f f

    u

    j

    0

    A

    A

    D

    t

    0

    t

    t

    D

    A

    f A

    u

    t )

    t

    A

    D

    A

    D

    t

    g

    g

    Y

    A

    t

    D

    t A

    e

    f

    tu

    A

    )

    A

    tD

    A

    D

    t

    g

    g

    Y

    t

    A

    D

    A

    A

    e

    U F ) H 6 8 F h H U h i 8 B U h P H

    D

    A

    H 8

    D

    t

    m

    P `H h B H 4 F h H i U h 6 8 4 h 8 H S X H 6

    m

    P `H S H h P 4 h 8 P H b 4 U X H P H b 4

    6 H i 8 B U h P X U B 8 H H 8 6 U b F 8 B U h P F S X U b H H 6 F B 4 h 8

    i ) H 6 8 6 U b F 8 B U h P H b r `H D F 4 8 B U h P B `H X H h 8 B H b b H

    ) u

    @

    i 3 4 4 b H F X P H ) 6 F X b H 6 i U h 8 U F X 6 H 6 8 B S U 6 `H H S 4 X

    w

    ) uA

    A

    tD

    A

    D

    t

    t

    A

    D

    A

    A

    e g

    Y

    C

    wD

    A

    A

    t

    A

    D

    A

    D

    t

    A

    t

    D

    tA

    e g

    Y

    C

    wD

    t

    H S 4 6 U F b B H X D F H 6 F X b H i U h 8 U F X

    m

    wD

    A

    H 8

    wD

    t 6 U h 8 b B `H 6 t

    i 3 4 i U h 6 8 4 h 8 H

    @

    H 6 8 P `H 8 H X B h `H H S 4 X

    0

    u

    e

    k

    )

    w

    k

    )

    D

    t

    wD

    A

    D

    A

    wD

    t B B B

    A

    t

    k

    a

    D

    A

    A

    D

    t

    D

    t A

    e g

    Y

    b

    w

    t

    A

    k

    a

    D

    A

    D

    t

    A

    D

    A

    A

    e g

    Y

    b

    w

    @

    P `H S H h P P U h i P H 0

    m

    A

    H 8 t

    t

    7 & 5 7 !

    #

    t ( 2

    s

    #

    q

    y 5 ( t

    s

    & # 7

    q

    ! # t #

    q

    w # ! & & t

    4 h 6 b H S b 4 h P H b 4 6 H i 8 B U h P X U B 8 H

    m

    b H i ~ 4 S 4 P H 6 S X U S X B `H 8 `H 6 B h 8 `H X H 6 6 4 h 8 H 6 D F B S H X H 8 8 H h 8 P r 4 U B X

    P H 6 X H h 6 H B h H H h 8 6 6 F X 6 4 h 6 i U h h 4 8 X H ) t

    t

    n

    0

    i

    j

    *

    S*

    t

    n

    0

    i

    j

    *

    S*

    A

    BB

    A

    a

    b d

    t

    f

    i

    l

    l

    U B 8 F h i U h 8 U F X H X `H 7 H h 8 B H X H H h 8 i U S X B 6 P 4 h 6 b 4 6 H i 8 B U h

    6 m

    H h 8 U F X 4 h 8 F h H S U X 8 B U h

    6

    P H

    6

    t

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    28/77

    ! # ( )

    T V V V

    3 H i U h 8 U F X 7

    7 i U S b `H 8 `H S 4 X b H 6 i ~ H B h 6 i U h U h P F 6

    @

    ( H 8 (

    @

    H h 8 U F X H F h H U h H 6 B S b H H h 8

    i U h h H | H t 3 H 8 ~ `H U X H H P H 8 U i H 6 S H X H 8 P r `H i X B X H

    k

    B u

    km

    G

    f

    B

    !

    w

    u

    km

    A

    f

    t

    t

    f A

    w

    H h X H S b 4 i 4 h 8

    f A

    H 8

    f

    t S 4 X b H F X 6 4 b H F X 6

    k

    B u

    @

    6

    Y

    g

    Y

    A

    A

    t

    @

    6

    P G t

    t

    A

    @

    6

    P G

    A

    C

    v X

    m

    S 4 X P `H h B 8 B U h P H 7

    m

    k

    B u

    k

    B

    k

    B

    k

    B

    k

    B u

    k

    B

    k

    B

    U F

    P `H 6 B h H b 4 i B X i F b 4 8 U h 6 F X b H i U h 8 U F X B h 8 `H X B H F X t

    v h H h 8 B X H b 4 i B X i F b 4 8 B U h i ~ H X i ~ `H H

    k

    B u

    @

    6

    Y

    g

    Y

    A

    A

    t

    @

    6

    P Gt

    t

    A

    @

    6

    P G

    A

    C

    9

    k

    B

    U F b H P H X h B H X 8 H X H H 6 8 b 4 6 U H P H 6 i B X i F b 4 8 B U h 6 P H b H b U h P H 6 i U h 8 U F X 6 B h 8 `H X B H F X 6 P `H i X B 8 6 P 4 h 6

    b H 6 H h 6 S U 6 B 8 B t

    T ! V !

    H b 4 H H 4 h B H X H D F H S U F X b 4 i B X i F b 4 8 B U h

    m

    U h i 4 b i F b H P r 4 U X P b H

    F | P H 4 8 X 4 H X 6 7

    t 3 H

    8 ~ `H U X H H P H b 4 P B H X H h i H S H X H 8 P r `H i X B X H

    k

    B R

    w

    D u

    k m

    P B

    w

    u

    k m

    A

    f A

    t

    f

    t

    w

    `H 8 4 h 8 8 4 h H h 8 4 F i U h 8 U F X

    m

    6 U h

    F | 4 8 X 4 H X 6 b H 6 i U h 8 U F X 6 B h 8 `H X B H F X 6 H 6 8 h F b t

    v h U 8 B H h 8 P U h i

    k

    B R

    w

    D u

    A

    t

    @

    6

    P G t

    t

    A

    @

    6

    P G

    A

    #

    % & 7 y

    q

    # ! & t # (

    5 &

    q s

    y # t

    3 H 8 H h 6 H F X P H 6 i U h 8 X 4 B h 8 H 6

    P

    `H 8 4 h 8 i U h h F

    m

    b 4 b U B P H i U S U X 8 H H h 8 `H b 4 6 8 B D F H B 6 U 8 X U S H P U h h H b H

    8 H h 6 H F X P H 6 S H 8 B 8 H 6 P `H U X 4 8 B U h 6 I

    V

    u

    g

    X

    !

    f f

    g

    Y

    f A

    g

    Y

    f

    t

    g

    Y

    f A

    Y

    f f

    g

    Y

    f

    t Y

    f f

    "

    %

    b H | B 6 8 H B H h F h i ~ 4 S P H P `H S b 4 i H H h 8 ' 8 H b D F H I u

    g

    e

    5

    '

    '

    9

    m

    i 4 X b H 6 `H D F 4 8 B U h 6 P H

    H b 8 X 4 B 4 X 4 h 8 B 6 6 H h 8 b r B h 8 `H X 4 B b B 8 `H P H I t

    U F X i 4 b i F b H X '

    m

    U h F 8 B b B 6 H b 4 `H 8 ~ U P H 6 8 4 h P 4 X P F H H h `H i 4 h B D F H P H 6 B b B H F | i U h 8 B h F 6 U h i 4 b i F b H

    P r 4 U X P b H 8 H h 6 H F X P H 6 X U 8 4 8 B U h 6 4 h 8 B 6 w `H 8 X B D F H )

    m

    S F B 6 b H i ~ 4 S ' t

    x # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    29/77

    ( ! # ! ) ( # )

    ! " ! ! "

    ) H 6 8 6 U b F 8 B U h P H

    ) u 1

    !

    H h i U U X P U h h `H H 6 i 4 X 8 `H 6 B H h h H 6

    m

    b H 6 i U S U 6 4 h 8 H 6 P H ) 6 U h 8 6 U b F 8 B U h P H 6 `H D F 4 8 B U h 6 P B `H X H h 8 B H b b H 6

    w

    7 9 u

    V 9

    #

    9 V

    #

    wD

    #

    ) `H 8 4 h 8 4 h 8 B 6 w `H 8 X B D F H B b 6 F 8 P H i 4 b i F b H X 7

    f A

    m

    7

    A

    t H 8 7 t

    f

    4 X H | H S b H

    m

    S U F X 7

    f A

    w

    7

    f A

    u

    A

    V

    f

    #

    f

    V

    #

    A

    wD

    #

    D F B `H D F B 4 F 8 4 F | 8 X U B 6 `H D F 4 8 B U h 6 P B `H X H h 8 B H b b H 6

    f

    7

    f A

    u

    A

    V

    f f

    f

    V

    f A

    A

    7

    f A

    u

    A

    V

    f A

    f

    V

    A A

    t 7

    f A

    u

    A

    V

    f

    t

    f

    V t

    A

    3 H b H i 8 H F X `H X B H X 4 6 4 h 6 P B i F b 8 `H

    m

    H h X H S b 4 i 4 h 8 I S F B 6

    P

    S 4 X b H F X 6 4 b H F X 6

    m

    D F r U h U 8 B H h 8

    7

    f A

    u

    g

    Y

    X

    t )

    @

    D

    t

    A

    X t

    a

    Y

    D

    A

    A

    e

    g

    Y

    D

    tA

    e

    b

    t

    X

    A

    D

    A

    D

    t

    A

    X t

    a

    D

    f

    D

    f

    A

    e

    b

    0

    t

    X t

    D

    f

    H H H

    m

    U h U 8 B H h 8

    7

    A

    tu Y

    A

    X t D

    t

    D

    f

    Y

    0

    t

    X t D

    t

    Y

    t

    X

    A

    D

    A

    D

    f

    Y

    0

    A

    X

    A

    D

    A

    g

    Y

    X

    @

    D

    f

    H 8

    7t

    f

    u

    g

    Y

    X

    A

    )

    @

    D

    A

    t

    X

    A

    a

    g

    Y

    D

    A

    A

    e

    Y

    D

    tA

    e

    b

    A

    X t D

    A

    D

    t

    t

    X

    A

    a

    D

    f

    D

    f

    A

    e

    b

    0

    A

    X

    A

    D

    f

    h B h 8 X U P F B 8 b H

    l

    EP H b 4 S 4 X 8 B i F b H H h 0

    $

    u

    g

    e

    1 )

    P U h 8 b H 6 i U S U 6 4 h 8 H 6 6 U h 8

    f

    u 7

    A

    t

    A

    u 7t

    f

    t

    u 7

    f A

    ! "

    "

    3 H i ~ 4 S P H 6 P `H S b 4 i H H h 8 6 H 6 8 6 U b F 8 B U h P H b r `H D F 4 8 B U h P B `H X H h 8 B H b b H

    ' u I

    )

    c R 0 y

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    30/77

    ! # ( )

    6 U B 8

    m

    H h i U U X P U h h `H H 6 i 4 X 8 `H 6 B H h h H 6

    w

    9 u V 9

    7 9

    wD

    4 X H | H S b H

    m

    S U F X b H i 4 b i F b P H

    f

    w

    f

    u V

    f

    7

    f

    wD

    i H D F B `H D F B 4 F 8 4 F | 8 X U B 6 `H D F 4 8 B U h 6 P B `H X H h 8 B H b b H 6

    f

    f

    u V

    f f

    7

    f f

    u V

    f f

    A

    f

    u V

    f A

    7

    f A

    t

    f

    u V

    f

    t

    7

    f

    t

    P U h 8 b 4 6 U b F 8 B U h H 6 8

    f

    u

    X

    j D

    f

    a

    e

    X t

    D

    A

    f

    X

    A

    D

    t

    b

    a

    D

    f

    D

    f

    A

    e

    b

    D

    f

    a

    0

    A

    X

    A

    D

    t

    0

    t

    X t

    D

    A

    b

    B B B

    A

    X t

    A Y D

    A

    t

    e

    Y D

    A

    D

    tA

    e

    C

    t

    X

    A

    A Y D

    t

    t

    e

    Y D

    A

    A

    D

    t

    e

    C

    B B B

    g

    Y

    X

    D

    A

    P

    D

    t

    D

    A

    D

    t

    3 4 U h i 8 B U h )

    D

    A

    P

    D

    t P `H S H h P 4 h 8 P H b 4 U X H P H b 4 6 H i 8 B U h P X U B 8 H

    m

    U h 4 B h 8 X U P F B 8 F h H U h i 8 B U h

    D

    A

    P

    D

    t S U F X S U F U B X `H i X B X H b 4 6 U b F 8 B U h t 3 4 U h i 8 B U h

    D

    A

    P

    D

    t H 6 8 6 U b F 8 B U h P F 6 w 6 8 H H P B `H X H h 8 B H b

    A

    ue

    t )

    @

    D

    t

    t

    u

    e

    t )

    @

    D

    A

    6 U B 8 H h i U X H H i 8 U X B H b b H H h 8

    u e

    )

    @

    y

    &

    G

    f

    ! "

    i

    D

    A

    P

    D

    t H 6 8 P `H h B H 4 F h H i U h 6 8 4 h 8 H S X H 6 D F B U F H b H H H X U b H D F H

    t v h S H F 8 P U h i

    S X H h P X H S 4 X H | H S b H

    P u t

    i v h H 6 8 4 6 6 F X `H P H b r H | B 6 8 H h i H P H

    D

    A

    P

    D

    t

    m

    i 4 X U h 4 B H h

    A

    t

    u

    t

    A

    i

    D

    A

    P

    D

    t H 6 8 F h H U h i 8 B U h ~ 4 X U h B D F H t

    3 H i 4 b i F b P H

    A

    H 8

    tH 6 8 S b F 6 6 B S b H i 4 X ) h r B h 8 H X B H h 8 S 4 6 P 4 h 6 b H 6 `H D F 4 8 B U h 6 t v h U 8 B H h 8

    A

    u Y

    X

    jD

    t

    Y

    D

    f

    A

    A

    e

    X t

    D

    A

    A

    D

    t

    A

    t

    X

    A

    D

    A

    D

    t

    C

    B B B

    Y A

    0

    t

    eX t

    D

    A

    A

    D

    t

    A

    0

    A

    X

    A

    D

    A

    D

    t

    C

    g

    Y

    X

    @

    D

    f

    D

    t

    B B B

    A

    0

    t

    X t

    A

    X t

    D

    f

    f

    C

    D

    f

    A

    e

    D

    f

    D

    t

    tu Y

    X

    j

    D

    t

    Y

    D

    f

    A

    t

    e

    X

    A

    D

    t

    A

    D

    A

    A

    A

    X t D

    A

    D

    t

    C

    B B B

    Y

    A

    0

    A

    e

    X

    A

    D

    t

    A

    D

    A

    A

    0 t

    X t

    D

    A

    D

    t

    C

    g

    Y

    X

    @

    D

    f

    D

    A

    B B B

    A

    0

    A

    X

    A

    t

    X

    A

    D

    f

    f

    C

    D

    f

    A

    e

    D

    f

    D

    A

    # & ( ) # & 4 8 9 @ B D D F G I P Q

  • 8/4/2019 statique des poutres lastiques

    31/77

    ! ( ) ! 1 ! ( )

    1 ! 1 )

    3 H 6 i U h 6 8 4 h 8 H 6

    P

    P

    P

    P

    P

    D F B 4 S S 4 X 4 B 6 6 H h 8 P 4 h 6 b H i ~ 4 S ' P `H h B 6 6 H h 8 F h i ~ 4 S P H P `H S b 4 i H

    H h 8 P H 6 U b B P H t H h H H 8

    m

    8 U F 8 i ~ 4 S P H P `H S b 4 i H H h 8 i 4 b i F b `H 4 S 4 X 8 B X P r F h 8 H h 6 H F X P H P `H U X 4 8 B U h 6

    H 6 8 P `H h B 4 F h i ~ 4 S P H P `H S b 4 i H H h 8 P H 6 U b B P H S X H 6 t

    7

    5 5 & !

    s q

    # ! & ( &

    q

    t & & 2 #% ! & ( %

    q

    ! # ' (

    q

    #

    q

    2 8 5 &" 2 6 # 7 t

    3 H i ~ 4 S P H P `H S b 4 i H H h 8 6 8 X U F `H H 6 8 F h i ~ 4 S P 4 h 6 8 U F 8 b H U b F H P H b 4 S U F 8 X H t H h 8 ~ `H U X B H P H 6

    S U F 8 X H 6

    m

    U h h H 6 r B h 8 `H X H 6 6 H D F r 4 F | U F H H h 8 6 P H 6 S U B h 8 6 P H b 4 b B h H U w H h h H t v h P `H h B 8 P U h i

    i 3 4 X U 8 4 8 B U h P H 6 S U B h 8 6 P H b 4 b B h H U w H h h H

    u

    $

    D

    f

    P P

    i 3 H P `H S b 4 i H H h 8 P H 6 S U B h 8 6 P H b 4 b B h H U w H h h H

    & u '

    D

    f

    P P

    v h 4 4 b U X 6

    f

    u

    @

    D

    f

    g

    Y

    X

    X

    A

    u

    A

    ) P

    g

    Y

    X

    a

    D

    f

    D

    f

    A

    e

    b

    t

    X

    A

    D

    f

    0

    A

    X

    A

    X

    tu

    t) P

    g

    Y

    X

    a

    D

    f

    D

    f

    A

    e

    b

    A

    X t

    D

    f

    0

    t

    X t

    X

    7

    f

    u

    D

    f

    X

    j

    X

    7

    A

    u

    D

    f

    A

    0 t

    eX

    t

    D

    f

    A

    e

    D

    f

    f

    A

    X t

    D

    f

    X

    X

    7t

    u

    D

    f

    A

    0

    A

    eX

    A

    D

    f

    A

    e

    D

    f

    f

    t

    X

    A

    D

    f

    X

    X

    U F X `H b B B h H X b H 6 i U h 6 8 4 h 8 H 6 P F H 6 4 F i ~ 4 S P H P `H S b 4 i H H h 8 P H 6 U b B P H

    m

    U h P `H X B H i H 6 X `H 6 F b 8 4 8 6 S 4 X

    X 4 S S U X 8 4

    D

    f

    t v h U B 8 4 b U X 6 4 S S 4 X 4 8 X H b H 6 i U S U 6 4 h 8 H 6 P F 8 U X 6 H F X P H 6 H U X 8 6 B h 8 `H X B H F X 6

    m

    H 8 U h

    U 8 B H h 8 h 4 b H H h 8 b H 6

    l

    D F B P U h h H h 8 b r `H U b F 8 B U h P H b 4 X U 8 4 8 B U h

    H 8 P F P `H S b 4 i H H h 8 & b H b U h P H b 4 b B h H U w H h h H

    i H U b F 8 B U h P H b 4 X U 8 4 8 B U h P H 8 U X 6 B U h H h X 4 P B 4 h 6 H h U h i 8 B U h P H

    D

    f

    w

    f

    wD

    f

    u

    @

    g

    Y

    X

    u

    @

    eB

    U F U h 4 S U 6 `H B u

    X

    e

    g

    Y

    u

    Q

    b H i U H i B H h 8 P H 3 4 `H b t

    i H U b F 8 B U h P H b 4 X U 8 4 8 B U h P H H | B U h H h U h i 8 B U h P H

    D

    f

    w

    A

    wD

    f

    u

    0 $

    A

    D

    f

    X

    A

    w

    t

    wD

    f

    u

    0 $ t

    D

    f

    X t

    h 1 k ` a c8 d e g c Dg e u sr x q p q x Dg

    x B u w s g B s u e ` a c d e g c g p q s u qt e e g ` g w x

    8 9 @ B D D F G I P Q # & ( ) # & 4

  • 8/4/2019 statique des poutres lastiques

    32/77

    ! # ( )

    6 U B 8 H h i U X H 6 U F 6 U X H H i 8 U X B H b b H

    w

    A

    t

    wD

    f

    u

    0 $

    A

    D

    f

    X

    A

    G

    A

    0 $t

    D

    f

    X t

    G t

    U F

    A

    tH 6 8 b 4 X U 8 4 8 B U h P H H | B U h

    A

    tu

    A

    G

    A

    tG

    tt

    i H U b F 8 B U h P F P `H S b 4 i H H h 8 b U h B 8 F P B h 4 b H h U h i 8 B U h P H

    D

    f

    4 b b U h H H h 8 P H b 4 b B h H U w H h h H

    w

    7

    f

    wD

    f

    u

    D

    f

    X

    j

    i H U b F 8 B U h P F P `H S b 4 i H H h 8 8 X 4 h 6 H X 6 4 b H h U h i 8 B U h P H

    D

    f

    w

    A 7

    A

    w D

    f

    A

    u

    0 $ t

    D

    f

    X t

    w

    A 7 t

    w D

    f

    A

    u

    0 $

    A

    D

    f

    X

    A

    z H 6 `H D F 4 8 B U h 6 P B `H X H h 8 B H b b H 6 S H X H 8 8 H h 8 P H i 4 b i F b H X b H 6 X U 8 4 8 B U h 6 H 8 b H 6 P `H S b 4 i H H h 8 6 P H 6 S U B h 8 6 P H b 4

    b B h H U w H h h H P r F h H S U F 8 X H P X U B 8 H

    m

    H h U h i 8 B U h P H 6 i U S U 6 4 h 8 H 6 P F 8 U X 6 H F X P H 6 H U X 8 6 B h 8 `H X B H F X 6 0 t

    7

    5 5 & !

    s q

    # ! &

    q

    2 8 5 & 2 # 7 t ( %

    q

    ! ( &

    s

    & 2 7 ( 2 7

    z U h h 4 B 6 6 4 h 8 b H 8 U X 6 H F X P H 6 H U X 8 6 B h 8 `H X B H F X 6 P 4 h 6 F h H 6 H i 8 B U h

    m

    b H S X U b H H P H 4 B h 8 H h 4 h 8 4 S H X B 6

    P H i 4 b i F b H X b H i ~ 4 S P F 8 H h 6 H F X P H 6 i U h 8 X 4 B h 8 H 6 P 4 h 6 i H 8 8 H 6 H i 8 B U h t H S b F 6

    m

    U h 6 4 B 8 i 4 b i F b H X b H 6

    `H U b F 8 B U h 6 b H b U h P H b 4 b B h H U w H h h H P H b 4 X U 8 4 8 B U h H 8 P F P `H S b 4 i H H h 8 P H 6 S U B h 8 6 P H b 4 b B h H

    U w H h h H t

    z H 6 X `H 6 F b 8 4 8 6 U h 8 `H 8 `H `H 8 4 b B 6 S U F X F h H S U F 8 X H P H b B h H U w H h h H X H i 8 B b B h H

    m

    H 8 P H 6 H i 8 B U h P X U B 8 H

    D F H b i U h D F H t U F X b H 6 S U F 8 X H 6 P X U B 8 H 6

    m

    U h i 4 b i F b H b H 6 X U 8 4 8 B U h 6 H 8 b H 6 P `H S b 4 i H H h 8 6 P H 8 U F 8 S U B h 8 P H

    b 4 b B h H U w H h h H S 4 X 6 B S b H B h 8 `H X 4 8 B U h P H 6 b U B 6 P H i U S U X 8 H H h 8 t

    v h 4 `H 8 H h P X H i H 6 X `H 6 F b 8 4 8 6 4 F | S U F 8 X H 6 i U F X H 6

    m

    H h 6 F S S U 6 4 h 8 D F H i ~ 4 D F H 8 X U h i U h P H S U F 8 X H

    i U F X H P H b U h F H F X

    w

    D 6 H i U S U X 8 H i U H F h 8 X U h i U h P H S U F 8 X H P X U B 8 H t z H 8 8 H 4 S S X U | B 4 8 B U h H 6 8

    i U X X H i 8 H 6 B b 4 i U F X F X H H 6 8 4 B b H

    m

    U F S b F 6 S X `H i B 6 `H H h 8

    m

    6 B b H 6 P B H h 6 B U h 6 8 X 4 h 6 H X 6 4 b H 6

    w

    P H b 4 6 H i 8 B U h

    P X U B 8 H X H 6 8 H h 8 S H 8 B 8 H 6 P H 4 h 8 b H X 4 w U h P H i U F X F X H P H b 4 b B h H U w H h h H t

    w G

    b h H 4 F 8 S 4 6 U F b B H X D F H S U F X b H 6 S U F 8 X H 6 i U F X H 6

    m

    b 4 4 6 H b U i 4 b H G

    f

    P G

    A

    P G t h r H 6 8 S b F 6 i U h 6 8 4 h 8 H

    b H b U h P H b 4 b B h H U w H h h H t 3 H 6 b U B 6 P H i U S U X 8 H H h 8 S X `H i `H P H h 8 H 6 P U B H h 8 H 8 X H X `H B h 8 H X S X `H 8 `H H 6

    H b b H 6 P U h h H h 8 b H 6 P `H X B `H H 6 S 4 X X 4 S S U X 8 4 b r 4 6 i B 6 6 H i F X B b B h H P F H i 8 H F X X U 8 4 8 B U h H 8 P F H i 8 H F X

    P `H S b 4 i H H h 8

    m

    H h U h i 8 B U h P H 6 i U S U 6 4 h 8 H 6 P F 8 U X 6 H F X B h 8 `H X B H F X 6 F X b 4 4 6 H b U i 4 b H t

    z U h 6 B P `H X U h 6 F h H S U F 8 X H i U F X H

    m

    H 8 P H F | S U B h 8 6 D F H b i U h D F H 6

    @

    H 8 ( 6 F X b 4 b B