isostatikoi foreis

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  • 7/24/2019 isostatikoi foreis

    1/16

    8

    200

    A

    _0,4kNm 0,4kNm

    8.1 Q, M

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    8. 220

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    8.1 Q, M 221

    8.1 Q, M

    -

    .

    (=0,01m4)

    =2,9107k/m

    2. 8m.

    , 4m.

    -

    (1) -

    (2).

    . -

    . -

    .

    , ,

    ,

    . -

    Q, ,

    .

    , Q

    .

    -

    . , Q, ,

    ,

    .

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    8. 222

    1.

    A B

    P=400kN

    1

    8,0

    1.

    _ _ __ _

    + + ++ +

    2.

    .

    1. 2.

    -

    ,

    . -

    -

    , .

    -

    -

    , -

    .

    (+++)

    (- - -) .

    , -

    .

  • 7/24/2019 isostatikoi foreis

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    8.1 Q, M 223

    +

    _

    200

    200

    +

    +

    200kN

    +

    _

    400kN

    200kN200kN

    200kN

    Q: Q

    .

    Q

    A B1

    AZ

    BZ

    M+

    +

    AZ=200kN

    200kN

    +

    +

    800kNm

    A B

    M:

    .

    1

    Mmax= PL/4 = 800,0m

    QA= P /2= 200,0kN

    QB= P /2= 200,0kN

    .

    . 1,

    1 . Q

    .

    -

    , Q

    .

    ,

    .

    -

    .

    -

    .

    . -

    -

    1 1.

    -

    , -

    . -

    -

    .

    -

    -

    .

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    8. 224

    2.

    A B

    p=50kN/m

    L=8,0m

    1.

    _ __ _ _

    + + ++ +

    2.

    -

    1.

    .

    1. 2.

    -

    -

    , -

    -

    .

    -

    -

    -

    , .

    -

    -

    ,

    -

    .

    (+++)

    (- - -) .

    , -

    .

  • 7/24/2019 isostatikoi foreis

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    8.1 Q, M 225

    +

    _

    200

    20

    +

    +

    0

    200kN

    200kN_pdx

    Q: Q

    .

    Q

    A B

    0p

    dx

    AZ

    BZ

    M+

    +

    AZ=200kN

    +

    +

    400kNm

    A B

    M:

    .

    Mmax= pL2/8 = 400,0m

    QA= pL /2=+200,0kN

    QB= pL /2= 200,0kN

    1 (

    ).

    .

    p

    -

    Q -

    . -

    -

    ,

    .

    .

    p

    .

    ,

    .

    .

    Q. To

    p ,

    .

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    8. 226

    3.

    L=4,0m

    A B

    P=200kN

    1

    2

    Q:

    +200

    _800

    M:

    M

    (+)

    AZ=200kN

    200kN

    :

    MA=800kNm(_)

    .

    .

    AZ

    MA

    MA= PL= 200,04= 800,0kNm

    MB=0,0kNm

    QA=P= 200,0kN QB=P= 200,0kN

    1, 2

    ,

    .

    -

    -

    .

    .

    (

    (+++) (- - -))

    -

    -

    .

    ,

    .

    .

    . -

    Q

    -

    . -

    ,

    .

    .

    . -

    -

    .

    .

    () .

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    8.1 Q, M 227

    4.

    L=4,0m

    A B

    p=50kN/m

    1

    2

    +200

    Q:

    .

    AZ

    _400

    M:

    f=pL2/8=100kNm

    .MA

    MA= pL2/2= 400,0kNm

    QA= pL = 200,0kN

    MB=0,0 kNm, QB=0,0kN

    p.

    1,2

    (

    (++) (--)

    ).

    .

    -

    .

    .

    -

    , -

    .

    .

    p Q

    -

    .

    .

    p -

    (

    Q). -

    ,. p

    ,

    .

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    8. 228

    5.

    1

    2

    1, 2

    ,

    -

    .

    -

    .

    -

    ( (++)

    (- - -)

    ).

    -

    -

    -

    . -

    -

    -

    . -

    (++) -

    (--). -

    .

    90

    400,0kN

    G

    3,0

    8,0

  • 7/24/2019 isostatikoi foreis

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    8.1 Q, M 229

    Q: To Q

    (Q

    G=200,0kN, Q

    G=

    200,0kN)

    266,6 266,6

    200,0

    200,0

    +

    +_

    _

    .

    M:To

    800,0800,0_

    __

    _

    .

    Z Z

    400,0

    A B 200,0k2= = =

    G

    GM 0 = X200,0 4

    A 266,66kN3

    = =

    M M 266,66 3 800,0km= = =

    . -

    -

    . -

    Q -

    .

    (

    ).

    .

    .

    Q

    G=200,0kN

    G=0, -

    G

    (3).

    G

    ()

    ,

    -

    .

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    8. 230

    90

    6.

    p=50kN/m

    1

    2

    1, 2

    ,

    -

    .

    -

    .

    -

    ( (++)

    (- -)

    ).

    -

    -

    .

    -

    .

    (++)

    (- -). -

    .

    3,0

    8,0

    G

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    8.1 Q, M 231

    Q: Q

    (Q

    G=Q

    G=0)

    133,3

    200,0

    200,0

    +

    +_

    _

    .

    33,3

    M:

    400,0_

    __

    _400,0

    f=pL2/8=100kNmf=pL2/8=100kNm

    .

    Z Z

    50,0 8A B 200,0k

    2

    = = =

    G

    GM 0 = X

    200,0 4 50,0 4 2A 133,33kN

    3

    = =

    M M 133,33 3 400,0km= = =

    ., . -

    Q ,

    p

    ,

    .

    -

    -

    -

    (-

    ).

    Q

    G=0kN G=0kNm, -

    G -

    (4).

    G ( -

    )

    ,

    .

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    8. 232

    7.

    8,0 2,02,0

    2 31

    P=400kN

    1

    2

    Q: Q

    +

    _

    200

    200

    A

    .

    +

    800kNm

    A B

    M:

    .

    -

    1, 2

    ,

    . -

    -

    , . -

    -

    . -

    (++)

    ( - - - ) .

    ,

    -

    .

    , .Q, M -

    -

    . -

    (Q=0, M=0)

    .

    (

    ),

    -

    .

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    8.1 Q, M 233

    8.

    8,0 2,02,0

    2 3

    P=200kN P=200kN

    1

    2

    Q: Q

    _

    200

    200

    A

    .

    +

    200

    A .

    _400 400

    M:

    -

    .

    1, 2

    -

    .

    , .

    -

    .

    -

    .

    , -

    -

    .

    ,

    , -

    -

    -

    .

    ,

    (

    )

    Q -

    .

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    8. 234

    9.

    8,0 2,02,0

    2 31

    p=50kN/m

    1

    2

    Q: Q

    +

    _

    200100

    A

    ._

    100

    200

    +

    +

    300

    A B

    M:

    .

    100 100

    +

    _ _f=400kNm

    1, 2

    -

    1 -

    .

    . -

    (++) -

    (++)

    . -

    (

    ).

    , . -

    -

    5012=600k.

    M -

    (-

    ) - .

    , -

    -

    AQ

    BQ .

    .