Chapter 3 Trusses - موقع المهندس حماده شعبان 3 final2 (2).pdfb + r 2 j statically indeterminate degree of indeterminacy = b + r – 2 j ،ٹپي ٽڃ٫پ ٽ ٲأ سٷڒ ٠ ى ڍض)ڄڍ ڒوئ حڂڍض( حڋڇ٪ جڍ كذج

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  • July 2011

    SMS

    Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

    C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

    Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

    neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

    Chapter 3

    Trusses

    .

    http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

  • July 2011

    SMS

    Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

    C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

    Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

    neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

    Trusses

    (members) *

    (joints) (forces) (joints)

    (member) (tension) (compression).

    (compression) (tension) *

    (members) (joint method) (member)

    (section method)

    *

    .

    (joint) (tension) (member) *

    (compression) (joint).

    .

    http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

  • July 2011

    SMS

    Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

    C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

    Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

    neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

    Analysis of Trusses

    considering:

    b = number of members.

    r = number of reactions.

    j = number of joints.

    :tabilityS

    :tructure will be unstable in the following casesS

    1) b + r < 2 j

    2) b + r 2 j (but all reactions are parallel)

    3) b + r 2 j (but all reactions are concurrent)

    : of stability) providedeterminacy (D

    b + r = 2 j statically determinate

    b + r > 2 j statically indeterminate

    degree of indeterminacy = b + r 2 j

    ( )

    http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

  • July 2011

    SMS

    Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

    C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

    Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

    neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

    members (zero) truss *

    (. )

    (only 2 members) (joint) *

    (.A, D) ((zero member

    (only 3 members) (joint) *

    (. C, D) ((zero member ((member

    zero members

    http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

  • July 2011

    SMS

    Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

    C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

    Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

    neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

    .((members

    .((support reactions 1

    (. )

    (only 2 members) (joint) 2

    . 3

    (joints) 3 ,2 4

    2 - members)) .

    .((members ( 4) 5

    (tension) ((member 6

    (compression) .

    . 7

    joint method

    .

    http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

  • July 2011

    SMS

    Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

    C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

    Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

    neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

    ((members

    . ( truss)

    .((support reactions 1

    ( )

    2

    members) .)

    ( ) 3

    4

    .

    ((members - 2 5

    .

    ((members 6

    .

    ( section method) ( joint method) 7

    . ((members

    ethodmection s

    , ,

    http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

  • July 2011

    SMS

    Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

    C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

    Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

    neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

    a)

    statically indeterminate to the 4th degree

    b)

    statically determinate.

    c)

    statically indeterminate to the first degree

    d)

    the left panel is a collapsible component

    (6)

    parallel are reactions all satisfied

    d

    be not can F

    < r b

    j

    r

    b

    r b

    j

    r

    b

    r b

    j

    r

    b

    r b

    j

    r

    b

    x 0

    11

    6

    2

    9

    9 2 19

    9

    4

    15

    8 2 16

    8

    3

    13

    10 2 24

    10

    4

    20

    unstable

    3-2 classify each of the following trusses as statically determinate, statically indeterminate, or unstable.

    http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

  • July 2011

    SMS

    Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

    C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

    Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

    neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

    a)

    stable, statically determinate.

    b)

    stable, statically indeterminate to 1.

    c)

    stable, statically indeterminate to 1.

    d)

    (r + b) 2 j = 1

    stable, statically indeterminate to 1.

    6

    10

    3

    12)(

    6

    9

    4

    12)(

    6

    9

    4

    2)(

    8

    13

    3

    j

    b

    r

    jbr

    j

    b

    r

    jbr

    j

    b

    r

    jbr

    j

    b

    r

    3-3 classify each of the following trusses as statically determinate, statically

    indeterminate, or unstable. If indeterminate, state its degree.

    http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

  • July 2011

    SMS

    Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics :

    C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts :

    Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics :

    neths.-eng, comhs.-eng @hs.com-enginfo 9 4444 260 .

    Gy

    Gx FGF = 20 kN

    FAG = 15 kN Ax

    FAB = 10 kN

    20 kN

    18 kN

    7.5kN

    FEF

    FBC = FCD

    15 kN

    FCD

    FED = 8.33 kN

    5 kN

    FCD = 6.67 kN

    5 kN

    10 kN 6.67 kN

    FBF

    G

    A C

    F

    B

    D

    FBE = 4.17 kN

    FAf = 18 kN 15 kN FAF = 18 kN

    ;

    members *

    ( C) ( T)

    .

    . ( , ) *

    joint F:

    3-8 Determine the force in each member of the roof truss. State if the members

    are in tension or compression. Assume all members are pin connected.

    56.3o

    56.3o

    http://www.eng-hs.net/http://eng-hs.net/http://eng-hs.net/

  • July 2011

    SMS

    Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Stre

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