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July 2011 ساا٠ دح٠ذ وـ ػ١ثرـذ ا ػلغزوشاخ ا خطـأ تح تشعاSMS ىرشذ ا٠ثش تا أد عام موا ة: Physics I/II, Circuits, English 123/221, Numerical, AutoCAD, Strength, Statics C++, Java, MATLAB, Data Structures, Algorithms, Discrete Math, Digital Logic, Concepts ذش:١ثاد و Mechanical Design I/II, Structural Analysis I/II, Concrete I/II, Soil, Dynamics, System Dynamics اد ذص م. حمادة شعبان260 4444 9 hs.com - eng [email protected] ولة محل شرح ومسائل مجانا بالموقعينnet hs. - eng , com hs. - eng Chapter 3 Trusses حؽ ٠اسذ زوشاخ ؽشغ ، اخرؽا اذ٠ؼذ عاتمحااد أد ا ػً اعا راؼح ١لؼ ا٠سزو اغضببة اافببر سبب ابب أ أعؼاخ١ض لد ا.

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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, 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 .

    FAH

    FAB

    15

    A

    (From symmetry)

    joint A:

    joint B:

    joint H:

    3-9 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.

    FBH

    B FAB

    10 kN

    .

    FBC

    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 .

    from and:

    joint G:

    3.9

    16.67 kN 16.67 kN

    FGC

    G

    !!

    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 .

    (From symmetry)

    (FCG) is a zero-force member

    (

    +

    E) FGF (

    3-10 The Howe truss is subjected to the loading shown. Determine the force in members GF, CD, and GC, and state if the members are in tension or

    compression.

    5 kN

    2 kN

    9.5 kN

    D

    F

    FGF

    FDG

    FCD

    3 m

    2 m 2 m

    G

    :

    M )

    .(

    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 .

    (From symmetry)

    .

    3-11 The Howe truss is subjected to the loading shown. Determine the force in

    members GH, BC, and BG, of the truss and state if the members are in tension or

    compression. (Fig. 3-11)

    B

    9.5 kN

    H

    G

    FBC

    FGH

    FBG

    5 kN

    2 m 2 m

    3 m 2 kN

    36.87o

    56.31o

    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 .

    .

    Solution:

    (From symmetry)

    3-14 Determine the force in members IH, BC, and BH of the bridge truss. Solve

    for each unknown using a single equation of equilibrium. State if the membrs are in tension or compression. Assume all members are pin connected.

    5 kN 3 kN

    O

    H FIH

    FBC

    FBH

    2 m

    4 m

    4 m

    B

    I

    63.43o

    26.56o

    A

    2 m

    Ey

    Ay

    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 .

    .

    .

    (reactions )

    3-17 Determine the force in members GF, FC, and CD of the cantilever truss. State if the membrs are in tension or compression. Assume all members are pin

    connected.

    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 .

    Intire truss:

    ;

    .

    3-18 Determine the forces in members KJ, CD, and CJ of the truss. state if the

    members are in tension or compression. (Fig. 3-18).

    5 kN 15 kN 15 kN

    3 m

    FKJ

    FCJ

    FCD

    Ay

    A

    C

    33.69o

    18.43o

    J

    3 m 3 m

    3 m

    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 .

    moment 2) members )

    joint D:

    (G FDE )

    3-19 Determine the forces in members JI, JD, and DE of the truss. state if the

    members are in tension or compression.

    FDJ

    97.5 kN 97.5 kN

    D

    J H G

    FJI

    5 10 20

    49.17

    43.18FDE

    E

    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 .

    from symmetry

    joint A:

    joint D:

    3-20 Determine the forces in each member of the truss in terms of the load P and

    state if the members are in tension or compression.

    FDB

    P

    0.687 P 0.687 P

    P/2

    FAB

    FAD

    A

    D

    !!

    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 .

    For maximum loads, choose the minimum, Pmax = 4.25 kN

    From symmetry

    Ay = Cy = 0.5 P

    joint A:

    joint B:

    FAD cos FAB cos 45 = 0

    FAD cos 14 = FAB cos 45

    FAD = 0.729 FAB

    FAD sin + .5 P FAB sin 45 = 0

    (0.729 FAB * sin 14) + 0.5 P - FAB sin 45 = 0

    FAB = 0.942 P ( C )

    FAD = 0.687 P ( T )

    - FBD + 2 FAB sin 45 = 0

    FBD = 1.33 P ( T )

    FAB = 0.942 P = 4 kN, Pmax = 4.25 kN

    FBD = 1.33 P = 10 kN, Pmax = 7.52 kN

    3-22 Members AB and BC can each support a maximum compressive force of 4 kN, and members AD, DC, and BD can support a maximum tensile force of 10

    kN. If a = 1.8m determine the greatest load P the truss can support.

    .

    Ay = 0.5 P

    FAD

    FAB

    FBC

    FBD

    FAB

    B

    = 14

    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 .

    from symmetry

    Due To Symmetry

    .

    3-24 Determine the forces in members GF, FB, and BC, of the fink truss and

    state if the members are in tension or compression.

    FBC

    FGF

    FFB

    4 kN

    30o 60

    o

    B

    3 cos2 30

    o

    4.5 tan 30

    o

    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 .

    .

    3-25 Determine the force in members GF, CF, and CD, of the roof truss and

    indicate if the members are in tension or compression.

    FGF

    Ey

    FCD

    FCF

    1 m 1 m

    F

    1.5 m

    C

    E

    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 .

    This is a compound truss

    Where ACB and FED are connected by

    Three bars FA, EC, and DB.

    Since

    b + r = 2 j

    9 + 3 = 2(6) = 12

    Statically determinate

    Truss is internally unstable.

    .

    3-26 Classify the truss and determine if it is stable.

    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 .

    From symmetry:

    joint A:

    joint B:

    joint F:

    6 kN

    A FAB

    FAF

    8 kN

    FBE

    FBF

    8 kN

    B

    3-30 Specify the type of compound truss and determine the force in each member.

    State if the members are in tension or compression. Assume all members are pin connected.

    .

    2 kN

    2 kN 10 kN

    F FEF

    FCF

    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 .

    3-31 Determine the forces in members IH , AH, and BC, of truss. State if the

    members are in tension or compression.

    5 m 5 m

    FIH

    FAH

    FBC

    10 kN 14 kN

    5 m

    B

    J I

    A

    26.56o

    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 .

    Supports Reaction:

    Method of joints: By inspection,

    members BN, NC, DO, OC, HJ, JE, and LG are zero Force members.

    . . . .

    3-39 Determine the force in members EF, EB, and LK, of the Baltimore bridge truss and state if the members are in tension or compression. Also, indicate all

    zero-force members. (Fig.3-39).

    FIK

    FEP

    FEF

    Iy 2 kN 3 kN

    K

    P

    F

    4 m 2m

    4 m

    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 .

    (

    BCF

    BGF

    BA

    kN9 kN6

    HGF

    G

    X X X m3 m3

    X

    X

    m3

    m5.1

    m3X X

    X

    X

    m5.1

    (

    6.26

    3

    5.1tan 1

    5.4

    33.56

    3

    5.4tan 1

    3-41 Determine the force in members BG, HG, and BC, of the truss and state if the members are in tension or compression. Also, indicate all zero-force

    members.

    .

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