Beams and Loadings

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    LOADS

    wrt TIME

    STATIC DYNAMIC

    wrt DIRECTION OFLOADS

    NORMAL SHEAR

    wrt AREA

    CONCENTRATEDDISTRIBUTED

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    STATIC

    DEAD LOAD

    BEARING ON ASTATIONARY SHAFT

    LOAD IS CONSTANT WRTTO TIME .

    GRADUALLY APPLIEDLOAD

    WHICH VARIES SLOWLYTO ITS MAXIMUMMAGNITUDE AND THENREMAIN CONSTANT.

    GENERALLY LOAD VARIESTO ITS MAXIMUMMAGNITUDE IN 0 TO 1SEC THEN REMAIN

    CONSTANT .

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    DYNAMIC

    IMPACT/SHOCK LOAD

    (QUICKLY) WHICH ARE ACTING IN SHORTINTERVAL OF TIME TOWARD MAXIMUM

    MAGNITUDE.

    WHEN ANY MASS IS DROPPED FROMSOME HEIGHT ON OTHER BODY , THEN

    LOAD APPLIED ON OTHER BODY ISIMPACT LOAD .

    FATIGUE/CYCLIC LOAD

    WHOSE MAGNITUDE OR DIRECTION or BOTHMAGNITUDE AND DIRECTION CHANGE wrtTIME AND THESE LOADS ARE REPEATEDLY

    APPLIED wrt TIME

    SUDDENLYAPPLIED LOAD

    IT IS ALSO SAME AS IMPACT LOAD , BUT THEDIFFERNCE IS THAT , THE LOAD APPLIED ON

    OTHER BODY IS NOW FROM NEGLIGIBLE HEIGHT. ( STRESS = 2* STRESS IN CASE OF GRADUALLY

    APPLIED LOAD i.e (W/A) )

    WHEN THE CUTTING TOOL JUST TOUCHES

    THE ROTATING WORKPIECE .

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    IMPACT LOAD = WHEN h (height of impact) has some value.

    SUDDEN LOAD = WHEN h is very small or negligible.

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    a) Straight two-force member AB is in

    equilibrium under application of F and -F.

    b) Internal forces equivalent to F and -F are

    required for equilibrium of free-bodies AC and

    CB.

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    A to B UNIFORMLY DISTRIBUTED LOAD.

    B to CUNIFORMLY VARYING LOAD.

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    BEAMS

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    CLASSIFICATION OF BEAMS TAKING OTHER FACTORS -

    (a) STATICALLY DETERMINATE OR INDETERMINATE -

    Statically determinate - Equilibrium conditions sufficient to compute reactions.

    Statically indeterminate - Deflections (Compatibility conditions) along with equilibrium

    equations should be used to find out reactions.

    OR

    STATICALLY DETERMINATE STRUCTURE

    No. of unknowns

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    BEAMS SUPPORTS

    SUPPORTS-Identified by the

    resistance offered to forces .

    (a) Rollers/Links:

    Resists forces in a direction along the

    line of action

    (b) Pins/HINGES:

    Resists forces in any direction of the

    plane

    (c) Fixed Support:

    Resists forces in any direction

    Resists moments.

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    SHEAR FORCE SIGN CONVENTION

    HOW TO REMEMBER -

    CLOCKWISE DIRECTION OF SHEAR FORCEWILL MAKE BEAM TO ROTATE IN

    CLOCKWISE DIRECTION, HENCE TAKEN AS

    POSITIVE.

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    BENDING MOMENT SIGN CONVENTION

    POSITIVE MOMENT = SAGGING

    NEGATIVE MOMENT = HOGGING

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    CALCULATION OF BEAMS -

    When all the forces are applied in a single plane, the three equations of static equilibrium

    are available for analysis.

    Fx = 0, Fy = 0 and Mz = 0

    Employing these, the reactions at supports could be found out

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    PLANE SECTIONS normal to the axis before

    bending remain plane and normal after

    bending also, as shown in Figure, ab, cd, ef

    are sections which remain plane and

    normal.

    Beam is subjected to pure bending

    (means no shear, only moments).

    Longitudinal top fibers are in compression

    and bottom fibres in tension.

    Layer of fibres in between which is neither

    in tension or compression, is called the

    neutral surface.

    Neutral axis is the intersection of such a

    surface with the right section through thebeam.