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1 CVG2140 Winter 2014 Mechanics of Materials Course Instructor Won Taek Oh A609(CBY) [email protected] 13 March 2014 Department of Civil Engineering (613)562-5800 Ext. 6687 Resultant Forces Produced by Bending Stress 2 (E 1 = E 2 )

CVG2140 Lecture 15 Shear Due to Bending 2in1 Color

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  • 1CVG2140 Winter 2014Mechanics of Materials

    Course InstructorWon Taek Oh

    A609(CBY)[email protected]

    13 March 2014 Department of Civil Engineering

    @(613)562-5800 Ext. 6687

    Resultant Forces Produced by Bending Stress

    2

    (E1 = E2)

  • 2 Resultant Forces Produced by Bending Stress

    2 2 2 211 0 6000 2 0 6000212

    BF . N mm / mm . N mm mm

    kN

    3

    2 2 2 211 5 6000 3 0 60002

    18

    CF . N mm / mm . N mm mm

    kN

    Resultant Forces Produced by Bending Stress

    Shear force

    4

  • 3 Example 1A beam segment if subjected to the internal bending moments shown. The cross-sectional dimensions of the beam are given. gDetermine the horizontal force required to satisfy equilibrium for the specified area and show the location and direction of this force in the sketch.

    5

    The Shear Stress Formula Shear stresses produced in a prismatic beam made of a

    homogeneous liner-elastic material

    6

  • 4 The Shear Stress Formula Shear stresses produced in a prismatic beam made of a

    homogeneous liner-elastic materialg

    7

    The Shear Stress Formula Shear stresses produced in a prismatic beam made of a

    homogeneous liner-elastic material

    0x HA Az z

    M MMF y dA y dA FI I

    0x HA A Az z z

    M M MF y dA y dA y dA FI I I

    M MF y dA y dA

    8

    H A Az z

    F y dA y dAI I

    H

    z

    MQFI

  • 5 The Shear Stress Formula Shear stresses produced in a

    prismatic beam made of a phomogeneous liner-elastic material

    34

    675 3000006

    33750000H z

    kN mm mmMQF kNI mm

    9

    The Shear Stress Formula Shear stress in a beam

    ,H

    H avgz z

    F M Q M Qt x t x I x I t

    0x

    10

    Hz

    dM Qdx I t

  • 6 The Shear Stress Formula Shear stress in a beam

    dM Vdx

    Hz

    VQI t

    11

    z

    VQI t

    Shear stress formula