DISPLACEMENT MEDTHOD OF ANALYSIS: MOMENT DISTRIBUTION - PowerPoint PPT Presentation

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DISPLACEMENT MEDTHOD OF ANALYSIS: MOMENT DISTRIBUTION

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Title: The Moment Distribution Method Author: Nildem Tay i Last modified by: Nildem Tay i Created Date: 10/17/2006 9:12:34 AM Document presentation format – PowerPoint PPT presentation

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Title: DISPLACEMENT MEDTHOD OF ANALYSIS: MOMENT DISTRIBUTION


1
DISPLACEMENT MEDTHOD OF ANALYSIS MOMENT
DISTRIBUTION
  • Member Stiffness Factor (K)
  • Distribution Factor (DF)
  • Carry-Over Factor
  • Distribution of Couple at Node
  • Moment Distribution for Beams
  • General Beams
  • Symmetric Beams
  • Moment Distribution for Frames No Sidesway
  • Moment Distribution for Frames Sidesway

2
General Principles and Definitions
  • Thus the Moment Distribution Method (also known
    as the Cross Method) became the preferred
    calculation technique for reinforced concrete
    structures.
  • The description of the moment distribution method
    by Hardy Cross is a little masterpiece. He wrote
    "Moment Distribution. The method of moment
    distribution is this
  • Imagine all joints in the structure held so that
    they cannot rotate and compute the moments at the
    ends of the members for this condition
  • at each joint distribute the unbalanced fixed-end
    moment among the connecting members in proportion
    to the constant for each member defined as
    "stiffness"
  • multiply the moment distributed to each member at
    a joint by the carry-over factor at the end of
    the member and set this product at the other end
    of the member
  • distribute these moments just "carried over"
  • repeat the process until the moments to be
    carried over are small enough to be neglected
    and
  • add all moments - fixed-end moments, distributed
    moments, moments carried over - at each end of
    each member to obtain the true moment at the
    end." Cross 19492

3
1. Restrain all possible displacements. 2.
Calculate Distribution FactorsThe distribution
factor DFi of a member connected to any joint J
is                                             
   where S is the rotational stiffness , and is
given by                                       

4
  • 3. Determine carry-over factorsThe carry-over
    factor to a fixed end is always 0.5, otherwise it
    is 0.0.
  • 4. Calculate Fixed End Moments. (Table 3.1).
    These could be due to in-span loads,
    temperature variation and/or
  • relative displacement between the ends of a
    member.
  • 5. Do distribution cycles for all joints
    simultaneously Each cycle consists of two
    steps1. Distribution of out of balance moments
    Mo,
  • 2.Calculation of the carry over moment at the far
    end of each member. The procedure is stopped
    when, at all joints, the out of balance moment is
    a negligible value. In this case, the joints
    should be balanced and no carry-over moments are
    calculated.

5
6. Calculate the final moment at either end
of each member. This is the sum of all moments
(including FEM) computed during the distribution
cycles.
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Example
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Stiffness-Factor Modification
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Example
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Symmetric Beam and Loading
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Symmetric Beam with Antisymmetric Loading
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Moment Distribution for frames No sidesway
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Moment Distribution for frames sidesway
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