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Uniformly distributed load of intensity qLinearly distributed load of maximum intensity q0
Concentrated load of magnitude P
Couple of magnitute M0
Example
http://en.wikipedia.org/wiki/File:Fem4.pnghttp://en.wikipedia.org/wiki/File:Fem2.pnghttp://en.wikipedia.org/wiki/File:Fem3.pnghttp://en.wikipedia.org/wiki/File:Fem1.png8/14/2019 Uniformly Distributed Load of Intensity q
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Example
The statically indeterminate beam shown in the figure is to be analysed.
Members AB, BC, CD have the same length.
Flexural rigidities are EI, 2EI, EI respectively.
Concentrated load of magnitude acts at a distance from the support A.
Uniform load of intensity acts on BC.
Member CD is loaded at its midspan with a concentrated load of magnitude.
In the following calcuations, counterclockwise moments are positive.
]edit] Fixed-end moments
]edit] Distribution factors
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=98/14/2019 Uniformly Distributed Load of Intensity q
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The distribution factors of joints A and D are DAB = 1,DDC = 0.
]edit] Carryover factors
The carryover factors are , except for the carryover factor from D (fixed support) to C which is zero.
]edit] Moment distribution
Joint A Joint B Joint C Joint D
Distrib.factors
0 1 0.2727 0.7273 0.6667 0.3333 0 0
Fixed-end
moments
14.700 -6.300 8.333 -8.333 12.500 -12.500
Step 1 -14.700 -7.350
Step 2 1.450 3.867 1.934
Step 3 -2.034 -4.067 -2.034 -1.017
Step 4 0.555 1.479 0.739
Step 5 -0.246 -0.493 -0.246 -0.123
Step 6 0.067 0.179 0.090
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/wiki/File:MomentDistributionMethod2.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=128/14/2019 Uniformly Distributed Load of Intensity q
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Step 7 -0.030 -0.060 -0.030 -0.015
Step 8 0.008 0.022 0.011
Step 9 -0.004 -0.007 -0.004 -0.002
Step 10 0.001 0.003
Sum ofmoment
s0 -11.569 11.569 -10.186 10.186 -13.657
Numbers in grey are balaced moments; arrows ( / ) represent the carry-over of moment from one end
to the other end of a member.
]edit] Result
Moments at joints determined by the moment distribution method
The conventional engineer's sign convention is used here, i.e. positive moments cause elongation atthe bottom part of a beam member.
For comparison purposes, the following are the results generated using a matrix method. Note that in theanalysis above, the iterative process was carried to >0.01 precision. The fact that the matrix analysis results
and the moment distribution analysis results match to 0.001 precision is mere coincidence.
Moments at joints determined by the matrix method
The complete shear and bending moment diagrams are as shown. Note that the moment distribution methodonly determines the moments at the joints. Developing complete bending moment diagrams require
additional calculations using the determined joint moments and internal section equilibrium.
SFD and BMD
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_methodhttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_method8/14/2019 Uniformly Distributed Load of Intensity q
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Shear force diagram Bending moment diagram
]edit] Notes
Example
Example
The statically indeterminate beam shown in the figure is to be analysed.
Members AB, BC, CD have the same length.
Flexural rigidities are EI, 2EI, EI respectively.
Concentrated load of magnitude acts at a distance from the support A.
Uniform load of intensity acts on BC.
Member CD is loaded at its midspan with a concentrated load of magnitude.
In the following calcuations, counterclockwise moments are positive.
]edit] Fixed-end moments
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=14http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=14http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=14http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=98/14/2019 Uniformly Distributed Load of Intensity q
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]edit] Distribution factors
The distribution factors of joints A and D are DAB = 1,DDC = 0.]edit] Carryover factors
The carryover factors are , except for the carryover factor from D (fixed support) to C which is zero.
]edit] Moment distribution
Joint A Joint B Joint C Joint D
Distrib.factors
0 1 0.2727 0.7273 0.6667 0.3333 0 0
Fixed-end
moment
14.700 -6.300 8.333 -8.333 12.500 -12.500
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/wiki/File:MomentDistributionMethod2.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=128/14/2019 Uniformly Distributed Load of Intensity q
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s
Step 1 -14.700 -7.350
Step 2 1.450 3.867 1.934
Step 3 -2.034 -4.067 -2.034 -1.017
Step 4 0.555 1.479 0.739
Step 5 -0.246 -0.493 -0.246 -0.123
Step 6 0.067 0.179 0.090
Step 7 -0.030 -0.060 -0.030 -0.015
Step 8 0.008 0.022 0.011
Step 9 -0.004 -0.007 -0.004 -0.002
Step 10 0.001 0.003
Sum ofmoment
s0 -11.569 11.569 -10.186 10.186 -13.657
Numbers in grey are balaced moments; arrows ( / ) represent the carry-over of moment from one endto the other end of a member.
]edit] Result
Moments at joints determined by the moment distribution method
The conventional engineer's sign convention is used here, i.e. positive moments cause elongation atthe bottom part of a beam member.
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=138/14/2019 Uniformly Distributed Load of Intensity q
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For comparison purposes, the following are the results generated using a matrix method. Note that in theanalysis above, the iterative process was carried to >0.01 precision. The fact that the matrix analysis results
and the moment distribution analysis results match to 0.001 precision is mere coincidence.
Moments at joints determined by the matrix method
The complete shear and bending moment diagrams are as shown. Note that the moment distribution methodonly determines the moments at the joints. Developing complete bending moment diagrams require
additional calculations using the determined joint moments and internal section equilibrium.
SFD and BMD
Shear force diagram Bending moment diagram
Example
Example
The statically indeterminate beam shown in the figure is to be analysed.
Members AB, BC, CD have the same length.
Flexural rigidities are EI, 2EI, EI respectively.
Concentrated load of magnitude acts at a distance from the support A.
http://en.wikipedia.org/wiki/Matrix_methodhttp://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/wiki/Matrix_method8/14/2019 Uniformly Distributed Load of Intensity q
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Uniform load of intensity acts on BC.
Member CD is loaded at its midspan with a concentrated load of magnitude.
In the following calcuations, counterclockwise moments are positive.
]edit] Fixed-end moments
]edit] Distribution factors
The distribution factors of joints A and D are DAB = 1,DDC = 0.
]edit] Carryover factors
The carryover factors are , except for the carryover factor from D (fixed support) to C which is zero.
]edit] Moment distribution
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=128/14/2019 Uniformly Distributed Load of Intensity q
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Joint A Joint B Joint C Joint D
Distrib.factors
0 1 0.2727 0.7273 0.6667 0.3333 0 0
Fixed-end
moments
14.700 -6.300 8.333 -8.333 12.500 -12.500
Step 1 -14.700 -7.350
Step 2 1.450 3.867 1.934
Step 3 -2.034 -4.067 -2.034 -1.017
Step 4 0.555 1.479 0.739
Step 5 -0.246 -0.493 -0.246 -0.123
Step 6 0.067 0.179 0.090
Step 7 -0.030 -0.060 -0.030 -0.015
Step 8 0.008 0.022 0.011
Step 9 -0.004 -0.007 -0.004 -0.002
Step 10 0.001 0.003
Sum ofmoment
0 -11.569 11.569 -10.186 10.186 -13.657
http://en.wikipedia.org/wiki/File:MomentDistributionMethod2.jpg8/14/2019 Uniformly Distributed Load of Intensity q
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s
Numbers in grey are balaced moments; arrows ( / ) represent the carry-over of moment from one endto the other end of a member.
]edit] Result
Moments at joints determined by the moment distribution method
The conventional engineer's sign convention is used here, i.e. positive moments cause elongation atthe bottom part of a beam member.
For comparison purposes, the following are the results generated using a matrix method. Note that in the
analysis above, the iterative process was carried to >0.01 precision. The fact that the matrix analysis resultsand the moment distribution analysis results match to 0.001 precision is mere coincidence.
Moments at joints determined by the matrix method
The complete shear and bending moment diagrams are as shown. Note that the moment distribution methodonly determines the moments at the joints. Developing complete bending moment diagrams require
additional calculations using the determined joint moments and internal section equilibrium.
SFD and BMD
Shear force diagram Bending moment
Example
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_methodhttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_method8/14/2019 Uniformly Distributed Load of Intensity q
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Example
The statically indeterminate beam shown in the figure is to be analysed.
Members AB, BC, CD have the same length.
Flexural rigidities are EI, 2EI, EI respectively.
Concentrated load of magnitude acts at a distance from the support A.
Uniform load of intensity acts on BC.
Member CD is loaded at its midspan with a concentrated load of magnitude.
In the following calcuations, counterclockwise moments are positive.
]edit] Fixed-end moments
]edit] Distribution factors
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=108/14/2019 Uniformly Distributed Load of Intensity q
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The distribution factors of joints A and D are DAB = 1,DDC = 0.
]edit] Carryover factors
The carryover factors are , except for the carryover factor from D (fixed support) to C which is zero.
]edit] Moment distribution
Joint A Joint B Joint C Joint D
Distrib.factors
0 1 0.2727 0.7273 0.6667 0.3333 0 0
Fixed-end
moments
14.700 -6.300 8.333 -8.333 12.500 -12.500
Step 1 -14.700 -7.350
Step 2 1.450 3.867 1.934
Step 3 -2.034 -4.067 -2.034 -1.017
Step 4 0.555 1.479 0.739
Step 5 -0.246 -0.493 -0.246 -0.123
Step 6 0.067 0.179 0.090
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/wiki/File:MomentDistributionMethod2.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=128/14/2019 Uniformly Distributed Load of Intensity q
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Step 7 -0.030 -0.060 -0.030 -0.015
Step 8 0.008 0.022 0.011
Step 9 -0.004 -0.007 -0.004 -0.002
Step 10 0.001 0.003
Sum ofmoment
s0 -11.569 11.569 -10.186 10.186 -13.657
Numbers in grey are balaced moments; arrows ( / ) represent the carry-over of moment from one end
to the other end of a member.
]edit] Result
Moments at joints determined by the moment distribution method
The conventional engineer's sign convention is used here, i.e. positive moments cause elongation atthe bottom part of a beam member.
For comparison purposes, the following are the results generated using a matrix method. Note that in theanalysis above, the iterative process was carried to >0.01 precision. The fact that the matrix analysis results
and the moment distribution analysis results match to 0.001 precision is mere coincidence.
Moments at joints determined by the matrix method
The complete shear and bending moment diagrams are as shown. Note that the moment distribution methodonly determines the moments at the joints. Developing complete bending moment diagrams require
additional calculations using the determined joint moments and internal section equilibrium.
SFD and BMD
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_methodhttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_method8/14/2019 Uniformly Distributed Load of Intensity q
15/29
Shear force diagram Bending moment diagram
Example
Example
The statically indeterminate beam shown in the figure is to be analysed.
Members AB, BC, CD have the same length.
Flexural rigidities are EI, 2EI, EI respectively.
Concentrated load of magnitude acts at a distance from the support A.
Uniform load of intensity acts on BC.
Member CD is loaded at its midspan with a concentrated load of magnitude.
In the following calcuations, counterclockwise moments are positive.
]edit] Fixed-end moments
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=98/14/2019 Uniformly Distributed Load of Intensity q
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]edit] Distribution factors
The distribution factors of joints A and D are DAB = 1,DDC = 0.
]edit] Carryover factors
The carryover factors are , except for the carryover factor from D (fixed support) to C which is zero.
]edit] Moment distribution
Joint A Joint B Joint C Joint D
Distrib.factors
0 1 0.2727 0.7273 0.6667 0.3333 0 0
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/wiki/File:MomentDistributionMethod2.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=128/14/2019 Uniformly Distributed Load of Intensity q
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Fixed-end
moments
14.700 -6.300 8.333 -8.333 12.500 -12.500
Step 1 -14.700 -7.350
Step 2 1.450 3.867 1.934
Step 3 -2.034 -4.067 -2.034 -1.017
Step 4 0.555 1.479 0.739
Step 5 -0.246 -0.493 -0.246 -0.123
Step 6 0.067 0.179 0.090
Step 7 -0.030 -0.060 -0.030 -0.015
Step 8 0.008 0.022 0.011
Step 9 -0.004 -0.007 -0.004 -0.002
Step 10 0.001 0.003
Sum ofmoment
s
0 -11.569 11.569 -10.186 10.186 -13.657
Numbers in grey are balaced moments; arrows ( / ) represent the carry-over of moment from one endto the other end of a member.
]edit] Result
Moments at joints determined by the moment distribution method
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=138/14/2019 Uniformly Distributed Load of Intensity q
18/29
The conventional engineer's sign convention is used here, i.e. positive moments cause elongation atthe bottom part of a beam member.
For comparison purposes, the following are the results generated using a matrix method. Note that in theanalysis above, the iterative process was carried to >0.01 precision. The fact that the matrix analysis results
and the moment distribution analysis results match to 0.001 precision is mere coincidence.
Moments at joints determined by the matrix method
The complete shear and bending moment diagrams are as shown. Note that the moment distribution methodonly determines the moments at the joints. Developing complete bending moment diagrams require
additional calculations using the determined joint moments and internal section equilibrium.
SFD and BMD
Shear force diagram Bending moment diagram
Example
http://en.wikipedia.org/wiki/Matrix_methodhttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/wiki/Matrix_method8/14/2019 Uniformly Distributed Load of Intensity q
19/29
Example
The statically indeterminate beam shown in the figure is to be analysed.
Members AB, BC, CD have the same length.
Flexural rigidities are EI, 2EI, EI respectively.
Concentrated load of magnitude acts at a distance from the support A.
Uniform load of intensity acts on BC.
Member CD is loaded at its midspan with a concentrated load of magnitude.
In the following calcuations, counterclockwise moments are positive.
]edit] Fixed-end moments
]edit] Distribution factors
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=108/14/2019 Uniformly Distributed Load of Intensity q
20/29
The distribution factors of joints A and D are DAB = 1,DDC = 0.
]edit] Carryover factors
The carryover factors are , except for the carryover factor from D (fixed support) to C which is zero.
]edit] Moment distribution
Joint A Joint B Joint C Joint D
Distrib.factors
0 1 0.2727 0.7273 0.6667 0.3333 0 0
Fixed-end
moments
14.700 -6.300 8.333 -8.333 12.500 -12.500
Step 1 -14.700 -7.350
Step 2 1.450 3.867 1.934
Step 3 -2.034 -4.067 -2.034 -1.017
Step 4 0.555 1.479 0.739
Step 5 -0.246 -0.493 -0.246 -0.123
Step 6 0.067 0.179 0.090
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/wiki/File:MomentDistributionMethod2.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=128/14/2019 Uniformly Distributed Load of Intensity q
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Step 7 -0.030 -0.060 -0.030 -0.015
Step 8 0.008 0.022 0.011
Step 9 -0.004 -0.007 -0.004 -0.002
Step 10 0.001 0.003
Sum ofmoment
s0 -11.569 11.569 -10.186 10.186 -13.657
Numbers in grey are balaced moments; arrows ( / ) represent the carry-over of moment from one end
to the other end of a member.
]edit] Result
Moments at joints determined by the moment distribution method
The conventional engineer's sign convention is used here, i.e. positive moments cause elongation atthe bottom part of a beam member.
For comparison purposes, the following are the results generated using a matrix method. Note that in theanalysis above, the iterative process was carried to >0.01 precision. The fact that the matrix analysis results
and the moment distribution analysis results match to 0.001 precision is mere coincidence.
Moments at joints determined by the matrix method
The complete shear and bending moment diagrams are as shown. Note that the moment distribution methodonly determines the moments at the joints. Developing complete bending moment diagrams require
additional calculations using the determined joint moments and internal section equilibrium.
SFD and BMD
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_methodhttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_method8/14/2019 Uniformly Distributed Load of Intensity q
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Shear force diagram Bending moment diagram
Example
Example
The statically indeterminate beam shown in the figure is to be analysed.
Members AB, BC, CD have the same length.
Flexural rigidities are EI, 2EI, EI respectively.
Concentrated load of magnitude acts at a distance from the support A.
http://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpg8/14/2019 Uniformly Distributed Load of Intensity q
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Uniform load of intensity acts on BC.
Member CD is loaded at its midspan with a concentrated load of magnitude.
In the following calcuations, counterclockwise moments are positive.
]edit] Fixed-end moments
]edit] Distribution factors
The distribution factors of joints A and D are DAB = 1,DDC = 0.
]edit] Carryover factors
The carryover factors are , except for the carryover factor from D (fixed support) to C which is zero.
]edit] Moment distribution
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=128/14/2019 Uniformly Distributed Load of Intensity q
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Joint A Joint B Joint C Joint D
Distrib.factors
0 1 0.2727 0.7273 0.6667 0.3333 0 0
Fixed-end
moments
14.700 -6.300 8.333 -8.333 12.500 -12.500
Step 1 -14.700 -7.350
Step 2 1.450 3.867 1.934
Step 3 -2.034 -4.067 -2.034 -1.017
Step 4 0.555 1.479 0.739
Step 5 -0.246 -0.493 -0.246 -0.123
Step 6 0.067 0.179 0.090
Step 7 -0.030 -0.060 -0.030 -0.015
Step 8 0.008 0.022 0.011
Step 9 -0.004 -0.007 -0.004 -0.002
Step 10 0.001 0.003
Sum ofmoment
0 -11.569 11.569 -10.186 10.186 -13.657
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s
Numbers in grey are balaced moments; arrows ( / ) represent the carry-over of moment from one endto the other end of a member.
]edit] Result
Moments at joints determined by the moment distribution method
The conventional engineer's sign convention is used here, i.e. positive moments cause elongation atthe bottom part of a beam member.
For comparison purposes, the following are the results generated using a matrix method. Note that in the
analysis above, the iterative process was carried to >0.01 precision. The fact that the matrix analysis resultsand the moment distribution analysis results match to 0.001 precision is mere coincidence.
Moments at joints determined by the matrix method
The complete shear and bending moment diagrams are as shown. Note that the moment distribution methodonly determines the moments at the joints. Developing complete bending moment diagrams require
additional calculations using the determined joint moments and internal section equilibrium.
SFD and BMD
Shear force diagram Bending moment diagram
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_methodhttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_method8/14/2019 Uniformly Distributed Load of Intensity q
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Example
Example
The statically indeterminate beam shown in the figure is to be analysed.
Members AB, BC, CD have the same length.Flexural rigidities are EI, 2EI, EI respectively.
Concentrated load of magnitude acts at a distance from the support A.
Uniform load of intensity acts on BC.
Member CD is loaded at its midspan with a concentrated load of magnitude.
In the following calcuations, counterclockwise moments are positive.
]edit] Fixed-end moments
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethod.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=98/14/2019 Uniformly Distributed Load of Intensity q
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]edit] Distribution factors
The distribution factors of joints A and D are DAB = 1,DDC = 0.
]edit] Carryover factors
The carryover factors are , except for the carryover factor from D (fixed support) to C which is zero.
]edit] Moment distribution
Joint A Joint B Joint C Joint D
Distrib.factors
0 1 0.2727 0.7273 0.6667 0.3333 0 0
Fixed-end
moments
14.700 -6.300 8.333 -8.333 12.500 -12.500
Step 1 -14.700 -7.350
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/wiki/File:MomentDistributionMethod2.jpghttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=128/14/2019 Uniformly Distributed Load of Intensity q
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Step 2 1.450 3.867 1.934
Step 3 -2.034 -4.067 -2.034 -1.017
Step 4 0.555 1.479 0.739
Step 5 -0.246 -0.493 -0.246 -0.123
Step 6 0.067 0.179 0.090
Step 7 -0.030 -0.060 -0.030 -0.015
Step 8 0.008 0.022 0.011
Step 9 -0.004 -0.007 -0.004 -0.002
Step 10 0.001 0.003
Sum ofmoments
0 -11.569 11.569 -10.186 10.186 -13.657
Numbers in grey are balaced moments; arrows ( / ) represent the carry-over of moment from one endto the other end of a member.
]edit] Result
Moments at joints determined by the moment distribution method
The conventional engineer's sign convention is used here, i.e. positive moments cause elongation atthe bottom part of a beam member.
For comparison purposes, the following are the results generated using a matrix method. Note that in theanalysis above, the iterative process was carried to >0.01 precision. The fact that the matrix analysis results
and the moment distribution analysis results match to 0.001 precision is mere coincidence.
Moments at joints determined by the matrix method
http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_methodhttp://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Moment_distribution_method&action=edit§ion=13http://en.wikipedia.org/wiki/Matrix_method8/14/2019 Uniformly Distributed Load of Intensity q
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The complete shear and bending moment diagrams are as shown. Note that the moment distribution methodonly determines the moments at the joints. Developing complete bending moment diagrams require
additional calculations using the determined joint moments and internal section equilibrium.
SFD and BMD
Shear force diagram Bending moment diagram
http://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodBMD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpghttp://en.wikipedia.org/wiki/File:MomentDistributionMethodSFD.jpgTop Related