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254:
The vertical deviation of a point A on an elastic curve with respect to the tangent which is extended from another point B equals the moment of the area under the M/EI diagram between those two points (A and B). This moment is computed about point A where the deviation from B to A is to be
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The deviation at any point on the elastic curve is positive if the point lies above the tangent, negative if the point is below the tangent; we measured it from left tangent, if θ is counterclockwise direction, the change in slope is positive, negative if θ is clockwise direction.
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in 1873. This method is advantageous when we solve problems involving beams, especially for those subjected to a series of concentrated loadings or having segments with different
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The following procedure provides a method that may be used to determine the displacement and slope at a point on the elastic curve of a beam using the moment-area theorem.
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If there are only concentrated loads on the structure, the problem will be easy to draw M/EI diagram which will results a series of triangular shapes.
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The change in slope between any two points on the elastic curve equals the area of the M/EI (moment) diagram between these two points.
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If there are mixed with distributed loads and concentrated, the moment diagram (M/EI) will results parabolic curves, cubic, etc.
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is an engineering tool to derive the slope, rotation and deflection of beams and frames. This theorem was developed by
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Find the rotations, change of slopes and deflections of the structure by using the geometric mathematics.
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Determine the reaction forces of a structure and draw the M/EI diagram of the structure.
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Then, assume and draw the deflection shape of the structure by looking at M/EI diagram.
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122:{\displaystyle \theta _{A/B}={\int _{A}}^{B}\left({\frac {M}{EI}}\right)dx}
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428:= deviation of tangent at point A with respect to the tangent at point B
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333:{\displaystyle t_{A/B}={\int _{A}}^{B}{\frac {M}{EI}}x\;dx}
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537:(8th ed.). Boston: Prentice Hall. p. 317.
512:(8th ed.). Boston: Prentice Hall. p. 316.
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217:= change in slope between points A and B
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558:Moment-Area Method Beam Deflection
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853:
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840:Timoshenko–Ehrenfest beam theory
1:
456:= points on the elastic curve
245:= points on the elastic curve
210:{\displaystyle \theta _{A/B}}
825:Euler–Bernoulli beam theory
24:and later stated namely by
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573:Area-Moment Method. (n.d.)
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615:
702:Theorem of three moments
697:Shear and moment diagram
533:Hibbeler, R. C. (2012).
508:Hibbeler, R. C. (2012).
461:Rule of sign convention
421:{\displaystyle t_{A/B}}
609:Structural engineering
470:Procedure for analysis
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667:Conjugate beam method
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662:Castigliano's method
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884:Structural analysis
830:Mohr–Coulomb theory
712:Structural elements
687:Moment-area theorem
535:Structural analysis
510:Structural analysis
449:{\displaystyle A,B}
391:= flexural rigidity
238:{\displaystyle A,B}
180:= flexural rigidity
26:Charles Ezra Greene
18:moment-area theorem
797:Structural support
756:Compression member
677:Flexibility method
636:Duhamel's integral
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384:{\displaystyle EI}
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173:{\displaystyle EI}
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30:moments of inertia
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682:Macaulay's method
544:978-0-13-257053-4
519:978-0-13-257053-4
359:{\displaystyle M}
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148:{\displaystyle M}
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879:Moment (physics)
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692:Stiffness method
629:Dynamic analysis
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641:Modal analysis
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567:External links
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835:Plate theory
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255:determined.
253:
131:
39:
17:
15:
873:Categories
495:References
290:∫
250:Theorem 2
191:θ
75:∫
52:θ
36:Theorem 1
858:Category
818:Theories
366:= moment
155:= moment
805:Bracket
620:History
343:where,
132:where,
737:Lintel
732:I-beam
541:
516:
761:Strut
782:Arch
749:Span
727:Beam
539:ISBN
514:ISBN
22:Mohr
16:The
766:Tie
672:FEM
875::
32:.
601:e
594:t
587:v
547:.
522:.
444:B
441:,
438:A
414:B
410:/
406:A
402:t
379:I
376:E
354:M
328:x
325:d
321:x
315:I
312:E
308:M
301:B
294:A
284:=
279:B
275:/
271:A
267:t
233:B
230:,
227:A
203:B
199:/
195:A
168:I
165:E
143:M
117:x
114:d
110:)
104:I
101:E
97:M
92:(
86:B
79:A
69:=
64:B
60:/
56:A
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.