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Theorem of three moments

Index Theorem of three moments

In civil engineering and structural analysis Clapeyron's theorem of three moments is a relationship among the bending moments at three consecutive supports of a horizontal beam. [1]

12 relations: Beam (structure), Bending moment, Benoît Paul Émile Clapeyron, Christian Otto Mohr, Civil engineering, Compression (physics), Deflection (physics), Elasticity (physics), Settlement (structural), Shear and moment diagram, Slope, Structural analysis.

Beam (structure)

A beam is a structural element that primarily resists loads applied laterally to the beam's axis.

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Bending moment

A bending moment is the reaction induced in a structural element when an external force or moment is applied to the element causing the element to bend.

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Benoît Paul Émile Clapeyron

Benoît Paul Émile Clapeyron (26 February 1799 – 28 January 1864) was a French engineer and physicist, one of the founders of thermodynamics.

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Christian Otto Mohr

Christian Otto Mohr (8 October 1835 – 2 October 1918) was a German civil engineer.

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Civil engineering

Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works such as roads, bridges, canals, dams, airports, sewerage systems, pipelines, and railways.

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Compression (physics)

In mechanics, compression is the application of balanced inward ("pushing") forces to different points on a material or structure, that is, forces with no net sum or torque directed so as to reduce its size in one or more directions.

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Deflection (physics)

A deflection, in physics, refers to the change in an object's velocity as a consequence of contact (collision) with a surface or the influence of a field.

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Elasticity (physics)

In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.

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Settlement (structural)

Settlement in a structure refers to the distortion or disruption of parts of a building due to.

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Shear and moment diagram

Shear and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear force and bending moment at a given point of a structural element such as a beam.

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Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

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Structural analysis

Structural analysis is the determination of the effects of loads on physical structures and their components.

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Three moment theorem, Three moment theorem and simple examples.

References

[1] https://en.wikipedia.org/wiki/Theorem_of_three_moments

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