Ch12--Deflection

# Ch12--Deflection - • Can use superposition for...

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Deflection of Beams and  Shafts Chapter 12

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Important Concepts Slope and Displacement:   ;     ; Singularity Functions Statically Indeterminate Beams
Slope and Displacement A Moment acting on a beam causes rotation  and deflection such that    where  ρ  is  the radius of curvature  Assuming dv/dx is small, Via substation and integration:

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Conditions Sign Convention: Continuity:
If you do not use discontinuous  functions Need to determine shear and moment functions  for each region of the beam between  discontinuous loadings The continuity conditions must be maintained  across discontinuities

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Unformatted text preview: • Can use superposition for trapezoidal loading Singularity Function • Concentrated Load P: • Couple Moment M : Integrating • Integration of Macaulay functions follows same rules as ordinary functions: • Integration of Singularity functions follows rules of operational calculus: Statically Indeterminate —Number of Unknowns exceeds number of available equations • Additional unneeded supports for equilibrium are called Redundants • # of Redundants is called Degree of indeterminacy • To determine reactions: – 1. Identify redundant reactions – 2. Express the moment in terms of the unknown redundants – 3. Integrate twice then determine constants of integration and all reactions via boundary,...
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## This note was uploaded on 04/14/2008 for the course E MCH 213 taught by Professor Lewisdean during the Spring '08 term at Penn State.

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Ch12--Deflection - • Can use superposition for...

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