Ch12--Deflection

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

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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
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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:
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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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Macaulay Functions: Distributed Loading: n=0: n=1:
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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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Ch12--Deflection - Can use superposition for trapezoidal...

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