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D'Alembert's principle allows a dynamic problem to be written as an equilibrium problem by introducing

  • A.a static load equal to the weight of the structure itself
  • B.a fictitious inertia force opposing the acceleration
  • C.an additional stiffness term proportional to displacement
  • D.a viscous damper at every degree of freedom in the model

Answer: B

Correct answer: a fictitious inertia force opposing the acceleration

D'Alembert's principle adds an inertia force of magnitude \( m\ddot{u} \) acting opposite to the acceleration, after which the system may be treated as though it were in static equilibrium.

The advantage is method rather than physics: the whole apparatus of statics - free bodies, equilibrium equations, virtual work - becomes available for a dynamic problem. The force is fictitious in the sense that no external agent applies it; it is the mass's resistance to acceleration written as though it were a load.

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