Which of the following statements is true with regard to the flexibility method of analysis? A) Difference of the area of moment and flexural rigidity B) The area of moment multiplied by the flexural rigidity C) Summation of the area of moment and flexural rigidity D) The area of moment divided by the flexural rigidity
Answer (1)
The flexibility method of analysis is a technique used in structural engineering to determine the internal forces and displacements in a system. This method uses the concept of flexibility, which is the inverse of stiffness, to analyze structures by considering their deflections.
In essence, the flexibility method involves working with the areas under the moment diagram and the flexural rigidity of the structure. The flexural rigidity is given by the product of the modulus of elasticity E and the moment of inertia I , represented as E I . This parameter quantifies the stiffness of a member in bending.
Regarding the specific question, we're asked to consider which statement accurately describes a relationship in the flexibility method. The true statement should reflect how the area under the moment diagram relates to the flexural rigidity E I . When using the flexibility method, the deflection Δ is typically calculated by dividing the integral of the moment area by the flexural rigidity, as it accounts for how much a structure will deflect under a certain loading.
Thus, the correct option is:
D) The area of moment divided by the flexural rigidity.
This implies that when calculating deflections using the flexibility method, the total influence of the applied loads (represented as the area under the moment graph) is considered relative to the structure's resistance to bending (the flexural rigidity). This division characterizes how flexibility affects the structural deflection.
