Q:

3.1 (a) Consider a single, uniform, simply supported beam whose length is L and whose stiffness coefficient is EI. The beam is loaded by a single, concentrated, lateral force of magnitude F ₀ placed at the center of the beam span. Using just one beam bending finite element for the left half of the beam, and another for the right half-span, determine the lateral deflection at midspan.

(b) Redo the previous problem, but this time let the boundary conditions be clamped supports at both beam ends. Note the percentage change in deflection between these two extremes of beam boundary condition modeling.

Q:

3.2 (a) As a variation on the above problem, consider the beam-spring structure shown in Figure 3.12(a), where the sole loading is an externally applied moment of magnitude M ₀ at midspan. Using the DOF shown in Figure 3.12(b), write the full seven-DOF { Q} = [ K]{ q} equation for this structural system and loading. Just use the generic symbol R to represent the support reactions. Then apply the boundary conditions to obtain the two DOF matrix equation to be solved for the unknown DOF.

Figure 3.12: Exercise 3.2(a): (a) Math model. (b) FEM model.

(b) Consider the cantilevered beam structure that is shown in Figure 3.13. The structure is loaded by a tip force whose three components are F ₁, F ₂, and F ₃. The beam...