2014년도 2학기 항공기 구조역학 기말고사

(25 points) A beam with the closed semi-circular thin-walled cross-section shown in figure is subjected to a vertical shear force, [eqn: V _{3}], with a line action passing through the section’s vertical web.

(1) Determine the location of the section’s shear ceter. (10 points)

(2) Determine the shear flow distribution due to shearing and torque. (15 points)

Figure 1. Thin-walled closed semi-circular section

(25 points) A root pivoted beam carries a concentrated mid-span load, [eqn: P]. and is supported by a three-bar truss, as shown in figure.

(1) Combine the unit load method for beams and trusses to determine the midpoint deflection for the beam. (15 points)

(2) Determine the vertical deflection of point [eqn: A]. (10 points)

Figure 2. Pivoted beam supported by three bar truss.

(25 points) A cantilevered beam with a mid-span support carries a uniformly distributed load, [eqn: p _{0}], as shown in the figure.

(1) Using the principle of least work, determine the reaction forces. (15 points)

(2) Find the bending moment distribution in the beam. (10 points)

Figure 3. the cantilevered beam.

(25 points) The uniform circular beam with centerline radius [eqn: R] shown in the figure is clamped at point [eqn: A] and constrained to move in the only in the vertical direction at point [eqn: B], where it is also subjected to an applied vertical load, [eqn: P].

(1) Find the displacement, [eqn: TRIANGLE], in the direction of the applied load. (15 points)

(2) Find the horizontal reaction [eqn: Q] at point [eqn: B]. (25 points)

(3) find the equivalent spring constant [eqn: k=P/ TRIANGLE].

Assume that only bending deformations are significant, i.e., ignore axial deformation.

Figure 4. Uniform spring under a vertical load, [eqn: P].