Theory of Structures. Takehome exam

Theory of structures

Academic year 2021/22

Ardito Raffaele
Prof. Homework

Theory of structures + stability of structures

February 11, 2022 (the solution should be delivered on the above date within 9:30 am, also in case of electronic submission)

Theory of structures problem T1

q = 15 kN/m

Data:
E = 30 GPa, l = 40 m, ν = 0.2, q = 15 kN/m

Section:
m m ℓ/4 = 10 ℓ/4 = 10 square = 40 m ℓ 125x125 cm

The problem is referred to a parabolic arch, whose geometry is depicted in the figure (hinge on the right). The material is homogeneous (E = 30 GPa, ν = 0.2) and the keystone section is square (side length 125 cm). The variation of the cross-section properties with respect to the arch inclination is A = A₀/cos α, I = I₀/cos α, where A₀ and I₀ are the keystone cross-section area and inertia, respectively. The external load is represented by a distributed force (q = 15 kN/m). The student should solve the problem by making use of symbolic variables and, finally, should obtain the numerical values of the reaction forces and the diagrams of shear, axial force, and bending moment.

Theory of structures + stability of structures

February 11, 2022 (the solution should be delivered on the above date within 9:30 am, also in case of electronic submission)

Theory of structures problem T2

Consider an axisymmetric annular plate, thickness h, fully clamped on the external edge and free on the interior edge. The applied pressure is uniformly distributed as pR/3 on the plate. The student should obtain the diagram of: displacement, rotation, shear force, and bending moments. Results must be obtained with both Kirchhoff and Mindlin model, providing specific comments on the variation with respect to the ratio h/R. (Assumption: E = 30 GPa, ν = 0.2)