Theory of structures
Academic Year 2021/22
Ardito Raffaele
Homework
Student:
Theory of structures problem T1
The structure is composed of a single beam with two torsional simple supports. The cross-section is depicted in the figure, and the building material is steel (Young's modulus 210000 MPa, Poisson's ratio 0.3). The beam length is 4 m; the distributed moment is linearly variable from 0 (left end section) to 0.5 kNm/m (right end section). The student should solve the structure in the non-uniform torsion regime, finally obtaining the diagrams of rotation, Wagner-Vlasov, and Saint Venant torsional moment, bimoment.
- h = 120 mm
- b1 = 5 mm
- b2 = 6 mm
- d = 110 mm
Problem T2
Consider a sandwich plate with three isotropic layers, characterized by the elastic parameters denoted in the figure. By assuming the Kirchhoff model, the student should write down the generalized constitutive model for the bending problem and the relevant governing equation (counterpart of the Germain-Lagrange equation). Finally, the student should apply a Navier-like solution to compute the maximum displacement for a square plate, with a side equal to 6 m, simply supported on the whole boundary and subject to a uniform pressure of 0.8 kPa. A critical comparison should be carried out with respect to the case E1 = E2 = 200 GPa (homogeneous plate).
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![Theory of Structures. Takehome exam]()
Theory of Structures. Takehome exam
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![Takehome Theory of structures]()
Takehome Theory of structures
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![Takehome Theory of structures]()
Takehome Theory of structures
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![Takehome Theory of structures]()
Takehome Theory of structures
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