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

th

(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, = 6 m

f

ν = 0.2

l = 40 m

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

section on the right). The material is homogeneous (E = 30 GPa, ν = 0.2)

left, clamped-in

the

and the keystone section is square (side length 125 cm). The variation of the cross-section

/cos α, I = I /cos α, where A and I are

properties with respect to the arch inclination is A = A

0 0 0 0

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

th

(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,

p thickness fully clamped on the external

h,

edge and free on the interior edge. The

applied pressure is uniformly distributed

p

R/3 on the plate. The student should obtain the

R diagram of: displacement, rotation,

shear force. Results must be obtained with both Kirchhoff and

bending moments,

Mindlin model, providing specific comments on the variation with respect to the ratio h/R.

(Assumption: E=30 GPa, ν=0.2)