The wall thickness of a 180 m long, circular reinforced concrete chimney with an outer diameter of 15 m and an inner diameter of 13 m at the base section is variable along the height of the chimney with the function r. In the case that a dynamic effect of 25% of the response spectrum given in the figure is applied within the framework of the assumptions that the structure is fixedly supported from the lower end to the ground, the damping ratio is 5% and the shape function suitable for the building behavior is u(x)=(3x²/2L²) - (x³/2L³): a) Find the natural angular frequency and period of the structure. b) Calculate the maximum shear force and bending moment that will occur at the base of the structure. c) Calculate the maximum compressive stress that will occur at the base of the structure. (The self-weight of the chimney will be included in the stress calculation.)

Consider the unit volume weight of the chimney material as 23 kN/m3 and the modulus of elasticity as 30000 MPa. (Circle area A=r², Circle moment of inertia: I=r⁴/4, r: radius, g=9.81m/s²)

H13 m a-a kesiti +Ar 113ml a a X X Ar= 0.25 +0.75(1- 180 m 15 m - moterims 27 co) (O) la- T genlik .. MON fa un u(t) = (0) cos wil www.sin wat p(t) sino(t - )]dt mon Jo H13 m a-a kesiti +Ar 113ml a a X X Ar= 0.25 +0.75(1- 180 m 15 m - moterims 27 co) (O) la- T genlik .. MON fa un u(t) = (0) cos wil www.sin wat p(t) sino(t - )]dt mon Jo