You are appointed to calculate the forces and moments in a w

You are appointed to calculate the forces and moments in a wall of a circular reservoir. Using the theory for beams on elastic foundations design a reservoir that is fixed against translation and rotation at the base as well as hinged at the base.
Solve the following problem with your program and by means of hand calculations:
(a) Height of wall = 10m, thickness of wall = 450mm, diameter of reservoir = 30m, Poisson’s ratio = 0 and fixed against translation but free to rotate at the base.
(b) Height of wall = 10m, thickness of wall = 450mm, diameter of reservoir = 30m, Poisson’s ratio = 0 and hinged at the base.

Solution

Assuming Tank resting on ground,

H = 10 m, D = 30 m

1) Case Walls restrained at Base

In this case wall will resist presssure of water partly by cantilever action and partly by hoop action.

it is assumed that cantilever effect of wall will be present for heaight equal to one fourth of height of tank, let it = h,

this cantilever will be subjected to triangular water pressure and it will act at h/3.

h = H/4 = 10/4 = 2.5 m

Maximum cantilever bending moment (BM),

water pressure at bottom = w x H = 9810 x 10 = 98100 N / m^2

BM = (1/2) x 98100 x 2.5 x (2.5 /3) = 102187.5 N-m

Max. Hoop tension per unit height = w x ( H-h) D / 2 = 9810 x (10 - 2.5) x 30 / 2

= 1103625 N

2) Wall Flexible at base

Wall of such tanks are designed as vertical cylinders subjected to water pressure.

hoop tension per meter height = T = wh x D / 2

consider 1m height of wall , pressure intensity corresponding to center of bottom 1 m height of wall be p

p = w x h = 9810 x ( 9 + 0.5 ) = 93195 N / m^2

Hoop tension = T = p x D/2 = 1397925 N = 1397. 9 KN