UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
SAN3701: Structural Analysis
Project Assignment — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
SAN3701
Module Code:
Structural Analysis
Module Name:
Circular Reservoir Wall & Matrix Stiffness
Assignment Topic:
Method
Project 2026
Assignment Number:
2026
Due Date:
100
Total Marks:
Submitted in partial fulfilment of the requirements for SAN3701 — UNISA 2026
,UNISA | SAN3701 Structural Analysis: Project 2026
Question 1: Circular Reservoir Wall Analysis [50 Marks]
Circular reservoir walls are commonly idealised as vertical structural elements subjected to
hydrostatic pressure. Their behaviour is analysed using the theory of beams on elastic founda-
tions to determine shear forces, bending moments, and deflections along the wall height (Tim-
oshenko and Gere, 1972).
Question 1.1: Excel Program Development [20 Marks]
Develop a complete Excel spreadsheet program to analyse a circular reservoir
wall. The program must compute hydrostatic pressure distribution along the wall
height, as well as shear force and bending moment distributions. It should be a
general model adaptable to different input parameters and reservoir geometries.
All inputs, formulas, calculations, results, and graphs must be clearly presented
and organised within the spreadsheet.
Given Data
Table 1: Input Parameters
Parameter Value
Height of wall (H) 14 m
Wall thickness (t) 500 mm = 0.5 m
Reservoir diameter (D) 35 m
Poisson’s ratio (ν) 0
Base condition Hinged at base
Excel Spreadsheet Structure
The spreadsheet follows the structure illustrated in the format below, replicating the semi-
infinite beam analysis approach shown in the provided Excel output.
A1 1.1 EXCEL PROGRAM
INPUT SECTION — Damping Factor Calculations
Page 2 of 25
,UNISA | SAN3701 Structural Analysis: Project 2026
Parameter Value Unit
Load from the fluid (γw ) 9.81 kN/m3
Height of wall (H) 14 m
Tank diameter (D) 35 m
Thickness of wall (t) 0.5 m
Poisson’s ratio (ν) 0 —
Semi-infinite beam model
ANALYSIS FOR SEMI-INFINITE BEAM CASE
Step 1 — Calculation for µ
The characteristic length parameter µ for a cylindrical shell wall on an elastic founda-
tion is: r
4 3(1 − ν 2 )
µ=
R2 t2
With ν = 0, R = 17.5 m, t = 0.5 m:
s
√
r
3(1 − 0) 3
= 0.039157 = 0.44481 m−1
4 4 4
µ= =
(17.5)2 (0.5)2 76.5625
Symbol Value
µ= 0.44481422
µL = 6.22879909
Step 2 — Coefficient Equations from Shell Theory
From equation 5.3 SG, the deflection distribution is calculated from coefficients A1 and
A2 . These coefficients form part of equation 01 for the matrix formation.
Note: B1 = B2 = 0
Calculation for Coefficient Equation 01:
Coefficient Value Expression
Result
Coefficient A1 = 0
4EIµ4 v − q =
−137.2
Coefficient A2 = 1
From equation 5.4 SG, the slope distribution is calculated from coefficients A1 and A2 .
These coefficients form part of equation 02 for the matrix formation.
Page 3 of 25
,UNISA | SAN3701 Structural Analysis: Project 2026
Calculation for Coefficient Equation 02:
Coefficient Value Expression
Result
Coefficient A1 = 1
dq 1 dq
4EIµ3 dx − µ dx
=
22.027
Coefficient A2 = −1
Matrix Formation and Solution
−137.2 0 1 A −115.173
A1
= 1 ⇒ =
22.027 1 −1 A2 A2 −137.200
Hydrostatic Pressure Distribution Table
Hydrostatic pressure at any depth:
p(h) = γw h = 9.81h [kN/m2 ]
Table 2: Pressure, Shear Force and Bending Moment Distribution
Depth h (m) Pressure p (kN/m2 ) Shear V (kN/m) Moment M (kNm/m)
0
0.00 0.00 0.00 19.62
2
19.62 13.08 39.24 78.48
4
104.64 58.86 176.58 353.16
6 8
78.48 313.92 837.12 98.10
10
490.50 1635.00 117.72 706.32
12
2825.28 137.34 961.38 4486.44
14
Excel formulas used:
Page 4 of 25
, UNISA | SAN3701 Structural Analysis: Project 2026
• Pressure: =$B$6*A15
• Shear Force: =($B$6*A15ˆ2)/2
• Bending Moment: =($B$6*A15ˆ3)/6
Graphical Outputs — TikZ Representation
The three graphs below replicate the Excel chart outputs.
Graph 1: Hydrostatic Pressure Distribution
Hydrostatic Pressure p (kN/m2 )
140 p = γw h
120
100
80
60
40
20
0
0 2 4 6 8 10 12 14
Depth h (m)
Figure 1: Linear hydrostatic pressure distribution along wall height
Graph 2: Shear Force Distribution
1,000
γw h2
V = 2
Shear Force V (kN/m)
800
600
400
200
0
0 2 4 6 8 10 12 14
Depth h (m)
Figure 2: Parabolic shear force distribution along wall height
Page 5 of 25
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
SAN3701: Structural Analysis
Project Assignment — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
SAN3701
Module Code:
Structural Analysis
Module Name:
Circular Reservoir Wall & Matrix Stiffness
Assignment Topic:
Method
Project 2026
Assignment Number:
2026
Due Date:
100
Total Marks:
Submitted in partial fulfilment of the requirements for SAN3701 — UNISA 2026
,UNISA | SAN3701 Structural Analysis: Project 2026
Question 1: Circular Reservoir Wall Analysis [50 Marks]
Circular reservoir walls are commonly idealised as vertical structural elements subjected to
hydrostatic pressure. Their behaviour is analysed using the theory of beams on elastic founda-
tions to determine shear forces, bending moments, and deflections along the wall height (Tim-
oshenko and Gere, 1972).
Question 1.1: Excel Program Development [20 Marks]
Develop a complete Excel spreadsheet program to analyse a circular reservoir
wall. The program must compute hydrostatic pressure distribution along the wall
height, as well as shear force and bending moment distributions. It should be a
general model adaptable to different input parameters and reservoir geometries.
All inputs, formulas, calculations, results, and graphs must be clearly presented
and organised within the spreadsheet.
Given Data
Table 1: Input Parameters
Parameter Value
Height of wall (H) 14 m
Wall thickness (t) 500 mm = 0.5 m
Reservoir diameter (D) 35 m
Poisson’s ratio (ν) 0
Base condition Hinged at base
Excel Spreadsheet Structure
The spreadsheet follows the structure illustrated in the format below, replicating the semi-
infinite beam analysis approach shown in the provided Excel output.
A1 1.1 EXCEL PROGRAM
INPUT SECTION — Damping Factor Calculations
Page 2 of 25
,UNISA | SAN3701 Structural Analysis: Project 2026
Parameter Value Unit
Load from the fluid (γw ) 9.81 kN/m3
Height of wall (H) 14 m
Tank diameter (D) 35 m
Thickness of wall (t) 0.5 m
Poisson’s ratio (ν) 0 —
Semi-infinite beam model
ANALYSIS FOR SEMI-INFINITE BEAM CASE
Step 1 — Calculation for µ
The characteristic length parameter µ for a cylindrical shell wall on an elastic founda-
tion is: r
4 3(1 − ν 2 )
µ=
R2 t2
With ν = 0, R = 17.5 m, t = 0.5 m:
s
√
r
3(1 − 0) 3
= 0.039157 = 0.44481 m−1
4 4 4
µ= =
(17.5)2 (0.5)2 76.5625
Symbol Value
µ= 0.44481422
µL = 6.22879909
Step 2 — Coefficient Equations from Shell Theory
From equation 5.3 SG, the deflection distribution is calculated from coefficients A1 and
A2 . These coefficients form part of equation 01 for the matrix formation.
Note: B1 = B2 = 0
Calculation for Coefficient Equation 01:
Coefficient Value Expression
Result
Coefficient A1 = 0
4EIµ4 v − q =
−137.2
Coefficient A2 = 1
From equation 5.4 SG, the slope distribution is calculated from coefficients A1 and A2 .
These coefficients form part of equation 02 for the matrix formation.
Page 3 of 25
,UNISA | SAN3701 Structural Analysis: Project 2026
Calculation for Coefficient Equation 02:
Coefficient Value Expression
Result
Coefficient A1 = 1
dq 1 dq
4EIµ3 dx − µ dx
=
22.027
Coefficient A2 = −1
Matrix Formation and Solution
−137.2 0 1 A −115.173
A1
= 1 ⇒ =
22.027 1 −1 A2 A2 −137.200
Hydrostatic Pressure Distribution Table
Hydrostatic pressure at any depth:
p(h) = γw h = 9.81h [kN/m2 ]
Table 2: Pressure, Shear Force and Bending Moment Distribution
Depth h (m) Pressure p (kN/m2 ) Shear V (kN/m) Moment M (kNm/m)
0
0.00 0.00 0.00 19.62
2
19.62 13.08 39.24 78.48
4
104.64 58.86 176.58 353.16
6 8
78.48 313.92 837.12 98.10
10
490.50 1635.00 117.72 706.32
12
2825.28 137.34 961.38 4486.44
14
Excel formulas used:
Page 4 of 25
, UNISA | SAN3701 Structural Analysis: Project 2026
• Pressure: =$B$6*A15
• Shear Force: =($B$6*A15ˆ2)/2
• Bending Moment: =($B$6*A15ˆ3)/6
Graphical Outputs — TikZ Representation
The three graphs below replicate the Excel chart outputs.
Graph 1: Hydrostatic Pressure Distribution
Hydrostatic Pressure p (kN/m2 )
140 p = γw h
120
100
80
60
40
20
0
0 2 4 6 8 10 12 14
Depth h (m)
Figure 1: Linear hydrostatic pressure distribution along wall height
Graph 2: Shear Force Distribution
1,000
γw h2
V = 2
Shear Force V (kN/m)
800
600
400
200
0
0 2 4 6 8 10 12 14
Depth h (m)
Figure 2: Parabolic shear force distribution along wall height
Page 5 of 25
