CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers
Job No.
Sheet No.
jXXX
Rev. 1
Member/Location Drg. Ref. Wall BS8110 v2015.01.xlsx Job Title Structure Design - Reinforced Concrete Arch (Dome), Ring Made by Structure Design - RC Arch (Dome), Ring Wall 19-08-15 Chd. XX Date
Arch Note it is assumed that the base of the arch is pinned; Arch rise, r
5.000 m
Arch span, L
31.000 m 1.000 m
Arch width, b Arch thickness, t
125 mm
Arch loading, ω = (DL+SDL+LL).b
4.50 kN/m
dead load, DL = 24kN/m3.t superimposed dead load, SDL
3.00 kPa 0.00 kPa 1.50 kPa
live load, LL 2
2
26.525 m
Arch radius, R = [(D/2) +r ]/(2r) Arch cosine angle, c = cosθ = (R-r)/R
0.811
Arch sine angle, s = sinθ = sin(acos(cosθ))
0.584
Arch angle, θ = acos(cosθ)
0.624 radians
Arch angle, θ = acos(cosθ)
35.8 degrees
Arch (unfactored) axial (comp) thrust, T = √(H2+V2)
133 kN
Arch (unfactored) axial (comp) thrust (small r/L for cosθ≈1), T = √(H2+V2)
129 kN
2
2
2
Arch (unfactored) horizontal thrust, H = -ω.R.[2θ sc-0.5θ-4.5sc+5θc ]/[2θc + 2
Arch (unfactored) horizontal thrust (small r/L for cosθ≈1), H = ω.L /(8r)
110 kN 108 kN
Arch (unfactored) vertical thrust, V = θ.R.ω
74 kN
Arch (unfactored) vertical thrust (small r/L for cosθ≈1), V = ω.L/2
70 kN
Job No.
CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers
jXXX
Sheet No.
Rev. 2
Member/Location Drg. Ref. Wall BS8110 v2015.01.xlsx Job Title Structure Design - Reinforced Concrete Arch (Dome), Ring Made by Structure Design - RC Arch (Dome), Ring Wall 19-08-15 Chd. XX Date
Dome Note it is assumed that the base of the arch is pinned; Note that the benefit of the dome to the arch is that whereas the 2D arch requires external thrust abutments or an internal tie that cut through the clear span, the dome utilizes the hoop tension ring within the dome structure to perform this function, thus alleviating the need for both the external abutment and the internal obstructive tie element;
5.000 m
Dome rise, r (usually D/6 to D/5) Dome span, D
31.000 m
Dome thickness, t
125 mm
Dome loading, ω = DL+SDL+LL
4.50 kPa
dead load, DL = 24kN/m3.t superimposed dead load, SDL
3.00 kPa 0.00 kPa
live load, LL
1.50 kPa
Dome radius, R = [(D/2)2+r2]/(2r) Dome cosine angle, cosθ = (R-r)/R
26.525 m 0.811
Dome angle, θ = acos(cosθ)
35.8 degrees
Note ensure θ ≤ 51.8 ° for no tensile circumferential force; 100 N/mm2
Allowable steel (tens) stress, fs,allow
Note that the allowable steel stress may be much higher (to 0.80fy) than that recommended in the table 3.1 if a full crack width calculation is undertaken; Dome (unfactored) meridional (comp) thrust, T1 = ωR/(1+cosθ)
66 kN/m
Dome (unfactored) circumferential (comp) force, T2 = ωR.(cosθ-1/(1+cosθ))
31 kN/m
Dome circumferential steel
φ
10
mm
s
150 mm
2 1 side(s) 524 mm2/m Dome circumferential steel area, As = sides.πφ /4/s Dome circumferential steel area percentage, ρ (>=0.40% or >=0.45%, <=4.0%) 0.42% Dome (unfactored) circumferential steel (tens) stress, σT2 = -T2 / As 0 N/mm2 Allowable steel (tens) stress utilisation, σT2 / fs,allow 0%
Dome (unfactored) horizontal thrust, H = T1.cosθ
829 kN
Dome ring beam
b
600
mm
h
Dome ring beam steel
φ
25
mm
no.
Dome ring beam steel area, As = no.πφ2/4 Dome ring beam steel area percentage, ρ (>=0.45%, <=4.0%) Dome ring beam (unfactored) steel (tens) stress, σTh = Th / As
900 mm 18 number(s) 8836 mm2 1.64% 94 N/mm2 94%
Note the dome horizontal force may be resisted by an external abutment resisting thrust H or the ring beam resisting hoop tension T h ; Dome (unfactored) vertical thrust, V = T1.sinθ
OK
53 kN/m
Dome ring beam (unfactored) hoop (tens) force, Th = H.D/2
Allowable steel (tens) stress utilisation, σTh / fs,allow
OK
39 kN/m
OK OK
CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers
Job No.
Sheet No.
jXXX
Rev. 3
Member/Location Drg. Ref. Wall BS8110 v2015.01.xlsx Job Title Structure Design - Reinforced Concrete Arch (Dome), Ring Made by Structure Design - RC Arch (Dome), Ring Wall 19-08-15 Chd. XX Date
Ring Wall
Ring wall height, H
5.000 m
Ring wall internal diameter, D Ring wall top thickness, t1
31.000 m 300 mm
Ring wall bottom thickness, t2
400 mm
Ring wall internal radius, r = D/2
15.500 m
Ring wall volume capacity (cubic metre), V = π.H.D2/4 2
Ring wall volume capacity (gallon), V = π.H.D /4
3774 m3 830128 gallon
Fluid density, γ
10.0 kN/m3
Thin-walled assumption r/t1 ≥ 5.0
51.7
OK
Thin-walled assumption r/t2 ≥ 5.0
38.8
OK
Allowable steel (tens) stress, fs,allow
100 N/mm2
Note that the allowable steel stress may be much higher (to 0.80fy) than that recommended in the table 3.1 if a full crack width calculation is undertaken;
Method of analysis Coefficients for "two way spanning hoop tension and vertical plane moment" method H2/Dt External cover to wall, cover Characteristic strength of concrete, fcu
2.3 50 mm 35 N/mm2
Job No.
CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers
Sheet No.
jXXX
Rev. 4
Member/Location Drg. Ref. Wall BS8110 v2015.01.xlsx Job Title Structure Design - Reinforced Concrete Arch (Dome), Ring Made by Structure Design - RC Arch (Dome), Ring Wall 19-08-15 Chd. XX Date
s (mm) As (mm2/m) ρw (%) 115 3497 1.17%
2
h (m)
t (mm)
p (kPa)
ktens
Fh (kN/m)
φ (mm)
0.000
300
0
0.205
159
16
0.417
308
4
0.260
202
16
115
3497
1.13%
58
0.833
317
8
0.321
249
16
115
3497
1.10%
71
1.250
325
13
0.347
269
16
115
3497
1.08%
77
1.667
333
17
0.373
289
16
115
3497
1.05%
83
2.083
342
21
0.411
319
16
115
3497
1.02%
91
2.500
350
25
0.434
336
16
115
3497
1.00%
96
2.917
358
29
0.419
325
16
115
3497
0.98%
93
3.333
367
33
0.394
305
16
115
3497
0.95%
87
3.750
375
38
0.369
286
16
115
3497
0.93%
82
4.167
383
42
0.280
217
16
115
3497
0.91%
62
4.583
392
46
0.151
117
16
115
3497
0.89%
33
5.000
400
50
0.151
117
16
115
3497
0.87%
33
fs (N/mm ) 45
Note ring wall pressure, p = γ .h; Note (unfactored) hoop (tens) force (thin-walled), F h = p.r or k tens . γ .h.r; Note steel area, A s = 2 πφ 2 /4/s; Note steel area percentage, ρ w = A s / 1000.t; Note (unfactored) steel (tens) stress, f s = F h / A s ; Maximum steel area percentage, ρwmax (<=4.0%)
1.17%
Minimum steel area percentage, ρwmin (>=0.45%)
0.87%
Maximum steel (tens) stress, MAX (fs)
OK OK
96 N/mm
Allowable steel (tens) stress utilisation, MAX (fs) / fs,allow Mv (kN/m) φv (mm)
2
96%
OK
s (mm) Asv (mm2/m) ρwv (%) fs (N/mm2) 115 983 0.33% 5
h (m)
t (mm)
kmom
0.000
300
0.0009
1
12
0.417
308
0.0009
1
12
115
983
0.32%
5
0.833
317
0.0033
4
12
115
983
0.31%
17
1.250
325
0.0053
7
12
115
983
0.30%
26
1.667
333
0.0073
9
12
115
983
0.30%
35
2.083
342
0.0114
14
12
115
983
0.29%
53
2.500
350
0.0158
20
12
115
983
0.28%
72
2.917
358
0.0199
25
12
115
983
0.27%
88
3.333
367
0.0219
27
12
115
983
0.27%
94
3.750
375
0.0212
27
12
115
983
0.26%
89
4.167
383
0.0205
26
12
115
983
0.26%
84
4.583
392
0.0145
18
12
115
983
0.25%
58
5.000
400
0.0000
0
12
115
983
0.25%
0
Note ring wall pressure, p = γ .h; 3
Note (unfactored) vertical plane moment, M v = 0.0 or k mom . γ .h ; Note steel area, A sv = (2 or 1). πφ v 2 /4/s; Note steel area percentage, ρ wv = A sv / 1000.t; Note (unfactored) steel (tens) stress, f s = M v /(z.A sv ) where z = d.MIN[0.95,0.5+(0.25-K/0.9) 0.5 ], d = t-cover- φ v /2 and K = M v /(1000.d 2 .f cu ); Maximum steel area percentage, ρwvmax (<=4.0%)
0.33%
OK
Minimum vertical steel area percentage, ρwvmin (>=0.25% or >=0.13%)
0.25%
OK
Maximum steel (tens) stress, MAX (fs) Allowable steel (tens) stress utilisation, MAX (fs) / fs,allow
94 N/mm2 94%
OK
CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers
Job No. jXXX
Sheet No.
Rev. 5
Member/Location Drg. Ref. Wall BS8110 v2015.01.xlsx Job Title Structure Design - Reinforced Concrete Arch (Dome), Ring Made by Structure Design - RC Arch (Dome), Ring Wall 19-08-15 Chd. XX Date
