CONSULTING Engineering Calculation Sheet E N G I N … No. Sheet No. Rev. Job Title XX Ring Wall...

Job No. Sheet No. Rev.

Job Title

XX

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

Arch width, b 1.000 m

Arch thickness, t 125 mm

Arch loading, ω = (DL+SDL+LL).b 4.50 kN/m

dead load, DL = 24kN/m3.t 3.00 kPa

superimposed dead load, SDL 0.00 kPa

live load, LL 1.50 kPa

Arch radius, R = [(D/2)2+r

2]/(2r) 26.525 m

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+V

2) 133 kN

Arch (unfactored) axial (comp) thrust (small r/L for cosθ≈1), T = √(H2+V

2) 129 kN

Arch (unfactored) horizontal thrust, H = -ω.R.[2θ2sc-0.5θ-4.5sc+5θc2]/[2θc2+ 110 kN

Arch (unfactored) horizontal thrust (small r/L for cosθ≈1), H = ω.L2/(8r) 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

CONSULTING

E N G I N E E R S

Engineering Calculation Sheet

Consulting Engineers jXXX 1

Structure Design - Reinforced Concrete Arch (Dome), Ring Wall BS8110 v2015.01.xlsx

Structure Design - RC Arch (Dome), Ring Wall 19-08-15Made by Date Chd.

Drg. Ref.

Member/Location


Job Title

XX

Dome

Note it is assumed that the base of the arch is pinned;

Dome rise, r (usually D/6 to D/5) 5.000 m

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 3.00 kPa

superimposed dead load, SDL 0.00 kPa

live load, LL 1.50 kPa

Dome radius, R = [(D/2)2+r

2]/(2r) 26.525 m

Dome cosine angle, cosθ = (R-r)/R 0.811

Dome angle, θ = acos(cosθ) 35.8 degrees

Note ensure θ ≤ 51.8 ° for no tensile circumferential force;

Allowable steel (tens) stress, fs,allow 100 N/mm2

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

Dome circumferential steel area, As = sides.πφ2/4/s 1 side(s) 524 mm2/m

Dome circumferential steel area percentage, ρ (>=0.40% or >=0.45%, <=4.0%)0.42% OK

Dome (unfactored) circumferential steel (tens) stress, σT2 = -T2 / As 0 N/mm2

Allowable steel (tens) stress utilisation, σT2 / fs,allow 0% OK

Dome (unfactored) horizontal thrust, H = T1.cosθ 53 kN/m

Dome ring beam (unfactored) hoop (tens) force, Th = H.D/2 829 kN

Dome ring beam b 600 mm h 900 mm

Dome ring beam steel φ 25 mm no. 18 number(s)

Dome ring beam steel area, As = no.πφ2/4 8836 mm2

Dome ring beam steel area percentage, ρ (>=0.45%, <=4.0%) 1.64% OK

Dome ring beam (unfactored) steel (tens) stress, σTh = Th / As 94 N/mm2

Allowable steel (tens) stress utilisation, σTh / fs,allow 94% OK

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 39 kN/m

CONSULTING

E N G I N E E R S





Drg. Ref.

Member/Location

Note that the allowable steel stress may be

much higher (to 0.80fy) than that

recommended in the table 3.1 if a full crackwidth calculation is undertaken;

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 ringwithin the dome structure to perform this function, thus alleviating

the need for both the external abutment and the internal

obstructive tie element;


Job Title

XX

Ring Wall

Ring wall height, H 5.000 m

Ring wall internal diameter, D 31.000 m

Ring wall top thickness, t1 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 3774 m

3

Ring wall volume capacity (gallon), V = π.H.D2/4 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

Method of analysis

Coefficients for "two way spanning hoop tension and vertical plane moment" method

H2/Dt 2.3

External cover to wall, cover 50 mm

Characteristic strength of concrete, fcu 35 N/mm2



CONSULTING

E N G I N E E R S


19-08-15Structure Design - RC Arch (Dome), Ring Wall Made by Date Chd.

Drg. Ref.

Member/Location

Note that the allowable steel stress may be

much higher (to 0.80fy) than that

recommended in the table 3.1 if a full crackwidth calculation is undertaken;


Job Title

XX

h (m) t (mm) p (kPa) ktens Fh (kN/m) φ (mm) s (mm) As (mm2/m) ρw (%) fs (N/mm

2)

0.000 300 0 0.205 159 16 115 3497 1.17% 45

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

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% OK

Minimum steel area percentage, ρwmin (>=0.45%) 0.87% OK

Maximum steel (tens) stress, MAX (fs) 96 N/mm2

Allowable steel (tens) stress utilisation, MAX (fs) / fs,allow 96% OK

h (m) t (mm) kmom Mv (kN/m) φv (mm) s (mm) Asv (mm2/m) ρwv (%) fs (N/mm

2)

0.000 300 0.0009 1 12 115 983 0.33% 5

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;

Note (unfactored) vertical plane moment, M v = 0.0 or k mom . γ .h 3 ;

Note steel area, A sv = (2 or 1). πφ v2/4/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) 94 N/mm2

Allowable steel (tens) stress utilisation, MAX (fs) / fs,allow 94% OK

jXXX 4


Consulting Engineers

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E N G I N E E R S



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Member/Location


Job Title

XX

5

CONSULTING

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Consulting Engineers jXXX



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CONSULTING Engineering Calculation Sheet E N G I N … No. Sheet No. Rev. Job Title XX Ring Wall...

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