DOHA METRO RED LINE NORTH
Calculation of Crack Width in Accordance with EN 1992-1-1:2004 (E)
Geometry and loads Materials Reinforcement
Notation Value Unit Notation Value Unit Notation Value Unit
Loads fck 40 MPa Tension reinforcement
z: Load duration, ST for short term and LT for long term LT fct,eff: Mean Value of tensile strength of concrete 3.5 Mpa øt1: Diameter of reinforcement, layer 1 32 mm
Ecm: Secant modulus of elasticity of concrete 35000 Mpa (c-c)t1: Distance of reinforcement, layer 1 150 mm
Permanent loads fyk: Characteristic tensile strength of reinforcement 500 Mpa ct1: Cover to reinforcement, layer 1 90 mm
N: Normal force along y axis, compression as positive 1 kN Es: Characteristic modulus of elasticity of reinforcement 200000 Mpa øt2: Diameter of reinforcement, layer 2 0 mm
M: Moment along x axis, positive always 600 kNm (c-c)t2: Distance of reinforcement, layer 2 150 mm
Crack Width Calculation (Input for formula 7.11) ct2: Cover to reinforcement, layer 2 147 mm
Temperature loads k1 1 øt3: Diameter of reinforcement, layer 3 0 mm
N: Normal force along y axis, compression as positive 0 kN k1: high bond bars 0.8 (c-c)t3: Distance of reinforcement, layer 3 150 mm
M: Moment along x axis, positive always 0 kNm k1: bars with an effectively plain surface 1.6 ct3: Cover to reinforcement, layer 3 200 mm
etemp Strain from temperature 0.00E+00 k2 1
k2: bending 0.5 Compression reinforcement
Section properties k2: pure tension 1 øc: Diameter of compressive reinforcement 32 mm
b: Width of the section 1000 mm k2: eccentric tension or local areas (use below cells) 1 (c-c)c: Distance of compressive reinforcement 150 mm
h: Reduced Depth of the section 800 mm e1: Input value for eccentric tension or local areas 1.00 cc: Cover to compressive reinforcement 115 mm
h: Depth of the section 800 mm ε2: Input value for eccentric tension or local areas 1.00
53 kg/m³
Calculations
Elastic Solution for Uncracked Section Stresses of Cracked Section (aj-method) Crack Width
Notation Value Unit Notation Value Unit Notation Value Unit
Asc: Area of compressive reinforcement 5362 mm2 a: M/N 600000 mm Sr,max: The maximum crack spacing 322 mm
As: Area of tensile reinforcement 5362 mm2 A0: a(Asc+As) 122552 mm2 εsm-εcm: The tensile strain at point being considered 5.90E-04
αe: Es/Ec 11.43 d0: a(cøAsc+hefAs)/A0 413 mm
cø: cc+øc/2 131 mm I0: a(cø2Asc+hef2As)-A0d02 9.7E+09 mm4 ρp,eff: As/Ac,eff 0.0284
tø: ct+øt/2 106 mm e: a-h/2 599600 mm kt: A factor dependent on the duration of the load 0.4
hef: h-ct-øt/2 694 mm c: e+d0 600013 mm For coefficients below see column P
Ae: Equivalent areas of concrete section 911828.73 mm2 a2: 3e 1798800 mm k1: A coefficient of the bond properities 0.8
ye: Distance from neutral axis of equivalent section to most tensile 398.5 mm a1: 6A0c/b 4.4E+08 mm2 k2: A coefficient of the distribution of strain 0.5
Ie: Moment of inertia of equivalent sections 5.2E+10 mm4 a0: -6(I0+A0cd0)/b -1.8E+11 mm3 k3: A coefficient 1.447
sbot: Elastic concrete stress at bottom face 4.64 Mpa x: The neutral axis depth 218.31 mm k4: A coefficient 0.425
stop: Elastic concrete stress at top face -4.68 Mpa
smax: Maximum concrete stress 4.64 Mpa hc,ef: The depth of the effective tension area 194 mm ø: The bar (equivalent) dimension 32.00 mm
Mcr: Cracking Moment 453 KNm
Ncr: Corresponding Cracking Normal Force 1 kN I: hc3b/3+I0+A0(hc-d0)2 1.8E+10 mm4 wk : Maximum allowed crack width 0.20 mm
e0: e+x 599818 mm
Ac,eff: The effective area of concrete in tension 188537 mm2 sc: Maximum compressive stress of concrete 7.36 Mpa
The section may be cracked! ssc: Maximum compressive stress of bars 33.6 Mpa wk : Design crack width 0.190 mm
ss: Maximum tensile stress of reinforcement 183.19 Mpa The crack width is OK!
file:///conversion/tmp/activity_task_scratch/624352075.xlsxSLS - Crackwidth Page 1 COWI 11/07/2022
ecu=0.0035 fcd
cc
hc Asc*ssc
h/2 esc
Asc
0.8*hc
hef
N
Ast Mu
h/2 Ast*sst
ct est
Ultimate Moment of Rectangular Section with Normal Force (In Accordance with DS411)
Project: Doha metro Cut & Cover Tunnel Element: AT COL LOCATION
Data Input
Geometry Materials and Load
Notation Value Unit Notation Value Unit
b: Width 1000 mm fck: Comp. streng. of conc. 40 MPa
h: Depth 800 mm fyck: Ten. streng. of com. bar 500 MPa
øc: Dia. of comp. bars 32 mm fytk: Ten. streng. of ten. bar 500 MPa
cc: Cover to comp. bar 115 mm gc: Safety fac. of con. 1.50
(c-c)c: Dist. of comp. bar 150 mm gs: Safety fac. of bar 1.15
øt: Dia. of ten. bars 32 mm N: Normal force 0.001 MN
ct: Cover to ten. bar 90 mm Note: N is positive for comp.
(c-c)t: Dist. of ten. bar 150 mm cø, ct is the pure cover!
Calculations
Geometries and Design Value of Materials Depth of Neutral Axis and Ultimate Moment
Notation Value Unit Notation Value Unit
Asc: Area of comp. bars 0.0 mm2 * (hc)1: Parameter 109.3 mm
Ast: Area of ten. bars 5361.7 mm 2
(hc)2: Parameter 109.3 mm
cc+øc/2: 0.0 mm * (hc)3: Parameter 109.3 mm
ct+øt/2: 106.0 mm hc: Depth of comp. area 109.3 mm
hef: Effective depth 694.0 mm esc: Strain of comp. bar 0.00350
fcd: Des. str. of conc. 26.7 MPa ssc: Stres. of comp. bar 434.8 MPa
fycdc: Comp. str. of comp. bar 434.8 MPa est: Strain of ten. bar 0.01872
fytdc: Ten. str. of comp. bar 434.8 MPa sst: Stres. of ten. bar 434.8 MPa
fytdt: Ten. str. of ten. bar 434.8 mm
7*(cc+øc/2)/3 0.0 mm
(cc+øc/2)/(1+fyd/700) 0.0 mm Mu: Ultimate moment 1.516 MNm
file:///conversion/tmp/activity_task_scratch/624352075.xlsx
COWI India Ltd. Proj: Doha Metro_Red Line_North Job No.:
Designed by: YYH
Checked by:
Design of Sidewall Bottom Reinforcement with struts Date: 7-Nov-22
Page:
Reference Output
Members Not requiring shear reinforcement: Clause 6.2.2, EN 1992-1-1
VRd,c, the design shear resistance of the member without shear reinforcement is
estimated as:
eqn.(6.2.a) VRd,c = [CRd,c k (100 r1 fck)1/3 + k1 scp] bw d
eqn.(6.2.b) Min VRd,c = (vmin + k1 scp) bw d
Characteristic compressive strength, fck = 40 N/mm2
Partail factor of safety of concrete, ϒc 1.5
Overall depth = 800 mm
Design value of concrete compressive strength, fcd = 26.67 N/mm2
cover to reinforcement ct+øt/2 = 106 mm
Effective depth, d = 694 mm
Smallest width of cross-section, bw = 1000 mm
k = Min ( 1+(200/d) , 2 )
0.5
1+(200/d)0.5 =1+(200/694)^0.5 = 1.54
k = 1.54
dia of bars = 32.00 mm
No of bars = 6.67
Ast = 5361.65 mm2
rl =5362/(694×1000) = 0.008
eqn.(6.2.a) CRdc = 0.18 / gc =0.18/1.5 = 0.12
(NA CRdc = 0.18 / γc ,stone > 16mm, or 0.15/ γc )
eqn.(6.3.N) v min =0.035 k3/2 fck0.5
=0.035×1.54^(3/2)×40^0.5 = 0.42 N/mm2
Axial force, NED due to loading or prestressing = 1 kN
scp = 0.00125 N/mm2
eqn.(6.2.a) k1 = 0.15
VRd,c =(0.12×1.54×(100×0.008×40)^(1/3) +0.15 x 0.0)×1000×694/1000
= 402 kN
VRd,c , Min =(0.42 +(0.15x0.00))×(694×1000)/1000 = 293 kN
VRd,c = 402 kN
32 0 0
150 150 150
5 / 12
COWI India Ltd. Proj: Doha Metro_Red Line_North Job No.:
Designed by: YYH
Checked by:
Design of Sidewall Bottom Reinforcement with struts Date: 7-Nov-22
Page:
Reference Design Check for Shear Reinforcement : Clause 6.2.3, EN 1992-1-1 Output
Ultimate shear force, VED = 2.1 MN
(includes all vertical and torsional effects)
Grade of concrete = 40 N/mm2
ϒc = 1.5
fcd =40/1.500 = 26.7 N/mm2
Yield Stress of Steel reinforcement = 500 N/mm2
ϒs = 1.15
fywd =500/1.150 = 434.8 N/mm2
Overall depth of beam, h = 0.800 m
Cover to reinforcement = 106 mm
Dia of bars = 32 mm
Effective Depth of beam, d = 0.694 m
Axial force, NED due to loading or prestressing = 1 kN
Ast = 5362 mm²
Neutra; axis depth 109.320 mm
z =0.9×0.694 = 0.625 m
Thickness of web, bw = 1.000 m
Theta Assumed = 22.0 degrees
= 0.384 radians
cot q = 2.48
Check, 1< cot q < 2.5: = OK
Shear capacity based on strength of concrete compressive strut, Vrd, max
eqn.(6.9) = acw bw z n1 fcd / ( cot q + tanq)
acw is based on the average stress in section due to prestressing, scp
scp = 0.00 N/mm2
scp / fcd =0.00/26.7 = 0.0000
scp / fcd lies between 0 < scp/fcp < 0.25 fcd
Therefore acw = 1+ scp / fcd = 1.000
eqn.(6.6N) n1 = 0.504
eqn.(6.9) Vrd, max =1.00×1.000×0.625×0.504×26.7/(1/TAN(0.384)+TAN(0.384))×1000
= 2916 kN
= 2.9 MN
2.1 MN < 2.9 MN OKAY
eqn.(6.8) Shear reinforcement required = VED x tan q / (z fywd)
Asw /sw =2.1×1000000×TAN(0.384)/(0.625×1000×434.8)
= 3.12 mm² /mm
Minimum shear reinforcement Asw/sw = bw (0.08 fck0.5 / fyk), Eqn 9.4
Asw /sw(min) =1.000×1000×(0.08×40^0.5/500) = 1.01 mm² /mm
Max Shear reinforcement: Asw/sw = 0.5 acw v1 fcd bw / fywd = 15.5 mm² /mm
Required Shear reinforcement = 3.12 mm² /mm
Provide 3.33 Legs -Dia 12 at a spacing of = 300 mm
=3.33×3.14×12^2/4/300 = 1.25 mm2/mm
=1.25 mm²/mm < 3.12mm²/mm NOT OK
COWI India Ltd. Proj: Doha Metro_Red Line_North Job No.:
6 / 12
Designed by: YYH
Checked by:
Design of Sidewall Bottom Reinforcement with struts Date: 7-Nov-22
Page:
Reference Output
Longitudinal Reinforcement:
Additional tensile force DFd, = 0.5 VED (cot q - cot a)
=0.5×2.10× cot(22.0) = 2.60 MN
Dast, =2.60×1e6 /434.8 = 5977 mm2
Check if reinforcement required for moment at section + additional reinforcement due to
DFd,is not greater than reinforcement provided for maximum moment.
ecu=0.0035 fcd
cc
hc Asc*ssc
h/2 esc
Asc
0.8*hc
hef
N
Ast Mu
h/2 Ast*sst
ct est
Ultimate Moment of Rectangular Section with Normal Force (In Accordance with DS411)
Project: Doha metro Cut & Cover Tunnel Element: AT COL LOCATION
Data Input
Geometry Materials and Load
Notation Value Unit Notation Value Unit
b: Width 1000 mm fck: Comp. streng. of conc. 40 MPa
h: Depth 800 mm fyck: Ten. streng. of com. bar 500 MPa
øc: Dia. of comp. bars 32 mm fytk: Ten. streng. of ten. bar 500 MPa
cc: Cover to comp. bar 115 mm gc: Safety fac. of con. 1.20
(c-c)c: Dist. of comp. bar 150 mm gs: Safety fac. of bar 1.00
øt: Dia. of ten. bars 32 mm N: Normal force 0.001 MN
ct: Cover to ten. bar 90 mm Note: N is positive for comp.
(c-c)t: Dist. of ten. bar 150 mm cø, ct is the pure cover!
Calculations
Geometries and Design Value of Materials Depth of Neutral Axis and Ultimate Moment
Notation Value Unit Notation Value Unit
Asc: Area of comp. bars 0.0 mm2 * (hc)1: Parameter 100.6 mm
Ast: Area of ten. bars 5361.7 mm 2
(hc)2: Parameter 100.6 mm
cc+øc/2: 0.0 mm * (hc)3: Parameter 100.6 mm
ct+øt/2: 106.0 mm hc: Depth of comp. area 100.6 mm
hef: Effective depth 694.0 mm esc: Strain of comp. bar 0.00350
fcd: Des. str. of conc. 33.3 MPa ssc: Stres. of comp. bar 500.0 MPa
fycdc: Comp. str. of comp. bar 500.0 MPa est: Strain of ten. bar 0.02065
fytdc: Ten. str. of comp. bar 500.0 MPa sst: Stres. of ten. bar 500.0 MPa
fytdt: Ten. str. of ten. bar 500.0 mm
7*(cc+øc/2)/3 0.0 mm
(cc+øc/2)/(1+fyd/700) 0.0 mm Mu: Ultimate moment 1.753 MNm
file:///conversion/tmp/activity_task_scratch/624352075.xlsx
Cover and Crack width:
Longitudunal
90 + 32 = 122 mm
Upper face, wk = 0.15 mm
90 + 16 = 106 mm
Longitudunal
Lower face, wk = 0.30 mm
The shear stirrups will be in the layer of longitudinal reinforcement at top face and at
outside face of the transverse reinforcemnt at bottom of the slab.
Minimum Reinforcement:
Transverse Reinforcement:
Roof slab thickness = 800 mm
Minimum reinforcement is max. of 0.26(fctm/fyk)bd or 0.13% of bd as per
EN 1992-1-1 clause 9.2.1.1
fctm = 3.5 MPa fyk = 500 MPa
Minimun Transverse reinforcement = 0.182 . 800 . 1000 mm² /m
required 100
= 1456 mm² /m
L1 - f 12 s 75 mm c/c is considered for actual reinforcement calculation .
= 1508 mm2/m Hence OK
Roof slab thickness = 1400 mm
Minimun Transverse reinforcement = 0.182 . 1400 . 1000 mm² /m
required 100
= 2548 mm² /m
L1 - f 25 s 150 mm c/c is considered for actual reinforcement calculation .
= 3272 mm2/m Hence OK
Roof slab thickness = 1800 mm
Minimun Transverse reinforcement = 0.182 . 1800 . 1000 mm² /m
required 100
= 3276 mm² /m
L1 - f 25 s 150 mm c/c + f 16 s 300 mm c/c
is considered for actual reinforcement calculation .
= 3942 mm2/m Hence OK
Roof slab thickness = 2000 mm
Minimun Transverse reinforcement = 0.182 . 2000 . 1000 mm² /m
required 100
= 3640 mm² /m
L1 - f 25 s 150 mm c/c + f 16 s 300 mm c/c
is considered for actual reinforcement calculation .
= 3942 mm2/m Hence OK
Roof slab thickness = 2300 mm
Minimun Transverse reinforcement = 0.182 . 2300 . 1000 mm² /m
required 100
= 4186 mm² /m
L1 - f 25 s 150 mm c/c + f 20 s 300 mm c/c
is considered for actual reinforcement calculation .
= 4319 mm2/m Hence OK
Roof slab thickness = 2800 mm
Minimun Transverse reinforcement = 0.182 . 2800 . 1000 mm² /m
required 100
= 5096 mm² /m
L1 - f 32 s 150 mm c/c is considered for actual reinforcement calculation .
= 5362 mm2/m Hence OK
Note -:In minimum reinforcement calculation value of d is taken as for overall depth
conservatively.
CIO
Design Calculations
Al Wahda station
Design of Base Slab Designed By: KVRY
Appendix-G: Minimum Reinforcement Date: 04/06/2014
Minimum reinforcement:
The minimum reinforcement in base slab, starter bars and in lining walls.
As per EN1992-1-1 cl. 7.1 and CIRIA C660 cl. 3.3.1 eq. 3.12
𝐴𝑠=𝑘. 𝑓𝑐𝑡.𝑒𝑓𝑓. 𝐴𝑐t/𝑓𝑦𝑘
Where,
fctm ,the mean value of the tensile strength of the concrete effective at the time when the cracks
may first be expected to occur = 3.5 MPa
σs is the absolute value of the maximum stress permitted in reinforcement , may be taken
as the yeild strength of the reinforcement = 500 MPa
From CIRIA C660 table 3.1
kc = 1.0
k = 0.75
Input Result
H c f Act Ast.min
Reinforcement%age kg/m³
mm mm mm mm2 mm2
250 90 12 250000 656 f 12 s 150 0.3 23.7
1400 122 25 1400000 3675 f 25 s 130 0.27 21.2
1500 90 25 1500000 3938 f 25 s 120 0.27 21.4
1500 122 25 1500000 3938 f 25 s 120 0.27 21.4
2500 90 32 2500000 6563 f 32 s 120 0.27 21
2500 122 32 2500000 6563 f 32 s 120 0.27 21
dia sp Ast
16 130 1546.6
20 130 2416.6
3963.2
Alternate sp dia Ast
130 25.61 3963.2
Bundlled sp dia Ast
130 25.61 3963.2
For CG of the reinforcement:
Layer Cover Dia Spacing Spacer CG of Ast Ast x Yi
(nominal) Dia bars, Yi
1 234 32 150 32 250 5362 1340413
2 298 32 150 32 314 5362 1683559
3 362 32 150 32 378 5362 2026704
4 426 0 150 32 426 0 0
5 458 0 150 32 458 0 0
6 490 0 150 32 490 0 0
7 522 0 150 32 522 0 0
Total 16085 5050676
55 150 314 16085
Effective 286 55 150 314 16085
