Wall Final Calcs

7/23/2019 Wall Final Calcs

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Euroget Wall Steel Estimation

Input Data

f ck 20 MPaCylinder Concrete Characteristic Strength

Concrete tensile strength f ctm 0.3 f ck MPa 1

2 3

1

MPa f ctm 2.21 MPa

Reinf. Yield Strength f yk 250 MPa

Conc. partial safety factor c 1.5

Steel partial safety factor s 1.15

Concrete Modulus (evaluated) Ec 5000 MPa f ck MPa 1

Ec 2.236 1010

Pa

Steel Modulus Es 200 GPa Es 2 1011

Pa

f cd f ck c1

Concrete design Strength f cd 1.333 10

7 Pa

f yd f yk s1

f yd 2.174 108

PaSteel design strength

yd f yk s Es 1

yd 1.087 10 3

Steel yield design strain

Minimum beam reinforcement ratio min

0.5 f ctm

f yk

min 0.442 %

Wall height hs 5000 mm

bs 3000 mmReal wall width (buttress to buttress)

Per meter wall run bw 1000 mm

Cover to main reinf. cv 75 mm

Thickness of wall thk 150 mm

Effective depth d thk cv d 0.075 m



Unit weight of concrete gw 24 kN m 3

pga acceration ag 0.15 g

spectral amplification ratio rSa 2.5

Sag rSa ag Sag 0.375 gbase spectral acceleration

fAc 2 Average amplification factor

Average acceleration over wall Sa_C fAc Sag Sa_C 0.75 g

Weight of wall Ww bs thk hs gw Ww 54 kN

Mass of wall mw Ww g 1

mw 5.506 s

2

mkN

Fc mw Sa_C Fc 40.5 kNSeismic lateral force

Corresponding distributed lateral pressure fcc Fc hs bs 1

fcc 2.7kPa

Moment Estimations

Wall is assumed to be bounded on all three sides with a distributed load imposed on it.

Two cases are analyzed using the Yield line theory approach:

Case 1: The bottom is fixed and the sides are also fixed

Case 2: The bottom is fixed and the sides are pin supported

The equations are taken from Reference [1],

Kennedy G, Goodchild, GH, Practical Yield Line Design, The Concrete Centre, UK, 2004.



Case 1:

nab fccDistributed load

No line load loads, thus line load factors = 0 pa 0 pb 0

pa pa nab bs 1

pa 0 pb pb nab hs 1

pb 0

Edge fixity ratio

Side ratios i1 1 i3 1 bottom ratio i2 1

Possibility 1, Separate Yield Line Case

br 2 bs

1 i1 1 i3

Kh2 hs 1 3 pb

3 br 1 pa 2 pb hH

hs

Kh Kh2 i2 br Kh

2 hs 1

br 2.121 m Kh 1.571 hH 1.42 m

h1 hH 1 i1 h1 2.008 m h3 hH 1 i3 h3 2.008 m

Combined horizontal distances greater than total width, NOT a valid possibility,

mabnab hs br 1 pa 2 pb

8i2 br

4 hs

hs

hH

mab 0.987

kN m

m

m1 mab m3 mab m2 mab

Possibility 2, Combined Yield Line Case

Nab nab 1 pb pa Ap br Ap 2.121 m

Bp2 hs

1 i2

1 pb 2 pa

1 3 pa

Bp 7.071 m



mba Nab Ap Bp

8 1 Bp

Ap

Ap

Bp

mba 1.093

kN m

m

h1 br

21 i1 h3

br

21 i3 h2

6 mba 1 i2( )

nab 1 3 pa

h1 1.5 m h3 1.5 m h2 2.204 m

m1 mba m3 mba m2 mba

M1end if mab mba mab mba( ) M1end 1.093 kN m

m

M1side mbaM1side 1.093

kN m

m

Case 2:

Edge fixity ratio

Side ratios i1 0 i3 0 bottom ratio i2 1

Possibility 1, Separate Yield Line Case

br 2 bs

1 i1 1 i3

Kh2 hs 1 3 pb

3 br 1 pa 2 pb hH

hs

Kh Kh2 i2 br Kh

2 hs 1

br 3 m Kh 1.111 hH 1.843 m

h1 hH 1 i1 h1 1.843 m h3 hH 1 i3 h3 1.843 m

Combined horizontal distances greater than total width, NOT a valid possibility

mabnab hs br 1 pa 2 pb

8i2 br

4 hs

hs

hH

mab 1.768

kN m

m



m2 mab

Possibility 2, Combined Yield Line Case

Nab nab 1 pb pa Ap br Ap 3 m

Bp2 hs

1 i2

1 pb 2 pa

1 3 pa

Bp 7.071 m

mba Nab Ap Bp8 1

Bp

Ap

Ap

Bp

mba 1.893

kN mm

h1 br

21 i1 h3

br

21 i3 h2

6 mba 1 i2( )

nab 1 3 pa

h1 1.5 m h3 1.5 m h2 2.901 m

m2 mba

M2end if mab mba mab mba( ) M2end 1.893 kN m

m

Summary of Moments

As noted in Ref [1], yield line moments should be increased by 10% to account for the

approach producing an upper bound solution

incfact 1.1

Maximum base moment, from pinned case Mbase incfact M2end Mbase 2.083 kN m

m

Maximum side moments, from fixed case Mside incfact M1side Mside 1.202 kN m

m



FLEXURAL DESIGN

Limiting depth ratio xdlim 0.448

Stress block factors 0.85 0.8

c 0.0035Maximum concrete strain

Wall design

Minimum reinforcement Af 0.26 f ctm f yk 1

Afmin if Af 0.15% 0.15% Af

Asmin Afmin bw d Asmin 172.413 mm2

Minimum steel Provide R10 @ 450 mm Aspv_min 174 mm

2

m

Positive moment per meter Mpm Mbase 1 m Mpm 2.083 kN m

Balanced moment capacity ratio mlim xdlim 1 xdlim mlim 0.23

Normalized moment ratio mk Mpm bw d2

f cd1

mk 0.033

Steel area, zero means need compression reinforcement

Asl if mk mlim 1 1 2 mk bw d f cd

f yd

0

Asl 129.899 mm

2

Provide R10@300 Aspv 262 mm

2

m

Provided steel in wall As_wall = R12@150 As_wall 753 mm

2

m



Buttess Loads Estimation

Buttress size (width) Ts 400 mm

Cover to main reinf. cv 30 mm

Effective depth d Ts cv d 0.37 m

From above, distributed lateral pressure fcc Fc hs bs 1

fcc 2.7kPa

UDL estimation on the buttress fh fcc bs fh 8.1kN m 1

Moment at base of buttress Mb 0.5 fh hs2

Mb 101.25kN m

Shear at the base Fb fh hs Fb 40.5kN

Minimum reinforcement Af 0.26 f ctm f yk 1

Afmin if Af 0.15% 0.15% Af

Asmin Afmin bw d Asmin 850.569 mm

2

Minimum steel Provide 3R20 Aspv_min 942 mm2

Positive moment Mpm Mb Mpm 101.25kN m

Balanced moment capacity ratio mlim xdlim 1 xdlim mlim 0.23

Normalized moment ratio mk Mpm bw d2

f cd1

mk 0.065

Steel area, zero means need compression reinforcement

Asl if mk mlim 1 1 2 mk bw d f cd

f yd

0

Asl 1.303 10

3

mm

2



Provide 4R20 Aspv 1256 mm2

Not far from that required.

Shear + Torsion Design

Torsional moment per meter for design mt Mside mt 1.202 kN m

m

Torsional moment at the base Mt mt hs Mt 6.009 kN m

Area of section A_but Ts2

A_but 0.16 m2

Circumference of section C_but 2 Ts Ts( ) C_but 1.6m

Thickness of box section t_but A_but C_but 1

t_but 0.1m

Area within centre line A_tors Ts t_but( )2

A_tors 0.09m2

Perimeter of centreline C_ctr 4 Ts t_but( ) C_ctr 1.2m

B: Crushing strength of concrete

g 22 Angle in radians rg g 180 1

cot cot rg

1 0.6 1 f ck 250 MPa( ) 1 1 0.552

VRdmx

0.9 Ts d 1 f cd

cot rg tan rg VRdmx 340.505 kN

Maximum Shear possible

Maximum Torsion possible TRdmx

1.33 1 f ck A_tors C_ctr

cot rg tan rg TRdmx 550.79 kN m



Check shear-torsion interaction equation

STratFb

VRdmx

Mt

TRdmx

STrat 0.13 We are ok

Shear reinforcment ratio AswS Fb 0.78d f yk cot 1

AswS 0.227 mm

2

mm

Torsional reinf. ratio AsTS Mt A_tors 0.87 f yk cot 1

AsTS 0.124 mm

2

mm

Total link reinforcement AsLS AswS AsTS AsLS 0.351 mm

2

mm

Use R8@275 mm AsLpv 0.3658 mm

2

mm

Link spacing should be based on longitudinal steel size to stop buckling

Use R8@150 mm as steel to be used. Note that we must have crossing links

since Torsion is an issue

Longitudinal Torsional steel

As_Tor Mt C_ctr cot

2 A_tors 0.87 f yk As_Tor 455.905 mm

2

Need to add 4R12 to the longitudinal steel at the corners to account for Torsion.

Wall Final Calcs

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