Method statement + design calculations PDF

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Method statement and design calculations of reinforced concrete building elements to detail...

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Job Number: 160602

5.1.

Structural Design Calculations

43 W:\Project File\Project Storage\2016\160602-25 Old Church Street\2.0.Calcs\CMS\cms croft\25 Old Church Street Subterranean Construction Method Statement .docx

Job Number: 160602

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Job Number: 160602

RETAINING WALL DESIGN TEMPORARY CONDITION The following calculations will consider the worst case. In the temporary condition no water will be taken into account.

RETAINING WALL ANALYSIS (BS 8002:1994) TEDDS calculation version 1.2.01.06

Wall details Retaining wall type

Cantilever propped at base

Height of retaining wall stem

hstem = 3500 mm

Thickness of wall stem Length of toe

twall = 350 mm ltoe = 3000 mm

Length of heel

lheel = 0 mm

Overall length of base Thickness of base

lbase = ltoe + l heel + twall = 3350 mm tbase = 350 mm

Depth of downstand Position of downstand

dds = 0 mm lds = 1900 mm

Thickness of downstand

tds = 350 mm

Height of retaining wall Depth of cover in front of wall

hwall = hstem + tbase + dds = 3850 mm dcover = 0 mm

Depth of unplanned excavation

dexc = 0 mm

Height of ground water behind wall Height of saturated fill above base

hwater = 0 mm hsat = max(hwater - tbase - dds , 0 mm) = 0 mm

Density of wall construction

Jwall = 23.6 kN/m3

Density of base construction

Jbase = 23.6 kN/m3

Angle of rear face of wall

D = 90.0 deg

Angle of soil surface behind wall

E = 0.0 deg

Effective height at virtual back of wall

heff = h wall + lheel u tan(E) = 3850 mm 45

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Job Number: 160602

Retained material details Mobilisation factor

M = 1.5

Moist density of retained material

Jm = 18.0 kN/m3

Saturated density of retained material

Js = 21.0 kN/m3

Design shear strength

I' = 24.2 deg

Angle of wall friction

G = 0.0 deg

Base material details Moist density

Jmb = 18.0 kN/m 3

Design shear strength

I' b = 24.2 deg

Design base friction

Gb = 18.6 deg

Allowable bearing pressure

P bearing = 100 kN/m2

Using Coulomb theory Active pressure coefficient for retained material Ka = sin(D+ I') 2 / (sin(D) 2 u sin(D- G) u [1 + (sin(I' + G) u sin(I' - E) / (sin(D- G) u sin(D+ E)))] 2) = 0.419 Passive pressure coefficient for base material Kp = sin(90- I' b )2 / (sin(90- Gb) u [1 - (sin(I' b + Gb) u sin(I'b) / (sin(90 + Gb)))] 2) = 4.187 At-rest pressure At-rest pressure for retained material

K0 = 1 – sin(I’) = 0.590

Loading details Surcharge load on plan

Surcharge = 10.0 kN/m 2

Applied vertical dead load on wall Applied vertical live load on wall

Wdead = 85.6 kN/m Wlive = 3.8 kN/m

Position of applied vertical load on wall

lload = 3150 mm

Applied horizontal dead load on wall Applied horizontal live load on wall

Fdead = 0.0 kN/m Flive = 0.0 kN/m

Height of applied horizontal load on wall

hload = 0 mm

Loads shown in kN/m, pressures shown in kN/m2 46 W:\Project File\Project Storage\2016\160602-25 Old Church Street\2.0.Calcs\CMS\cms croft\25 Old Church Street Subterranean Construction Method Statement .docx

Job Number: 160602

Vertical forces on wall Wall stem

w wall = hstem u twall u J wall = 28.9 kN/m

Wall base Applied vertical load

w base = l base u tbase u J base = 27.7 kN/m Wv = Wdead + W live = 89.4 kN/m

Total vertical load

Wtotal = wwall + wbase + Wv = 146 kN/m

Horizontal forces on wall Fsur = Ka u Surcharge u heff = 16.1 kN/m

Surcharge Moist backfill above water table

Fm_a = 0.5 u K a u Jm u (heff - hwater)2 = 55.8 kN/m

Total horizontal load

Ftotal = Fsur + Fm_a = 71.9 kN/m

Calculate propping force Passive resistance of soil in front of wall

Fp = 0.5 u K p u cos(Gb) u (d cover + tbase + dds - dexc )2 u Jmb = 4.4

kN/m Propping force

Fprop = max(Ftotal - Fp - (Wtotal - W live) u tan(Gb ), 0 kN/m) Fprop = 19.7 kN/m

Overturning moments Surcharge

Msur = Fsur u (h eff - 2 u dds) / 2 = 31 kNm/m

Moist backfill above water table

Mm_a = Fm_a u (h eff + 2 u hwater - 3 u d ds) / 3 = 71.7 kNm/m Mot = M sur + M m_a = 102.7 kNm/m

Total overturning moment Restoring moments Wall stem

Mwall = wwall u (ltoe + twall / 2) = 91.8 kNm/m

Wall base

Mbase = w base u lbase / 2 = 46.3 kNm/m

Design vertical dead load

Mdead = Wdead u lload = 269.6 kNm/m

Total restoring moment

Mrest = Mwall + Mbase + Mdead = 407.8 kNm/m

Check bearing pressure Design vertical live load

Mlive = Wlive u lload = 12 kNm/m

Total moment for bearing Total vertical reaction

Mtotal = M rest - Mot + Mlive = 317.1 kNm/m R = Wtotal = 146.0 kN/m

Distance to reaction Eccentricity of reaction

xbar = Mtotal / R = 2172 mm e = abs((lbase / 2) - xbar) = 497 mm

Bearing pressure at toe

ptoe = (R / lbase ) - (6 u R u e / lbase2) = 4.8 kN/m2

Reaction acts within middle third of base Bearing pressure at heel

pheel = (R / lbase) + (6 u R u e / l base2) = 82.4 kN/m 2 PASS - Maximum bearing pressure is less than allowable bearing pressure

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Job Number: 160602

RETAINING WALL DESIGN (BS 8002:1994) TEDDS calculation version 1.2.01.06

Ultimate limit state load factors Dead load factor

Jf_d = 1.4

Live load factor

Jf_l = 1.6

Earth and water pressure factor

Jf_e = 1.4

Factored vertical forces on wall Wall stem

w wall_f = Jf_d u hstem u twall u Jwall = 40.5 kN/m

Wall base

w base_f = Jf_d u lbase u t base u J base = 38.7 kN/m

Applied vertical load Total vertical load

Wv_f = Jf_d u Wdead + Jf_l u Wlive = 125.9 kN/m Wtotal_f = w wall_f + wbase_f + W v_f = 205.1 kN/m

Factored horizontal at-rest forces on wall Surcharge

Fsur_f = Jf_l u K 0 u Surcharge u heff = 36.3 kN/m

Moist backfill above water table

Fm_a_f = Jf_e u 0.5 u K0 u Jm u (heff - hwater)2 = 110.2 kN/m

Total horizontal load

Ftotal_f = Fsur_f + Fm_a_f = 146.6 kN/m

Calculate propping force Passive resistance of soil in front of wall 6.1 kN/m Propping force

Fp_f = Jf_e u 0.5 u K p u cos(Gb) u (dcover + tbase + dds - dexc )2 u J mb = Fprop_f = max(F total_f - Fp_f - (W total_f - J f_l u Wlive ) u tan(Gb), 0 kN/m) Fprop_f = 73.4 kN/m

Factored overturning moments Surcharge

Msur_f = Fsur_f u (heff - 2 u d ds) / 2 = 70 kNm/m

Moist backfill above water table

Mm_a_f = Fm_a_f u (h eff + 2 u h water - 3 u dds) / 3 = 141.4 kNm/m

Total overturning moment

Mot_f = Msur_f + M m_a_f = 211.4 kNm/m

Restoring moments Wall stem

Mwall_f = wwall_f u (lt oe + twall / 2) = 128.5 kNm/m

Wall base

Mbase_f = wbase_f u lbase / 2 = 64.9 kNm/m

Design vertical load

Mv_f = Wv_f u lload = 396.6 kNm/m

Total restoring moment

Mrest_f = Mwall_f + M base_f + Mv_f = 590 kNm/m

Factored bearing pressure Total moment for bearing Total vertical reaction

Mtotal_f = Mrest_f - M ot_f = 378.6 kNm/m Rf = Wtotal_f = 205.1 kN/m

Distance to reaction

xbar_f = Mtotal_f / Rf = 1846 mm

Eccentricity of reaction

ef = abs((lbase / 2) - xbar_f) = 171 mm Reaction acts within middle third of base

Bearing pressure at toe

ptoe_f = (Rf / l base) - (6 u Rf u e f / lbase2 ) = 42.5 kN/m2

Bearing pressure at heel

pheel_f = (R f / l base) + (6 u Rf u ef / lbase2 ) = 80 kN/m 2

Rate of change of base reaction

rate = (ptoe_f - pheel_f) / lbase = -11.19 kN/m2/m

Bearing pressure at stem / toe

pstem_toe_f= max(pheel_f + (rate u (lheel + twall)), 0 kN/m 2) = 76.1

kN/m2 Bearing pressure at mid stem

pstem_mid_f = max(pheel_f + (rate u (l heel + twall / 2)), 0 kN/m2) = 78

kN/m2 Bearing pressure at stem / heel

pstem_heel_f= max(pheel_f + (rate u l heel), 0 kN/m 2) = 80 kN/m2

Design of reinforced concrete retaining wall toe (BS 8002:1994) Material properties Characteristic strength of concrete

fcu = 40 N/mm 2 48

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Job Number: 160602

Characteristic strength of reinforcement

fy = 500 N/mm2

Base details Minimum area of reinforcement Cover to reinforcement in toe

k = 0.13 % ctoe = 30 mm

Calculate shear for toe design Shear from bearing pressure

V toe_bear= (p toe_f + pstem_toe_f) u ltoe / 2 = 177.8 kN/m

Shear from weight of base

Vtoe_wt_base= Jf_d u Jbase u l toe u tbase = 34.7 kN/m

Total shear for toe design

V toe = Vtoe_bear - V toe_wt_base = 143.1 kN/m

Calculate moment for toe design Moment from bearing pressure

Mtoe_bear = (2 u p toe_f + pstem_mid_f) u (ltoe + twall / 2)2 / 6 = 273.9

kNm/m Moment from weight of base kNm/m

Mtoe_wt_base = (Jf_d u Jbase u t base u (ltoe + twall / 2) 2 / 2) = 58.3

Total moment for toe design

Mtoe = M toe_bear- M toe_wt_base = 215.6 kNm/m

Check toe in bending Width of toe

b = 1000 mm/m

Depth of reinforcement

dtoe = tbase – ctoe – (Itoe/ 2) = 310.0 mm

Constant

K toe = Mtoe / (b u d toe2 u f cu) = 0.056 Compression reinforcement is not required

Lever arm

ztoe = min(0.5 + (0.25 - (min(Ktoe, 0.225) / 0.9)),0.95) u d toe ztoe = 289 mm

Area of tension reinforcement required

As_toe_des = Mtoe / (0.87 u fy u ztoe) = 1713 mm2 /m

Minimum area of tension reinforcement Area of tension reinforcement required

As_toe_min = k u b u tbase = 455 mm 2/m As_toe_req= Max(As_toe_des, As_toe_min) = 1713 mm 2/m

Reinforcement provided

20 mm dia.bars @ 150 mm centres

Area of reinforcement provided

As_toe_prov= 2094 mm 2/m PASS - Reinforcement provided at the retaining wall toe is adequate

Check shear resistance at toe Design shear stress Allowable shear stress

vtoe = Vtoe / (b u d toe) = 0.462 N/mm2 vadm = min(0.8 u (fcu / 1 N/mm2), 5) u 1 N/mm 2 = 5.000 N/mm 2 PASS - Design shear stress is less than maximum shear stress

From BS8110:Part 1:1997 – Table 3.8 Design concrete shear stress

vc_toe = 0.691 N/mm2 vtoe < vc_toe - No shear reinforcement required

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Job Number: 160602

Design of reinforced concrete retaining wall stem (BS 8002:1994) Material properties fcu = 40 N/mm 2 fy = 500 N/mm2

Characteristic strength of concrete Characteristic strength of reinforcement Wall details Minimum area of reinforcement

k = 0.13 %

Cover to reinforcement in stem

cstem = 30 mm

Cover to reinforcement in wall

cwall = 30 mm

Factored horizontal at-rest forces on stem Surcharge

Fs_sur_f = Jf_l u K 0 u Surcharge u (heff - tbase - dds ) = 33 kN/m

Moist backfill above water table

Fs_m_a_f = 0.5 u Jf_e u K0 u Jm u (heff - t base - dds - hsat )2 = 91.1

kN/m Calculate shear for stem design Shear at base of stem

Vstem= Fs_sur_f + Fs_m_a_f - Fprop_f = 50.7 kN/m

Calculate moment for stem design Surcharge

Ms_sur = Fs_sur_f u (h stem + t base) / 2 = 63.6 kNm/m

Moist backfill above water table

Ms_m_a = Fs_m_a_f u (2 u h sat + heff - d ds + tbase / 2) / 3 = 122.2

kNm/m Total moment for stem design

Mstem = M s_sur + M s_m_a = 185.8 kNm/m

Check wall stem in bending Width of wall stem

b = 1000 mm/m

Depth of reinforcement

dstem = twall – cstem – (Istem / 2) = 310.0 mm

Constant

K stem= M stem / (b u d stem2 u f cu) = 0.048

Lever arm

zstem = min(0.5 + (0.25 - (min(Kstem , 0.225) / 0.9)),0.95) u d stem

Compression reinforcement is not required zstem = 292 mm Area of tension reinforcement required

As_stem_des= M stem / (0.87 u fy u zstem ) = 1461 mm2/m

Minimum area of tension reinforcement Area of tension reinforcement required

As_stem_min= k u b u twall = 455 mm2/m As_stem_req= Max(As_stem_des, A s_stem_min) = 1461 mm 2/m

Reinforcement provided

20 mm dia.bars @ 150 mm centres

Area of reinforcement provided

As_stem_prov= 2094 mm 2 /m PASS - Reinforcement provided at the retaining wall stem is adequate

Check shear resistance at wall stem Design shear stress

vstem = V stem / (b u dstem ) = 0.163 N/mm 2

Allowable shear stress

vadm = min(0.8 u (fcu / 1 N/mm2), 5) u 1 N/mm 2 = 5.000 N/mm 2 50

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Job Number: 160602

PASS - Design shear stress is less than maximum shear stress From BS8110:Part 1:1997 – Table 3.8 Design concrete shear stress

vc_stem = 0.691 N/mm2 v stem < vc_stem - No shear reinforcement required

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Job Number: 160602

Indicative retaining wall reinforcement diagram

Stem reinforcement

Toe reinforcement

Toe bars - 20 mm dia.@ 150 mm centres - (2094 mm 2/m) Stem bars - 20 mm dia.@ 150 mm centres - (2094 mm2/m)

RETAINING WALL DESIGN PERMANENT DESIGN The following calculations will take into consideration the hydrostatic pressure to the rear of the wall.

RETAINING WALL ANALYSIS (BS 8002:1994) TEDDS calculation version 1.2.01.06

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Job Number: 160602

Wall details Retaining wall type

Cantilever propped at base

Height of retaining wall stem Thickness of wall stem

hstem = 3500 mm twall = 350 mm

Length of toe

ltoe = 3000 mm

Length of heel Overall length of base

lheel = 0 mm lbase = ltoe + l heel + twall = 3350 mm

Thickness of base Depth of downstand

tbase = 350 mm dds = 0 mm

Position of downstand

lds = 1900 mm

Thickness of downstand Height of retaining wall

tds = 350 mm hwall = hstem + tbase + dds = 3850 mm

Depth of cover in front of wall

dcover = 0 mm

Depth of unplanned excavation Height of ground water behind wall

dexc = 0 mm hwater = 2500 mm

Height of saturated fill above base

hsat = max(hwater - tbase - dds , 0 mm) = 2150 mm

Density of wall construction

Jwall = 23.6 kN/m3

Density of base construction

Jbase = 23.6 kN/m3

Angle of rear face of wall

D = 90.0 deg

Angle of soil surface behind wall

E = 0.0 deg

Effective height at virtual back of wall

heff = hwall + lheel u tan(E) = 3850 mm

Retained material details Mobilisation factor

M = 1.5

Moist density of retained material

Jm = 18.0 kN/m3

Saturated density of retained material

Js = 21.0 kN/m3

Design shear strength

I' = 24.2 deg

Angle of wall friction

G = 0.0 deg

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Job Number: 160602

Base material details Moist density

Jmb = 18.0 kN/m 3

Design shear strength

I' b = 24.2 deg

Design base friction

Gb = 18.6 deg

Allowable bearing pressure

P bearing = 100 kN/m2

Using Coulomb theory Active pressure coefficient for retained material Ka = sin(D+ I') 2 / (sin(D) 2 u sin(D- G) u [1 + (sin(I' + G) u sin(I' - E) / (sin(D- G) u sin(D+ E)))] 2) = 0.419 Passive pressure coefficient for base material Kp = sin(90- I' b )2 / (sin(90- Gb) u [1 - (sin(I' b + Gb) u sin(I'b) / (sin(90 + Gb)))] 2) = 4.187 At-rest pressure At-rest pressure for retained material

K0 = 1 – sin(I’) = 0.590

Loading details Surcharge load on plan Applied vertical dead load on wall

Surcharge = 10.0 kN/m 2 Wdead = 85.6 kN/m

Applied vertical live load on wall

Wlive = 3.8 kN/m

Position of applied vertical load on wall Applied horizontal dead load on wall

lload = 3150 mm Fdead = 0.0 kN/m

Applied horizontal live load on wall

Flive = 0.0 kN/m hload = 0 mm

Height of applied horizontal load on wall

Loads shown in kN/m, pressures shown in kN/m2

Vertical forces on wall Wall stem

w wall = hstem u t wall u J wall = 28.9 kN/m

Wall base

w base = lbase u tbase u Jbase = 27.7 kN/m

Applied vertical load

Wv = Wdead + Wlive = 89.4 kN/m

Total vertical load

Wtotal = wwall + wbase + Wv = 146 kN/m

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Horizontal forces on wall Surcharge

Fsur = Ka u Surcharge u heff = 16.1 kN/m

Moist backfill above water table

Fm_a = 0.5 u Ka u Jm u (heff - hwater)2 = 6.9 kN/m

Moist backfill below water table

Fm_b = Ka u Jm u (heff - hwater)...