5.1. Structural Design Calculations - RBKC

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5.1. Structural Design Calculations

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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 baseHeight of retaining wall stem hstem = 3500 mm Thickness of wall stem twall = 350 mm Length of toe ltoe = 3000 mm Length of heel lheel = 0 mm Overall length of base lbase = ltoe + lheel + twall = 3350 mm Thickness of base tbase = 350 mm Depth of downstand dds = 0 mm Position of downstand lds = 1900 mm Thickness of downstand tds = 350 mm Height of retaining wall hwall = hstem + tbase + dds = 3850 mm Depth of cover in front of wall dcover = 0 mm Depth of unplanned excavation dexc = 0 mm Height of ground water behind wall hwater = 0 mm Height of saturated fill above base hsat = max(hwater - tbase - dds, 0 mm) = 0 mm Density of wall construction �wall = 23.6 kN/m3

Density of base construction �base = 23.6 kN/m3

Angle of rear face of wall � = 90.0 deg Angle of soil surface behind wall � = 0.0 deg Effective height at virtual back of wall heff = hwall + lheel � tan(�) = 3850 mm

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Retained material details Mobilisation factor M = 1.5Moist density of retained material �m = 18.0 kN/m3

Saturated density of retained material �s = 21.0 kN/m3

Design shear strength �' = 24.2 deg Angle of wall friction � = 0.0 deg

Base material details Moist density �mb = 18.0 kN/m3

Design shear strength �'b = 24.2 deg Design base friction �b = 18.6 deg Allowable bearing pressure Pbearing = 100 kN/m2

Using Coulomb theory Active pressure coefficient for retained material

Ka = sin(�+ �')2 / (sin(�)2 � sin(�- �) � [1 + (sin(�' + �) � sin(�' - �) / (sin(�- �) � sin(�+ �)))]2) = 0.419Passive pressure coefficient for base material

Kp = sin(90- �'b)2 / (sin(90- �b) � [1 - (sin(�'b + �b) � sin(�'b) / (sin(90 + �b)))]2) = 4.187

At-rest pressure At-rest pressure for retained material K0 = 1 – sin(�’) = 0.590

Loading details Surcharge load on plan Surcharge = 10.0 kN/m2

Applied vertical dead load on wall Wdead = 85.6 kN/m Applied vertical live load on wall Wlive = 3.8 kN/m Position of applied vertical load on wall lload = 3150 mm Applied horizontal dead load on wall Fdead = 0.0 kN/m Applied horizontal live load on wall 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

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Vertical forces on wall Wall stem wwall = hstem � twall � �wall = 28.9 kN/m Wall base wbase = lbase � tbase � �base = 27.7 kN/m Applied vertical load Wv = Wdead + Wlive = 89.4 kN/m Total vertical load Wtotal = wwall + wbase + Wv = 146 kN/m

Horizontal forces on wall Surcharge Fsur = Ka � Surcharge � heff = 16.1 kN/m Moist backfill above water table Fm_a = 0.5 � Ka � �m � (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 � Kp � cos(�b) � (dcover + tbase + dds - dexc)2 � �mb = 4.4kN/mPropping force Fprop = max(Ftotal - Fp - (Wtotal - Wlive) � tan(�b), 0 kN/m) Fprop = 19.7 kN/m

Overturning moments Surcharge Msur = Fsur � (heff - 2 � dds) / 2 = 31 kNm/m Moist backfill above water table Mm_a = Fm_a � (heff + 2 � hwater - 3 � dds) / 3 = 71.7 kNm/m Total overturning moment Mot = Msur + Mm_a = 102.7 kNm/m

Restoring moments Wall stem Mwall = wwall � (ltoe + twall / 2) = 91.8 kNm/m Wall base Mbase = wbase � lbase / 2 = 46.3 kNm/m Design vertical dead load Mdead = Wdead � 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 � lload = 12 kNm/m Total moment for bearing Mtotal = Mrest - Mot + Mlive = 317.1 kNm/m Total vertical reaction R = Wtotal = 146.0 kN/m Distance to reaction xbar = Mtotal / R = 2172 mm Eccentricity of reaction e = abs((lbase / 2) - xbar) = 497 mm

Reaction acts within middle third of base Bearing pressure at toe ptoe = (R / lbase) - (6 � R � e / lbase2) = 4.8 kN/m2

Bearing pressure at heel pheel = (R / lbase) + (6 � R � e / lbase2) = 82.4 kN/m2

PASS - Maximum bearing pressure is less than allowable bearing pressure

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

Ultimate limit state load factors Dead load factor �f_d = 1.4Live load factor �f_l = 1.6Earth and water pressure factor �f_e = 1.4

Factored vertical forces on wall Wall stem wwall_f = �f_d � hstem � twall � �wall = 40.5 kN/m Wall base wbase_f = �f_d � lbase � tbase � �base = 38.7 kN/m Applied vertical load Wv_f = �f_d � Wdead + �f_l � Wlive = 125.9 kN/m Total vertical load Wtotal_f = wwall_f + wbase_f + Wv_f = 205.1 kN/m

Factored horizontal at-rest forces on wall Surcharge Fsur_f = �f_l � K0 � Surcharge � heff = 36.3 kN/m Moist backfill above water table Fm_a_f = �f_e � 0.5 � K0 � �m � (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 Fp_f = �f_e � 0.5 � Kp � cos(�b) � (dcover + tbase + dds - dexc)2 � �mb = 6.1 kN/m Propping force Fprop_f = max(Ftotal_f - Fp_f - (Wtotal_f - �f_l � Wlive) � tan(�b), 0 kN/m) Fprop_f = 73.4 kN/m

Factored overturning moments Surcharge Msur_f = Fsur_f � (heff - 2 � dds) / 2 = 70 kNm/m Moist backfill above water table Mm_a_f = Fm_a_f � (heff + 2 � hwater - 3 � dds) / 3 = 141.4 kNm/m Total overturning moment Mot_f = Msur_f + Mm_a_f = 211.4 kNm/m

Restoring moments Wall stem Mwall_f = wwall_f � (ltoe + twall / 2) = 128.5 kNm/m Wall base Mbase_f = wbase_f � lbase / 2 = 64.9 kNm/m Design vertical load Mv_f = Wv_f � lload = 396.6 kNm/m Total restoring moment Mrest_f = Mwall_f + Mbase_f + Mv_f = 590 kNm/m

Factored bearing pressure Total moment for bearing Mtotal_f = Mrest_f - Mot_f = 378.6 kNm/m Total vertical reaction 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 / lbase) - (6 � Rf � ef / lbase2) = 42.5 kN/m2

Bearing pressure at heel pheel_f = (Rf / lbase) + (6 � Rf � ef / lbase2) = 80 kN/m2

Rate of change of base reaction rate = (ptoe_f - pheel_f) / lbase = -11.19 kN/m2/mBearing pressure at stem / toe pstem_toe_f = max(pheel_f + (rate � (lheel + twall)), 0 kN/m2) = 76.1kN/m2

Bearing pressure at mid stem pstem_mid_f = max(pheel_f + (rate � (lheel + twall / 2)), 0 kN/m2) = 78kN/m2

Bearing pressure at stem / heel pstem_heel_f = max(pheel_f + (rate � lheel), 0 kN/m2) = 80 kN/m2

Design of reinforced concrete retaining wall toe (BS 8002:1994)

Material properties Characteristic strength of concrete fcu = 40 N/mm2

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Characteristic strength of reinforcement fy = 500 N/mm2

Base details Minimum area of reinforcement k = 0.13 % Cover to reinforcement in toe ctoe = 30 mm

Calculate shear for toe design Shear from bearing pressure Vtoe_bear = (ptoe_f + pstem_toe_f) � ltoe / 2 = 177.8 kN/m Shear from weight of base Vtoe_wt_base = �f_d � �base � ltoe � tbase = 34.7 kN/m Total shear for toe design Vtoe = Vtoe_bear - Vtoe_wt_base = 143.1 kN/m

Calculate moment for toe design Moment from bearing pressure Mtoe_bear = (2 � ptoe_f + pstem_mid_f) � (ltoe + twall / 2)2 / 6 = 273.9kNm/mMoment from weight of base Mtoe_wt_base = (�f_d � �base � tbase � (ltoe + twall / 2)2 / 2) = 58.3kNm/mTotal moment for toe design Mtoe = Mtoe_bear - Mtoe_wt_base = 215.6 kNm/m

Check toe in bending Width of toe b = 1000 mm/m Depth of reinforcement dtoe = tbase – ctoe – (�toe / 2) = 310.0 mm Constant Ktoe = Mtoe / (b � dtoe2 � fcu) = 0.056

Compression reinforcement is not required Lever arm ztoe = min(0.5 + (0.25 - (min(Ktoe, 0.225) / 0.9)),0.95) � dtoe

ztoe = 289 mm Area of tension reinforcement required As_toe_des = Mtoe / (0.87 � fy � ztoe) = 1713 mm2/mMinimum area of tension reinforcement As_toe_min = k � b � tbase = 455 mm2/m Area of tension reinforcement required As_toe_req = Max(As_toe_des, As_toe_min) = 1713 mm2/m Reinforcement provided 20 mm dia.bars @ 150 mm centresArea of reinforcement provided As_toe_prov = 2094 mm2/m

PASS - Reinforcement provided at the retaining wall toe is adequate

Check shear resistance at toe Design shear stress vtoe = Vtoe / (b � dtoe) = 0.462 N/mm2

Allowable shear stress vadm = min(0.8 � (fcu / 1 N/mm2), 5) � 1 N/mm2 = 5.000 N/mm2

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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Design of reinforced concrete retaining wall stem (BS 8002:1994)



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 = �f_l � K0 � Surcharge � (heff - tbase - dds) = 33 kN/m Moist backfill above water table Fs_m_a_f = 0.5 � �f_e � K0 � �m � (heff - tbase - dds - hsat)2 = 91.1kN/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 � (hstem + tbase) / 2 = 63.6 kNm/m Moist backfill above water table Ms_m_a = Fs_m_a_f � (2 � hsat + heff - dds + tbase / 2) / 3 = 122.2kNm/mTotal moment for stem design Mstem = Ms_sur + Ms_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 – (�stem / 2) = 310.0 mm Constant Kstem = Mstem / (b � dstem2 � fcu) = 0.048

Compression reinforcement is not required Lever arm zstem = min(0.5 + (0.25 - (min(Kstem, 0.225) / 0.9)),0.95) � dstem

zstem = 292 mm Area of tension reinforcement required As_stem_des = Mstem / (0.87 � fy � zstem) = 1461 mm2/m Minimum area of tension reinforcement As_stem_min = k � b � twall = 455 mm2/m Area of tension reinforcement required As_stem_req = Max(As_stem_des, As_stem_min) = 1461 mm2/m Reinforcement provided 20 mm dia.bars @ 150 mm centresArea of reinforcement provided As_stem_prov = 2094 mm2/m

PASS - Reinforcement provided at the retaining wall stem is adequate

Check shear resistance at wall stem Design shear stress vstem = Vstem / (b � dstem) = 0.163 N/mm2


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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

vstem < vc_stem - No shear reinforcement required

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Indicative retaining wall reinforcement diagram

Toe bars - 20 mm dia.@ 150 mm centres - (2094 mm2/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

Toe reinforcement

Stem reinforcement

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Wall details Retaining wall type Cantilever propped at baseHeight of retaining wall stem hstem = 3500 mm Thickness of wall stem twall = 350 mm Length of toe ltoe = 3000 mm Length of heel lheel = 0 mm Overall length of base lbase = ltoe + lheel + twall = 3350 mm Thickness of base tbase = 350 mm Depth of downstand dds = 0 mm Position of downstand lds = 1900 mm Thickness of downstand tds = 350 mm Height of retaining wall hwall = hstem + tbase + dds = 3850 mm Depth of cover in front of wall dcover = 0 mm Depth of unplanned excavation dexc = 0 mm Height of ground water behind wall hwater = 2500 mm Height of saturated fill above base hsat = max(hwater - tbase - dds, 0 mm) = 2150 mm Density of wall construction �wall = 23.6 kN/m3

Density of base construction �base = 23.6 kN/m3

Angle of rear face of wall � = 90.0 deg Angle of soil surface behind wall � = 0.0 deg Effective height at virtual back of wall heff = hwall + lheel � tan(�) = 3850 mm

Retained material details Mobilisation factor M = 1.5Moist density of retained material �m = 18.0 kN/m3

Saturated density of retained material �s = 21.0 kN/m3

Design shear strength �' = 24.2 deg Angle of wall friction � = 0.0 deg

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Base material details Moist density �mb = 18.0 kN/m3

Design shear strength �'b = 24.2 deg Design base friction �b = 18.6 deg Allowable bearing pressure Pbearing = 100 kN/m2

Using Coulomb theory Active pressure coefficient for retained material

Ka = sin(�+ �')2 / (sin(�)2 � sin(�- �) � [1 + (sin(�' + �) � sin(�' - �) / (sin(�- �) � sin(�+ �)))]2) = 0.419Passive pressure coefficient for base material

Kp = sin(90- �'b)2 / (sin(90- �b) � [1 - (sin(�'b + �b) � sin(�'b) / (sin(90 + �b)))]2) = 4.187

At-rest pressure At-rest pressure for retained material K0 = 1 – sin(�’) = 0.590

Loading details Surcharge load on plan Surcharge = 10.0 kN/m2

Applied vertical dead load on wall Wdead = 85.6 kN/m Applied vertical live load on wall Wlive = 3.8 kN/m Position of applied vertical load on wall lload = 3150 mm Applied horizontal dead load on wall Fdead = 0.0 kN/m Applied horizontal live load on wall 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

Vertical forces on wall Wall stem wwall = hstem � twall � �wall = 28.9 kN/m Wall base wbase = lbase � tbase � �base = 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 � Surcharge � heff = 16.1 kN/m Moist backfill above water table Fm_a = 0.5 � Ka � �m � (heff - hwater)2 = 6.9 kN/m Moist backfill below water table Fm_b = Ka � �m � (heff - hwater) � hwater = 25.4 kN/m Saturated backfill Fs = 0.5 � Ka � (�s- �water) � hwater2 = 14.6 kN/m Water Fwater = 0.5 � hwater2 � �water = 30.7 kN/m Total horizontal load Ftotal = Fsur + Fm_a + Fm_b + Fs + Fwater = 93.7 kN/m

Calculate propping force Passive resistance of soil in front of wall Fp = 0.5 � Kp � cos(�b) � (dcover + tbase + dds - dexc)2 � �mb = 4.4kN/mPropping force Fprop = max(Ftotal - Fp - (Wtotal - Wlive) � tan(�b), 0 kN/m) Fprop = 41.5 kN/m

Overturning moments Surcharge Msur = Fsur � (heff - 2 � dds) / 2 = 31 kNm/m Moist backfill above water table Mm_a = Fm_a � (heff + 2 � hwater - 3 � dds) / 3 = 20.3 kNm/m Moist backfill below water table Mm_b = Fm_b � (hwater - 2 � dds) / 2 = 31.8 kNm/m Saturated backfill Ms = Fs � (hwater - 3 � dds) / 3 = 12.2 kNm/m Water Mwater = Fwater � (hwater - 3 � dds) / 3 = 25.5 kNm/m Total overturning moment Mot = Msur + Mm_a + Mm_b + Ms + Mwater = 120.8 kNm/m

Restoring moments Wall stem Mwall = wwall � (ltoe + twall / 2) = 91.8 kNm/m Wall base Mbase = wbase � lbase / 2 = 46.3 kNm/m Design vertical dead load Mdead = Wdead � 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 � lload = 12 kNm/m Total moment for bearing Mtotal = Mrest - Mot + Mlive = 299 kNm/m Total vertical reaction R = Wtotal = 146.0 kN/m Distance to reaction xbar = Mtotal / R = 2048 mm Eccentricity of reaction e = abs((lbase / 2) - xbar) = 373 mm

Reaction acts within middle third of base Bearing pressure at toe ptoe = (R / lbase) - (6 � R � e / lbase2) = 14.5 kN/m2

Bearing pressure at heel pheel = (R / lbase) + (6 � R � e / lbase2) = 72.7 kN/m2

PASS - Maximum bearing pressure is less than allowable bearing pressure

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

Ultimate limit state load factors Dead load factor �f_d = 1.4Live load factor �f_l = 1.6Earth and water pressure factor �f_e = 1.4

Factored vertical forces on wall Wall stem wwall_f = �f_d � hstem � twall � �wall = 40.5 kN/m Wall base wbase_f = �f_d � lbase � tbase � �base = 38.7 kN/m Applied vertical load Wv_f = �f_d � Wdead + �f_l � Wlive = 125.9 kN/m Total vertical load Wtotal_f = wwall_f + wbase_f + Wv_f = 205.1 kN/m

Factored horizontal at-rest forces on wall Surcharge Fsur_f = �f_l � K0 � Surcharge � heff = 36.3 kN/m Moist backfill above water table Fm_a_f = �f_e � 0.5 � K0 � �m � (heff - hwater)2 = 13.6 kN/m Moist backfill below water table Fm_b_f = �f_e � K0 � �m � (heff - hwater) � hwater = 50.2 kN/m Saturated backfill Fs_f = �f_e � 0.5 � K0 � (�s- �water) � hwater2 = 28.9 kN/m Water Fwater_f = �f_e � 0.5 � hwater2 � �water = 42.9 kN/m Total horizontal load Ftotal_f = Fsur_f + Fm_a_f + Fm_b_f + Fs_f + Fwater_f = 171.9 kN/m

Calculate propping force Passive resistance of soil in front of wall Fp_f = �f_e � 0.5 � Kp � cos(�b) � (dcover + tbase + dds - dexc)2 � �mb = 6.1 kN/m Propping force Fprop_f = max(Ftotal_f - Fp_f - (Wtotal_f - �f_l � Wlive) � tan(�b), 0 kN/m) Fprop_f = 98.8 kN/m

Factored overturning moments Surcharge Msur_f = Fsur_f � (heff - 2 � dds) / 2 = 70 kNm/m Moist backfill above water table Mm_a_f = Fm_a_f � (heff + 2 � hwater - 3 � dds) / 3 = 40 kNm/m Moist backfill below water table Mm_b_f = Fm_b_f � (hwater - 2 � dds) / 2 = 62.7 kNm/m Saturated backfill Ms_f = Fs_f � (hwater - 3 � dds) / 3 = 24.1 kNm/m Water Mwater_f = Fwater_f � (hwater - 3 � dds) / 3 = 35.8 kNm/m Total overturning moment Mot_f = Msur_f + Mm_a_f + Mm_b_f + Ms_f + Mwater_f = 232.5 kNm/m

Restoring moments Wall stem Mwall_f = wwall_f � (ltoe + twall / 2) = 128.5 kNm/m Wall base Mbase_f = wbase_f � lbase / 2 = 64.9 kNm/m Design vertical load Mv_f = Wv_f � lload = 396.6 kNm/m Total restoring moment Mrest_f = Mwall_f + Mbase_f + Mv_f = 590 kNm/m

Factored bearing pressure Total moment for bearing Mtotal_f = Mrest_f - Mot_f = 357.5 kNm/m Total vertical reaction Rf = Wtotal_f = 205.1 kN/m Distance to reaction xbar_f = Mtotal_f / Rf = 1743 mm Eccentricity of reaction ef = abs((lbase / 2) - xbar_f) = 68 mm

Reaction acts within middle third of base Bearing pressure at toe ptoe_f = (Rf / lbase) - (6 � Rf � ef / lbase2) = 53.8 kN/m2

Bearing pressure at heel pheel_f = (Rf / lbase) + (6 � Rf � ef / lbase2) = 68.7 kN/m2

Rate of change of base reaction rate = (ptoe_f - pheel_f) / lbase = -4.45 kN/m2/m Bearing pressure at stem / toe pstem_toe_f = max(pheel_f + (rate � (lheel + twall)), 0 kN/m2) = 67.1kN/m2

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Bearing pressure at mid stem pstem_mid_f = max(pheel_f + (rate � (lheel + twall / 2)), 0 kN/m2) = 67.9kN/m2

Bearing pressure at stem / heel pstem_heel_f = max(pheel_f + (rate � lheel), 0 kN/m2) = 68.7 kN/m2

Design of reinforced concrete retaining wall toe (BS 8002:1994)



Base details Minimum area of reinforcement k = 0.13 % Cover to reinforcement in toe ctoe = 30 mm

Calculate shear for toe design Shear from bearing pressure Vtoe_bear = (ptoe_f + pstem_toe_f) � ltoe / 2 = 181.4 kN/m Shear from weight of base Vtoe_wt_base = �f_d � �base � ltoe � tbase = 34.7 kN/m Total shear for toe design Vtoe = Vtoe_bear - Vtoe_wt_base = 146.7 kN/m

Calculate moment for toe design Moment from bearing pressure Mtoe_bear = (2 � ptoe_f + pstem_mid_f) � (ltoe + twall / 2)2 / 6 = 294.8kNm/mMoment from weight of base Mtoe_wt_base = (�f_d � �base � tbase � (ltoe + twall / 2)2 / 2) = 58.3kNm/mTotal moment for toe design Mtoe = Mtoe_bear - Mtoe_wt_base = 236.5 kNm/m

Check toe in bending Width of toe b = 1000 mm/m Depth of reinforcement dtoe = tbase – ctoe – (�toe / 2) = 310.0 mm Constant Ktoe = Mtoe / (b � dtoe2 � fcu) = 0.062

Compression reinforcement is not required Lever arm ztoe = min(0.5 + (0.25 - (min(Ktoe, 0.225) / 0.9)),0.95) � dtoe

ztoe = 287 mm Area of tension reinforcement required As_toe_des = Mtoe / (0.87 � fy � ztoe) = 1894 mm2/mMinimum area of tension reinforcement As_toe_min = k � b � tbase = 455 mm2/m Area of tension reinforcement required As_toe_req = Max(As_toe_des, As_toe_min) = 1894 mm2/m Reinforcement provided 20 mm dia.bars @ 150 mm centresArea of reinforcement provided As_toe_prov = 2094 mm2/m

PASS - Reinforcement provided at the retaining wall toe is adequate

Check shear resistance at toe Design shear stress vtoe = Vtoe / (b � dtoe) = 0.473 N/mm2

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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

Design of reinforced concrete retaining wall stem (BS 8002:1994)



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 = �f_l � K0 � Surcharge � (heff - tbase - dds) = 33 kN/m Moist backfill above water table Fs_m_a_f = 0.5 � �f_e � K0 � �m � (heff - tbase - dds - hsat)2 = 13.6kN/mMoist backfill below water table Fs_m_b_f = �f_e � K0 � �m � (heff - tbase - dds - hsat) � hsat = 43.2 kN/m Saturated backfill Fs_s_f = 0.5 � �f_e � K0 � (�s- �water) � hsat2 = 21.4 kN/m Water Fs_water_f = 0.5 � �f_e � �water � hsat2 = 31.7 kN/m

Calculate shear for stem design Shear at base of stem Vstem = Fs_sur_f + Fs_m_a_f + Fs_m_b_f + Fs_s_f + Fs_water_f - Fprop_f = 44.1 kN/m

Calculate moment for stem design Surcharge Ms_sur = Fs_sur_f � (hstem + tbase) / 2 = 63.6 kNm/m Moist backfill above water table Ms_m_a = Fs_m_a_f � (2 � hsat + heff - dds + tbase / 2) / 3 = 37.6kNm/mMoist backfill below water table Ms_m_b = Fs_m_b_f � hsat / 2 = 46.4 kNm/m Saturated backfill Ms_s = Fs_s_f � hsat / 3 = 15.3 kNm/m Water Ms_water = Fs_water_f � hsat / 3 = 22.7 kNm/m Total moment for stem design Mstem = Ms_sur + Ms_m_a + Ms_m_b + Ms_s + Ms_water = 185.7 kNm/m

Check wall stem in bending Width of wall stem b = 1000 mm/m Depth of reinforcement dstem = twall – cstem – (�stem / 2) = 310.0 mm Constant Kstem = Mstem / (b � dstem2 � fcu) = 0.048

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Compression reinforcement is not required Lever arm zstem = min(0.5 + (0.25 - (min(Kstem, 0.225) / 0.9)),0.95) � dstem

zstem = 292 mm Area of tension reinforcement required As_stem_des = Mstem / (0.87 � fy � zstem) = 1460 mm2/m Minimum area of tension reinforcement As_stem_min = k � b � twall = 455 mm2/m Area of tension reinforcement required As_stem_req = Max(As_stem_des, As_stem_min) = 1460 mm2/m Reinforcement provided 20 mm dia.bars @ 150 mm centresArea of reinforcement provided As_stem_prov = 2094 mm2/m

PASS - Reinforcement provided at the retaining wall stem is adequate

Check shear resistance at wall stem Design shear stress vstem = Vstem / (b � dstem) = 0.142 N/mm2


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

vstem < vc_stem - No shear reinforcement required

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Indicative retaining wall reinforcement diagram

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

RETAINING WALL DEFLECTION

Toe reinforcement

Stem reinforcement

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CONCRETE BEAM ANALYSIS

Concrete beam dimensions:-

Beam width b = 1000 mm

Beam depth h = 350 mm

Cross-section area A = b � h = 350000 mm2

Major axis second moment of area Ixx = b � h3 / 12 = 3.57�109 mm4

fcu = 35 N/mm2

E = 20 kN/mm2 + 200 � fcu = 27.0 kN/mm2

Ref BS8110:1985:Pt 2 - Eq 17

� = �C.norm = 2400 kg/m3

CONTINUOUS BEAM ANALYSIS - INPUTBEAM DETAILS

Number of spans = 1Material Properties:

Modulus of elasticity = 27 kN/mm2 Material density = 2400 kg/m3

Support Conditions: Support A Vertically "Restrained" Rotationally "Restrained"

1089

Prop

14.5 72.74.2 10.2 11.7 24.525.0

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Support B Vertically "Free" Rotationally "Free"Span Definitions: Span 1 Length = 3500 mm Cross-sectional area = 350000 mm2 Moment of inertia = 3.57�109 mm4

LOADING DETAILS Beam Loads: Load 1 UDL Imposed load 4.2 kN/m Load 2 Partial VDL Dead load 10.2 kN/m at 2.700 m to 0.0 kN/m at 3.500 m Load 3 Partial UDL Dead load 10.2 kN/m from 0.000 m to 2.700 m Load 4 Partial VDL Dead load 11.7 kN/m at 0.000 m to 0.0 kN/m at 2.700 m Load 5 Partial VDL Imposed load 24.5 kN/m at 0.000 m to 0.0 kN/m at 2.700 m LOAD COMBINATIONS Load combination 1Span 1 1.4�Dead + 1.6�Imposed Load combination 2Span 1 1�Dead + 1�Imposed

CONTINUOUS BEAM ANALYSIS - RESULTSSupport Reactions - Combination SummarySupport A Max react = -95.2 kN Min react = -142.8 kN Max mom = -119.0 kNm Min mom = -177.7 kNm Support B Max react = 0.0 kN Min react = 0.0 kN Max mom = 0.0 kNm Min mom = 0.0 kNm Beam Max/Min results - Combination Summary

Maximum shear = 142.8 kN Minimum shearFmin = 0.0 kN Maximum moment = 0.0 kNm Minimum moment = -177.7 kNm Maximum deflection = 4.7 mm Minimum deflection = 0.0 mm

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6. Noise Vibration and DustBest construction method should be chosen to reduce the unnecessary Noise, Vibration and dust. The following table is a guidance to minimise the effect of the same.

Borehole test, soil investigation, CTMP and CMS. Full investigations and reports have to be carried out ahead of building works to formalize the best practical means to be used

CONSTRUCTION

METHOD

Measure, NOISE DUST VIBRATION

In accordance with the best practical means, to be used

To minimize, noise, vibration and dust during the construction of the basement, including the excavation, that is likely to affect adjacent residential premises and school(if any)

1. Preparation of site to fully contain the area

Boarding to front of house enclosing entrance, and windows kept in place for complete duration of construction

Boarding keeps noise inside the house and keeps house more rigid stopping attenuation, absorbs sound and

Stops airborne sound escaping

Dust from debris stored internally is contained within boarded up house preventing it from escaping to neighbours before collection.

Any internal vibration is further reduced by additional boarding to absorb before emitting to neighbour: as timber absorbs vibration better than metal or glass. The house is also more rigid, stopping vibration

Windows retained and sealed shut during construction, including front door and terrace doors kept closed

Airborne noise is contained within development

Airborne dust is contained within the development

Windows being sealed shut (taped) stops any rattling of windows or accentuation of any vibrations on site

Hording and sheeting to cover roof terrace.

Covering with hording and sheeting restricts airborne noise from escaping as best can be.

Sheeting to roof terrace stops window blowing up dust from excavation and any dust generated from

Hording and sheeting stops vibration as best is practicable.

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CONSTRUCTION

METHOD


works escaping to vicinity.

Retention of internal floors and structure during excavation works

Keeping the internal floors in situ during works allows the house to work as a buffer to contain noise and reduces the site area to the smallest volume reducing the effect noise can have.

Dust is contained to a smaller area and has several filters (ie floors and walls) to pass through and thus get stopped before it can affect neighbours, thus reduced.

Retaining the existing structure reduces vibration by keeping the house rigid and secondly by having a mix of materials all with different attenuation frequencies; vibration is absorbed and not accentuated, lastly floors and walls act as a break in otherwise continuous structure which acts as a buffer to stop vibration continuing out to neighbours.

Temporaryworks and structure

Temporary works allow the house to be kept rigid and allow for small scale, less noise emitting methods of construction to be used.

Temporary works keep the house rigid and safe so stop other areas of the house degenerating through works and thus dust being created.

Temporary works keep the house rigid which stops vibrations.

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CONSTRUCTION

METHOD


2. Management and hours of working

Project manager to manage all works on site, member of Considerate Contractors Scheme

Hours of working are restricted and staff supervised to use tools appropriately. No radio on site.

Small team working reducing noise. Coordination between workers ensured.

Hours of working are restricted and staff supervised to use tools appropriately with appropriate guarding to prevent dust migration.

Hours of working are restricted and staff supervised to use tools appropriately and reduced use of power tools to minimize vibration.

3. Excavation of basement

Non-percussive tools used for excavation (ie hand dug)

Hand tools are quieter. Method chosen reduces need for any heavy noisy machinery

Less dust generated by hand tools than fast repetitive motor driven tools.

Vibration is minimized by not using percussive tools

Excavation limited to 1m runs and shuttered for reinforced concretefoundations.

Each underpin is restricted to 1m lengths containing noise and amount of work that can be done at once to small area thus reducing overall hubbub. Method is quieter than piling or machine methods.

Dust is contained within shuttering, area is dampened with water to allow digging and eliminate dust.

Shuttering contains any subsequent vibration from excavation and keeping surrounding area soil intact.

Removal of spoil

All spoil is hand bagged and stored internally by hand so no noise from skip or large refuse area, removed as per CTMP by small

Spoil hand bagged, not using electric conveyor belt, and reducing emission of dust.

Spoil bagged by hand (ie shovel) so no machinery to transmit vibration

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CONSTRUCTION

METHOD


van and hand loaded

Removal of debris

Bagged debris is stored internally in a covered area and removed by waiting small van as per CTMP timed to cause least disruption

Debris removed by hand; dust contained within refuse sack, sealed shut.

Debris removed by hand, vibration minimized, in bags.

Mixing and pouring of concrete for underpins

Concrete is mixed on site for small quantities for underpin, contained within the site for noise and for short period of time once underpin and shuttering formed (ie

Separate activity)

Area set aside and shuttered off for mixing concrete to contain dust. Only small quantities mixed at time. Only small amounts of dry concrete

Stored on site in internal area to avoid unnecessary dust.

Concrete mixer put on level base in clear working area to avoid vibration.

Delivery of concrete for floor reinforced floor slabs

Large quantities are not mixed on site but delivered and pumped by specialist lorry to site in speedy low noise method from front of house through hording

No dust emitted from delivery of liquid concrete, area of road washed down before and after delivery. Area cordoned off as per CTMP (approx. ½ hour).

Large quantities of concrete mixed off site to reduce continuous vibration and delivered to site.

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Appendix A

Construction Sequence

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1. Basement Formation Suggested Method Statement

1.1. This method statement provides an approach that will allow the basement design to be correctly considered during construction. The statement also contains proposals for the temporary support to be provided during the works. The Contractor is responsible for the works on site and the final temporary works methodology and design on this site and any adjacent sites

1.2. This method statement has been written by a Chartered Engineer. The sequencing has been developed using guidance from ASUC (Association of Specialist Underpinning Contractors).

1.3. This method has been produced to allow for improved costings and for inclusion in the Party Wall Award. Final site conditions need there to be flexibility in the method statement: Should the site staff require alterations to the Method statement this is allowed once an alternative methodology, of the changes is provided, and an Addendum to the Party Wall Award will be required.

1.4. Contact Party Wall Surveyors to inform them of any changes to this method statement.

1.5. On this development, the approach is: construct the underpin segments that will support the permanent steel work insert the new steelwork remove load from above and place it onto new supporting steelwork cast the remainder of the retaining walls that will form the perimeter of the basement.

1.6. Temporary props will be provided along the height of the pin in the temporary condition. Before the base is cast cross props are needed. The base/ground slab provides propping in the final condition. In the temporary condition, the edge of the slab is buttressed against the soil in the middle of the property. Also the skin friction between the concrete base and the soil provides further resistance. The central soil mass is to be removed in portions (thirds but no greater than 8m) and cross propping subsequently added as the central soil ass is removed

1.7. A ground investigation has been undertaken. The soil present is made ground over gravels, over clay with decreasing sandy content and increased density as the depth increased with accorded with other investigations made in the area.

1.8. The bearing pressures have been limited to 100kN/m2

1.9. The water table was encountered at 8.9m BGL and hence on this site it will not be an issue during the construction.

1.10. The structural waterproofer (not Croft) must comment on the proposed design and ensure that he is satisfied that the proposals will provide adequate waterproofing.

1.11. Provide engineers with concrete mix, supplier, delivery and placement methods two weeks prior to the first pour. Site mixing of concrete should not be employed apart from in small

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sections (less than 1m3). The contractor must provide a method on how to achieve site mixing to the correct specification. The contractor must undertake toolbox talks with staff to ensure site quality is maintained.

2. Enabling Works

2.11. The site is to be hoarded with ply board sheets, at least 2.2m high, to prevent unauthorised public access.

2.12. Licences for skips and conveyors should be posted on the hoarding.

2.13. Provide protection to public where conveyor extends over footpath. Depending on the requirements of the local authority, construct a plywood bulkhead over the pavement. Hoarding to have a plywood roof covering over the footpath, night-lights and safety notices.

2.14. Dewater: No significant dewatering is expected. Localised removal of water may be required to deal with rain from perched water or localised water. This is to be dealt with by localised pumping. Typically achieved by a small sump pump in a bucket.

2.15. On commencement of construction, the contractor will determine the foundation type, width and depth. Any discrepancies will be reported to the structural engineer in order that the detailed design may be modified as necessary.

3. Basement Sequencing

3.11. Begin by placing cantilevered walls 1 2 noted on plans. (Cantilevered walls to be placed in accordance with Section 4.)

3.12. Needle and prop the first floor/ walls over.

3.13. Insert steel over and sit on cantilevered walls.

3.13.1. Beams over 6m to be jacked on site to reduce deflections of floors.

3.13.2. Dry pack to steelwork. Ensure a minimum of 24 hours from casting cantilevered walls to dry-packing. Grout column bases

3.14. Excavate lightwell to front of property down to 600mm below external ground level.

3.15. Excavate first front corner of lightwell. (Follow methodology in Section 4)

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3.16. Excavate second front corner of lightwell. (Follow methodology in Section 4)

3.17. Continue excavating section pins to form front lightwell. (Follow methodology in Section 4)

3.18. Place cantilevered retaining wall to the left side of front opening. After 48 hours place cantilevered retaining wall to the right side of front opening.

3.19. Needle and prop front wall. Insert support

Figure 17 Example of needling to existing wall

3.20. Excavate out first 1m around front opening, prop floor and erect conveyor.

3.21. Continue cantilevered wall formation around perimeter of basement following the numbering sequence on the drawings.

3.21.1. Excavation for the next numbered sequential sections of underpinning shall not commence until at least 8 hours after drypacking of previous works. Excavation of adjacent pin to not commence until 48 hours after drypacking. (24hours possible due to inclusion of Conbextra 100 cement accelerator to dry pack mix). No more than

3.21.2. Floor over to be propped as excavation progresses. Steelwork to support floor to be inserted as works progress.

3.22. Excavate and cast floor slab

3.22.1. Excavate 1/3 of the middle section of basement floor. As excavation proceeds, place Slim Shore props at a maximum of 2.5m c/c across the basement. Locate props at a third of the height of the wall.

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3.22.2. Continue excavating the next 1/3 and prop then repeat for the final 1/3.

3.22.3. Place below-slab drainage. Croft recommends that all drainage is encased in concrete below the slab and cast monolithically with the slab. Placing drainage on pea shingle below the slab allows greater penetration for water ingress.

3.22.4. Place reinforcement for basement slab.

3.22.5. Building Control Officer and Engineer are to be informed five working days before reinforcement is ready and invited for inspection.

3.22.6. Once inspected, pour concrete.

3.23. Provide structure to ground floor and water proofing to retaining walls as required. It is recommended to leave 3-4 weeks between completion of the basement and installing drained cavity. This period should be used to locate and fill any localised leakage of the basement

4. Underpinning and Cantilevered Walls 4.11. Prior to installation of new structural beams in the superstructure, the contractor may

undertake the local exploration of specific areas in the superstructure. This will confirm the exact form and location of the temporary works that are required. The permanent structural work can then be undertaken whilst ensuring that the full integrity of the structure above is maintained.

4.12. Provide propping to floor where necessary.

4.13. Excavate first section of retaining wall (no more than 1000mm wide). Where excavation is greater than 1.2m deep, provide temporary propping to sides of excavation to prevent earth collapse (Health and Safety). A 1000mm width wall has a lower risk of collapse to the heel face.

4.14. Excavation of pins involves working in confined spaces and the following measures should be applied:

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o Operatives must wear a harness and there must be a winch above the excavation.

o An attendant must be present at all times, at ground level, while excavation is occupied.

o A rescue plan must be produced prior to the works as well as a task-specific risk and method statement.

o Working in the confined space should require a permit to work.

Figure 18 – Schematic Plan view of soil propping

Figure 19 Propping examples

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Figure 20 Examples of excavations of pins

Figure 21 Examples of completed walls and back propping to central soil mass

4.15. Backpropping of rear face: Rear face to be propped in the temporary conditions with a minimum of 2 trench sheets. Trench sheets are to extend over entire height of excavation. Trench sheets can be placed in short sections as the excavation progresses.

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Figure 22 Example of trench sheet back propping

4.15.1. If the ground is stable, trench sheets can be removed as the wall reinforcement is placed and the shuttering is constructed.

4.15.2. Where trench sheets are left in, slight over spill may occur past the neighbours boundary wall line. Where this slight over spill is not allowed by the Party Wall Surveyors then cement particle board should be used as noted below.

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4.15.3. Where soft spots are encountered, leave in trench sheets or alternatively back prop with precast lintels or sacrificial boards. If the soil support to the ends of the lintels is insufficient, then brace the ends of the PC lintels with 150x150 C24 timbers and prop with Acrows diagonally back to the ground.

4.15.4. Where voids are present behind the lintels or trench sheeting, grout voids behind sacrificial propping. Grout to be 3:1 sand/cement packed into voids.

4.15.5. Prior to casting, place layer of DPM between trench sheeting (or PC lintels) and new concrete. The lintels are to be cut into the soil by 150mm either side of the pin. A site stock of a minimum of 10 lintels should be present to prevent delays due to ordering.

4.16. If cut face is not straight, or sacrificial boards noted previously have been used, place a 15mm cement particle board between sacrificial sheets or against the soil prior to casting. Cement particle board is to line up with the adjacent owner’s face of wall. The method adopted, to prevent localised collapse of the soil, is to install these progressively, one at a time. Cement particle board must be used in any condition where overspill onto the adjacent owner’s land is possible.

4.17. Excavate base. If soil over is unstable, prop top with PC lintel and sacrificial prop.

4.18. Visually inspect the footings and provide propping to local brickwork. If necessary install sacrificial Acrow, or pit props, and cast into the retaining wall.

4.19. Clear underside of existing footing.

4.20. Local Authority inspection to be carried out for approval of excavation base.

4.21. Place reinforcement for retaining wall base and stem. Drive H16 Bars U-bars into soil along centre line of stem to act as shear ties to adjacent wall underpin.

4.22. Site supervisor to inspect and sign off works before proceeding to next stage.

4.22.1. For pins 1, 3 and 5, inform the engineer five days before the reinforcement is ready, to allow for inspection of the reinforcement prior to casting.

4.23. Cast base. On short stems it is possible to cast base and wall at the same time. It is essential that pokers/vibrators are used to compact concrete.

4.24. Concrete Testing:

4.24.1. For first 3 pins take 4 cubes and test at 7 days then at 14 days and inform engineer of results. Test last cube at 28 days. If cube test results are low then action into concrete specification and placement method must be considered.

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4.24.2. If results are good from first three pins, then from the 4th pin onwards take 2 cubes of concrete from every third pin and store for testing. Test one at 28 days. If result is low, test second cube. Provide results to client and design team on request or if values are below those required.

4.24.3. A record of dates for the concrete pouring of each pin must be kept on site.

4.24.4. The location of where cubes were taken and their reference number must be recorded.

4.25. Horizontal temporary prop to base of wall to be inserted. Alternatively cast base against soil.

4.26. Place shuttering and pour concrete for retaining wall. Stop a minimum of 75mm from the underside of existing footing. It is essential that pokers/vibrators are used, hitting shutters is notconsidered adequate.

4.27. 24 hours after pouring the concrete pin, the gap shall be filled using a dry-pack mortar. Ram in dry-pack between the top of the retaining wall and existing masonry.

4.27.1. If gap is greater than 120mm, place a line of engineering bricks to the top of the wall. Dry pack from the engineering bricks to existing masonry.

4.28. After 24 hours, the temporary wall shutters can be removed.

4.29. Trim back existing masonry corbel and concrete on internal face.

4.30. Site supervisor to inspect and sign off for proceeding to the next stage. A record will be kept of the sequence of construction, which will be in strict accordance with recognised industry procedures.

5. Floor Support Timber Floor 5.11. The timber floor will remain in situ and be supported by a series of steel beams, to provide

open areas in the basement.

5.12. Position 100 x 100mm temporary timber beams, lightly packed, to underside of joists either side of existing sleeper wall and support with vertical Acrow props @ 750 centres. Remove sleeper walls and insert steel beams as a replacement. Steel beams to bear onto concrete padstones built into the masonry walls (refer to Structural Engineer’s details for padstone and beam sizes)

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5.13. Dismantle props and remove timber plates on completion of installation of permanent steel beams.

Concrete Ground bearing slabs 5.14. The support of the existing concrete floor will be undertaken in conjunction with the

underpinning process. Two opposite pins are constructed and allowed to cure as described elsewhere.

5.15. Locally prop concrete floors with Acrows at 2m centres with timbers between. If the underside is found be in poor condition then temporary boarding and props are to be introduced.

5.16. Insert steelwork and dry pack to underside of floor

5.17. Between steelwork, place 215wide x 65dp PC lintels at a maximum spacing of 600mm

5.18. If necessary, brick up to 50mm below the underside of the floor

5.19. Dry pack between lintel/brickwork to underside of slab.

5.20. Remove props

5.21. This process is to continue one pin width at a time.

6. Supporting existing walls above basement excavation 6.11. Where steel beams need to be installed directly under load-bearing walls, temporary works

will be required to enable this installation. Support comprises the temporary installation of steel needle beams at high level, supported on vertical props. This will enable safe removal of brickwork below and installation of the new beams and columns.

6.11.1. The condition of the brickwork must be inspected by the foreman to determine its condition and to assess the centres of needles. The foreman must inspect upstairs to consider where loads are greatest. Point loads between windows should be given greater consideration.

6.11.2. Needles are to be spaced to prevent the brickwork above ‘saw toothing’. Where brickwork is good, needles must be placed at a maximum of 1100mmcenters. Lighter needles or Strongboys should be placed at tighter centres under door thresholds

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6.12. Props are to be placed on sleepers on firm ground or, if necessary, temporary footings will be cast.

6.13. Once the props are fully tightened, the brickwork will be broken out carefully by hand. All necessary platforms and crash decks will be provided during this operation.

6.14. Decking and support platforms to enable handling of steel beams and columns will be provided as required.

6.15. Once full structural bearing is provided via beams and columns down to the new basement floor level, the temporary works will be redundant and can be safely removed.

6.16. Any voids between the top of the permanent steel beams and the underside of the existing walls will be packed out as necessary. Voids will be drypacked with a 1:3 (cement: sharp sand) drypack layer, between the top of the steel and underside of brickwork above.

6.17. Any voids in the brickwork left after removal of needle beams can at this point be repaired by bricking up and/or drypacking, to ensure continuity of the structural fabric.

7. Approval

7.11. Building Control Officer/Approved Inspector to inspect pin bases and reinforcement prior to casting concrete.

7.12. Contractor to keep list of dates of pins inspected and cast.

7.13. One month after the work is completed, the contractor is to contact Adjoining Party Wall Surveyor to attend site and complete final condition survey and to sign off works.

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8. Basement Temporary Works Design Lateral Propping

This calculation has been provided for the trench sheet and prop design of standard underpins in the temporary condition. There are gaps left between the sheeting and as such no water pressure will occur. Any water present will flow through the gaps between the sheeting and will be required to be pumped out.

Trench sheets should be placed at regular centres to deal with the ground. It is expected that the soil between the trench sheeting will arch. Looser soil will require tighter centres. It is typical for underpins to be placed at 1200c/c in this condition the highest load on a trench sheet is when 2 No.s trench sheets are used. It is for this design that these calculations have been provided.

Soil and ground conditions are variable. Typically one finds that, in the temporary condition, clays are more stable and the Cu (cohesive) values in clay reduce the risk of collapse. It is this cohesive nature that allows clays to be cut into a vertical slope. For these calculations, weak sand and gravels have been assumed. The soil properties are:

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Trench Sheet Design

Soil Depth Dsoil = 3500mm

Surcharge sur = 10kN/m2

Soil Density � = 20kN/m3

Angle of Friction � = 25�

ka = (1 - sin(�)) / (1 + sin(�)) = 0.406 kp = 1 / ka = 2.464

Soil pressure bottom soil = ka * �*Dsoil = 21.916kN/m2

Surcharge pressure surcharge = sur * ka = 4.059 kN/m2

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Sxx = 15.9 cm3

py = 275N/mm2

Ixx = 26.9cm4

A = (1m * 32.9kg/m2 ) / (7750kg/m3 ) = 4245.161mm2

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CONTINUOUS BEAM ANALYSIS - INPUTBEAM DETAILS

Number of spans = 3Material Properties:

Modulus of elasticity = 205 kN/mm2 Material density = 7860 kg/m3

Support Conditions: Support A Vertically "Restrained" Rotationally "Free"Support B Vertically "Restrained" Rotationally "Free"Support C Vertically "Restrained" Rotationally "Free"Support D Vertically "Free" Rotationally "Free"Span Definitions: Span 1 Length = 1000 mm Cross-sectional area = 4245 mm2 Moment of inertia = 269.�103 mm4

Span 2 Length = 1600 mm Cross-sectional area = 4245 mm2 Moment of inertia = 269.�103 mm4

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Span 3 Length = 1000 mm Cross-sectional area = 4245 mm2 Moment of inertia = 269.�103 mm4

LOADING DETAILS Beam Loads: Load 1 UDL Dead load 4.1 kN/m Load 2 VDL Dead load 21.9 kN/m to 0.0 kN/m LOAD COMBINATIONS Load combination 1Span 1 1.4�Dead Span 2 1.4�Dead Span 3 1.4�Dead

CONTINUOUS BEAM ANALYSIS - RESULTSSupport Reactions - Combination SummarySupport A Max react = -12.3 kN Min react = -12.3 kN Max mom = 0.0 kNm Min mom = 0.0 kNm Support B Max react = -38.5 kN Min react = -38.5 kN Max mom = 0.0 kNm Min mom = 0.0 kNm Support C Max react = -24.8 kN Min react = -24.8 kN Max mom = 0.0 kNm Min mom = 0.0 kNm Support D Max react = 0.0 kN Min react = 0.0 kN Max mom = 0.0 kNm Min mom = 0.0 kNm Beam Max/Min results - Combination Summary

Maximum shear = 18.8 kN Minimum shearFmin = -19.8 kN Maximum moment = 2.4 kNm Minimum moment = -4.4 kNm Maximum deflection = 17.1 mm Minimum deflection = -0.1 mm

Number of sheets Nos = 3

Moment M_allowable = Sxx * py * Nos = 13.118kNm

Deflection D = / Nos = 5.699mm

Acro Load Acro = Rmax_B / 2 = -19.272kN

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Acrow Props A or B are acceptable placed 0.5m from top, middle and 1m from bottom

Cross Props

Props should be placed a third up the wall measured from the bottom slab.

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Surcharge sur = 10kN/m2

Soil Density � = 20kN/m3

Angle of Friction � = 25�

Soil Depth Dsoil = 3000mm

ka = (1 - sin(�)) / (1 + sin(�)) = 0.406 kp = 1 / ka = 2.4641 - sin(�) = 0.577

Soil force bottomsoilforce = ka * �* Dsoil * Dsoil / 2 = 36.527kN/m

Surcharge Force Surchargeforce = ka * sur * Dsoil = 12.176kN/m

Place Props every other pin spacing = 2m

Propforce Propforce = spacing * (soilforce + Surchargeforce) = 97.406kN

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Figure 23 Mabey Mass 25 Load Chart

Job Number: 160602

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Figure 24 Mabey Mass 50 Load Chart

Provide Mabey Mass 50 at 2m Centres at 1/3 the height of the wall.

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Appendix B – Structural Plans & Details

Structural Drawings Plans 1:100

Structural Sections 1:50

Documents

5.1. Structural Design Calculations - RBKC