Example 3.16 Design of a cantilever retaining wall (BS 8110)

Transcription

1 Retaining walls Exaple 3.16 Design of a cantilever retaining wall (BS 8110) The cantilever retaining wall shown below is backfilled with granular aterial having a unit weight, ρ, of 19 kn 3 and an internal angle of friction, φ, of 30. Assuing that the allowable bearing pressure of the soil is 10 kn, the coefficient of friction is 0.4 and the unit weight of reinforced concrete is 4 kn 3 1. Deterine the factors of safety against sliding and overturning.. Calculate ground bearing pressures. 3. Design the wall and base reinforceent assuing f cu = 35 kn, f y = 500 kn and the cover to reinforceent in the wall and base are, respectively, 35 and W W W s F A k a 1 sin φ = 1 + sin φ 1 sin 30 = 1 + sin = = A W b Active pressure (p a ) = k a ρh = 1 / = 34. kn SLIDING Consider the forces acting on a 1 length of wall. Horizontal force on wall due to backfill, F A, is F A = 0.5p a h = = 9.34 kn and Weight of wall (W w ) = = 48.0 kn Weight of base (W b ) = = 38.4 kn Weight of soil (W s ) = = 75.5 kn Total vertical force (W t ) = kn Friction force, F F, is F F = µw t = = kn Assue passive pressure force (F P ) = 0. Hence factor of safety against sliding is OVERTURNING = 1.56 > Taking oents about point A (see above), su of overturning oents (M over ) is F A = = 166. kn _C03b 15 9/3/09, 1:14 PM

2 Design of reinforced concrete eleents to BS 8110 Exaple 3.16 continued Su of restoring oents (M res ) is M res = W w W b + W s.55 = = 8.5 kn Factor of safety against overturning is GROUND BEARING PRESSURE = Moent about centre line of base (M) is M = F A W W 1.1 W S = 3 N = kn M N = 67.5 kn = =. D = = Therefore, the axiu ground pressure occurs at the toe, p toe, which is given by p toe = + = 116 kn < allowable (10 kn ) 4 4 Ground bearing pressure at the heel, p heel, is BENDING REINFORCEMENT p heel = = 65 kn 4 4 Wall Height of ste of wall, h s = 5. Horizontal force on ste due to backfill, F s, is F s = 0.5k a ρh s Design oent at base of wall, M, is = / = kn 1 width γ Fh.. M = f s s = = kn 3 3 Effective depth Assue diaeter of ain steel (Φ) = 0. Hence effective depth, d, is d = 400 cover Φ/ = / = 355 Ultiate oent of resistance M u = 0.156f cu bd = = 688 kn Since M u > M, no copression reinforceent is required _C03b 16 9/3/09, 1:14 PM

3 Retaining walls Exaple 3.16 continued Steel area K A 6 M = = f bd cu 3 z = d[ ( 05. K / 09. )] s = = 355[ ( / 0. 9)] = M = = = 160 / 087. fz y Hence fro Table 3., provide H0 at 00 centres (A s = 1570 /) in near face (NF) of wall. Steel is also required in the front face (FF) of wall in order to prevent excessive cracking. This is based on the iniu steel area, i.e. = 0.13%bh = 0.13% = 50 / Hence, provide H1 at 00 centres (A s = 566 ) Base Heel = kn Toe A B C 900 D Heel p = = 91 kn p 1 p 3 p 1 = = 16.4 kn.( ) p 3 = 91 + = 14.8 kn 4 Design oent at point C, M c, is = kn 4 3 Assuing diaeter of ain steel (Φ) = 0 and cover to reinforceent is 50, effective depth, d, is d = / = K = = z = 340 [ ( / 0. 9 )] 0.95d = 33 A s 6 M = = = 114 / 087. fz y Hence fro Table 3., provide H0 at 00 centres (A s = 1570 /) in top face (T) of base _C03b 17 9/3/09, 1:14 PM

4 Design of reinforced concrete eleents to BS 8110 Exaple 3.16 continued Toe Design oent at point B, M B, is given by M B = kn A s = = 60 / < iniu steel area = 50 / Hence provide H1 at 00 centres (A s = 566 /), in botto face (B) of base and as distribution steel in base and ste of wall. REINFORCEMENT DETAILS The sketch below shows the ain reinforceent requireents for the retaining wall. For reasons of buildability the actual reinforceent details ay well be slightly different. U-bars H1-00 H1-00(FF) (FF) far face (NF) near face (T) top face (B) botto face Distribution steel H1-00 H0-00 (NF) 00 kicker Starter bars H0-00 H0-00 (T) 3.13 Design of short braced coluns Distribution steel H1-00 The function of coluns in a structure is to act as vertical supports to suspended ebers such as beas and roofs and to transit the loads fro these ebers down to the foundations (Fig. 3.83). Coluns are priarily copression ebers although they ay also have to resist bending oents transitted by beas. H1-00 (B) Coluns ay be classified as short or slender, braced or unbraced, depending on various diensional and structural factors which will be discussed below. However, due to liitations of space, the study will be restricted to the design of the ost coon type of colun found in building structures, naely short-braced coluns COLUMN SECTIONS Soe coon colun cross-sections are shown in Fig Any section can be used, however, _C03b 18 9/3/09, 1:14 PM

5 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN GEOMETRY Conc. Ste Height... Ste Thickness Top... Ste Thickness Bot... Footing Thickness... Toe Length... Heel Length... Soil Toe... Backfill Height... Backfill Slope Angle SEISMIC EARTH FORCES Hor. Seisic Coeff. kh... Ver. Seisic Coeff kv... Seisic Active Coeff. Kae Seisic Force Pae-Pa... SOIL BEARING PRESSURES Allow. Bearing Pressure.. 1 Max. Toe Min. Heel Total Footing Length Footing Length / Resultant Eccentricity e Resultant is Within the Middle Third c c deg KN/ APPLIED LOADS Unifor Surcharge... Strip Pressure... Strip 0.6 deep, fro Ste Ste Vertical (Dead)... Ste Vertical (Live)... Vertical Load Eccentricity Wind Load on Ste BACKFILL PROPERTIES Backfill Density... Earth Pressure Theory... Internal Friction Angle... Active Pressure Coeff. Ka Active Wall... Active Wall Pa... Water Table Height... SHEAR KEY DESIGN Shear Key Depth... Shear Key Thickness... Max. Shear Key.. Shear Capacity Ratio... No shear key has been specified Moent Capacity Ratio... KN/ KN/ c 19.0 KN/³ Rankine Active deg / KN/ c c KN/ 1

6 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN Backfill Pa... Water Table... Surcharge Hor... Strip Load Hor... Wind Load... Seisic Pae-Pa... Seisic Water... Seisic Selfweight OVERTURNING CALCULATIONS (Cob. D+H+W) OVERTURNING Force Ar Moent KN/ KN-/ Rh = 9.34 OTM = Ar of Horizontal Resultant = 9.34 = Ar of Vertical Resultant = =.8 Overturning Safety Factor = = 4.94 > Ste Top... Ste Taper... CMU Ste at Top.. Footing Weight... Shear Key... Soil Toe. Ste Wedge... Backfill Weight... Backfill Slope... Water Weight... Seisic Pae-Pa... Pa Heel... Vertical Load... Surcharge Ver... Strip Load Ver... RESISTING Force Ar Moent KN/ KN-/ Rv = RM = 80.3 STEM DESIGN (Cob. 0.9D+1.6H+E) Height d Mu ϕmn Ratio c KN-/ KN-/ Shear Crit. Height.. Resisting Shear ϕvc... Use vertical bars 0 c at backfill side Cut off alternate bars. Cut off length =.13 Vert. Bars Ebed. Ldh Reqd.. Vert. Bars Splice Length Ld KN/ KN/ c c SLIDING CALCS (Cob. D+H+W) Footing-Soil Friction Coeff... Friction Force at Base... Passive Pressure Coeff. Kp. Depth to Neglect Passive... Passive Wall... Passive Wall Pp... Horiz. Resisting Force... Horiz. Sliding Force... Sliding Safety Factor = Infinity KN/ / KN/ KN/ KN/ = 1.56 > 1.5 LOAD COMBINATIONS (ASCE 7) STABILITY STRENGTH 1 D+H+W D+L+H+W 3 D+H+0.7E 4 D+L+H+0.7E 1 1.4D 1.D+1.6(L+H) 3 1.D+0.8W 4 1.D+L+1.6W 5 1.D+L+E 6 0.9D+1.6H+1.6W 7 0.9D+1.6H+E

7 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN HEEL DESIGN (Cob. 0.9D+1.6H+E) Force Ar Moent KN/ KN-/ Upward Pressure. Concrete Weight.. Backfill Weight... Backfill Slope... Water Weight... Surcharge Ver.... Strip Load Ver.... Shear Crit. Sect... Resisting Shear ϕvc Mu = KN/ KN/ Use top bars 0 c, Transv. 0 c Resisting Moent ϕmn KN-/ Develop. Length Ratio at End... Develop. Length Ratio at Toe TOE DESIGN (Cob. 1.D+1.6(L+H)) Force Ar Moent KN/ KN-/ Upward Presssure Concrete Weight.. Soil Cover... Shear Crit. Sect... Resisting Shear ϕvc Mu = KN/ KN/ Use bott. bars 0 c, Transv. 0 c Resisting Moent ϕmn KN-/ Develop. Length Ratio at End... Develop. Length Ratio at Ste Concrete f'c... Rebars fy... MATERIALS Ste Footing MPa MPa 3

8 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN DESIGN CODES General Analysis... Concrete Design... Masonry Design... Load Cobinations... IBC-1 ACI MSJC-11 ASCE

9 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN Conc. Ste Height... Unifor Surcharge... Ste Thickness Top... c Strip Pressure... Ste Thickness Bot... c Footing Thickness... Ste Vertical (Dead)... KN/ Toe Length... Ste Vertical (Live)... KN/ Heel Length... Vertical Load Eccentricity... c Soil Toe... Wind Load on Ste... Backfill Height... Wind Height fro Top... Backfill Slope Angle... deg Wall taper atan ((4-4) / 100 / 5.00) = 00 rad Backfill slope * 3.14 / 180 = 00 rad Internal friction 3 * 3.14 / 180 = 0.54 rad Wall-soil friction 0.54 / = 0.6 rad Seisic angle atan (0 / (1-0)) = 00 rad Footing length / = 4.00 Height for Stability / 100 = 5.40 Earth pressure theory = Rankine Active Moist density = 19 KN/³ Saturated density =0 KN/³ Active coefficient = 0.33 Active pressure 0.33 * 19.0 = 6.3 / of height - For stability analysis (non-seisic) Active force 0.33 * 19.0 * 5.40² / = 9.3 KN/ 9.3 * Cos (00) = 9.3 KN/, 9.3 * Sin (00) = KN/ Water force Pw = (0.33 * ( ) + 9.8) * (0 + 4 / 100)² / = KN/ - For ste design (non-seisic) Active force 0.33 * 19.0 * 5.00² / = 79. KN/ 79. * Cos (00) = 79. KN/, 79. * Sin (00) = KN/ Water force Pw = (0.33 * ( ) + 9.8) * 0² / = KN/ 1

10 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN Active seisic coeff. = For stability analysis (seisic) Seisic force 0.30 * 19.0 * 5.40² / * (1 - ) = 83.5 KN/ 83.5 * Cos ( ) = 80.7 KN/ 83.5 * Sin ( ) = 1.6 KN/ Water force Pwe = 0 * ( ) * (0 + 4 / 100)² / = KN/ - For ste design (seisic) Seisic force 0.30 * 19.0 * 5.00² / = 71.6 KN/ 71.6 * Cos ( ) = 69.1 KN/ 71.6 * Sin ( ) = 18.5 KN/ Water force Pwe = 0 * ( ) * 0² / = KN/ Backfill = 1.0 * 9.3 = 9.3 KN/ Ar = 5.40 / 3 = 1.80 Moent = 9.3 * 1.80 = 166. KN-/ Water table = 1.0 * = KN/ Ar = (0 + 4 / 100) / 3 = 0.13 Moent = * 0.13 = KN-/ Surcharge = 1.0 * 0.33 * * 5.40 = KN/ Ar = 5.40 / =.70 Moent = *.70 = KN-/ Strip load = KN/ Ar =.50 Moent = *.50 = KN-/ Wind load = 1.0 * * 1.5 = KN/ Ar = 4 / / = 4.64 Moent = * 4.64 = KN-/ Backfill seisic = * ( ) = KN/ Ar = 0.6 * 5.40 = 3.4 Moent = * 3.4 = KN-/ Water seisic = * = KN/ Ar = (0 + 4 / 100) / 3 = 0.13 Moent = * 0.13 = KN-/ Wall seisic = * ( ) * 0 = KN/ Moent = = * ( * (4 / / ) + * (4 / / 3) * 4 / 100 / ) * 0 = KN-/ Hor. resultant Rh = = 9.3 KN/ Overturning oent OTM = = 166. KN-/ Ar of hor. resultant = 166. / 9.3 = 1.80

11 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN Ste weight 1.0 * 4 / 100 * 5.00 * 3.56 = 47.1 KN/ Ar = / 100 / = 0.90 Moent = 47.1 * 0.90 = 4.4 KN-/ Ste taper 1.0 * (4-4) / 100 * 5.00 / * 3.56 = KN/ Ar = / (4-4) / 100 * / 3 = 1.10 Moent = * 1.10 = KN-/ CMU ste at top = KN/ Ar = / 100 / = 0 Moent = * 0 = KN-/ Ftg. weight 1.0 * 4.00 * 4 / 100 * 3.56 = 37.7 KN/ Ar = 4.00 / =.00 Moent = 37.7 *.00 = 75.4 KN-/ Key weight 1.0 * 0 / 100 * / 100 * 3.56 = KN/ Ar = / 100 / = 0.70 Moent = * 0.70 = KN-/ Soil cover = 1.0 * 0.70 * 0 * 19.0 = KN/ Ar = 0.70 / = 0.35 Moent = * 0.35 = KN-/ Ste wedge = 1.0 * (4-4) / 100 * 5.00 / * 19.0 = KN/ Ar = / (4-4) / 100 / 3 = 1.10 Moent = * 1.10 = KN-/ Backfill weight = 1.0 *.90 * 5.00 * 19.0 = 75.5 KN/ Ar = / =.55 Moent = 75.5 *.55 = 70.5 KN-/ Backfill slope = = 1.0 * (.9 + (4-4) / 100) * 0 / * 19.0 = KN/ Ar = (.90 + (4-4) / 100) / 3 = 3.03 Moent = * 3.03 = KN-/ Water = 1.0 *.90 * 0 * ( ) = KN/ Ar = / =.55 Moent = *.55 = KN-/ Seisic Pae-Pa = * ( ) = KN/ Ar = 4.00 Moent = * 4.00 = KN-/ Backfill Pav = 1.0 * 1.6 = KN/ Ar = 4.00 Moent = * 4.00 = KN-/ Concentrated = 1.0 * + * = KN/ Ar = (4-15.) / 100 = 0.95 Moent = * 0.95 = KN-/ 3

12 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN Surcharge = 1.0 * (.9 + (4-4) / 100) * = KN/ Ar = (.90 + (4-4) / 100) / =.55 Moent = *.55 = KN-/ Strip = 1.0 * *.90 = KN/ Ar = / =.55 Moent = *.55 = KN-/ Ver. resultant Rv = KN/ Resisting oent RM = 80.3 KN-/ Ar of ver. resultant = 80.3 / =.8 Overturning ratio = 80.3 / 166. = 4.94 >.00 Eccentricity = - = = 0.18 Bearing length = Min (4.00, 3 * (4.00 / )) = 4.00 Toe bearing = + = * * ² = < 1 Heel bearing = - = * * ² =

13 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN Passive coefficient 1 / 0.33 = 3.00 Passive depth 0 + (4 + ) / = 0 Passive pressure top = 3.00 * 19.0 * 0.40 =.80 Passive pressure bot = 3.00 * 19.0 * ( ) =.80 Passive force = ( ) / * 0 = KN/ Friction force = Max (0, * 0.40) = KN/ Sliding ratio = ( ) / 9.3 = 1.56 > 1.50 Backfill = 1.6 * 78.7 = 16.7 KN/ Ar = 5.00 / 3 = 1.67 Moent = 16.7 * 1.67 = 11.1 KN-/ Water table = 1.6 * = KN/ Ar = 0 / 3 = 0 Moent = * 0 = KN-/ Surcharge = 1.6 * 0.33 * * 5.00 = KN/ Ar = 5.00 / =.50 Moent = *.50 = KN-/ Strip load = Ar =.50 Wind load = KN/ Moent = *.50 = KN-/ * * 1.5 = KN/ Ar = / = 4.4 Moent = * 4.4 = KN-/ Backfill seisic = 1.0 * ( ) = KN/ Ar = 0.6 * 5.00 = 3.00 Moent = * 3.00 = KN-/ Water seisic = 1.0 * = KN/ Ar = 0 / 3 = 0 Moent = * 0 = KN-/ Max. shear = = 16.7 KN/ Shear at critical section = Max. oent = = 11.1 KN-/ / 5.00 * 35.5 / 100 = KN/ Shear strength ACI Eq. (11-3) φ Vn = 0.75 * 0.17 * (35)½ * 10 * 35.5 = 61.5 KN/> KN/ Use c As = c²/ / (100 * 35.5) = 044 Bending strength φ Mn = 0.90 * 35.5² * 35.0 * 63 * ( * 63) = 41.6 KN-/> 11.1 KN-/ ACI Hooked 0.4 * 50 / (35.0)½ *.00 * 0.7 = 8.4 c ACI 1.5 Dev. length at footing = = = 35.0 c > 8.4 c 5

14 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN Bearing force = ( ) / *.90 = 18.4 KN/ Ar = = (15.0 *.90² / + ( ) *.90² / 6) / 18.4 = 1.08 Moent = 18.4 * 1.08 = KN-/ Concrete weight = 0.9 * 4 / 100 *.90 * 3.56 = 4.6 KN/ Ar = =.90 / = 1.45 Moent =4.6 * 1.45 = 35.7 KN-/ Backfill weight = 0.9 *.90 * 5.00 * 19.0 = 48.0 KN/ Ar = =.90 / = 1.45 Moent = 48.0 * 1.45 = KN-/ Backfill slope = = 0.9 * (.9 + (4-4) / 100) * 0 / * 19.0 = KN/ Ar =.90 * / 3 = 1.93 Moent = * 1.93 = KN-/ Water = 0.9 *.90 * 0 * ( ) = KN/ Ar = =.90 / = 1.45 Moent = * 1.45 = KN-/ 6

15 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN Surcharge = 0.9 * (.9 + (4-4) / 100) * = KN/ Ar = =.90 / = 1.45 Moent = * 1.45 = KN-/ Strip = Ar = Moent = * 1.45 = KN-/ 0.9 * * 1. = KN/ (4-4) / / = 1.45 Max. Shear Vu = = 90.1 KN/ Max. Moent Mu = = KN/ Shear strength ACI Eq. (11-3) φ Vn = 0.75 * 0.17 * (35)½ * 10 * 33.9 = 49.7 KN/> Vu = 90.1 KN/ Use c As = c²/ / (100 * 33.9) = 046 Bending strength φ Mn = 0.90 * 33.9² * 35.0 * 66 * ( * 66) = 30.3 KN-/> Mu = KN-/ Cover factor = Min (.5, ( /, / ) /.00) =.5 Straight = 50 / 1.1 / (35)½ * 0.8 * 1.3 /.5 *.00 = 63.9 c Hooked 0.4 * 50 / (35.0)½ *.00 * 0.7 = 8.4 c ACI 1.5 Dev. length at toe side = = ( ) / = c> 63.9 c Dev. length at heel side = =.90 / = 84.9 c > 63.9 c ACI ACI Eq. (1-1) Bearing force = ( ) / * 0.70 = KN/ Ar = = (143.8 * 0.70² / + ( ) * 0.70² / 3) / = 0.36 Moent = * 0.36 = 38.4 KN-/ Concrete weight = 1. * 4 / 100 * 0.70 * 3.56 = 7.9 KN/ Ar = = 0.70 / = 0.35 Moent =7.9 * 0.35 =.8 KN-/ Soil cover = 1. * 0.70 * 0 * 19.0 = KN/ Ar = = 0.70 / = 0.35 Moent = * 0.35 = KN-/ Max. Shear Vu = = 99.4 KN/ Shear at crit. section Vu = 99.4 * ( / 100) / 0.70 = 50.6 KN/ Max. Moent Mu = = 35.6 KN/ Shear strength ACI Eq. (11-3) φ Vn = 0.75 * 0.17 * (35)½ * 10 * 34.4 = 53.4 KN/> Vu = 50.6 KN/ Use c As = 5.65 c²/ 5.65 / (100 * 34.4) = 016 Bending strength ACI φ Mn = 0.90 * 34.4² * 35.0 * 3 * ( * 3) = 86. KN-/ > Mu = 35.6 KN-/ 7

16 Project: Verification Exaple ASDIP Retain 3. CANTILEVER RETAINING WALL DESIGN Cover factor = Min (.5, ( /, / ) / 1.0) =.5 Straight = 50 / 1.1 / (35)½ * 0.8 * 1.0 /.5 * 1.0 = 9.5 c ACI Eq. (1-1) Hooked 0.4 * 50 / (35.0)½ * 1.0 * 0.7 = 17.0 c ACI 1.5 Dev. length at toe side = = ( ) / = 35.0 c> 9.5 c Dev. length at toe side = = 0.70 / = 65.0 c> 9.5 c Shear key depth = c Shear key thickness = c Passive force = 1.6 * (.8 +.8) / * / 100 = KN/ Shear at crit. section Vu = * ( - 0.1) / = KN/ Ar = = (.8 * 0² / + (.8 -.8) * 0² / 3) / = 0 Max. oent Mu = * 0 = KN-/ Shear strength ACI Eq. (11-3) φ Vn = 0.75 * 0.17 * (35)½ * 10 * 0.1 = 0.7 KN/ > Vu = KN/ Use 30.5 c As = 4.3 c²/ 4.3 / (100 * 0.1) = Bending strength ACI φ Mn = 0.90 * 0.1² * 35.0 * * ( * 6.044) = 0.1 KN-/ > Mu = KN-/ 8