Job Number
Sheet
Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail :
[email protected]
Client Calcs by
Checked by
Date
Retaining Wall Design : Cantilever wall example C14
Input Data H1 H2 H3 Hw Hr B D
(m) (m) (m) (m) (m) (m) (m)
Wall Dimensions 5.5 C 0.5 F 0 xf 5.5 At 0.36 Ab 0.5 Cov wall 2.5 Cov base
0.5 0.3 2.40 0.3 0.4 50 50
(m) (m) (m) (m) (m) mm mm
Unfactored Live Loads W 1.5 (kN/m²) P 1 (kN) xp 1 (m) L 1 (kN/m) xl 1 (m) Lh (kN/m) x 0 (m)
General Parameters 20 (°) Soil frict φ 0 Fill slope β (°) 15 Wall frict δ (°) 25 ρ Conc kN/m3 18 kN/m3 ρ Soil fcu 30 (MPa) fy 450 (MPa)
Design Parameters SF Overt. 1.5 SF Slip 1.5 DL Factor 1.2 LL Factor 1.6 Pmax 150 (kPa)
Seepage allowed Active pressure applied on back of shear key for sliding Theory : Coulomb Wall type : Cantilever
SEISMIC ANALYSIS SETTINGS: Seismic Analysis ON/OFF:ON
Hor Accel. (g) 0.02 Vert Accel. (g) 0.01 Include LL's Y
VALUES OF PRESSURE COEFFICIENTS: Active Pressure coefficient Ka Passive Pressure coefficient Kp Seismic Active Pressure coefficient Kas Seismic Passive Pressure coefficient Kps Base frictional constant µ
:0.442 :3.029 :0.454 :1.345 :0.364
FORCES ACTING ON THE WALL: All forces/moments are per m Description Destabilizing forces: Total Active pressure Pa Siesmic component of Pa Triangular W-table press Pw Seismic component of Pw Hydrostatic pressure on bot of base: uniform portion Hydrostatic pressure on bot of base: triangular portion As a result of surcharge w As a result of Point load P As a result of Line Load L Siesmic wall inertia Stabilizing forces: Passive pressure on base Pp Siesmic component of Pp Weight of the wall + base Weight of soil on the base Hydrostatic pressure on top of rear portion of base Hydrostatic pressure on top of front portion of base
width
FORCES (kN ) and their LEVER ARMS (m ) F Horizontal Lever arm F Vertical Lever arm left (+) down (+) 121.722 2.973 85.328 2.597
1.845 3.300 1.878 3.300
3.560 0.223 0.223 1.767
2.750 5.055 5.055 1.582
-2.592 3.791
-0.000 0.300
34.356 0.861 0.000 0.000 -16.510
0.866 0.840 0.872 0.844 1.700
-82.551
2.267
1.031 0.065 0.065
0.855 0.809 0.809
88.358 103.378 121.399
1.228 2.125 2.150
0.000
0.250
Job Number
Sheet
Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail :
[email protected]
Client Calcs by
Checked by
Point load of 0.99 kN on backfill Line load of 0.99 kN/m on backfill UDL of 1.5 kPa
Date
0.090 0.990 3.861
1.500 1.500 2.100
EQUILIBRIUM CALCULATIONS AT SLS All forces/moments are per m
width
1.Moment Equilibrium Point of rotation: bottom front corner of base. For Overturning moment Mo calculate as follows: Mo = Sum(hor. forces x l.a.) - Sum(vert. forces x l.a.) For Stabilizing moment Mr calculate as follows: Mr = -Sum(hor. forces x l.a.) + Sum(vert. forces x l.a.) where l.a. = lever arm of each force. Stabilizing moment Mr : 598.93 kNm Destabilizing moment Mo : 583.24 kNm Safety factor against overturning = Mr/Mo = 1.027
*** SAFETY FACTOR IS LOWER THAN SPECIFIED MINIMUM OF
1.5 ***
2.Force Equilibrium Sum of Vertical forces Pv Frictional resistance Pfric Passive Pressure on shear key Passive pressure on base => Horizontal resistance Fr
: 254.48 kN : 92.62 kN : 5.15 kN : 2.59 kN : 100.37 kN
Horizontal sliding force on wall Fhw : 212.64 kN Horizontal sliding force on shear key Fht : -23.28 kN => Total Horizontal sliding force Fh : 189.37 kN Safety factor against overall sliding = Fr/Fh = 0.530
*** SAFETY FACTOR IS LOWER THAN SPECIFIED MINIMUM OF
1.50 ***
SOIL PRESSURES UNDER BASE Maximum pressure :2750.33 kPa Minimum pressure : 0 kPa at 3.21 m from right hand side of base. Maximum pressure occurs at left hand side of base
*** MAXIMUM PRESSURE EXCEEDS SPECIFIED ALLOWABLE PRESSURE BY 2600.3 kPa *** WALL MOMENTS (ULS) AND REINFORCEMENT TO BS8110 - 1997 Position from base top (m ) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50
Moment (kNm ) 366.56 346.82 326.82 307.61 289.16 271.47 254.51 238.27 222.74 207.90 193.74 180.23 167.37 155.13 143.50 132.47
Front Reinforcing Back Reinforcing Nominal (0.13%) (mm²/m ) (mm²/m ) (mm²/m ) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
2901.92 2740.12 2576.72 2421.20 2273.15 2132.20 1998.00 1870.24 1748.64 1632.93 1522.88 1418.24 1318.81 1224.39 1134.79 1049.83
522.60 520.00 517.40 514.80 512.20 509.60 507.00 504.40 501.80 499.20 496.60 494.00 491.40 488.80 486.20 483.60
Job Number
Sheet
Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail :
[email protected]
1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00
Client Calcs by
122.02 112.14 102.80 94.00 85.71 77.93 70.63 63.80 57.42 51.49 45.98 40.87 36.16 31.82 27.85 24.21 20.91 17.92 15.23 12.82 10.68 8.79 7.13 5.69 4.46 3.41 2.54 1.82 1.24 0.79 0.44 0.22 0.09 0.02 0.00
Checked by
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Date
969.35 896.48 827.21 761.34 698.82 639.58 583.57 530.70 480.93 434.18 390.37 349.44 311.31 275.90 243.14 212.94 185.23 159.90 136.88 116.08 97.40 80.74 66.00 53.09 41.89 32.30 24.20 17.48 12.02 7.70 4.38 2.14 0.87 0.20 0.01
481.00 478.40 475.80 473.20 470.60 468.00 465.40 462.80 460.20 457.60 455.00 452.40 449.80 447.20 444.60 442.00 439.40 436.80 434.20 431.60 429.00 426.40 423.80 421.20 418.60 416.00 413.40 410.80 408.20 405.60 403.00 400.40 397.80 395.20 392.60
BASE MOMENTS (ULS) AND REINFORCEMENT TO BS8110 - 1997 Position from left (m ) 0.07 0.14 0.20 0.27 0.34 0.41 0.48 0.54 0.61 0.68 0.75 0.82 0.88 0.95 1.02 1.09 1.16 1.22 1.29 1.36 1.43 1.50 1.56 1.63 1.70 1.77 1.84 1.90
Moment (kNm ) -0.00 -1.90 -7.61 -17.12 -30.43 -47.54 -68.46 -93.19 -121.71 -154.04 -190.18 -209.67 273.79 253.88 241.03 228.51 216.32 204.47 192.96 181.77 170.92 160.41 150.23 140.38 130.86 121.68 112.84 104.32
Top Reinforcing (mm²/m ) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1542.19 1423.55 1348.83 1278.77 1210.58 1144.26 1079.81 1017.22 956.51 897.66 840.68 785.57 732.33 680.95 631.44 583.81
Bot Reinforcing (mm²/m ) 0.00 10.64 42.57 95.78 170.28 266.06 383.13 521.49 681.13 862.05 1064.26 1173.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Nominal (0.13%) (mm²/m ) 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00
Job Number
Sheet
Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail :
[email protected]
1.97 2.04 2.11 2.18 2.24 2.31 2.38 2.45 2.52 2.58 2.65 2.72 2.79 2.86 2.92 2.99 3.06 3.13 3.20 3.26 3.33 3.40
Client Calcs by
96.14 88.30 80.79 73.61 66.77 60.26 54.08 48.24 42.73 37.56 32.72 28.21 24.04 20.20 16.69 13.52 10.68 8.18 6.01 4.17 2.67 1.50
Checked by
538.04 494.13 452.10 411.93 373.64 337.21 302.64 269.95 239.13 210.17 183.08 157.86 134.51 113.02 93.41 75.66 59.78 45.77 33.63 23.35 14.95 8.41
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Date
650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00 650.00
SHEAR CHECK AT WALL-BASE JUNCTION TO BS8110 - 1997 Shear force at bottom of wall V = 259.7 kN Shear stress at bottom of wall v = 0.76 MPa INADEQUATE Allowable shear stress vc = 0.66 MPa (based on Wall tensile reinf.)
Sketch of Wall
Design code: BS8110 - 1997 1.00 0.99kN/m 0.99kN
kh =0.02g kv =0.01g
0.50
2750.3kPa Wall type: Cantilever Theory: Coulomb
1.49
20.00°
0.50 0.40
0.30
0.50
5.50
15.00°
5.50
1.00 0.30 0.00°
2.50
2.40
SFslip = 0.53 SFovt = 1.03
Kas=0.45 Kps=1.34 µ=0.36 V=259.7kN v= 0.76MPa vc= 0.66MPa
Job Number
Sheet
Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail :
[email protected]
Client Calcs by
Checked by
Date
Wall Bending Moments
Moment max = 367 kNm @ -.500m
Wall Moments 5.00 4.50 4.00 3.50
2.50 2.00 1.50
Bending moment (kNm)
350
300
250
200
150
100
.500
50.0
1.00 0.00
Height (m)
3.00
Job Number
Sheet
Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail :
[email protected]
Client Calcs by
Checked by
Date
Base Bending Moments
300
Base Moments
Moment max = 274 kNm @ .703m
250
150
3.40
3.20
3.00
2.80
2.60
2.40
2.20
2.00
1.80
1.60
1.40
1.20
1.00
.800
.600
50.0
.400
100 .200
Bending moment (kNm)
200
-50.0 -100 -150 -200 Position (m)
Wall Reinforcement Wall Reinforcement Reinf. max = 2900mm²/m @ 0.00m
5.00 4.50
Nominal
4.00
3.00 Back
2.50 2.00 1.50
Reinforcement (mm²/m)
3000
2500
2000
.500
1500
Front
1000
1.00
500
Height (m)
3.50
Job Number
Sheet
Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail :
[email protected]
Client Calcs by
Checked by
Date
Base Reinforcement
Base Reinforcement
Reinf. max = 1540mm²/m @ .703m
1600 1400
1000 800 Nominal 600 400
Top
Position (m) Schematic Reinforcement
T12@200 (Hor) T12@200 (Hor) T32@250 (NF) T12@200 (FF) 1-R10/m2 clips 1-R10/m2 clips T12@200 starters
FRONT
T32@220 starters T20@200 (T1) T20@250 (B1) T16@300 (T2) T16@300 (B2) T12@200
SECTION
T12@200 (EF)
3.40
3.20
3.00
2.80
2.60
2.40
2.00
1.80
1.60
1.40
1.20
1.00
.800
.600
.200
.400
Bottom
200
2.20
Reinforcement (mm²/m)
1200
