Castillo Muro Calculos
Castillo Muro Calculos
Castillo Muro Calculos
inasa
Muro de Contencion Residencia Castillo
20 cm
80 cm = 18 kN/m³
30 cm = 30°
0.3 m
c = 0.5 kPa
#5 bars @ 20 cm 1.85 m #5 bars @ 20 cm
30 cm
0.6 m 1.2 m
Wall Loads
General 2.15 m Backfill Assumptions
Burial Depth 0.8 m Retained Height 3.3 m Restrained Against Sliding No
Material Slope 0° Neglect Bearing @ Heel Yes
Rebar Fy 413.7 MPa Gamma (weight) 16 kN/m³ Use Vert. Comp. for OT No
Concrete F'c 20.69 MPa Use Equiv. Fluid Pressure (EFP) No Use Vert. Comp. for Sliding No
Unit Weight 23.56 kN/m³ Analysis Type Rankine Use Vert. Comp. for Bearing Yes
Footing Phi (friction angle) 30° Use Surcharge for Sliding & OT Yes
Footing Thickness 30 cm Cohesion 0.5 kPa Use Surcharge for Bearing Yes
Heel Length 1.2 m Has Water in Backfill No Neglect soil over toe No
Toe Length 0.6 m Passive Pressure @ Toe Neglect Backfill Wt. for Coulomb No
Heel Bar Size #5 Calculation Method Rankine Factor Soil Wt as Dead Yes
Heel Bar Spacing 20 cm Phi (friction angle) 30° Use Passive Force for OT Yes
Hook Heel Bars Downward No Cohesion 0.5 kPa Assume Pressure to Top Yes
Heel Bar Ld 60 cm Gamma (weight) 18 kN/m³
Heel Bar Cover 5.08 cm Apply Only to Key No
Toe Bars Hook Into Stem Yes Overburden Depth To Ignore 0.3 m
Toe Bar Cover 7.62 cm Surcharge (Uniform)
Key Surcharge Type None
Has Key Yes Surcharge (Line/Strip)
Key Depth 0.3 m Type None
Key Width 30 cm Axial Load
Key Position Heel End Apply Axial Load On Stem No
Lateral Load
General Apply Lateral Pressure To Stem No
Stem Type Single / Tapered Seismic Loading
Bars Developed @ Top No Has Backfill Seismic Load No
Has Lateral Support (Restrained Wall)
No Geotechnical
Extension Above Backfill 0m Friction Coefficent 0.40
Geometry Wall Friction Angle 25°
Stem Top Thickness 20 cm
Tapered Yes
Stem Toe Side Offset 0 cm
Stem Heel Side Offset 15 cm
Bar Cover 5.08 cm Stability Criteria
Reinforcement Required F.S. for Overturning 1.20
Dowel Bar Size #5 Required F.S. for Sliding 1.50
Dowel Bar Spacing 20 cm Allowable Bearing Pressure 200 kPa
Bars are Centered No Req'd Bearing Location Middle third
Dowel Bar Embedment Hook into Toe
Has Lapped Bars No
Cutoff Alternate Bars Yes
Length of Cutoff Bars 220 cm
Force Calculations
Backfill Pressure
= 16 kN/m³
= 30°
c = 0.5 kPa
43.64 kN/m
1.37 m
21.29 kPa
[
Ka = tan² 45° -
2] [
= tan² 45° -
2]
30°
= 0.33
a = HKa - 2c*sqrt (Ka) = (16 kN/m³) (4.1 m) 0.33 - 2 (0.5 kPa) *sqrt (0.33) = 21.29 kPa
1 1 H 4.1 m
Pa = H = (4.1 m) (21.29 kPa) = 43.64 kN/m Location = = = 1.37 m
2 a 2 3 3
= 18 kN/m³
= 30° 17.76 kN/m -0.03 m
c = 0.5 kPa 44.67 kPa
[
Kp = tan² 45° +
2 ] [
= tan² 45° +
30°
2 ] = 3.00
p = (db + Hkey) Kp + 2c*sqrt (Kp) = (18 kN/m³) (0.8 m + 0.3 m) 3.00 + 2 (0.5 kPa) *sqrt (3.00) = 44.67 kPa
Force Calculations
Wall Weights
W1 = 1A1 = (23.56 kN/m³) (0.65 m²) = 15.2 kN/m
W2 = 2A2 = (23.56 kN/m³) (0.76 m²) = 17.91 kN/m
W3 = 3A3 = (23.56 kN/m³) (0.29 m²) = 6.72 kN/m
W4 = 4A4 = (23.56 kN/m³) (0.09 m²) = 2.12 kN/m
d1 = 1.08 m
2 W2 d2 = 0.7 m
d2 d3 = 0.85 m
3 W3 d4 = 2 m
d3
1 W1
4 d1 W4
d4
Backfill Weights
W5 = 5A5 = (16 kN/m³) (4.56 m²) = 72.96 kN/m
W6 = 6A6 = (16 kN/m³) (0.29 m²) = 4.56 kN/m
W7 = 7A7 = (18 kN/m³) (0.3 m²) = 5.4 kN/m
d5 = 1.55 m
6 W6 d6 = 0.9 m
d6 d7 = 0.3 m
5 W5
d5
8 W7
d7
Force Calculations
Bearing Pressure
R 11.04 kPa
L 105.1 kPa
dR
R
R = W1 + W2 + W3 + W4 + W5 + W6 + W7 + Pav
= 15.2 kN/m + 17.91 kN/m + 6.72 kN/m + 2.12 kN/m + 72.96 kN/m + 4.56 kN/m + 5.4 kN/m + 0 kN/m
= 124.9 kN/m (100.0% dead, 0.0% live, 0.0% earth )
H
M = W1d1 + W2d2 + W3d3 + W4d4 + W5d5 + W6d6 + W7d7 + Pavbf - Pah
3
= (1.08 m) (15.2 kN/m) + (0.7 m) (17.91 kN/m) + (0.85 m) (6.72 kN/m) + (2 m) (2.12 kN/m) + (1.55 m) (72.96 kN/m) + (0.9 m) (4.56 kN/m)
4.1 m
+ (0.3 m) (5.4 kN/m) + (0 kN/m) (2.15 m) - (43.64 kN/m)
3
= 97.99 kN·m/m
M 97.99 kN·m/m
dR = = = 0.78 m
R 124.9 kN/m
L =
R
L [ d
1+3 1-2 R
L ( )] =
124.9 kN/m
2.15 m [
1+3 1-2 (
0.78 m
2.15 m )] = 105.1 kPa
R =
R
L [ ( d
1-3 1-2 R
L )] =
124.9 kN/m
2.15 m [ (
1-3 1-2
0.78 m
2.15 m )] = 11.04 kPa
Friction Force
F = R = (0.40) (124.9 kN/m) = 49.95 kN/m
Note: Bearing resultant used here was decreased by 0 kN/m to remove vertical backfill component effect.
(prevent vertical backfill component from contributing to sliding resistance)
Stability Checks
Overturning Check Sliding Check
Overturning Moments Sliding Force(s)
Force Distance Moment Backfill lateral pressure 43.64 kN/m
Backfill pressure 43.64 kN/m 1.37 m 59.65 kN·m/m Total: 43.64 kN/m
Total: 59.65 kN·m/m Resisting Force(s)
Resisting Moments Passive pressure @ toe 17.76 kN/m
Force Distance Moment Friction 49.95 kN/m
W1 (footing) 15.2 kN/m 1.08 m 16.34 kN·m/m Total: 67.71 kN/m
W2 (stem) 17.91 kN/m 0.7 m 12.54 kN·m/m RF 67.71 kN/m
F.S. = = = 1.551 (OK)
W3 (stem) 6.72 kN/m 0.85 m 5.71 kN·m/m SF 43.64 kN/m
W4 (key) 2.12 kN/m 2m 4.24 kN·m/m
W5 (soil) 72.96 kN/m 1.55 m 113.1 kN·m/m
W6 (soil) 4.56 kN/m 0.9 m 4.1 kN·m/m
W7 (soil) 5.4 kN/m 0.3 m 1.62 kN·m/m
Passive pressure @ toe 17.76 kN/m -0.03 m -0.62 kN·m/m
Total: 157 kN·m/m
RM 157 kN·m/m
F.S. = = = 2.632 (OK)
OTM 59.65 kN·m/m
Heel Check
Min Reinforcement Check
Mn 85.45 kN·m/m
b = 60.8 kPa (backfill) Not needed: capacity 1/3 greater than req'd: = = 1.457
Mu 58.64 kN·m/m
c = 7.07 kPa (concrete)
Ld=60 cm
Design Forces
Controlling combination: 1.2D + 1.6H
1 1 1 1
Mu = 1.20 L² + 1.20 bL² = 1.20 (7.07 kPa) (1.2 m) ² + 1.20 (60.8 kPa) (1.2 m) ² = 58.64 kN·m/m
2 c 2 2 2
M u @ stem base = 75.98 kN·m/m > 58.64 kN·m/m (does not control for heel)
Vu = 1.20cL + 1.20bL = 1.20 (7.07 kPa) (1.2 m) + 1.20 (60.8 kPa) (1.2 m) = 97.73 kN/m
Shear Check
Vn = [2 sqrt (f'c)] d = (0.75) [2 sqrt (3000 psi)] (9.5 in) = 136.7 kN/m Vn > Vu
Flexure Check
Mn = AsFy (d - a/2) = 0.90 (1000 mm²/m) (413.7 MPa) [24.13 cm - (2.35 cm) /2] = 85.45 kN·m/m Mn > Mu
Heel Check
Development
Ld 3 fy 3 60000 psi (1.0) (1.0) (0.8) (1.0)
= = = 26.29
db
db [
40 sqrt (f'c) c + Ktr
] 40 sqrt (3000 psi) 2.50
c + Ktr 5.87 cm + 0
where: = = 3.70 > 2.5 use 2.5
db 15.88 mm
where: = 1.0 (12" fresh concrete below) = 1.0 (bars not coated) = 0.8 (bar size #6) = 1.0 (normal wt concrete)
K tr = 0 (no transverse reinforcement) c = 5.87 cm (lesser of bar ctr to outer edge or half of ctr - to ctr spacing)
Ld
Ld = d = (26.29) (15.88 mm) = 41.74 cm
db b
Toe Check
Min Reinforcement Check
Mn 75.99 kN·m/m
c = 7.07 kPa (concrete)
Not needed: capacity 1/3 greater than req'd: = = 3.940
Mu 19.29 kN·m/m
30 cm
#5 bars @ 20 cm
78.86 kPa
105.1 kPa
Ldh=29.92 cm
Design Forces
Controlling combination: 1.2D + 1.6H
Bearing load factor: take weighted average of factors from all sources based on contribution (see bearing calcs) :
100.0% (1.20 - Dead) + 0.0% (0.00 - Live) + 0.0% (1.60 - Earth) = 1.20
M u @ stem base = 75.98 kN·m/m > 19.29 kN·m/m (does not control for toe)
Vu = - 1.20cL + 1.20 [brL + (bl - br) L/2] = - 1.20 (7.07 kPa) (0.38 m) + 1.20 [(88.3 kPa) (0.38 m) + (105.1 kPa - 88.3 kPa) (0.38 m) /2] = 41.32 kN/m
(taken @ 'd' from the base of the stem: d = 21.59 cm, bearing pressure @ d = 88.3 kPa)
Shear Check
Vn = [2 sqrt (f'c)] d = (0.75) [2 sqrt (3000 psi)] (8.5 in) = 122.3 kN/m Vn > Vu
Flexure Check
Mn = AsFy (d - a/2) = 0.90 (1000 mm²/m) (413.7 MPa) [21.59 cm - (2.35 cm) /2] = 75.99 kN·m/m Mn > Mu
Toe Check
Development
#5 bars @ 20 cm: Developed by 90° hook
L dh = (0.02fy/sqrt (f'c)) db = (0.02 (1.0) (1.0) (413.7 MPa) /sqrt (20.69 MPa)) (15.88 mm) = 34.78 cm
Excess reinforcement reduction of 12.5.3 (d) : 25.4%Ld = 25.4% (24.35 cm) = 6.18 cm
Minimum inside bend diameter = 6db = 6 (15.88 mm) = 95.25 mm 127 mm (actual diameter)
Stem Check
3.04
2.66
2.28
C
Ld = 0.42 m
1.9 (m)
B
1.52
2.2 m 1.14
#5 @ 40 cm
0.76
0.38
db 1.59 cm
d = th - cover - = 35 cm - 5.08 cm - = 29.13 cm
2 2
Mn = AsFy (d - a/2) = 0.90 (1000 mm²/m) (413.7 MPa) [29.13 cm - (2.35 cm) /2] = 104.1 kN·m/m
db 1.59 cm
d = th - cover - = 27.96 cm - 5.08 cm - = 22.09 cm
2 2
Mn = AsFy (d - a/2) = 0.90 (1000 mm²/m) (413.7 MPa) [22.09 cm - (2.35 cm) /2] = 77.87 kN·m/m
Stem Check
Negative Moment Capacity @ C
As 200 mm² 200 mm²
= 100% + 0% = 500 mm²/m
b 40 cm 40 cm
db 1.59 cm
d = th - cover - = 26.32 cm - 5.08 cm - = 20.44 cm
2 2
Mn = AsFy (d - a/2) = 0.90 (500 mm²/m) (413.7 MPa) [20.44 cm - (1.18 cm) /2] = 36.96 kN·m/m
db 1.59 cm
d = th - cover - = 21.65 cm - 5.08 cm - = 15.77 cm
2 2
Mn = AsFy (d - a/2) = 0.90 (500 mm²/m) (413.7 MPa) [15.77 cm - (1.18 cm) /2] = 28.27 kN·m/m
c + Ktr 5.87 cm + 0
where: = = 3.70 > 2.5 use 2.5
db 15.88 mm
where: = 1.0 (12" fresh concrete below) = 1.0 (bars not coated) = 0.8 (bar size #6) = 1.0 (normal wt concrete)
K tr = 0 (no transverse reinforcement) c = 5.87 cm (lesser of bar ctr to outer edge or half of ctr - to ctr spacing)
Ld
Ld = d = (26.29) (15.88 mm) = 41.74 cm
db b
c + Ktr 5.87 cm + 0
where: = = 3.70 > 2.5 use 2.5
db 15.88 mm
where: = 1.0 (12" fresh concrete below) = 1.0 (bars not coated) = 0.8 (bar size #6) = 1.0 (normal wt concrete)
K tr = 0 (no transverse reinforcement) c = 5.87 cm (lesser of bar ctr to outer edge or half of ctr - to ctr spacing)
Ld
Ld = d = (26.29) (15.88 mm) = 41.74 cm
db b
Stem Check
Shear checks
@ base: Vu = 59.98 kN/m Vn = [2 sqrt (f'c)] d = (0.75) [2 sqrt (3000 psi)] (11.47 in) = 165 kN/m Vn > Vu
@ 380 cm: V u = 0 kN/m Vn = [2 sqrt (f'c)] d = (0.75) [2 sqrt (3000 psi)] (5.56 in) = 80.02 kN/m Vn > Vu
Bar cutoffs
#5 @ 15.75 in cut off at 220 cm:
2 2(
In tension zone: V = 115.8 kN/m) = 77.2 kN/m > V u = 10.63 kN/m
3 n 3
12d b = 19.05 cm, d = 20.44 cm bar must extend 20.44 cm past point required, actual length = 138.9 cm
L dh = (0.02fy/sqrt (f'c)) db = (0.02 (1.0) (1.0) (413.7 MPa) /sqrt (20.69 MPa)) (15.88 mm) = 34.78 cm
Excess reinforcement reduction of 12.5.3 (d) : 73.0%Ld = 73.0% (24.35 cm) = 17.78 cm
Minimum inside bend diameter = 6db = 6 (15.88 mm) = 95.25 mm 127 mm (actual diameter)
At 220 cm:
At 380 cm:
As 200 mm² As A
= = 500 mm²/m > s,min
b 40 cm b b
Stem Check
Check Min Tensile Strain
At 0 cm:
At 220 cm:
At 380 cm: