Calcu Calcu latio n Sheet Sheet
8D
ISOLATED FOOTING, F-1
REFERENCE
Reference:C:\Users\Bong\Desktop\01 MathCad\Utilities.mcd(R) DESCRIPTION
This section section pr ovides ovides the design of IS OLATED FOOTING P AGE
C ONTENTS
2
A.
DIM ENS ION S
2
B.
M ATERIAL P ROP ERTIES
4
C.
DES IGN LOADS
5
C.
ANALYS IS RES ULTS
11
D.
FACTORE D S OIL BE ARIN G P RES S URE
13
E.
CHE CK S HE AR
22
F.
REI NFORCEM ENT DES IG N
25
G.
S U M MARY/DETAI LS
Footing F-2.mcd
LNT - Page 1 of 38
Calcu Calcu latio n Sheet Sheet
Customer
SATORP
Proj No
04811179
Project Title
JUBAIL EXPORT REFINERY (PACKAGE-8)
Calc No
SA-JER-PI903-GCCC-070113 SA-JER-PI903-GCCC-070113
Calculation Calculation Title Elec File Location
KFIP BERTH-22 MAINTENANCE MA INTENANCE BUILDING \ENG\ST\CA\References\MB\MATHCAD\
Phase/CTR
Project File Location
J:\ONSHORE\04811225
Re v
Da te
By
Che ck ed
C
Jun 11
LNT
VKJ
A.
Re v
Page Da t e
By
Check e d
Re v
Dat e
2 By
of
26 Check e d
DIMENSIONS A.1
FOOTING AND PIER DATA
FOOTING DATA
Footing Length, L =
4.000 m
Footing Width, B =
3.000 m
Footing Thickness, T =
0.500 m
Concrete Unit Wt., Yc = Soil Depth, D = Soil Unit Unit Wt., Ys =
24.000 kN/m³ 0.800 m 18.000 kN/m³
Pass. Press. Coef., Kp =
3.000
Coef. of Base Friction, µ =
0.400
Uniform Surcharge, Q =
0.000 kPa
Net Allow. SB Pressure, qs =
140 kPa
PIER DATA
Number of Piers =
1
Nomenclature
Pier #1
B.
Xp (m) =
0.000
Zp (m) =
0.500
Lpx (m) =
0.500
Lpz (m) =
0.500
h (m) =
0.000
MATERIALS PR PROP ERTIES B.1
B.2
C ON CRETE
Compressive Strength
f c := 30MPa
Modulus of Elasticity
Ec := 4700 ⋅
Concrete strain
εc := 0.003
Concrete Protection
cov := 75mm
Ec = 25743MPa
REBARS
Yield Strength of of Steel Steel
Footing F-2.mcd
fc ⋅ MPa
f y := 414MPa
Modulus of Elasticity
5 Es := 2 × 10 MPa
LNT - Page 2 of 38
Calcu Calcu latio n Sheet Sheet
BAR DESIGNATIONS, SIZES AND AREAS
Table No
0
1
2
3
4
5
6
7
8
9
10 10
db (mm)
0
0
8
10
12
16
20
22
25
28
32
As (mm²)
0
0
50
79
113
201
314
380
491
616
804
T No := No
T dia := db mm
Example for for b ar at
bar := 4
=4 No bar
Bar diameter is:
dia = 12mm bar
Area of of bar is: is:
T 2 As := As mm
As = 113mm bar
2
SKETCH PLAN
S I X A X L c
cL Z-AXIS
Footing F-2.mcd
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Calcu latio n Sheet
C.
DESIGN LOADS
T NODES =
1
From STAAD Analysis and Design Output
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Node_No := k 8 9
SUPPORT REACTIONS NODE
LOAD
8
100 101 102 103 104 105 106
ALL UNITS ARE IN -FORCE-X 2.94 -7.26 2.32 -4.14 3.05 -8.16 1.42
SUPPORT REACTIONS NODE
LOAD
8
200 201 202 203 204 2 05 206 2 07
Footing F-2.mcd
FORCE-Y 799.73 640.25 647.81 719.18 724.85 352.34 359.89
FORCE-Z -5.24 -2.57 21.87 -3.75 14.58 -1.55 22.89
ALL UNITS ARE IN -FORCE-X 3.16 3.80 -3.82 3.85 -11.84 3.49 -13.20 2.14
FORCE-Y 1007.71 991.65 928.02 934.07 816.43 828.52 520.55 532.64
FORCE-Z -3.55 -7.36 -7.39 12.17 -5.80 33.31 -2.34 36.77
KN METER MOM-X -12.30 -5.53 71.80 -7.98 50.01 -3.35 73.98
MOM-Y -0.35 -0.14 0.38 -0.18 0.21 -0.06 0.46
MOM-Z -4.44 28.06 -4.01 18.68 -5.37 29.49 -2.58
KN METER MOM-X -7.61 -17.50 -17.58 44.29 -13.53 110.20 -5.04 118.69
MOM-Y -0.29 -0.48 -0.43 -0.01 -0.29 0.54 -0.08 0.75
MOM-Z -5.00 -5.67 19.63 -6.02 45.45 -5.86 47.39 -3.92
LNT - Page 4 of 38
Calcu latio n Sheet
D.
ANALYSIS RESULTS D.1
LOAD NUMBER
SERVICE LOADS
100
Pier #1 Py (kN) =
-799.7
Fx (kN) =
2.9
Fz (kN) =
-5.2
Mx (kN·m) =
-12.3
Mz (kN·m) =
-4.4
⎡ ⎣
Npier
( PyT )0 ( FxT )0 ( FzT )0 ( MxT )0 ( MzT )0 ⎤ kN
kN
kN
kN m
kN m
⎦
CALCULATE FOOTING STABILITY D.2
WEIGHTS AND LOADS
FOUNDATION CENTROID: Xc := 0m
Y c := 0m
FOUNDATION, SOIL AND SURCHARGE: Base weight:
Wtbase := L ⋅ B ⋅ T ⋅ γc
Wtbase = 144.0kN
Soil weight:
Wtsoil := L ⋅ B ⋅ D ⋅ γs
Wtsoil = 172.8kN
Surcharge wt:
Wtsurc := L ⋅ B ⋅ Q
Wtsurc = 0.0kN
Total wt:
WTotal := Wtbase + Wtsoil + Wtsurc
WTotal = 316.8kN
PIER WEIGHTS AND LOADS: Excess Pier Weights
ExcessPier_wt := n
Lpx ⋅ Lpz ⋅ h ⋅ ( γc − γs) if h ≤ D n n n n Lpx ⋅ Lpz ⋅ D ⋅ ( γc − γs) + h − D ⋅ γc n n n
(
)
otherwise
T ExcessPier_wt = ( 0.0 ) kN Applied load + Excess pier weight
Pty := − Py + ExcessPier_wt n n n
TOTAL VERTICAL LOAD: P Total := WTotal +
∑ Ptyn n
T P Total = ( 1116.5 957.1 964.6 1036.0 1041.7 669.1 676.7 ) kN
Footing F-2.mcd
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Calcu latio n Sheet
D.3
j := 0 .. rows( ASD_Comb) − 1
CHECK STABILITY
SLIDING CHECK: Passive Soil Pressure Passivex := T ⋅ B ⋅
( K p) ⋅ γs ⋅ ( D + T) + K p ⋅ γs ⋅ ( D)
⋅ 0.5
Passivex = 85.1kN
Passivez := T ⋅ L ⋅
( K p) ⋅ γs ⋅ ( D + T) + K p ⋅ γs ⋅ ( D)
⋅ 0.5
Passivez = 113.4kN
Friction Forces Frictionx := j
0kN if P Total ≤ 0kN j
(
)
μ ⋅ P Total − Wtsurc j
otherwise
T Frictionx = ( 446.6 382.8 385.8 414.4 416.7 267.7 270.7 ) kN Frictionz := j
0kN if P Total ≤ 0kN j
(
)
μ ⋅ P Total − Wtsurc j
otherwise
T Frictionz = ( 446.6 382.8 385.8 414.4 416.7 267.7 270.7 ) kN Factor of Safety:
FSSL.x := j
Passivex + Frictionx j
⎛ ∑ Fxn ⎞ ⎝ n ⎠ j
Fx ⎞ , 3⎤ ≠ 0kN ⎢ ∑ n ⎥ ⎣ ⎝ n ⎠ j ⎦
if round⎡ ⎛
"INFINITY" otherwise T FSSL.x =
Check_FS SLx := j
"N.A." if FSSL.x j
=
"INFINITY"
Check_FS SLx =
otherwise "OK,Safe against sliding @ X" if FSSL.x ≥ 1.5 j "N.G. Redesign" otherwise
FSSL.z := j
Passivez + Frictionz j
⎛ ∑ Fzn ⎞ ⎝ n ⎠ j
⎛ Fz ⎞ , 3⎤ ≠ 0kN ⎢ ∑ n ⎥ ⎣ ⎝ n ⎠ j ⎦
if round⎡
"INFINITY" otherwise T FSSL.z =
Footing F-2.mcd
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Calcu latio n Sheet
Check_FS SLz := j
"N.A." if FSSL.z j
=
Check_FS SLz =
"INFINITY"
otherwise "OK,Safe against sliding @ Z" if FSSL.z ≥ 1.5 j "N.G. Redesign" otherwise
UPLIFT CHECK: Upward Loads P y.up := n
for j ∈ 0 .. 6
( )
( )
Up ← if Py > 0 ⋅ kN , Py , 0 ⋅ kN j n j n j Uplift ← Up n Uplift n
⎡⎛ 0.0 ⎞ ⎤ ⎢⎜ 0.0 ⎟ ⎥ ⎢⎜ 0.0 ⎟ ⎥ ⎟⎥ T ⎢⎜ P y.up = 0.0 kN ⎢⎜ ⎟ ⎥ ⎢⎜ 0.0 ⎟ ⎥ ⎢⎜ 0.0 ⎟ ⎥ ⎣⎝ 0.0 ⎠ ⎦ Downward Loads Pty.down := P Total + j j
⎛ ∑ Py.upn ⎞ − Wtsurc ⎝ n ⎠ j
T Pty.down = ( 1116.5 957.1 964.6 1036.0 1041.7 669.1 676.7 ) kN Pty.uplift := j
⎛ ∑ P y.upn ⎞ ⎝ n ⎠ j
T Pty.uplift = ( 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ) kN Factor of Safety:
FSUL := j
Pty.down j Pty.uplift j
if Pty.uplift > 0kN j
"INFINITY" otherwise
FSUL =
"INFINITY" "INFINITY" "INFINITY" "INFINITY" "INFINITY" "INFINITY" "INFINITY"
Footing F-2.mcd
LNT - Page 7 of 38
Calcu latio n Sheet
Check_FS UL := j
"N.A." if FSUL j
=
"INFINITY"
Check_FS UL =
"N.A." "N.A."
otherwise "OK,Safe against sliding @ X" if FSUL ≥ 1.2 j
"N.A."
"N.G. Redesign" otherwise
"N.A." "N.A." "N.A." "N.A."
OVERTURNING ABOUT X-AXIS CHECK: Moment due to Py: Mex := Pty ⋅ − Zp n n n
⎡⎛ − 399.87 ⎞ ⎤ ⎢⎜ − 320.13 ⎟ ⎥ ⎢⎜ − 323.90 ⎟ ⎥ ⎟⎥ T ⎢⎜ Mex = − 359.59 kN m ⎢⎜ ⎟⎥ ⎢⎜ − 362.43 ⎟ ⎥ ⎢⎜ − 176.17 ⎟ ⎥ ⎣⎝ − 179.94 ⎠ ⎦
⎛ − 399.87 ⎞ ⎜ − 320.13 ⎟ ⎜ − 323.90 ⎟ ⎜ ⎟ ∑ Mexn = ⎜ −359.59 ⎟ kN m n ⎜ − 362.43 ⎟ ⎜ − 176.17 ⎟ ⎝ − 179.94 ⎠
Due to Fz and Mx:
(
)
Mox := − Fz ⋅ h + T + Mx n n n n
⎡⎛ − 9.68 ⎞ ⎤ ⎢⎜ − 4.25 ⎟ ⎥ ⎢⎜ 60.86 ⎟ ⎥ ⎟⎥ T ⎢⎜ Mox = − 6.10 kN m ⎢⎜ ⎟⎥ ⎢⎜ 42.72 ⎟ ⎥ ⎢⎜ − 2.57 ⎟ ⎥ ⎣⎝ 62.54 ⎠ ⎦
⎛ − 9.68 ⎞ ⎜ − 4.25 ⎟ ⎜ 60.86 ⎟ ⎜ ⎟ ∑ Moxn = ⎜ −6.10 ⎟ kN m n ⎜ 42.72 ⎟ ⎜ − 2.57 ⎟ ⎝ 62.54 ⎠
Eccentricity:
ez := − j
⎛ ∑ Mexn ⎞ + ⎛ ∑ Moxn ⎞ ⎝ n ⎠ j ⎝ n ⎠ j P Total j
T ez = ( 0.367 0.339 0.273 0.353 0.307 0.267 0.174 ) m
Footing F-2.mcd
LNT - Page 8 of 38
Calcu latio n Sheet
Overturning Moment du e to Py: Mot.x := n
for j ∈ 0 .. 6
(
if Pty n
) j < 0 ⋅ kN
⎛ B − Z ⎞ if Z < 0 m pn ⎝ 2 pn ⎠ ⎛ B − Z ⎞ if Z > 0m OT ← − ( Pty ) ⋅ pn pn j n j ⎝ 2 ⎠
(
)
⋅ OT ← Pty j n j
if Zp
n
=
0m
⎛ B ⎞ if e < 0m z j ⎝ 2 ⎠ ⎛ B ⎞ if ez > 0m OT ← ( Pty ) ⋅ j n j ⎝ 2 ⎠ j
(
)
OT ← − Pty ⋅ j n j
OT ← 0 kN ⋅ m otherwise j OT
⎡⎛ 0.0 ⎞ ⎤ ⎢⎜ 0.0 ⎟ ⎥ ⎢⎜ 0.0 ⎟ ⎥ ⎟⎥ T ⎢⎜ Mot.x = 0.0 kN m ⎢⎜ ⎟ ⎥ ⎢⎜ 0.0 ⎟ ⎥ ⎢⎜ 0.0 ⎟ ⎥
⎛ 0.00 ⎞ ⎜ 0.00 ⎟ ⎜ 0.00 ⎟ ⎜ ⎟ ∑ Mot.xn = ⎜ 0.00 ⎟ kN m n ⎜ 0.00 ⎟ ⎜ 0.00 ⎟
⎣⎝ 0.0 ⎠ ⎦
⎝ 0.00 ⎠
Total Overturning Moment about X-axis: MOT.x :=
∑ Moxn + ∑ Mot.xn n
n
T MOT.x = ( − 9.68 − 4.25 60.86 − 6.10 42.72 −2.57 62.54 ) kN m Resisting Moment about X-axis due to Py: Mrm.x := n
for j ∈ 0 .. 6
(
)
if Pty > 0 ⋅ kN n j
⎛ B ⎝ 2 ⎛ B OT ← ( Pty ) ⋅ j n j ⎝ 2
(
)
OT ← Pty ⋅ j n j
+ Zp ⎞ if MOT.x > 0 kN m n ⎠
j
− Zp ⎞ if MOT.x < 0 kN m n ⎠
j
OT ← 0 kN ⋅ m otherwise j OT ← 0 kN ⋅ m otherwise j OT
Footing F-2.mcd
LNT - Page 9 of 38
Calcu latio n Sheet
⎡⎛ 799.7 ⎞ ⎤ ⎢⎜ 640.3 ⎟ ⎥ ⎢⎜ 1295.6 ⎟ ⎥ ⎟⎥ T ⎢⎜ Mrm.x = ⎢⎜ 719.2 ⎟ ⎥ kN m ⎢⎜ 1449.7 ⎟ ⎥ ⎢⎜ 352.3 ⎟ ⎥
⎛ 799.7 ⎞ ⎜ 640.3 ⎟ ⎜ 1295.6 ⎟ ⎜ ⎟ ∑ Mrm.xn = ⎜ 719.2 ⎟ kN m n ⎜ 1449.7 ⎟ ⎜ 352.3 ⎟
⎣⎝ 719.8 ⎠ ⎦
⎝ 719.8 ⎠
Total Resisting Moment ab out X-axis: MRM.x :=
B
∑ Mrm.xn + (Wtbase + Wtsoil ) ⋅ 2 n
T MRM.x = ( 1274.9 1115.5 1770.8 1194.4 1924.9 827.5 1195.0 ) kN m
Factor of Safety: FSOT.x := j
MRM.x j MOT.x j
if MOT.x ≠ 0 kN m j
"INFINITY" otherwise T FSOT.x = ( 131.7 262.8 29.1 195.6 45.1 321.4 19.1 ) Check_FS OTx := j
"N.A." if FSOT.x j
=
"INFINITY"
otherwise "OK,Safe against overturning @ X" if FSOT.x ≥ 1.5 j "N.G. Redesign" otherwise Check_FS OTx =
"OK,Safe against overturning @ X" "OK,Safe against overturning @ X" "OK,Safe against overturning @ X" "OK,Safe against overturning @ X" "OK,Safe against overturning @ X" "OK,Safe against overturning @ X" "OK,Safe against overturning @ X"
OVERTURNING ABOUT Z-AXIS CHECK: Moment due to Py: Mez := Pty ⋅ Xp n n n
Footing F-2.mcd
LNT - Page 10 of 38
Calcu latio n Sheet
⎡⎛ 0.00 ⎤ ⎢⎜ 0.00 ⎟ ⎥ ⎢⎜ 0.00 ⎟ ⎥ ⎟⎥ T ⎢⎜ Mez = 0.00 kN m ⎢⎜ ⎟ ⎥ ⎢⎜ 0.00 ⎟ ⎥ ⎢⎜ 0.00 ⎟ ⎥
⎛ 0.00 ⎜ 0.00 ⎟ ⎜ 0.00 ⎟ ⎜ ⎟ ∑ Mezn = ⎜ 0.00 ⎟ kN m n ⎜ 0.00 ⎟ ⎜ 0.00 ⎟
⎣⎝ 0.00 ⎠ ⎦
⎝ 0.00 ⎠
Due to Fx and Mz:
(
)
Moz := Fx ⋅ h + T + Mz n n n n
⎡⎛ − 3.0 ⎞ ⎤ ⎢⎜ 24.4 ⎟ ⎥ ⎢⎜ − 2.9 ⎟ ⎥ ⎟⎥ T ⎢⎜ Moz = 16.6 kN m ⎢⎜ ⎟⎥ ⎢⎜ − 3.8 ⎟ ⎥ ⎢⎜ 25.4 ⎟ ⎥
⎛ − 3.0 ⎞ ⎜ 24.4 ⎟ ⎜ − 2.9 ⎟ ⎜ ⎟ ∑ Mozn = ⎜ 16.6 ⎟ kN m n ⎜ − 3.8 ⎟ ⎜ 25.4 ⎟
⎣⎝ − 1.9 ⎠ ⎦
⎝ − 1.9 ⎠
Eccentricity:
ex := j
⎛ ∑ Mezn ⎞ + ⎛ ∑ Mozn ⎞ ⎝ n ⎠ j ⎝ n ⎠ j P Total j
T ex = ( − 0.003 0.026 −0.003 0.016 − 0.004 0.038 − 0.003 ) m
Footing F-2.mcd
LNT - Page 11 of 38
Calcu latio n Sheet
Overturning Moment du e to Py: Mot.z := n
for j ∈ 0 .. 6
(
)
if Pty < 0 ⋅ kN n j
⎛ L − X ⎞ if X < 0 m pn ⎝ 2 pn ⎠ ⎛ L − Xp ⎞ if Xp > 0m OT ← ( Pty ) ⋅ j n j ⎝ 2 n ⎠ n
(
)
⋅ OT ← − Pty j n j
if Xp n
=
0m
⎛ L ⎞ if e < 0m z j ⎝ 2 ⎠ ⎛ L ⎞ if e > 0m OT ← ( Pty ) ⋅ z j j n j ⎝ 2 ⎠
(
)
⋅ OT ← − Pty j n j
OT ← 0 kN ⋅ m otherwise j OT
⎡⎛ 0.0 ⎞ ⎤ ⎢⎜ 0.0 ⎟ ⎥ ⎢⎜ 0.0 ⎟ ⎥ ⎟⎥ T ⎢⎜ Mot.z = 0.0 kN m ⎢⎜ ⎟ ⎥ ⎢⎜ 0.0 ⎟ ⎥ ⎢⎜ 0.0 ⎟ ⎥
⎛ 0.00 ⎞ ⎜ 0.00 ⎟ ⎜ 0.00 ⎟ ⎜ ⎟ ∑ Mot.zn = ⎜ 0.00 ⎟ kN m n ⎜ 0.00 ⎟ ⎜ 0.00 ⎟
⎣⎝ 0.0 ⎠ ⎦
⎝ 0.00 ⎠
Total Overturning Moment about X-axis:
MOT.z :=
∑ Mozn + ∑ Mot.zn n
n
T MOT.z = ( − 3.0 24.4 −2.9 16.6 −3.8 25.4 −1.9 ) kN m
Resisting Moment about Z-axis due to Py: Mrm.z := n
for j ∈ 0 .. 6
(
)
> 0 ⋅ kN if Pty n j
⎛ L ⎝ 2 ⎛ L OT ← ( Pty ) ⋅ j n j ⎝ 2
(
)
OT ← Pty ⋅ j n j
− Xp ⎞ if MOT.z > 0 kN m n ⎠ j + Xp ⎞ if MOT.z < 0 kN m n ⎠
j
OT ← 0 kN ⋅ m otherwise j OT ← 0 kN ⋅ m otherwise j OT
Footing F-2.mcd
LNT - Page 12 of 38
Calcu latio n Sheet
⎡⎛ 1599.5 ⎞ ⎤ ⎢⎜ 1280.5 ⎟ ⎥ ⎢⎜ 1295.6 ⎟ ⎥ ⎟⎥ T ⎢⎜ Mrm.z = 1438.4 kN m ⎢⎜ ⎟⎥ ⎢⎜ 1449.7 ⎟ ⎥ ⎢⎜ 704.7 ⎟ ⎥
⎛ 1599.5 ⎞ ⎜ 1280.5 ⎟ ⎜ 1295.6 ⎟ ⎜ ⎟ ∑ Mrm.zn = ⎜ 1438.4 ⎟ kN m n ⎜ 1449.7 ⎟ ⎜ 704.7 ⎟
⎣⎝ 719.8 ⎠ ⎦
⎝ 719.8 ⎠
Total Resisting Moment ab out X-axis: MRM.z :=
L
∑ Mrm.zn + (Wtbase + Wtsoil) ⋅ 2 n
T MRM.z = ( 2233.1 1914.1 1929.2 2072.0 2083.3 1338.3 1353.4 ) kN m Factor of Safety: FSOT.z := j
M RM.z j M OT.z j
if MOT.z ≠ 0 kN m j
"INFINITY" otherwise T FSOT.z = ( 751.872 78.350 676.919 124.742 541.821 52.667 723.733 ) Check_FS OTz := j
"N.A." if FSOT.z j
=
"INFINITY"
otherwise "OK,Safe against overturning @ Z" if FSOT.z ≥ 1.5 j "N.G. Redesign" otherwise Check_FS OTz =
"OK,Safe against overturning @ Z" "OK,Safe against overturning @ Z" "OK,Safe against overturning @ Z" "OK,Safe against overturning @ Z" "OK,Safe against overturning @ Z" "OK,Safe against overturning @ Z" "OK,Safe against overturning @ Z" CALCULATE FOOTING STABILITY
Footing F-2.mcd
LNT - Page 13 of 38
Calcu latio n Sheet
TOTAL RESULTANT LOAD AND ECCENTRICITIES: Total Vertical Load
T P Total = ( 1116.5 957.1 964.6 1036.0 1041.7 669.1 676.7 ) kN
Eccentricity along X-axis
T ex = ( − 0.003 0.026 −0.003 0.016 −0.004 0.038 − 0.003 ) m
Eccentricity along Z-axis
T ez = ( 0.367 0.339 0.273 0.353 0.307 0.267 0.174 ) m
K Coefficient Using K c oefficient ex L
ez
= 0.012
B
= 0.268
K = j
1.754 1.737 1.574 1.748 1.648 1.612 1.356
hence qmax =
⎛ K ⋅ ⎝ j
P Total ⎞ j = B ⋅ L ⎠
163.21 138.51
kPa
126.54 150.95 143.03 89.90 76.45
OVERTURNING CHECK: Resisting Moment about X-axis
T MRM.x = ( 1274.9 1115.5 1770.8 1194.4 1924.9 827.5 1195.0 ) kN m
Overturning Moment about X-axis
T MOT.x = ( − 9.7 − 4.2 60.9 −6.1 42.7 −2.6 62.5 ) kN m
Factor of Safety
⎛ "YES!.. SATISFACTORY" ⎞ T = FSOT.x ( 131.708"YES!.. 262.768 29.094 195.64 45.059 321.375 19.109 ) SATISFACTORY"
131.7 262.8
⎜ ⎜ "YES!.. ⎜ FSOT.x >=? 1.5 = "YES!.. j ⎜ ⎜ "YES!.. ⎜ "YES!..
⎟ SATISFACTORY" ⎟ ⎟ SATISFACTORY" ⎟ SATISFACTORY" ⎟ SATISFACTORY" ⎟
29.1
⎝ "YES!..
SATISFACTORY" ⎠
FSOT.x = j
195.6 45.1 Footing F-2.mcd
LNT - Page 14 of 38
Calcu latio n Sheet
. 19.1
Resisting Moment about Z-axis
T MRM.z = ( 2233.1 1914.1 1929.2 2072.0 2083.3 1338.3 1353.4 ) kN m
Overturning Moment about Z-axis
T MOT.z = ( − 3.0 24.4 −2.9 16.6 −3.8 25.4 −1.9 ) kN m
Factor of Safety
⎛ "YES!.. SATISFACTORY" ⎞ T FSOT.z = ( 751.87 "YES!.. 78.35 676.92 124.74 541.82 52.67 723.73 ) SATISFACTORY" ⎜ ⎟
751.9 78.4
⎜ "YES!.. ⎜ FSOT.z >=? 1.5 = "YES!.. j ⎜ ⎜ "YES!.. ⎜ "YES!..
676.9
⎝ "YES!..
FSOT.z = j
⎟ ⎟ SATISFACTORY" ⎟ SATISFACTORY" ⎟ SATISFACTORY" ⎟ SATISFACTORY"
SATISFACTORY" ⎠
124.7 541.8 52.7 723.7 SLIDING CHECK: Passive Soil Pressure along X-axis
Passivex = 85.1kN
Friction Force along X-axis
T Frictionx = ( 446.6 382.8 385.8 414.4 416.7 267.7 270.7 ) kN
Factor of Safety
FSSL.x >=? 1.5 = j
Passive Soil Pressure along Z-axis
Passivez = 113.4kN
Friction Forces along Z-axis
T Frictionz = ( 446.6 382.8 385.8 414.4 416.7 267.7 270.7 ) kN
Factor of Safety
Footing F-2.mcd
FSSL.x = j
FSSL.z = j
FSSL.z >=? 1.5 = j
LNT - Page 15 of 38
Calcu latio n Sheet
UPLIFT CHECK: Downward Force
T Pty.down = ( 1116.5 957.1 964.6 1036.0 1041.7 669.1 676.7 ) kN
Uplift Force
"INFINITY" ⎞ ⎛ ⎛ "N.A." ⎞ T = ( 0.0 0.0 0.0 0.0 0.0 0.0 "N.A." Pty.uplift "INFINITY" 0.0 ) kN ⎜ ⎟ ⎜ ⎟
Factor of Safety
⎜ "INFINITY" ⎟ ⎜ "N.A." ⎟ ⎜ ⎟ ⎜ ⎟ FSUL = "INFINITY" FSUL >=? 1.2 = "N.A." j ⎜ j ⎟ ⎜ ⎟ ⎜ "INFINITY" ⎟ ⎜ "N.A." ⎟ ⎜ "INFINITY" ⎟ ⎜ "N.A." ⎟ ⎝ "INFINITY" ⎠
Footing F-2.mcd
⎝ "N.A." ⎠
LNT - Page 16 of 38
Calcu latio n Sheet
CALCULATE SOIL BEARING PRESSURE NO OF BEARING CORNERS 1 b ( a) :=
6
−
2 a 6
+
1− a+
NBC := j
3 a 12
2 a 3
⎛ 4ex j ⎞ ⋅B ⎝ L ⎠ ⎛ 4ez j ⎞ ⋅L tope x ← b ⎝ B ⎠
T NBC = ( 4 4 4 4 4 4 4 )
tope z ← b
−B L ⋅ ex + 3 if ex ≤ tope x ∧ ez ≤ tope z ∧ ez > j j j j L 6 −B L ⋅ ex + 4 if ez ≤ j j 6 L B L ∧ ex ≥ 1 if ez ≥ j 4 j 4 2 otherwise
Solution for Biaxial Resultant Eccentricity for 1, 2, or 3 Corners with Zero Pressure ( when: ABS(6*ex/L)+ABS(6*ey/B) > 1.0 )
BIAX2 Check Ecc.:
0.351
ABS(6*ex/L)+ABS(6*ey/B) <= 1.0
P3 =
N.A.
kPa
P2 =
N.A.
kPa
P4 =
N.A.
kPa
P1 =
N.A.
kPa
Distance dx =
N.A.
m
Distance dz =
N.A.
m
Footing F-2.mcd
LNT - Page 17 of 38
Calcu latio n Sheet
⎛ P1 j ⎜ P2 ⎟ ⎜ j ⎟ := ⎜ P3 ⎟ ⎜ j ⎟ ⎝ P4 j ⎠
(
) (
)
if ex ≠ 0 ⋅ m ⋅ ez ≠ 0 ⋅ m j j if Ecc ≤ 1 j P1 ← j P2 ← j P3 ← j P4 ← j
P Total ⎛ 6 ⋅ ex 6 ⋅ ez ⎞ j j j ⋅ 1+ +− L⋅ B L B ⎠ ⎝
⎛ L⋅ B ⎝ P Total ⎛ j ⋅ 1− L⋅ B ⎝ P Total ⎛ j ⋅ 1− L⋅ B ⎝ P Total j
⋅ 1+
6 ⋅ ex j L 6 ⋅ ex j L 6 ⋅ ex j L
+
6 ⋅ ez ⎞ j
⎛ P1 j ⎞ ⎜ P2 ⎟ ⎜ j ⎟ ⎜ P3 ⎟ ⎜ j ⎟ ⎝ P4 j ⎠
T
⎡( 24.42 160.93 161.67 25.16 ) ⎤ ⎢( 28.75 136.87 130.76 22.64 ) ⎥ ⎢ ( 36.19 123.87 124.58 36.9 ) ⎥ ⎢ ⎥ = ( 27.46 149.36 145.2 23.31 ) kPa ⎢ ⎥ ⎢ ( 33.04 139.61 140.57 34 ) ⎥ ⎢ ( 29.15 88.73 82.38 22.79 ) ⎥ ⎣
( 36.59 75.73 76.19 37.06 )
⎦
⎠ 6 ⋅ ez ⎞ j + B ⎠ 6 ⋅ ez ⎞ j +− B ⎠ B
otherwise P1 ← P 1 ⋅ kPa j j P2 ← P 2 ⋅ kPa j j P3 ← P 3 ⋅ kPa j j P4 ← P 4 ⋅ kPa j j otherwise 6 ⋅ ez ⎞ ⎡ PTotal j ⎛ 6 ⋅ ex j ⎤ j ⋅ 1+ +− , 0 ⋅ kPa P1 ← max j L B ⎠ ⎣ L ⋅ B ⎝ ⎦
⎡ PTotal j ⎛ 6 ⋅ ex j 6 ⋅ ez j ⎞ ⎤ ⋅ 1+ + , 0 ⋅ kPa P2 ← max j L B ⎠ ⎣ L ⋅ B ⎝ ⎦ ⎡ PTotal j ⎛ 6 ⋅ ex j 6 ⋅ ez j ⎞ ⎤ ⋅ 1− + , 0 ⋅ kPa P3 ← max j L B ⎠ ⎣ L ⋅ B ⎝ ⎦ 6 ⋅ ez ⎞ ⎡ PTotal j ⎛ 6 ⋅ ex j ⎤ j ⋅ 1− +− , 0 ⋅ kPa P4 ← max j L B ⎠ ⎣ L ⋅ B ⎝ ⎦
⎛ P1 j ⎞ ⎜ P2 ⎟ ⎜ j ⎟ ⎜ P3 ⎟ ⎜ j ⎟ ⎝ P4 j ⎠
Footing F-2.mcd
LNT - Page 18 of 38
Calcu latio n Sheet
Case := j
(
) (
)
if ex ≠ 0m ⋅ ez ≠ 0m j j
Case =
if Ecc > 1.0 j dx ← dx ⋅ m j dz ← dz ⋅ m j Case ← 1 if ( d x > L) ⋅ ( d z > B) j Case ← 2 if ( d x > L) ⋅ ( d z ≤ B) j Case ← 3 if ( d x ≤ L) ⋅ ( d z > B) j Case ← 4 if ( d x ≤ L) ⋅ ( d z ≤ B) j Case ← "N.A." otherwise j Case ← "N.A." otherwise j
⎛ dx j ⎞ ⎝ dz j ⎠
:=
⎛ "N.A." ⎞ ⎝ "N.A." ⎠ ⎛ dx j ⋅ m ⎞ ⎝ dz j ⋅ m ⎠
Footing F-2.mcd
if Case j
=
"N.A."
⎛ dx j ⎞ ⎝ dz j ⎠
T
=
otherwise
LNT - Page 19 of 38
Calcu latio n Sheet
⎛ L1 j ⎞ ⎝ L2 j ⎠
:=
if Case j
=
⎛ L1 j ⎞
"N.A."
⎝ L2 j ⎠
L1 ← L j
T
=
L2 ← B j otherwise if Case = 1 dx j L1 ← d z − B ⋅ j j dz j
(
)
dz j L2 ← d x − L ⋅ j j dx j
(
)
if Case = 2 dz j L1 ← d x − L ⋅ j j dx j
(
)
L2 ← d z j j if Case = 3 dx j L1 ← d z − B ⋅ j j dz j
(
)
L2 ← d x j j if Case = 4 L1 ← d x j j L2 ← d z j j
⎛ L1 j ⎞ ⎝ L2 j ⎠ Brg_Area := j
100% if Case j
=
"N.A."
otherwise L⋅ B −
( L − L1 j) ⋅ ( B − L2 j) 2
⋅ 100% if Case
j
L⋅ B
(
L⋅ L1 + L2 j j 2
⋅ 100% if Case
=
2
⋅ 100% if Case
=
3
j
B⋅ L1 + L2 j j 2 L⋅ B
1
)
L⋅ B
(
=
) j
dx ⋅ dz j j 2 L⋅ B
Footing F-2.mcd
⋅ 100% if Case
j
=
4
LNT - Page 20 of 38
Calcu latio n Sheet
Brg_Plan := j
"Case NA" if Case j
=
"N.A."
otherwise "Case 1" if Case j
=
1
"Case 2" if Case j
=
2
"Case 3" if Case j
=
3
"Case 4" if Case j
=
4
T Brg_Plan =
T Case =
T
⎛ dx ⎞ ⎝ dz ⎠
P = kPa
P_Eqn := j
(
) (
= m
⎛ L1 ⎞ ⎝ L2 ⎠
T
= m
)
if ex ≠ 0 ⋅ m ⋅ ez ≠ 0 ⋅ m j j "P 1" if E cc ≤ 1 j "P 2" otherwise "P 3" if
(ex j ≠ 0 ⋅ m) ⋅ ( ez j = 0 ⋅ m)
+
( ex j = 0 ⋅ m) ⋅ ( ez j ≠ 0 ⋅ m)
"P 4" otherwise
T P_Eqn = ( "P 1" "P 1" "P 1" "P 1" "P 1" "P 1" "P 1" )
Footing F-2.mcd
LNT - Page 21 of 38
Calcu latio n Sheet
CALCULATE SOIL BEARING PRESSURE
BEARING AREA: Dist x
T dx =
Dist z
T dz =
Brg. L1
T L1 =
Brg. L2
T L2 =
%Brg. Area
Brg_Area
Biaxial Case
T Case =
T
= %
GROSS SOIL BEARING CORNER PRESSURES:
T P1 = ( 24.42 28.75 36.19 27.46 33.04 29.15 36.59 ) kPa
T P2 = ( 160.93 136.87 123.87 149.36 139.61 88.73 75.73 ) kPa
T P3 = ( 161.67 130.76 124.58 145.20 140.57 82.38 76.19 ) kPa
P1 = j
24.42 28.75
Footing F-2.mcd
P2 = j kPa
160.93 136.87
P3 = j kPa
161.67 130.76
P4 = j kPa
25.16 22.64
kPa
LNT - Page 22 of 38
Calcu latio n Sheet
.
.
.
.
27.46
149.36
145.20
23.31
33.04
139.61
140.57
34.00
29.15
88.73
82.38
22.79
36.59
75.73
76.19
37.06
MAXIMUM NET SOIL PRESSURE:
(
)
P max.net := max P1 , P2 , P3 , P4 − γs ⋅ ( D + T) j j j j j
⎛ "OK, q max < q allowable" ⎞ Check_qs := if P max.net ≤ q s , "OK, q max < q allowable" , "N.G. Redesign" j j ⎜ "OK, q max < q allowable" ⎟
(
P max.net = j
138.27 113.47
kPa
⎛ "YES!.. ) ⎜ "YES!.. ⎜ "OK, q max < q allowable" ⎟ ⎜ "YES!.. ⎜ ⎟ ⎜ Check_qs = "OK, q max < q allowable"P max.net <=? q s = "YES!.. j ⎜ j ⎟ ⎜ ⎜ "OK, q max < q allowable" ⎟ ⎜ "YES!.. ⎜ "OK, q max < q allowable" ⎟ ⎜ "YES!.. ⎝ "OK, q max < q allowable" ⎠
101.18
⎝ "YES!..
SATISFACTORY" ⎞
⎟ ⎟ ⎟ SATISFACTORY" ⎟ SATISFACTORY" ⎟ SATISFACTORY" ⎟ SATISFACTORY" SATISFACTORY"
SATISFACTORY" ⎠
125.96 117.17 65.33 52.79
E.
FACTORED SOIL BEARING PRESSURE E.1
FACTORED LOADS
LOAD NUMBER
200
Pier #1
Footing F-2.mcd
Puy (kN) =
-32.100
Vux (kN) =
12.870
Vuz (kN) =
-6.490
Mux (kN·m) =
0.000
Muz (kN·m) =
0.000
LNT - Page 23 of 38
Calcu latio n Sheet
CALCULATE ULTIMATE LOADS E.2
Use Load Factor
TOTAL FACTORED VERTICAL LOAD AND ECCENTRICITIES
LF := 1.4
FOUNDATION, SOIL AND SURCHARGE: WuTotal := WTotal ⋅ LF
WuTotal = 443.5kN
TOTAL VERTICAL LOAD: Puty := − Pu + ExcessPier_wt ⋅ LF n n n
Applied load + Excess pier weight T Puty = ( 32.1 ) kN
∑ Puty = 32.1kN
PuTotal := WuTotal +
∑ Puty
PuTotal = 475.6kN
ECCENTRICITY ALONG Z -AXIS: Muex := Puty ⋅ − Zp n n n
Moment due to Py: T Muex = ( − 16.1 ) kN m
∑ Muex = −16.1 kN m (
)
Muox := − Vuz ⋅ h + T + Mux n n n n
Due to Fz and Mx: T Muox = ( 3.2 ) kN m
Eccentricity:
euz := −
∑ Muox = 3.2kN m
∑Muex + ∑ Muox
euz = 0.027m
PuTotal
ECCENTRICITY ALONG X-AXIS: Muez := Puty ⋅ Xp n n n
Moment due to Py: T Muez = ( 0.0 ) kN m
∑ Muez = 0.0kN m (
)
Muoz := Vux ⋅ h + T + Muz n n n n
Due to Fx and Mz:
T Muoz = ( 6.4 ) kN m
Eccentricity:
eux :=
∑ Muoz = 6.4kN m
∑ Muez + ∑ Muoz PuTotal
eux = 0.014m
CALCULATE ULTIMATE LOADS CALCULATE ULTIMATE SOIL BEARING TOTAL RESULTANT ULTIMATE LOAD AND ECCENTRICITIES:
Footing F-2.mcd
Total Vertical Load
PuTotal = 475.6kN
Eccentricity along X-axis
eux = 0.014m
Eccentricity along Z-axis
euz = 0.027m
LNT - Page 24 of 38
Calcu latio n Sheet
ULTIMATE SOIL BEARING CORNER PRESSURES: P u = 38.31kPa 1 P u = 42.57kPa 2 P u = 40.96kPa 3 P u = 36.70kPa 4 F.
CHECK SHEAR F .1
F OO TI NG AN AL YSI S A LO NG X-D IREC TI ON S
L = 4m
q uL :=
Pu + Pu 3 4
q uR :=
2
q uL = 38.8kPa
Pu + P u 1 2 2
q uR = 40.4kPa
qx CALCULATIONS q at critical sections:
( )
( )
q d1 = n
39.9
Footing F-2.mcd
( )
q d6 = n kPa
39.4
( )
q d2 = n kPa
39.8
( )
q d5 = n kPa
39.5
( )
q d3 = n kPa
39.7
q d4 = n kPa
39.5
kPa
LNT - Page 25 of 38
Calcu latio n Sheet
Diagrams
Soil Bearing Pressure Diagram 0.25m1
) a P k ( u q
q uL = 38.8kPa
q uR = 40.4kPa
− 0.25m1 max( B , L)
0
mm L (mm)
Footing F-2.mcd
LNT - Page 26 of 38
Calcu latio n Sheet
Shear Diagram 0.25m1
) N k ( u V
− 0.25m1 max( B , L)
0
mm L (mm)
Footing F-2.mcd
LNT - Page 27 of 38
Calcu latio n Sheet
Moment Diagram 0.25m1
) m N k ( u M
− 0.25m1 max( B , L)
0
mm L (mm)
Footing F-2.mcd
LNT - Page 28 of 38
Calcu latio n Sheet
Max Beam Shear & Bending Moment Wide-beam shear along Z direction
Max negative moment at face of support
Muneg.z = 14.9kN m
VuLz = 8.6kN
Max positive moment:
Mupos.z = kN m
VuRz = 12.9kN
F .2
F OO TI NG AN AL YSI S A LO NG Z-D IREC TI ON S
B = 3m
q uL :=
Pu + Pu 1 4
q uR :=
2
q uL = 37.5kPa
Pu + P u 3 2 2
q uR = 41.8kPa
qz CALCULATIONS q at critical sections:
( )
( )
q d1 = n
41.3
Footing F-2.mcd
( )
q d6 = n kPa
39.4
( )
q d2 = n kPa
41.0
( )
q d5 = n kPa
39.7
( )
q d3 = n kPa
40.7
q d4 = n kPa
40.0
kPa
LNT - Page 29 of 38
Calcu latio n Sheet
Diagrams
Soil Bearing Pressure Diagram 0.25m1
q uL = 37.5kPa
) a P k ( u q
q uR = 41.8kPa
− 0.25m1 max( B , L)
0
mm B (mm)
Footing F-2.mcd
LNT - Page 30 of 38
Calcu latio n Sheet
Shear Diagram 0.25m1
) N k ( u V
− 0.25m1 max( B , L)
0
mm B (mm)
Footing F-2.mcd
LNT - Page 31 of 38
Calcu latio n Sheet
Moment Diagram 0.25m1
) m N k ( u M
− 0.25m1 max( B , L)
0
mm B (mm)
Footing F-2.mcd
LNT - Page 32 of 38
Calcu latio n Sheet
Max Beam Shear & Bending Moment Wide-beam shear along X direction
Max negative moment at face of support
Muneg.x = 8.4kN m
VuLx = 8.0kN
Max positive moment:
Mupos.x = kN m
F.4
VuRx = 6.1kN
PUNCHING SHEAR ϕv := 0.85
Capacity redu ction factor Shear strength pr ovided
(
ϕ Vc := ϕv ⋅ 0.33 ⋅
)
f c ⋅ MPa ⋅ ( b ox + b oz) ⋅ d e
T ϕ Vc = ( 1167 ) kN Punching Shear Perimeter around column/pier: Along x-d irection
T b ox = ( 0.915 ) m
Along z-direction
T b oz = ( 0.915 ) m
Area of Punc hing Sh ear: T 2 A p = ( 0.837 ) m
A p := b ox ⋅ b oz n n n Total force from column/pier:
P uy := Puty + LF ⋅ A p ⋅ ( T ⋅ γc + D ⋅ γs + Q) n n n T P uy = ( 63.0 ) kN q at d/2 distance from supports: Along x-d irection
T q x.2 = ( 39.8 ) kPa T q x.5 = ( 39.5 ) kPa
Along z-direction
T q z.2 = ( 41.0 ) kPa T q z.5 = ( 39.7 ) kPa
Total force acting on pun ched ar ea R q := n
1 2
(
⋅ max qx.5 + q x.2 , q z.5 + q z.2 n
n
n
n
) ⋅ A pn
T R q = ( 33.8 ) kN Net punching shear: Vup := P uy − R q n n n T Vup = ( 29.3 ) kN
Footing F-2.mcd
LNT - Page 33 of 38
Calcu latio n Sheet
Check if shear strength p rovided by c oncrete is greater than the maximum shear force. ACI31811.3.1.1.Eq.11.3.p := if ( min( ϕ Vc ) > max( Vup) , "OK,shear strength provided > Vu." , "NG!" ) min( ϕ Vc) >=? max( Vup) = "YES!.. SATISFACTORY"
ACI31811.3.1.1.Eq.11.3.p = "OK,shear strength provided > Vu." F.5
WIDE BEAM SHEAR
Wide-beam shear along Z direction VuLz = 8.6kN Shear strength pr ovided
VuRz = 12.9kN
(
ϕ Vn b := ϕv ⋅ 0.17 ⋅
)
fc ⋅ MPa ⋅ B ⋅ d e
ϕ Vn b = 985.4kN
Check if shear strength p rovided by c oncrete is greater than the maximum shear force. ACI31811.3.1.1.Eq.11.3.bsz := if ( ϕ Vn b > max( VuLz , VuRz) , "OK,shear strength provided > Vu." , "NG!" ) ϕ Vn b >=? max ( VuLz , VuRz) = "YES!.. SATISFACTORY"
ACI31811.3.1.1.Eq.11.3.bsz = "OK,shear strength provided > Vu."
Wide-beam shear along X direction VuLx = 8.0kN Shear strength pr ovided
VuRx = 6.1kN
(
ϕ Vn b := ϕv ⋅ 0.17 ⋅
)
fc ⋅ MPa ⋅ L ⋅ d e
ϕ Vn b = 1313.8kN
Check if shear strength p rovided by c oncrete is greater than the maximum shear force. ACI31811.3.1.1.Eq.11.3.bsx := if ( ϕ Vn b > max( VuLx , VuRx) , "OK,shear strength provided > Vu." , "NG!" ) ϕ Vn b >=? max ( VuLx , VuRx) = "YES!.. SATISFACTORY"
ACI31811.3.1.1.Eq.11.3.bsx = "OK,shear strength provided > Vu." G.
REINFORCEMENT DESIGN G.1
G.2
D ESI GN MO MEN T F OR B OTTO M B ARS
Capacity redu ction factor
ϕf := 0.90
Moment at face of pedestal X-direction
Muneg.z = 14.9kN m
Moment at face of pedestal Z-direction
Muneg.x = 8.4kN m
BOTTOM REINFORCEMENTS
Temp steel reinforcement ratio
Minimum steel reinf ratio
ρ temp := 0.0018
[ACI 318 7.12.2]
ρmin := ρ temp
[ACI 318 10.5.4]
ρmin = 0.0018
Bars in X- direction
⎡ ⎣
ϕf ⋅ A s ⋅ f y ⋅ d s −
1
⋅
⎛ A s ⋅ f y ⎞⎤ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
Factored resistance
Mr
Mr := max( Muneg.z , 0.001 kN m)
Mr = 14.9kN m
b := B
barx ≡ 6
Bar diameter
=
2
Reinforcement provided Size of bar
Footing F-2.mcd
dia = 20mm barx
LNT - Page 34 of 38
Calcu latio n Sheet
Proposed bar spacing
Area of steel provided
S x.bot := 200mm
A s :=
= 314mm As barx
Bar area
⋅b As barx
2
2 A s = 4710mm
S x.bot
Distance from extreme compr essive fiber to centroid of reinforcing steel
d := T − cov − 0.5 ⋅ dia
Solve the quadratic equation for the area of steel required
Given
d = 415mm
barx Mr
=
⎡ ⎣
ϕf ⋅ A s ⋅ f y ⋅ d −
A s.reqd := Find( As )
1 2
⋅
⎛ A s ⋅ f y ⎞⎤ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
A s.reqd = 96mm
⎛ ⎝
4
⎞ ⎠
Minimum reinforcement
A s.min := min ρ min b d ,
Temperature reinforcement
A s.temp := ρ temp b
Reinforcing steel required
A s.reqd := max( As.reqd , A s.min , A s.temp)
Check As pr ovided
A s >=? A s.reqd = "YES!.. SATISFACTORY"
3
2
A s.min = 129mm
A s.reqd
T
2
2 A s.temp = 1350mm
2
A s.reqd = 1350mm
2
Bars in Z- direction
⎡ ⎣
ϕf ⋅ A s ⋅ f y ⋅ d s −
1
⋅
⎛ A s ⋅ f y ⎞⎤ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
Factored resistance
Mr
Mr := max( Muneg.x , 0.001 kN m)
Mr = 8.4kN m
b := L
Size of bar
barz ≡ 6
Bar diameter
Proposed bar spacing
S z.bot := 200mm
Bar area
=
2
Reinforcement provided
Area of steel provided
A s :=
As = 314mm barz
As ⋅b barz
2
2 A s = 6280mm
S z.bot
Distance from extreme compr essive fiber to centroid of reinforcing steel
− 0.5 dia d := T − cov − dia barx barz
Solve the quadratic equation for the area of steel required
Given
Mr
=
d = 395mm
⎡ ⎣
ϕf ⋅ A s ⋅ f y ⋅ d −
A s.reqd := Find( As )
G.3
= 20mm dia barz
1 2
⋅
⎛ A s ⋅ f y ⎞⎤ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
A s.reqd = 57mm
⎛ ⎝
4
⎞ ⎠
Minimum reinforcement
A s.min := min ρ min b d ,
Temperature reinforcement
A s.temp := ρ temp b
Reinforcing steel required
A s.reqd := max( As.reqd , A s.min , A s.temp)
Check As pr ovided
A s >=? A s.reqd = "YES!.. SATISFACTORY"
3
A s.reqd
T
A s.min = 76mm
2
2
2 A s.temp = 1800mm
2
A s.reqd = 1800mm
2
TOP REINFORCEMENTS
Bars in X- direction
Footing F-2.mcd
Mr
Mr := max( Mupos.z , 0.001 kN m)
Mr = kN m
=
⎡ ⎣
ϕf ⋅ A s ⋅ f y ⋅ d s −
Factored resistance
1 2
⋅
⎛ A s ⋅ f y ⎞⎤ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦ b := B
LNT - Page 35 of 38
Calcu latio n Sheet
Reinforcement provided Size of bar
barx.top := 6
Bar diameter
Proposed bar spacing
S x.top := 200mm
Bar area
Area of steel provided
A s :=
= 20mm dia barx.top = 314mm As barx.top
⋅b As barx.top
2 A s = 4710mm
S x.top
Distance from extreme compr essive fiber to centroid of reinforcing steel
d := T − cov − 0.5 dia
Solve the quadratic equation for the area of steel required
Given
d = 415mm
barx.top Mr
=
⎡ ⎣
ϕf ⋅ A s ⋅ f y ⋅ d −
1 2
⋅
⎛ A s ⋅ f y ⎞⎤ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
2 A s.reqd = mm
A s.reqd := Find( As ) Minimum reinforcement
2
⎛ ⎝
A s.min := min ρ min b d ,
4 3
⎞ ⎠
2 A s.min = mm
A s.reqd
T
2 A s.temp = 1350mm
Temperature reinforcement
A s.temp := ρ temp b
Reinforcing steel required
A s.reqd := max( A Ass.reqd .reqd, A s.min , A s.temp)
Check As pr ovided
A s >=? A A s.reqd =
2
2 A s.reqd = mm
Bars in Z- direction
⎡ ⎣
ϕf ⋅ A s ⋅ f y ⋅ d s −
1
⋅
⎛ A s ⋅ f y ⎞⎤ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
Factored resistance
Mr
Mr := max( Mupos.x , 0.001 kN m)
Mr = kN m
b := L
Size of bar
barz.top := 6
Bar diameter
Proposed bar spacing
S z.top := 200mm
Bar area
=
2
Reinforcement provided
Area of steel provided
A s :=
2
2 A s = 6280mm
S z.top
d := T − cov − dia − 0.5 dia barx.top barz.top
Solve the quadratic equation for the area of steel required
Given
Mr
=
d = 395mm
⎡ ⎣
ϕf ⋅ A s ⋅ f y ⋅ d −
1 2
⋅
⎛ A s ⋅ f y ⎞⎤ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
2 A s.reqd = mm
A s.reqd := Find( As )
Footing F-2.mcd
As = 314mm barz.top
As ⋅b barz.top
Distance from extreme compr essive fiber to centroid of reinforcing steel
Minimum reinforcement
dia = 20mm barz.top
⎛ ⎝
A s.min := min ρ min b d ,
4 3
⎞ ⎠
A s.reqd
T
Temperature reinforcement
A s.temp := ρ temp b
Reinforcing steel required
A s.reqd := max( A Ass.reqd .reqd, A s.min , A s.temp)
Check As pr ovided
A s >=? A A s.reqd =
2
2 A s.min = mm 2 A s.temp = 1800mm 2 A s.reqd = mm
LNT - Page 36 of 38
Calcu latio n Sheet
H.
SUMMARY/DETAILS
PLAN REINFORCEMENTS
L = 4.000 m
BARS PARALLEL TO 'L'
B = 3.000 m s i x A X L c
BARS PARALLEL TO 'B'
cL Z-Axis
Footing F-2.mcd
LNT - Page 37 of 38
