Mathcad - Footing F-4
February 27, 2018 | Author: lnt4 | Category: N/A
Short Description
Descripción: F-4...
Description
Calculation Sheet
8D
ISOLATED FOOTING, F-1
REFERENCE
Reference:C:\Users\Bong\Desktop\01 MathCad\Utilities.mcd(R) DESCRIPTION This section provides the design of ISOLATED FOOTING PAGE
CONTENTS
2
A.
DIMENSIONS
2
B.
MATERIAL PROPERTIES
4
C.
DESIGN LOADS
5
C.
ANALYSIS RESULTS
11
D.
FACTORED SOIL BEARING PRESSURE
13
E.
CHECK SHEAR
22
F.
REINFORCEMENT DESIGN
25
G.
SUMMARY/DETAILS
Footing F-4.xmcd
LNT - Page 1 of 41
Calculation Sheet
Customer
SATORP
Proj No
04811179 SA-JER-PI903-GCCC-070113
Project Title
JUBAIL EXPORT REFINERY (PACKAGE-8)
Calc No
Calculation Title Elec File Location
KFIP BERTH-22 MAINTENANCE BUILDING \ENG\ST\CA\References\MB\MATHCAD\
Phase/CTR
Project File Location
J:\ONSHORE\04811225
Rev
Date
By
Checked
C
Jun 11
LNT
VKJ
A.
Page
Rev
Date
By
Checked
Rev
Date
2 By
of
26 Checked
DIMENSIONS A.1
FOOTING AND PIER DATA
FOOTING DATA Footing Length, L =
5.000 m
Footing Width, B =
6.000 m
Footing Thickness, T =
0.500 m
Concrete Unit Wt., Yc =
24.000 kN/m³
Soil Depth, D =
0.800 m
Soil Unit Wt., Ys =
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 =
100 kPa
PIER DATA Number of Piers =
3 Nomenclature
Pier #1
B.
Pier #2
Pier #3
Xp (m) =
0.000
0.000
0.000
Zp (m) =
-2.000
0.000
2.000
Lpx (m) =
0.500
0.500
0.500
Lpz (m) =
0.500
0.500
0.500
h (m) =
1.000
1.000
1.000
MATERIALS PROPERTIES B.1
B.2
Footing F-4.xmcd
CONCRETE Compressive Strength
fc := 30MPa
Modulus of Elasticity
E c := 4700 ⋅
Concrete strain
εc := 0.003
Concrete Protection
cov := 75mm
Yield Strength of Steel
fy := 414MPa
fc ⋅ MPa
E c = 25743 ⋅ MPa
REBARS Modulus of Elasticity
5 E s := 2 × 10 MPa
LNT - Page 2 of 41
Calculation Sheet
BAR DESIGNATIONS, SIZES AND AREAS
Table No
0
1
2
3
4
5
6
7
8
9
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 := d b mm
T 2 As := As mm
Example for bar at
bar := 4
No =4 bar
Bar diameter is:
dia = 12 ⋅ mm bar
Area of bar is:
As = 113 ⋅ mm bar
2
cL X-AXIS
SKETCH PLAN
cL Z-AXIS
Footing F-4.xmcd
LNT - Page 3 of 41
Calculation Sheet
C.
DESIGN LOADS
From STAAD Analysis and Design Output
ASD LOAD COMBINATIONS T NODES =
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Node_No := k
k := 0 .. Npier − 1
9 8 10
〈0〉 r := match⎛Node_No , ASD ⎞ k k ⎝ ⎠
N LC := rows( ASD_Comb)
( )
( )
FX := − ASD_Data 2 , r ⋅ kN k k
MX := ASD_Data 5 , r ⋅ kN ⋅ m k k
( )
MY := ASD_Data 6 , r ⋅ kN ⋅ m k k
( )
( )
MZ := ASD_Data 7 , r ⋅ kN ⋅ m k k
FY := ASD_Data 3 , r ⋅ kN k k
( )
FZ := ASD_Data 4 , r ⋅ kN k k
FX1 :=
k←0
FY1 :=
for i ∈ 0 .. N pier − 1
k←0
for i ∈ 0 .. N pier − 1
for j ∈ 0 .. NLC − 1
for j ∈ 0 .. NLC − 1
F ← FX k ij
F ← FY k ij
F ← FZ k ij
( )
k←k+1
( )
k←k+1
F
k←k+1
F
k←0
MY1 :=
F
k←0
MZ1 :=
k←0
for i ∈ 0 .. Npier − 1
for i ∈ 0 .. Npier − 1
for i ∈ 0 .. Npier − 1
for j ∈ 0 .. N LC − 1
for j ∈ 0 .. N LC − 1
for j ∈ 0 .. N LC − 1
F ← MX k ij
F ← MY k ij
F ← MZ k ij
( )
( )
k←k+1 F
LOAD1 :=
k←0
for j ∈ 0 .. NLC − 1
( )
MX1 :=
FZ1 :=
for i ∈ 0 .. N pier − 1
( )
k←k+1
k←k+1
F
k←0 for i ∈ 0 .. N pier − 1
F
NODE1 :=
k←0 for i ∈ 0 .. N pier − 1
for j ∈ 0 .. NLC − 1
for j ∈ 0 .. NLC − 1
(
)
F ← ASD_Comb k j
F ← Node_No if mod k , N LC = 0 k i
k←k+1
F ← " " otherwise k
F
k←k+1 F
Footing F-4.xmcd
LNT - Page 4 of 41
Calculation Sheet
ASD LOAD COMBINATIONS
SUPPORT REACTIONS NODE
LOAD
9
100 101 102 103 104 105 106 100 101 102 103 104 105 106 100 101 102 103 104 105 106
8
10
Footing F-4.xmcd
ALL UNITS ARE IN -FORCE-X 0.20 8.95 -0.22 6.58 -0.29 9.10 -0.06 -2.94 7.26 -2.32 4.14 -3.05 8.16 -1.42 -0.53 8.95 -0.37 6.43 -0.56 9.22 -0.10
FORCE-Y 441.82 406.58 386.44 420.57 405.46 235.58 215.43 799.73 640.25 647.81 719.18 724.85 352.34 359.89 574.79 472.30 499.49 539.38 559.77 274.88 302.06
FORCE-Z -2.75 -2.33 32.87 -2.12 24.28 -1.48 33.72 -5.24 -2.57 21.87 -3.75 14.58 -1.55 22.89 8.52 5.80 35.73 8.25 30.70 3.52 33.46
KN METER MOM-X -7.62 -5.24 79.41 -4.95 58.54 -3.31 81.35 -12.30 -5.53 71.80 -7.98 50.01 -3.35 73.98 16.41 11.70 85.73 16.52 72.04 7.09 81.12
MOM-Y -2.30 -0.97 -1.18 -1.18 -1.33 -0.39 -0.59 -0.35 -0.14 0.38 -0.18 0.21 -0.06 0.46 -0.82 -0.62 0.85 -0.65 0.46 -0.41 1.07
MOM-Z 0.30 28.40 -1.16 20.75 -1.42 29.01 -0.55 -4.44 28.06 -4.01 18.68 -5.37 29.49 -2.58 -1.42 28.63 -1.00 20.66 -1.57 29.41 -0.22
LNT - Page 5 of 41
Calculation Sheet
LRFD COMBINATIONS 〈0〉 r := match⎛Node_No , LRFD ⎞ k k ⎝ ⎠
N LC := rows( LRFD_Comb)
( )
( )
FXU := − LRFD_Data 2 , r ⋅ kN k k
MXU := LRFD_Data 5 , r ⋅ kN ⋅ m k k
( )
MYU := LRFD_Data 6 , r ⋅ kN ⋅ m k k
( )
( )
MZU := LRFD_Data 7 , r ⋅ kN ⋅ m k k
FYU := LRFD_Data 3 , r ⋅ kN k k
( )
FZU := LRFD_Data 4 , r ⋅ kN k k
FXU1 :=
k←0
FYU1 :=
k←0
for i ∈ 0 .. Npier − 1
for i ∈ 0 .. Npier − 1
for j ∈ 0 .. N LC − 1
for j ∈ 0 .. N LC − 1
for j ∈ 0 .. N LC − 1
F ← FXU k ij
F ← FYU k ij
F ← FZU k ij
k←k+1
k←k+1
k←k+1
)
(
F
)
( )
F
k←0
MYU1 :=
for i ∈ 0 .. N pier − 1
F
k←0
MZU1 :=
k←0
for i ∈ 0 .. Npier − 1
for i ∈ 0 .. Npier − 1
for j ∈ 0 .. NLC − 1
for j ∈ 0 .. N LC − 1
for j ∈ 0 .. N LC − 1
F ← MXU k ij
F ← MYU k ij
F ← MZU k ij
k←k+1
k←k+1
k←k+1
(
)
F
LOAD1 :=
FZU1 :=
for i ∈ 0 .. Npier − 1
(
MXU1 :=
k←0
(
)
(
F
k←0 for i ∈ 0 .. N pier − 1
)
F
NODE1 :=
k←0 for i ∈ 0 .. N pier − 1
for j ∈ 0 .. NLC − 1
for j ∈ 0 .. NLC − 1
(
)
F ← LRFD_Comb k j
F ← Node_No if mod k , N LC = 0 k i
k←k+1
F ← " " otherwise k
F
k←k+1 F
LRFD COMBINATIONS Footing F-4.xmcd
LNT - Page 6 of 41
Calculation Sheet SUPPORT REACTIONS NODE
LOAD
9
200 201 202 203 204 205 206 207 200 201 202 203 204 205 206 207 200 201 202 203 204 205 206 207
8
10
Footing F-4.xmcd
ALL UNITS ARE IN -FORCE-X -0.55 0.48 7.95 0.62 15.06 0.40 14.59 -0.07 -3.16 -3.80 3.82 -3.85 11.84 -3.49 13.20 -2.14 -0.95 -0.58 7.12 -0.33 14.74 -0.17 14.79 -0.11
FORCE-Y 598.50 535.91 519.17 503.05 493.84 461.61 351.27 319.04 1007.71 991.65 928.02 934.07 816.43 828.52 520.55 532.64 691.00 722.24 705.23 726.97 639.48 682.97 410.19 453.68
FORCE-Z -2.98 -3.55 -3.71 24.45 -3.50 52.82 -2.24 54.07 -3.55 -7.36 -7.39 12.17 -5.80 33.31 -2.34 36.77 7.96 11.36 11.46 35.40 9.84 57.74 5.30 53.19
KN METER MOM-X -6.78 -10.26 -10.58 57.14 -9.23 126.21 -5.00 130.45 -7.61 -17.50 -17.58 44.29 -13.53 110.20 -5.04 118.69 16.15 21.64 21.78 81.00 18.99 137.43 10.65 129.09
MOM-Y -2.04 -3.10 -2.71 -2.88 -1.81 -2.14 -0.53 -0.86 -0.29 -0.48 -0.43 -0.01 -0.29 0.54 -0.08 0.75 -0.75 -1.09 -1.16 0.02 -1.06 1.30 -0.62 1.74
MOM-Z -2.14 1.09 25.03 1.39 47.88 0.58 46.51 -0.78 -5.00 -5.67 19.63 -6.02 45.45 -5.86 47.39 -3.92 -2.73 -1.49 22.98 -0.73 47.13 -0.29 47.18 -0.23
LNT - Page 7 of 41
Calculation Sheet
D.
ANALYSIS RESULTS D.1
WEIGHTS AND LOADS FOUNDATION CENTROID: Xc := 0m
Yc := 0m
FOUNDATION, SOIL AND SURCHARGE: Base weight:
Wtbase := L ⋅ B ⋅ T ⋅ γc
Wtbase = 360.0 ⋅ kN
Soil weight:
Wtsoil := L ⋅ B ⋅ D ⋅ γs
Wtsoil = 432.0 ⋅ kN
Surcharge wt:
Wtsurc := L ⋅ B ⋅ Q
Wtsurc = 0.0 ⋅ kN
Total wt:
WTotal := Wtbase + Wtsoil + Wtsurc
WTotal = 792.0 ⋅ kN
PIER WEIGHTS AND LOADS: Excess Pier Weights
ExcessPier_wt := n
( ) if hn ≤ D Lpx ⋅ Lpz ⋅ ⎡D ⋅ ( γc − γs) + ( h − D) ⋅ γc⎤ n n ⎣ n ⎦ Lpx ⋅ Lpz ⋅ h ⋅ γc − γs n n n
otherwise
T ExcessPier_wt = ( 2.4 2.4 2.4 ) ⋅ kN Applied load + Excess pier weight
Pty := − Py + ExcessPier_wt n n n
TOTAL VERTICAL LOAD: P Total := WTotal +
∑ Ptyn n
CALCULATE FOOTING STABILITY D.3
CHECK STABILITY SLIDING CHECK: Passive Soil Pressure Passivex := T ⋅ B ⋅
⎡⎣( Kp ) ⋅ γs ⋅ ( D + T)
+ Kp ⋅ γs ⋅ ( D)⎤⎦ ⋅ 0.5
Passivex = 170.1 ⋅ kN
Passivez := T ⋅ L ⋅
⎡⎣( Kp ) ⋅ γs ⋅ ( D + T)
+ Kp ⋅ γs ⋅ ( D)⎤⎦ ⋅ 0.5
Passivez = 141.8 ⋅ kN
Friction Forces Frictionx := j
0kN if P Total ≤ 0kN j
(
)
μ ⋅ P Total − Wtsurc j
Frictionz := j
0kN if P Total ≤ 0kN j
(
)
μ ⋅ P Total − Wtsurc j
otherwise
otherwise
Factor of Safety:
FSSL.x := j
Passivex + Frictionx j
⎛∑ Fxn⎞ ⎜ ⎟ ⎝n ⎠j
if round⎡⎢
⎛∑ Fxn⎞ ⋅ ⎟ ⎢ ⎜⎝ n ⎠j ⎣
1 , 3⎥⎤ ≠ 0kN kN
⎥ ⎦
"INFINITY" otherwise
Footing F-4.xmcd
LNT - Page 8 of 41
Calculation Sheet
Check_FS SLx := j
"N.A." if FSSL.x = "INFINITY" j otherwise "OK,Safe against sliding @ X" if FSSL.x ≥ 1.5 j "N.G. Redesign" otherwise
SLIDING ALONG X-DIRECTION Comb
Passive + Ff
100 101 102 103 104 105 106
FSSL.z := j
Sum FX
1216.32 1097.43 1103.28 1161.43 1165.81 834.90 840.73
Passivez + Frictionz j
⎛∑ Fzn⎞ ⎜ ⎟ ⎝n ⎠j
FS Sliding
3.27 -25.16 2.91 -17.15 3.90 -26.48 1.58
⎡ ⎛ Fz ⎞ ⋅ ∑ n⎟ ⎢ ⎜⎝ n ⎠j ⎣
if round⎢
371.96 43.62 379.13 67.72 298.93 31.53 532.11
1 kN
Remarks OK,Safe against OK,Safe against OK,Safe against OK,Safe against OK,Safe against OK,Safe against OK,Safe against
sliding @ X sliding @ X sliding @ X sliding @ X sliding @ X sliding @ X sliding @ X
⎤
, 3⎥ ≠ 0kN
⎥ ⎦
"INFINITY" otherwise Check_FS SLz := j
"N.A." if FSSL.z = "INFINITY" j otherwise "OK,Safe against sliding @ Z" if FSSL.z ≥ 1.5 j "N.G. Redesign" otherwise
SLIDING ALONG Z-DIRECTION Comb 100 101 102 103 104 105 106
Passive + Ff 1187.97 1069.08 1074.93 1133.08 1137.46 806.55 812.38
Sum FZ
FS Sliding
0.53 0.90 90.47 2.38 69.56 0.49 90.07
2241.45 1187.87 11.88 476.08 16.35 1646.02 9.02
Remarks OK,Safe against sliding @ Z OK,Safe against sliding @ Z OK,Safe against sliding @ Z OK,Safe against sliding @ Z OK,Safe against sliding @ Z OK,Safe against sliding @ Z OK,Safe against sliding @ Z
UPLIFT CHECK: Upward Loads
P y.up := n
for j ∈ 0 .. 6
( )
( )
Up ← if ⎡ Py > 0 ⋅ kN , Py , 0 ⋅ kN⎤ j n j ⎣ nj ⎦ Uplift ← Up n Uplift n
Pty.uplift := j
Footing F-4.xmcd
⎛∑ P y.upn⎞ ⎜ ⎟ ⎝n ⎠j
LNT - Page 9 of 41
Calculation Sheet
Pty.down := P Total + j j
Downward Loads
⎛∑ P y.upn⎞ − Wtsurc ⎜ ⎟ ⎝n ⎠j
Factor of Safety: FSUL := j
Pty.down
j if Pty.uplift > 0kN j Pty.uplift j
"INFINITY" otherwise Check_FS UL := j
"N.A." if FSUL = "INFINITY" j otherwise "> 1.2, OK,Safe against sliding @ X" if FSUL ≥ 1.2 j "< 1.2, N.G. Redesign" otherwise
UPLIFT Comb
Downward F
100 101 102 103 104 105 106
Uplift F
2615.54 2318.33 2332.94 2478.33 2489.28 1662.00 1676.58
0.00 0.00 0.00 0.00 0.00 0.00 0.00
FS Uplift
Remarks
INFINITY INFINITY INFINITY INFINITY INFINITY INFINITY INFINITY
N.A. N.A. N.A. N.A. N.A. N.A. N.A.
OVERTURNING ABOUT X-AXIS CHECK: Moment due to Py:
Mex := Pty ⋅ − Z p n n n
Due to Fz and Mx:
Mox := − Fz ⋅ h + T + Mx n n n n
(
Eccentricity:
ez := − j
)
⎛∑ Mexn⎞ + ⎛∑ Moxn⎞ ⎜ ⎟ ⎜ ⎟ ⎝n ⎠j ⎝ n ⎠j P Total j
Overturning Moment due to Py: Mot.x := n
for j ∈ 0 .. 6 if
( Ptyn) j < 0 ⋅ kN (
)
OT ← Pty ⋅ j n j
(
⎛⎜ B ⎝2
)
OT ← − Pty ⋅ j n j
− Zp
⎞⎟
if Z p < 0 m n
n⎠
⎛⎜ B ⎝2
− Z p ⎞⎟ if Z p > 0m n n
)
⎛⎜ B ⎞⎟ ⎝ 2⎠
⎠
if Z p = 0m n
(
⋅ OT ← − Pty j n j
(
)
OT ← Pty ⋅ j n j
⎛⎜ B ⎞⎟ ⎝ 2⎠
if ez < 0m j if ez > 0m j
OT ← 0 kN ⋅ m otherwise j OT
Footing F-4.xmcd
LNT - Page 10 of 41
Calculation Sheet
Total Overturning Moment about X-axis:
MOT.x :=
∑ Moxn + ∑ Mot.xn n
Resisting Moment about X-axis due to Py:
n
Mrm.x := n
for j ∈ 0 .. 6
( Ptyn) j > 0 ⋅ kN
if
OT ← Pty ⋅ j n j
(
)
⎛⎜ B ⎝2
+ Zp
(
)
⎛⎜ B ⎝2
− Z p ⎟ if MOT.x < 0 kN m n⎠ j
OT ← Pty ⋅ j n j
⎞
n⎟⎠
if MOT.x > 0 kN m j
⎞
OT ← 0 kN ⋅ m otherwise j OT ← 0 kN ⋅ m otherwise j OT
Total Resisting Moment about X-axis:
MRM.x :=
B
∑ Mrm.xn + ( Wtbase + Wtsoil) ⋅ 2 n
Factor of Safety:
FSOT.x := j
MRM.x MOT.x
j
if
j
MOT.x
≠ 0 kN m
j
"INFINITY" otherwise Check_FS OTx := j
"N.A." if FSOT.x = "INFINITY" j otherwise "> 1.5, OK,Safe against overturning @ X" if FSOT.x ≥ 1.5 j "< 1.5, N.G. Redesign" otherwise
OVERTURNING MOMENT ABOUT X Comb 100 101 102 103 104 105 106
RM 8112.56 6823.55 6772.72 7197.37 7159.22 4907.40 4856.48
OM
FS OT
2.72 -2.28 -372.65 -7.16 -284.93 -1.17 -371.56
2988.05 2992.79 18.17 1005.22 25.13 4212.36 13.07
Remarks > 1.5, > 1.5, > 1.5, > 1.5, > 1.5, > 1.5, > 1.5,
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
Due to Fx and Mz:
Moz := Fx ⋅ h + T + Mz n n n n
Eccentricity:
Footing F-4.xmcd
(
ex := j
)
⎛∑ Mezn⎞ + ⎛∑ Mozn⎞ ⎜ ⎟ ⎜ ⎟ ⎝n ⎠j ⎝ n ⎠j P Total j
LNT - Page 11 of 41
Calculation Sheet
Overturning Moment due to Py:
Total Overturning Moment about X-axis:
Mot.z := n
MOT.z :=
for j ∈ 0 .. 6
(
if
)
Pty < 0 ⋅ kN n j
(
n
⎛⎜ L ⎝2
)
OT ← − Pty ⋅ j n j
)
⎛⎜ L ⎝2
(
)
(
OT ← Pty ⋅ j n j
∑ Mozn + ∑ Mot.zn
− Xp
⎞⎟
n⎠
n
if Xp < 0 m n
− Xp ⎞⎟ if Xp > 0m n⎠ n
if Xp = 0m n OT ← − Pty ⋅ j n j
(
)
OT ← Pty ⋅ j n j
⎛⎜ L ⎞⎟ ⎝ 2⎠
⎛⎜ L ⎞⎟ ⎝ 2⎠
if ez < 0m j if ez > 0m j
OT ← 0 kN ⋅ m otherwise j OT Resisting Moment about Z-axis due to Py:
Total Resisting Moment about X-axis:
Mrm.z := n
MRM.z :=
for j ∈ 0 .. 6 if
( Ptyn) j > 0 ⋅ kN
n
OT ← Pty ⋅ j n j
(
)
⎛⎜ L ⎝2
− Xp ⎟ if MOT.z > 0 kN m n⎠ j
(
)
⎛⎜ L ⎝2
+ Xp
OT ← Pty ⋅ j n j
L
∑ Mrm.zn + ( Wtbase + Wtsoil) ⋅ 2
⎞ ⎞
n⎟⎠
if MOT.z < 0 kN m j
OT ← 0 kN ⋅ m otherwise j OT ← 0 kN ⋅ m otherwise j OT Factor of Safety:
FSOT.z := j
MRM.z j MOT.z j
if
MOT.z ≠ 0 kN m j
Check_FS OTz := j
"N.A." if FSOT.z = "INFINITY" j otherwise
"INFINITY" otherwise
"> 1.5, OK,Safe against overturning @ Z" if FSOT.z ≥ 1.5 j "< 1.5, N.G. Redesign" otherwise
OVERTURNING MOMENT ABOUT Z Comb 100 101 102 103 104 105 106
RM 6538.85 5795.83 5832.35 6195.83 6223.20 4155.00 4191.45
OM
FS OT -0.66 47.35 -1.81 34.37 -2.51 48.19 -0.98
9982.98 122.40 3231.22 180.29 2479.36 86.22 4276.99
Remarks > 1.5, > 1.5, > 1.5, > 1.5, > 1.5, > 1.5, > 1.5,
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-4.xmcd
LNT - Page 12 of 41
Calculation Sheet
NET SOIL BEARING PRESSURE:
MAX NET SOIL BEARING PRESSURE Comb
P Total (kN)
100 101 102 103 104 105 106
ex (m)
2615.54 2318.33 2332.94 2478.33 2489.28 1662.00 1676.58
CRITICAL LOAD COMBINATION
Pier #1
ez (m)
0.000 0.020 -0.001 0.014 -0.001 0.029 -0.001
K Coeff
0.101 0.058 0.257 0.099 0.238 0.048 0.325
1.10 1.08 1.26 1.12 1.24 1.08 1.33
P max (kPa) 95.99 83.63 97.80 92.14 102.86 59.99 74.09
P max.net (kPa) 72.59 60.23 74.40 68.74 79.46 36.59 50.69
Remarks < qs = 100 kPa, < qs = 100 kPa, < qs = 100 kPa, < qs = 100 kPa, < qs = 100 kPa, < qs = 100 kPa, < qs = 100 kPa,
O.K.! O.K.! O.K.! O.K.! O.K.! O.K.! O.K.!
ASD_Comb = 104 SL
Pier #2
Pier #3
Py (kN) =
-405.5
-724.9
-559.8
Fx (kN) =
0.3
3.1
0.6
Fz (kN) =
24.3
14.6
30.7
Mx (kN·m) =
-58.5
-50.0
-72.0
Mz (kN·m) =
-1.4
-5.4
-1.6
CALCULATE SOIL BEARING PRESSURE
Footing F-4.xmcd
LNT - Page 13 of 41
Calculation Sheet BEARING AREA: Dist x
d x = "N.A."
Dist z
d z = "N.A."
Brg. L1
L1 = 5.000 m
Brg. L2
L2 = 6.000 m
%Brg. Area
Brg_Area = 100.00 ⋅ %
Biaxial Case
Case = "N.A."
GROSS SOIL BEARING CORNER PRESSURES:
MAXIMUM NET SOIL PRESSURE:
P = 63.09 ⋅ kPa 1
P = 102.86 ⋅ kPa 3
P = 102.66 ⋅ kPa 2
P = 63.29 ⋅ kPa 4
P max.net := max ( P ) − γs ⋅ ( D + T) P max.net = 79.46 ⋅ kPa
(
Check_qs := if P max.net ≤ q s , "OK, q max < q allowable" , "N.G. Redesign" Check_qs = "OK, q max < q allowable"
E.
)
P max.net q uR
otherwise
x otherwise
⎛L d 6 := max ⎜ + Xp − n n ⎝2
Lpx ⎞ n − d e , 0m⎟ 2 ⎠
T d 6 = ( 1.835 1.835 1.835 ) m
⎛L d 5 := max ⎜ + Xp − n n ⎝2
Lpx ⎞ de n − , 0m⎟ 2 2 ⎠
T d 5 = ( 2.042 2.042 2.042 ) m
⎛L d 4 := max ⎜ + Xp − n n ⎝2
Lpx ⎞ n , 0m⎟ 2 ⎠
T d 4 = ( 2.25 2.25 2.25 ) m
⎛L d 3 := min⎜ + Xp + n n ⎝2
Lpx n ⎞⎟ ,L 2 ⎠
T d 3 = ( 2.75 2.75 2.75 ) m
⎛L d 2 := min⎜ + Xp + n n ⎝2
Lpx de ⎞ n + , L⎟ 2 2 ⎠
T d 2 = ( 2.957 2.957 2.957 ) m
⎛L d 1 := min⎜ + Xp + n n ⎝2
Lpx ⎞ n + d e , L⎟ 2 ⎠
T d 1 = ( 3.165 3.165 3.165 ) m
T b ox = ( 0.915 0.915 0.915 ) m
b ox := d 2 − d 5
qx CALCULATIONS
q at critical sections:
( )
q d1 = n
103.1 103.1 103.1
Footing F-4.xmcd
( )
⋅ kPa
q d6 = n
103.1 103.1 103.1
( )
⋅ kPa
q d2 = n
103.1 103.1 103.1
( )
⋅ kPa
q d5 = n
103.1 103.1 103.1
( )
⋅ kPa
q d3 = n
103.1 103.1 103.1
( )
⋅ kPa
q d4 = n
103.1 103.1
⋅ kPa
103.1
LNT - Page 17 of 41
Calculation Sheet
Diagrams
⎛L ⎜ ⎜2 ⎜ ⎜L ⎜2 ⎜ xp ( n ) := ⎜ L ⎜2 ⎜ ⎜L ⎜2 ⎜ ⎜L ⎝2
⎞ ⎟ ⎟ Lpx ⎟ n ⎟ 2 ⎟ Lpx ⎟ n⎟ 2 ⎟ Lpx ⎟ n ⎟ 2 ⎟ Lpx ⎟ n⎟ 2 ⎠ Lpx n 2
+ Xp − n + Xp + n + Xp + n + Xp − n + Xp − n
⎛ T ⎞ ⎜ ⎟ ⎜ T ⎟ y1p := ⎜ T + 0.5m ⎟ ⎜ T + 0.5m ⎟ ⎜ ⎟ ⎝ T ⎠
⎛ 0m ⎞ ⎜ ⎟ ⎜L⎟ xf := ⎜ L ⎟ ⎜ 0m ⎟ ⎜ ⎟ ⎝ 0m ⎠
L
0kN if x <
( Putyn) FL Vp_ ( x) :=
2
+ Xp
Mp_ ( x , n ) :=
n
Mp_ ( x) :=
⋅x
Mssf ( x) :=
Mp ← 0kN ⋅ m
Wu Total L
⋅
x
2
2
Moment due to Soil Pressure:
if q uR = 0 ⋅ kPa
Msbp ( x) :=
1 − ⎡⎢ ⋅ ( q uL + q ( x) ) ⋅ x⎤⎥ ⋅ Brgz if x ≤ Brgx ⎣2 ⎦ ⎛1 ⎞ − ⎜ ⋅ Brgx ⋅ q uL ⋅ Brgz⎟ otherwise ⎝2 ⎠ 1 − ⎡⎢ ⋅ q ( x) ⋅ ⎡⎣x − ( L − Brgx)⎤⎦⎥⎤ ⋅ Brgz ⎣2 ⎦
if q uR = 0 ⋅ kPa − ⎛⎜
1 2 1 2 ⋅ q uL ⋅ x + ⋅ q ( x) ⋅ x ⎞⎟ ⋅ Brgz 6 ⎝3 ⎠ 1 1 ⎡ ⎛ ⎞⎤ − ⎢ ⋅ Brgx ⋅ q uL ⋅ Brgz ⋅ ⎜x − ⋅ Brgx⎟⎥ ⎣2 ⎝ 3 ⎠⎦
if q uL = 0 ⋅ kPa
(
if x ≥ L − Brgx
)
if q uL = 0 ⋅ kPa 1 2 − ⎡⎢ ⋅ q ( x) ⋅ ⎡⎣x − L − Brgx ⎤⎦ ⎥⎤ ⋅ Brgz i ⎣6 ⎦
(
0 ⋅ kN otherwise
Footing F-4.xmcd
n
Moment due to Soil, Surcharge and Foundation:
Shear due to Soil Pressure:
⎡1 −⎢ ⎣2
+ Xp
Mp ← Mp + Mp_ ( x , i − 1)
Shear due to Soil, Surcharge and Foundation:
L
2
for i ∈ 1 .. Npier
Vp ← Vp + Vp_ ( x , i − 1)
Wu Total
L
L
for i ∈ 1 .. Npier
Vssf ( x) :=
0kN ⋅ m if x <
( Putyn) FL ⋅ ⎡⎢⎣x − ⎛⎜⎝ 2 + Xpn⎞⎟⎠⎤⎥⎦ − ( Muozn) F
otherwise
Vp ← 0kN
Vsbp ( x) :=
⎛ T ⎞ ⎜ ⎟ ⎜ T ⎟ ⎜ T + hn ⎟ yp ( n ) := ⎜ ⎟ ⎜ T + hn ⎟ ⎜ ⎟ ⎝ T ⎠
Moment due to Py:
Shear due to Py: Vp_ ( x , n ) :=
⎛ 0m ⎞ ⎜ ⎟ ⎜ 0m ⎟ yf := ⎜ T ⎟ ⎜T⎟ ⎜ ⎟ ⎝ 0m ⎠
( quL + q( x) ) x⎤⎥ ⋅ Brgz ⎦
)
0 ⋅ kN ⋅ m otherwise otherwise
⎛1
−⎜
⎝3
2 1 2⎞ ⋅ q uL ⋅ x + ⋅ q ( x) ⋅ x ⎟ ⋅ Brgz othe 6 ⎠
LNT - Page 18 of 41
Calculation Sheet
TOTAL SHEAR:
TOTAL MOMENT:
V( x) :=
M( x) :=
0 ⋅ kN if ( x = 0 ⋅ m) + ( x = L) Vsbp ( x) + Vssf ( x) + Vp_ ( x) otherwise
0 ⋅ kN ⋅ m if ( x = 0 ⋅ m) + ( x = L) Mssf ( x) + Msbp ( x) + Mp_ ( x) otherwise
a := 1000 L .. L a
Let
x := 0m ,
M1 :=
for i ∈ 0 .. a
V1 :=
for i ∈ 0 .. a
⎛ i ⋅ L ⎟⎞ M1 ← M⎜ i ⎝ a ⎠
⎛ i ⋅ L ⎟⎞ M ← V⎜ i ⎝ a ⎠
M1
M
X( c ) := match⎛⎜
⎝
max ( c ) 1 c ⎞ , ⎟0 ⋅ L ⋅ mm a mm ⎠
m1 := 100 ⋅ ⎛⎜ceil ⎛⎜0.011 ⋅
⎝
⎝
v1 := 100 ⋅ ⎛⎜ceil ⎛⎜0.011 ⋅
M( X( M1) ) ⎞⎞ ⎟⎟ kN m ⎠⎠
⎝
m1 = 0
⎝
M( X( M1) ) ⎞⎞ ⎟⎟ kN m ⎠⎠
v1 = 0
⎛ ⎝
⎛ ⎝
m1 := 100 ⋅ ⎜ceil ⎜0.011 ⋅
m1 = 1.7 × 10
(
max yp ( 0) , yp ( 1) , yp ( 2) mm
) ⎞⎞ ⎟⎟ ⎠⎠
⎛ 0.25m1 ⎞ y1 := ⎜ ⎟ ⎝ − 0.25m1 ⎠
⎛L⎞ ⎜2⎟ x1 := ⎜ ⎟ ⎜L⎟ ⎝2⎠
3
( )
q x.5 := q d 5 n n
( )
q x.2 := q d 2 n n
Diagrams
Footing F-4.xmcd
LNT - Page 19 of 41
Calculation Sheet
q uL = 103.1 ⋅ kPa
qu (kPa)
Soil Bearing Pressure Diagram
q uR = 103.0 ⋅ kPa
0
2× 10
3
4× 10
3
6× 10
3
L (mm)
Footing F-4.xmcd
LNT - Page 20 of 41
Calculation Sheet
Vu (kN)
Shear Diagram
0
2× 10
3
4× 10
3
6× 10
3
L (mm)
Footing F-4.xmcd
LNT - Page 21 of 41
Calculation Sheet
Mu (kN-m)
Moment Diagram
0
2× 10
3
4× 10
3
6× 10
3
L (mm)
Footing F-4.xmcd
LNT - Page 22 of 41
Calculation Sheet
Max Beam Shear & Bending Moment Beam Shear along Z-axis at d distance from face of col:
( )
( )
V d1 = n
V d6 = n
⋅ kN
727.6 727.6
-728.0 -728.0
727.6
Bending moment about Z-axis at critical sections:
( )
⋅ kN
-728.0
( )
M d3 = n
⋅ kN m
-1003.7 -1003.7
M d4 = n
-1003.7
-1004.3 -1004.3
⋅ kN m
-1004.3
Mupos.z := max ( M1)
MuRz := VuRz :=
for i ∈ 0 .. N pier − 1
VuRz = 727.6 ⋅ kN
( )
for i ∈ 0 .. N pier − 1
( )
m ← M d3 i i
v ← V d1 i i
min( m)
max ( v) MuRz = − 1003.7 ⋅ kN m MuLz := VuLz :=
for i ∈ 0 .. Npier − 1
( )
m ← M d4 i i
for i ∈ 0 .. Npier − 1
( )
v ← V d6 i i
min( m)
max ( v)
MuLz = − 1004.3 ⋅ kN m
VuLz = − 728.0 ⋅ kN
(
(
)
(
))
Muneg.z := if min MuLz , MuRz ≥ 0kN ⋅ m , 0kN ⋅ m , min MuLz , MuRz
Max Beam Shear & Bending Moment Wide-beam shear along Z direction
Max negative moment at face of support
Muneg.z = 1004.3 ⋅ kN m
VuLz = − 728.0 ⋅ kN
Max positive moment:
Mupos.z = 0.0 ⋅ kN m
F.2
Footing F-4.xmcd
VuRz = 727.6 ⋅ kN
FOOTING ANALYSIS ALONG Z-DIRECTIONS
LNT - Page 23 of 41
Calculation Sheet
B = 6m
q uL :=
Pu + Pu 1 4 2
q uR :=
q uL = 68.7 ⋅ kPa
Pu + Pu 3 2 2
q uR = 137.5 ⋅ kPa
qz CALCULATIONS
q at critical sections:
Δq :=
q ( x) :=
q uL − q uR
Δq = 11.471 ⋅
Brgz
kPa m
if q uR = 0kPa x ⎞ ⎟ if x ≤ Brgz Brgz ⎠
q uL ⋅ ⎛⎜1 −
⎝
0kPa otherwise if q uL = 0kPa
⎛ ⎝
q uR ⋅ ⎜1 +
x − B⎞
⎟
Brgz ⎠
0kPa otherwise
(
)
min q uL , q uR + Δq ⋅
(
)
if x ≥ B − Brgz
( Brgz − x)
if q uL > q uR
otherwise
x otherwise
⎛B d 6 := max ⎜ + Z p − n n ⎝2
Lpz n
⎛B d 5 := max ⎜ + Z p − n n ⎝2
Lpz n
Footing F-4.xmcd
2
2
⎞
− d e , 0m⎟
⎠
−
de 2
⎞
, 0m⎟
⎠
T d 6 = ( 0.335 2.335 4.335 ) m
T d 5 = ( 0.542 2.542 4.543 ) m
LNT - Page 24 of 41
Calculation Sheet ⎛B d 4 := max ⎜ + Z p − n n ⎝2
Lpz n 2
⎛B d 3 := min⎜ + Z p + n n ⎝2
Lpz
⎛B d 2 := min⎜ + Z p + n n ⎝2
Lpz
⎛B d 1 := min⎜ + Z p + n n ⎝2
Lpz
n
⎞
T d 4 = ( 0.75 2.75 4.75 ) m
, 0 ⋅ m⎟
⎠
⎞
T d 3 = ( 1.25 3.25 5.25 ) m
, B⎟
⎠
2 n
2 n
2
+
de 2
⎞
T d 2 = ( 1.458 3.458 5.457 ) m
, B⎟
⎠
⎞
T d 1 = ( 1.665 3.665 5.665 ) m
+ d e , B⎟
⎠
b oz := d 2 − d 5
T b oz = ( 0.915 0.915 0.915 ) m
WzR := Brgx − d 1
T WzR = ( 3.335 1.335 − 0.665 ) m
WzL := d 6
T WzL = ( 0.335 2.335 4.335 ) m
azL := d 4
T azL = ( 0.75 2.75 4.75 ) m
azR := Brgz − d 3
T azR = ( 4.75 2.75 0.75 ) m
qz CALCULATIONS
q at critical sections:
( )
q d1 = n
87.8 110.7 133.6
Footing F-4.xmcd
( )
⋅ kPa
q d6 = n
72.5 95.4 118.4
( )
⋅ kPa
q d2 = n
85.4 108.3 131.3
( )
⋅ kPa
q d5 = n
74.9 97.8 120.8
( )
⋅ kPa
q d3 = n
83.0 105.9 128.9
( )
⋅ kPa
q d4 = n
77.3 100.2
⋅ kPa
123.1
LNT - Page 25 of 41
Calculation Sheet
Diagrams
⎛B ⎜ ⎜2 ⎜ ⎜B ⎜2 ⎜ xp ( n ) := ⎜ B ⎜2 ⎜ ⎜B ⎜2 ⎜ ⎜B ⎝2
+ Zp − n + Zp + n + Zp + n + Zp − n + Zp − n
⎞ ⎟ 2 ⎟ Lpz ⎟ n ⎟ 2 ⎟ Lpz ⎟ n⎟ 2 ⎟ Lpz ⎟ n ⎟ 2 ⎟ Lpz ⎟ n⎟ 2 ⎠ Lpz n
⎛ 0m ⎞ ⎜ ⎟ ⎜B⎟ xf := ⎜ B ⎟ ⎜ 0m ⎟ ⎜ ⎟ ⎝ 0m ⎠
Moment due to Py:
Shear due to Py: Vp_ ( x , n ) :=
0kN if x <
( Vp_ ( x) :=
Puty n
) FL
B 2
+ Zp
Mp_ ( x , n ) :=
n
Mp_ ( x) :=
Vp ← 0kN
Mp ← 0kN ⋅ m
Moment due to Soil, Surcharge and Foundation: Mssf ( x) :=
⋅x
Wu Total B
Shear due to Soil Pressure:
Moment due to Soil Pressure:
Vsbp ( x) :=
Msbp ( x) :=
if q uR = 0 ⋅ kPa 1 − ⎡⎢ ⋅ ( q uL + q ( x) ) ⋅ x⎤⎥ ⋅ Brgx if x ≤ Brgz ⎣2 ⎦ 1 ⎛ ⎞ − ⎜ ⋅ Brgz ⋅ q uL ⋅ Brgx⎟ otherwise ⎝2 ⎠ 1 − ⎡⎢ ⋅ q ( x) ⋅ ⎡⎣x − ( B − Brgz)⎤⎦⎥⎤ ⋅ Brgx ⎣2 ⎦ 0 ⋅ kN otherwise
⎤ − ⎢ ( q uL + q ( x) ) x⎥ ⋅ Brgx ⎣2 ⎦
Footing F-4.xmcd
⋅
2 x 2
if q uR = 0 ⋅ kPa
⎛ 1 ⋅ q ⋅ x2 + 1 ⋅ q ( x) ⋅ x2⎞⎟ ⋅ Brg if uL x 6 ⎝3 ⎠ 1 1 − ⎡⎢ ⋅ Brgz ⋅ q uL ⋅ Brgx ⋅ ⎛⎜x − ⋅ Brgz⎞⎟⎥⎤ ⎣2 ⎝ 3 ⎠⎦ −⎜
if q uL = 0 ⋅ kPa
⎡1
otherwise
Mp ← Mp + Mp_ ( x , i − 1)
Shear due to Soil, Surcharge and Foundation: B
B + Zp n 2
for i ∈ 1 .. Npier
Vp ← Vp + Vp_ ( x , i − 1)
Wu Total
0kN ⋅ m if x <
( Putyn) FL ⋅ ⎡⎢⎣x − ⎛⎜⎝ B2 + Zpn⎞⎟⎠⎤⎥⎦ + ( Muoxn) FL
otherwise
for i ∈ 1 .. Npier
Vssf ( x) :=
⎛ 0m ⎞ ⎜ ⎟ ⎜ 0m ⎟ yf := ⎜ T ⎟ ⎜T⎟ ⎜ ⎟ ⎝ 0m ⎠
x ≤ Brgz otherwise
if q uL = 0 ⋅ kPa
(
)
if x ≥ B − Brgz
2⎤ ⎡1 − ⎢ ⋅ q ( x) ⋅ ⎡⎣x − B − Brgz ⎤⎦ ⎥ ⋅ Brgx if x ≥ B − Brgz ⎣6 ⎦
(
)
(
)
0 ⋅ kN ⋅ m otherwise otherwise
1 2 1 2 − ⎛⎜ ⋅ q uL ⋅ x + ⋅ q ( x) ⋅ x ⎞⎟ ⋅ Brgx otherwise 6 ⎝3 ⎠
LNT - Page 26 of 41
Calculation Sheet
TOTAL SHEAR:
TOTAL MOMENT:
V( x) :=
M( x) :=
0 ⋅ kN if ( x = 0 ⋅ m) + ( x = B) Vsbp ( x) + Vssf ( x) + Vp_ ( x) otherwise
0 ⋅ kN ⋅ m if ( x = 0 ⋅ m) + ( x = B) Mssf ( x) + Msbp ( x) + Mp_ ( x) otherwise
a := 1000
Let
x := 0m ,
B .. B a
B = 6 ⋅ mm a
⎛B⎞ ⎜2⎟ x1 := ⎜ ⎟ ⎜B⎟ ⎝2⎠
M1 :=
for i ∈ 0 .. a
V1 :=
for i ∈ 0 .. a
⎛ i ⋅ B⎞
M1 ← M⎜ i ⎝ a
⎛ i ⋅ B ⎞⎟ M ← V⎜ i ⎝ a ⎠
⎟ ⎠
M1
M
X( c ) := match⎛⎜
⎝
max ( c ) 1 c ⎞ , ⎟0 ⋅ B ⋅ mm a mm ⎠
( )
q z.5 := q d 5 n n
( )
q z.2 := q d 2 n n
Diagrams
Footing F-4.xmcd
LNT - Page 27 of 41
Calculation Sheet
q uL = 68.7 ⋅ kPa
qu (kPa)
Soil Bearing Pressure Diagram
q uR = 137.5 ⋅ kPa
0
2× 10
3
4× 10
3
6× 10
3
B (mm)
Footing F-4.xmcd
LNT - Page 28 of 41
Calculation Sheet
Vu (kN)
Shear Diagram
0
2× 10
3
4× 10
3
6× 10
3
B (mm)
Footing F-4.xmcd
LNT - Page 29 of 41
Calculation Sheet
Mu (kN-m)
Moment Diagram
0
2× 10
3
4× 10
3
6× 10
3
B (mm)
Footing F-4.xmcd
LNT - Page 30 of 41
Calculation Sheet
Max Beam Shear & Bending Moment Beam Shear along X-axis at d distance from face of col:
( )
( )
V d1 = n
V d6 = n
⋅ kN
121.6 330.9
-56.3 -61.4
165.1
VuRx :=
Bending moment about X-axis at critical sections:
( )
M d3 = n
⋅ kN
-231.7 -276.5
71.0
( )
⋅ kN m
M d4 = n
-48.6 -189.8
-137.3
⋅ kN m
21.6
for i ∈ 0 .. Npier − 1
( )
v ← V d1 i i max ( v
Mupos.x := max ( M1)
) MuRx :=
VuRx = 389.3 ⋅ kN
for i ∈ 0 .. Npier − 1
( )
m ← M d3 i i min( m)
VuLx :=
for i ∈ 0 .. N pier − 1
( )
MuRx = − 276.5 ⋅ kN m
v ← V d6 i i max ( v
)
MuLx :=
for i ∈ 0 .. N pier − 1
( )
m ← M d4 i i
VuLx = 109.5 ⋅ kN
min( m) MuLx = − 189.8 ⋅ kN m
(
(
)
(
Muneg.x := if min MuLx , MuRx ≥ 0kN ⋅ m , 0kN ⋅ m , min MuLx , MuRx
))
Max Beam Shear & Bending Moment Wide-beam shear along X direction
Max negative moment at face of support
Muneg.x = 276.5 ⋅ kN m
VuLx = 109.5 ⋅ kN
Max positive moment:
Mupos.x = 34.1 ⋅ kN m
F.4
VuRx = 389.3 ⋅ kN
PUNCHING SHEAR Capacity reduction factor
ϕv := 0.85
Shear strength provided
(
ϕVc := ϕv ⋅ 0.33 ⋅
) (
)
fc ⋅ MPa ⋅ b ox + b oz ⋅ d e
T ϕVc = ( 1167 1167 1167 ) ⋅ kN Punching Shear Perimeter around column/pier: Along x-direction
T b ox = ( 0.915 0.915 0.915 ) m
Along z-direction
T b oz = ( 0.915 0.915 0.915 ) m
Area of Punching Shear:
Footing F-4.xmcd
LNT - Page 31 of 41
Calculation Sheet T 2 Ap = ( 0.837 0.837 0.837 ) m
Ap := b ox ⋅ b oz n n n Total force from column/pier:
(
)
(
)
P uy := Puty + LF ⋅ ⎡Ap ⋅ T ⋅ γc + D ⋅ γs + Q ⎤ n n FL ⎣ n ⎦ T P uy = ( 495.9 862.8 717.3 ) ⋅ kN q at d/2 distance from supports: Along x-direction
T q x.2 = ( 103.1 103.1 103.1 ) ⋅ kPa T q x.5 = ( 103.1 103.1 103.1 ) ⋅ kPa
Along z-direction
T q z.2 = ( 85.4 108.3 131.3 ) ⋅ kPa T q z.5 = ( 74.9 97.8 120.8 ) ⋅ kPa
Total force acting on punched area Rq := n
1 2
(
)
⋅ max q x.5 + q x.2 , q z.5 + q z.2 ⋅ Ap n n n n n
T Rq = ( 86.3 86.3 105.5 ) ⋅ kN Net punching shear: Vup := P uy − Rq n n n T Vup = ( 409.6 776.5 611.8 ) ⋅ kN
Check if shear strength provided by concrete is greater than the maximum shear force.
(
(
)
ACI31811.3.1.1.Eq.11.3.p := if min( ϕVc ) > max Vup , "OK,shear strength provided > Vu." , "NG!"
(
ACI31811.3.1.1.Eq.11.3.p = "OK,shear strength provided > Vu." F.5
) )
min( ϕVc ) >=? max Vup = "YES!.. SATISFACTORY"
WIDE BEAM SHEAR Wide-beam shear along Z direction VuLz = − 728.0 ⋅ kN
VuRz = 727.6 ⋅ kN
(
Shear strength provided
ϕVn b := ϕv ⋅ 0.17 ⋅
)
fc ⋅ MPa ⋅ B ⋅ d e
ϕVn b = 1970.7 ⋅ kN
Check if shear strength provided by concrete is greater than the maximum shear force.
(
(
)
ACI31811.3.1.1.Eq.11.3.bsz := if ϕVn b > max VuLz , VuRz , "OK,shear strength provided > Vu." , "NG!"
(
ACI31811.3.1.1.Eq.11.3.bsz = "OK,shear strength provided > Vu."
) )
ϕVn b >=? max VuLz , VuRz = "YES!.. SATISFACTORY"
Wide-beam shear along X direction VuLx = 109.5 ⋅ kN
VuRx = 389.3 ⋅ kN
( Footing F-4.xmcd
) LNT - Page 32 of 41
Calculation Sheet (
Shear strength provided
ϕVn b := ϕv ⋅ 0.17 ⋅
)
fc ⋅ MPa ⋅ L ⋅ d e
ϕVn b = 1642.3 ⋅ kN
Check if shear strength provided by concrete is greater than the maximum shear force.
(
(
)
) ϕVn b >=? max ( VuLx , VuRx) = "YES!.. SATISFACTORY"
ACI31811.3.1.1.Eq.11.3.bsx := if ϕVn b > max VuLx , VuRx , "OK,shear strength provided > Vu." , "NG!" ACI31811.3.1.1.Eq.11.3.bsx = "OK,shear strength provided > Vu." G.
REINFORCEMENT DESIGN G.1
G.2
DESIGN MOMENT FOR BOTTOM BARS Capacity reduction factor
ϕf := 0.90
Moment at face of pedestal X-direction
Muneg.z = 1004.3 ⋅ kN m
Moment at face of pedestal Z-direction
Muneg.x = 276.5 ⋅ kN m
BOTTOM REINFORCEMENTS Temp steel reinforcement ratio
[ACI 318 7.12.2]
ρ temp := 0.0018 ρ min := ρ temp
Minimum steel reinf ratio
[ACI 318 10.5.4]
ρ min = 0.0018 Bars in X-direction
⎡ ⎣
Mr = ϕf ⋅ As ⋅ fy ⋅ ⎢d s −
Factored resistance
(
)
Mr := max Muneg.z , 0.001 kN m
⎛ As ⋅ fy ⎞⎤ ⎜ ⎟⎥ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
1 ⋅ 2
Mr = 1004.3 ⋅ kN m
b := B
Size of bar
barx ≡ 6
Bar diameter
dia = 20 ⋅ mm barx
Proposed bar spacing
S x.bot := 200mm
Bar area
As = 314 ⋅ mm barx
Reinforcement provided
As ⋅b barx S x.bot
Area of steel provided
As :=
Distance from extreme compressive fiber to centroid of reinforcing steel
d := T − cov − 0.5 ⋅ dia barx
Solve the quadratic equation for the area of steel required
Given
As = 9420 ⋅ mm
2
d = 415 ⋅ mm
⎡ ⎣
Mr = ϕf ⋅ As ⋅ fy ⋅ ⎢d −
( )
As.reqd := Find As
1 ⋅ 2
⎛ As ⋅ fy ⎞⎤ ⎜ ⎟⎥ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
As.reqd = 6638 ⋅ mm
Minimum reinforcement
As.min := min⎛⎜ρ min b d ,
Temperature reinforcement
As.temp := ρ temp b
Reinforcing steel required
As.reqd := max As.reqd , As.min , As.temp
Check As provided
As >=? As.reqd = "YES!.. SATISFACTORY"
⎝
(
2
4 As.reqd⎟⎞ 3 ⎠
As.min = 4482 ⋅ mm
T 2
2
2
As.temp = 2700 ⋅ mm
)
As.reqd = 6638 ⋅ mm
2
2
Bars in Z-direction
Footing F-4.xmcd
LNT - Page 33 of 41
Calculation Sheet ⎡ ⎣
Mr = ϕf ⋅ As ⋅ fy ⋅ ⎢d s −
Factored resistance
(
)
Mr := max Muneg.x , 0.001 kN m
1 2
⋅
⎛ As ⋅ fy ⎞⎤ ⎜ ⎟⎥ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
Mr = 276.5 ⋅ kN m
b := L
Size of bar
barz ≡ 6
Bar diameter
dia = 20 ⋅ mm barz
Proposed bar spacing
S z.bot := 200mm
Bar area
As = 314 ⋅ mm barz
Reinforcement provided
As ⋅b barz
Area of steel provided
As :=
Distance from extreme compressive fiber to centroid of reinforcing steel
d := T − cov − dia − 0.5 dia barx barz
Solve the quadratic equation for the area of steel required
Given
As = 7850 ⋅ mm
S z.bot
2
d = 395 ⋅ mm
⎡ ⎣
Mr = ϕf ⋅ As ⋅ fy ⋅ ⎢d −
( )
As.reqd := Find As
G.3
2
1 2
⋅
⎛ As ⋅ fy ⎞⎤ ⎜ ⎟⎥ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
As.reqd = 1893 ⋅ mm
⎛ ⎝
4
⎞ ⎠
Minimum reinforcement
As.min := min⎜ρ min b d ,
Temperature reinforcement
As.temp := ρ temp b
Reinforcing steel required
As.reqd := max As.reqd , As.min , As.temp
Check As provided
As >=? As.reqd = "YES!.. SATISFACTORY"
3
As.reqd⎟
As.min = 2525 ⋅ mm
T
2
2
As.temp = 2250 ⋅ mm
2
(
)
As.reqd = 2525 ⋅ mm
2
2
TOP REINFORCEMENTS Bars in X-direction
⎡ ⎣
Mr = ϕf ⋅ As ⋅ fy ⋅ ⎢d s −
Factored resistance
(
)
Mr := max Mupos.z , 0.001 kN m
1 2
⋅
⎛ As ⋅ fy ⎞⎤ ⎜ ⎟⎥ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
Mr = 0.0 ⋅ kN m
b := B
Size of bar
barx.top := 5
Bar diameter
dia = 16 ⋅ mm barx.top
Proposed bar spacing
S x.top := 300mm
Bar area
As = 201 ⋅ mm barx.top
Reinforcement provided
As ⋅b barx.top
Area of steel provided
As :=
Distance from extreme compressive fiber to centroid of reinforcing steel
d := T − cov − 0.5 dia barx.top
Solve the quadratic equation for the area of steel required
Given
As = 4020 ⋅ mm
S x.top
⎡ ⎣
( )
As.reqd := Find As
Footing F-4.xmcd
1 2
⋅
⎛ As ⋅ fy ⎞⎤ ⎜ ⎟⎥ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
As.reqd = 0 ⋅ mm 4
⎞ ⎠
Minimum reinforcement
As.min := min⎜ρ min b d ,
Temperature reinforcement
As.temp := ρ temp b
Reinforcing steel required
As.reqd := max As.reqd , As.min , As.temp
(
2
d = 417 ⋅ mm
Mr = ϕf ⋅ As ⋅ fy ⋅ ⎢d −
⎛ ⎝
3
2
As.reqd⎟
As.min = 0 ⋅ mm
T
2
2
As.temp = 2700 ⋅ mm
2
)
As.reqd = 2700 ⋅ mm
2
2
LNT - Page 34 of 41
Calculation Sheet Check As provided
As >=? As.reqd = "YES!.. SATISFACTORY"
Bars in Z-direction
⎡ ⎣
Mr = ϕf ⋅ As ⋅ fy ⋅ ⎢d s −
Factored resistance
(
)
Mr := max Mupos.x , 0.001 kN m
1 ⋅ 2
⎛ As ⋅ fy ⎞⎤ ⎜ ⎟⎥ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
Mr = 34.1 ⋅ kN m
b := L
Size of bar
barz.top := 5
Bar diameter
dia = 16 ⋅ mm barz.top
Proposed bar spacing
S z.top := 300mm
Bar area
As = 201 ⋅ mm barz.top
Reinforcement provided
As ⋅b barz.top S z.top
Area of steel provided
As :=
Distance from extreme compressive fiber to centroid of reinforcing steel
d := T − cov − dia − 0.5 dia barx.top barz.top
Solve the quadratic equation for the area of steel required
Given
As = 3350 ⋅ mm
⎡ ⎣
( )
H.
2
d = 401 ⋅ mm
Mr = ϕf ⋅ As ⋅ fy ⋅ ⎢d −
As.reqd := Find As
1 ⋅ 2
⎛ As ⋅ fy ⎞⎤ ⎜ ⎟⎥ ⎝ 0.85 ⋅ fc ⋅ b ⎠⎦
As.reqd = 228 ⋅ mm
Minimum reinforcement
As.min := min⎛⎜ρ min b d ,
Temperature reinforcement
As.temp := ρ temp b
Reinforcing steel required
As.reqd := max As.reqd , As.min , As.temp
Check As provided
As >=? As.reqd = "YES!.. SATISFACTORY"
⎝
4 As.reqd⎟⎞ 3 ⎠
As.min = 304 ⋅ mm
T 2
(
2
2
As.temp = 2250 ⋅ mm
)
2
As.reqd = 2250 ⋅ mm
2
2
SUMMARY/DETAILS
PLAN REINFORCEMENTS
⎛
⎛ diabarx ⎞ ⎞ ⎟ , "mmØ at " , num2str⎛⎜ S x.bot ⎞⎟ , "mm O.C." ⎟ ⎝ mm ⎠ ⎝ mm ⎠ ⎠
Bot_BarsParallel.L := concat⎜num2str⎜
⎝
⎛
Top_Bars Parallel.L :=
⎛ diabarx.top ⎞ ⎞ ⎟ , "mmØ at " , num2str⎛⎜ S x.top ⎞⎟ , "mm O.C." ⎟ ⎝ mm ⎠ ⎝ mm ⎠ ⎠
concat⎜num2str⎜
⎝
if S x.top ≠ 0mm
"Rebars Not Required" otherwise
⎛
⎛ diabarz ⎞ ⎞ ⎟ , "mmØ at " , num2str⎛⎜ S z.bot ⎞⎟ , "mm O.C." ⎟ ⎝ mm ⎠ ⎝ mm ⎠ ⎠
Bot_BarsParallel.B := concat⎜num2str⎜
⎝
Footing F-4.xmcd
LNT - Page 35 of 41
Calculation Sheet
⎛
Top_Bars Parallel.B :=
⎛ diabarz.top ⎞ ⎞ ⎟ , "mmØ at " , num2str⎛⎜ S z.top ⎟⎞ , "mm O.C." ⎟ ⎝ mm ⎠ ⎝ mm ⎠ ⎠
concat⎜num2str⎜
⎝
if S z.top ≠ 0mm
"Rebars Not Required" otherwise
Center lines:
⎛ 0m ⎞ y1 := ⎜ ⎟ ⎝ 0m ⎠
⎛ − Scale ⋅ 2 ⋅ max ( L , B) ⎜ 2 x1 := ⎜ 1.2 ⋅ L ⎜ 2 ⎝
⎛ 1.2 ⋅ B ⎞ ⎜ 2 ⎟ y2 := ⎜ ⎟ ⎜ − 1.2 ⋅ B ⎟ 2 ⎠ ⎝
x2 :=
Footing:
⎛ −L ⎞ ⎜ 2 ⎟ ⎜ ⎟ ⎜ L ⎟ ⎜ 2 ⎟ ⎜ L ⎟ xf := ⎜ ⎟ ⎜ 2 ⎟ ⎜ −L ⎟ ⎜ 2 ⎟ ⎜ −L ⎟ ⎜ ⎟ ⎝ 2 ⎠
⎛ −B ⎞ ⎜ 2 ⎟ ⎜ ⎟ ⎜ −B ⎟ ⎜ 2 ⎟ ⎜ B ⎟ yf := ⎜ ⎟ ⎜ 2 ⎟ ⎜ B ⎟ ⎜ 2 ⎟ ⎜ −B ⎟ ⎜ ⎟ ⎝ 2 ⎠
Rebars:
⎛ − L − 2cov ⎞ ⎜ ⎟ 2 x1rebar := ⎜ ⎟ ⎜ L − 2cov ⎟ 2 ⎝ ⎠
⎛ − B − 2cov ⎞ ⎜ ⎟ 2 y2rebar := ⎜ ⎟ ⎜ B − 2cov ⎟ 2 ⎝ ⎠
⎛ B − 2cov ⎞ ⎜ 4 ⎟ y1rebar := ⎜ ⎟ ⎜ B − 2cov ⎟ ⎝ 4 ⎠
⎛ L − 2cov ⎞ ⎜ 4 ⎟ x2rebar := ⎜ ⎟ ⎜ L − 2cov ⎟ ⎝ 4 ⎠
Footing F-4.xmcd
⎛ 0m ⎞ ⎜ ⎟ ⎝ 0m ⎠
⎞ ⎟ ⎟ ⎟ ⎠
⎛ − B − 2cov ⎞ ⎜ ⎟ 5 y3 := ⎜ ⎟ ⎜ − down ⋅ m ⎟ ⎝ − down ⋅ m ⎠
⎛ B − 2cov ⎞ ⎜ 4 ⎟ y4 := ⎜ ⎟ ⎜ up ⋅ m ⎟ ⎝ up ⋅ m ⎠
LNT - Page 36 of 41
Calculation Sheet
Columns/pedestal:
⎛ ⎜ Xp − ⎜ n ⎜ ⎜ Xp + ⎜ n ⎜ xp ( n ) := ⎜ X p + ⎜ n ⎜ ⎜ Xp − ⎜ n ⎜ ⎜ Xp − ⎝ n
⎞ ⎟ 2 ⎟ Lpx ⎟ n⎟ 2 ⎟ Lpx ⎟ n ⎟ 2 ⎟ Lpx ⎟ n⎟ 2 ⎟ Lpx ⎟ n ⎟ 2 ⎠ Lpx n
⎛ ⎜ Zp − ⎜ n ⎜ ⎜ Zp − ⎜ n ⎜ yp ( n ) := ⎜ Z p + ⎜ n ⎜ ⎜ Zp + ⎜ n ⎜ ⎜ Zp − ⎝ n
⎞ ⎟ ⎟ Lpz ⎟ n⎟ 2 ⎟ Lpz ⎟ n ⎟ 2 ⎟ Lpz ⎟ n⎟ 2 ⎟ Lpz ⎟ n ⎟ 2 ⎠
Lpz n 2
PLAN REINFORCEMENTS
L = 5.000 m
BARS PARALLEL TO 'L'
cL X-Axis
B = 6.000 m
BARS PARALLEL TO 'B'
Footing F-4.xmcd
LNT - Page 37 of 41
Calculation Sheet
cL Z-Axis
SUMMARY OF REINFORCEMENTS: Bot_BarsParallel.L = "20mmØ at 200mm O.C."
Bot_BarsParallel.B = "20mmØ at 200mm O.C."
Top_Bars Parallel.L = "16mmØ at 300mm O.C."
Top_Bars Parallel.B = "16mmØ at 300mm O.C."
FOOTING DIMENSIONS:
L = 5.000 m
B = 6.000 m
T = 0.500 m
ELEVATION ALONG X-AXIS
T − ⎛cov + dia + 1⋅ barx ⎝
Center lines:
Footing F-4.xmcd
y1 :=
⎛ 0m ⎞ ⎜ ⎟ ⎝ 0m ⎠
⎛ − 1.2 ⋅ L ⎞ ⎜ 2 ⎟ x1 := ⎜ ⎟ 1.2 ⋅L ⎟ ⎜ ⎝ 2 ⎠
⎡T − ⎛cov + diabarx + 1 ⋅ diab ⎢ ⎝ ⎢ cov + dia + 1 ⋅ dia barx ba y3 := ⎢ ⎢ − down ⋅ m ⎢ − down ⋅ m ⎣
LNT - Page 38 of 41
Calculation Sheet
⎛ 1.2 ⋅ max ( h + T) ⎞ y2 :=
⎜ ⎜ ⎝
−
T 2
⎟ ⎟ ⎠
x2 :=
⎛ 0m ⎞ ⎜ ⎟ ⎝ 0m ⎠
Footing:
⎛ −L ⎞ ⎜ 2 ⎟ ⎜ ⎟ ⎜ L ⎟ ⎜ 2 ⎟ ⎜ L ⎟ xf := ⎜ ⎟ ⎜ 2 ⎟ ⎜ −L ⎟ ⎜ 2 ⎟ ⎜ −L ⎟ ⎜ ⎟ ⎝ 2 ⎠
⎛ 0m ⎞ ⎜ ⎟ ⎜ 0m ⎟ yf := ⎜ T ⎟ ⎜T⎟ ⎜ ⎟ ⎝ 0m ⎠
Rebars:
⎛ − L − 2cov ⎞ ⎜ ⎟ 2 x1rebar := ⎜ ⎟ ⎜ L − 2cov ⎟ 2 ⎝ ⎠
y2rebar :=
⎛ cov + 0.5 diabarx ⎞ ⎜ ⎟ y1rebar := ⎜ cov + 0.5 ⋅ dia ⎟ barx ⎠ ⎝
⎛ − L − 2cov ⎞ ⎜ ⎟ 2 x2rebar := ⎜ ⎟ ⎜ L − 2cov ⎟ 2 ⎝ ⎠
⎛ − L − 3cov ⎞ ⎜ ⎟ 2 ⎜ ⎟ ⎜ L − 3cov ⎟ ⎜ 2 ⎟ ⎜ L − 3cov ⎟ x3rebar := ⎜ ⎟ 2 ⎜ ⎟ ⎜ − L − 3cov ⎟ ⎜ ⎟ 2 ⎜ L − 3cov ⎟ ⎜− ⎟ 2 ⎝ ⎠
⎡ ⎛cov + diabarx + 1 ⋅ diabarz⎞ ⎤ ⎠ ⎥ ⎢ ⎝ ⎢ ⎛cov + dia ⎥ + 1 ⋅ dia barx barz⎞⎠ ⎥ ⎢ ⎝ ⎢ ⎥ y3rebar := T − ⎛⎝cov + diabarx + 1 ⋅ diabarz⎞⎠ ⎢ ⎥ ⎢T − ⎛cov + dia ⎥ + 1 ⋅ dia ⎞ barx barz⎠ ⎥ ⎢ ⎝ ⎢ ⎛cov + dia ⎥ + 1 ⋅ dia barx barz⎞⎠ ⎦ ⎣ ⎝
Footing F-4.xmcd
⎡ cov + 0.5 ⋅ diabarx ⎤ ⎢ ⎥ ⎢T − ⎛cov + 0.5 ⋅ dia ⎞ ⎥ barx⎠ ⎥ y4 := ⎢ ⎝ ⎢ ⎥ up ⋅ m ⎢ ⎥ up ⋅ m ⎣ ⎦
⎡T − ⎛cov + 0.5 ⋅ diabarx⎞ ⎤ ⎠⎥ ⎢ ⎝ ⎢T − ⎛cov + 0.5 ⋅ dia ⎞ ⎥ barx⎠ ⎦ ⎣ ⎝
LNT - Page 39 of 41
Calculation Sheet
Columns/pedestal:
⎛ ⎜ Xp − ⎜ n ⎜ ⎜ Xp + ⎜ n ⎜ xp ( n ) := ⎜ X p + ⎜ n ⎜ ⎜ Xp − ⎜ n ⎜ ⎜ Xp − ⎝ n
⎞ ⎟ 2 ⎟ Lpx ⎟ n⎟ 2 ⎟ Lpx ⎟ n ⎟ 2 ⎟ Lpx ⎟ n⎟ 2 ⎟ Lpx ⎟ n ⎟ 2 ⎠ Lpx n
⎛ T ⎞ ⎜ ⎟ ⎜ T ⎟ ⎜ T + hn ⎟ yp ( n ) := ⎜ ⎟ ⎜ T + hn ⎟ ⎜ ⎟ ⎝ T ⎠
ELEVATION ALONG X-AXIS
BARS PARALLEL TO 'L'
T = 0.500 m
BARS PARALLEL TO 'B' L = 5.000 m
Footing F-4.xmcd
LNT - Page 40 of 41
Calculation Sheet
END OF FTG DESIGN
Footing F-4.xmcd
LNT - Page 41 of 41
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