02 machine foundation on piles
DESCRIPTION
machine foundations on pilesTRANSCRIPT
Static Design
Static Design for Foundation:
Foundation Size:Length of the Foundation, L = 9.20 mBreadth of the Foundation, B = 3.00 mThickness of the Foundation, D = 1.60 mThickness of the Base-grout = 0.40 m
Pile Vertical Load Carrying Capacity = 600 kN
Total Weight of Pump assembly = 237.00 kN (Refer Vender Doc.)Center of Shaft of Motor from TOG = 1.35 m (Refer Vender Doc.)
Minimum Thickness of Foundation Block
Minimum thickness of the foundation block = m
= 1.62 mProvided Thickness of Foundation = Thickness of Fdn +Thichness of Grout
= 2.0 m > 1.62
Minimum Concrete Foundation MassMinimum Concrete Foundation Mass = 3 x Mass of Machine
= 711 kNProvided Foundation Mass = 1380 kN > 711.00
Check for Pile Vertical Load Carrying CapacityStatic weight of foundation + machine = 1617 kN
Total Number of 350mm dia. Piles = 8 Nos.
Load combination 1Lateral forces acting perpendicular to the shaft = 25 % of machine weight
= 59.25 kNDistance from the base of fdn to the point of force = 2.95 m
Maximum Pile Load, Pmax = 220.72 kN<
Minimum Pile Load, Pmin = 183.53 kN<
Foundation Block ReinforcementVolume of concrete = 44.16
= 2208.00 kgMinimum Dia of bars = 20 mmWeight of bar = 2.47 kg/mTotal Surface area of foundation = 94.24
Reinforcement per square meter of surface = 23.43Required No. of bars for B/W Reinforcement (per m) = 4.75 Nos. per mRequired Spacing of Reinforcement (B/W & T/B) = 211 mmProvided Spacing of Rreinforcement (B/W & T/B) = 200 mm ……..OK
Reinforcement for 450 dia. PilesDia of bars = 16 mmArea of Reinforcement bar = 201
Required Reinforcement (1% of sectional area) = 962
0.6+Lx/9
m…..OK
kN…..OK
50% of 450 kN…OK
50% of 450 kN…OK
m3
Quantity of steel required (@ 50 kg/m3)
m2
kg/m2
mm2
mm2
Static Design
Required Number of bars = 4.79 Nos.Provided Number of bars = 6 Nos. ……..OK
C.G. & Mass M.I. Calculation 04/22/2023
Calculation of Centre of gravity and Mass moment of inertia 4.00
(Refer foundation Plan and Vendor documents for item markings)
Item mass moment of inertia (individuals) C.G. diatances mass moment of inertia due to eccentricity
No. (m) (m) (m) Weight Mass (m) (m) (m) x y z
(t) (m) (m) (m) (m) (m) (m)total 151.260 15.419 72.473 23.165 50.801 96.109 11.704 89.253 4.700 1.502 3.295 1.344 7.132 8.475Plinth 9.200 3.000 1.600 110.400 11.254 4.600 1.500 2.900 51.768 16.881 32.636 87.817 10.841 81.778 4.700 1.502 3.295 0.100 0.002 0.395 0.113 1.753 1.866
Base Grout 7.150 2.400 0.400 17.160 1.749 5.525 1.500 3.900 9.665 2.624 6.822 8.292 0.863 7.475 4.700 1.502 3.295 -0.825 0.002 -0.605 1.190 0.641 1.831Pump (Total) 0.000 0.000 0.000 23.700 2.416 4.570 1.515 4.695 11.041 3.660 11.343 0.000 0.000 0.000 4.700 1.502 3.295 0.130 -0.013 -1.400 0.041 4.738 4.778
0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.700 1.502 3.295 4.700 1.502 3.295 0.000 0.000 0.000
Note: Consider origin at h/2 distance below pilecap bottom & in x-y plane. Eccentricity of common centre of gravity with respect to centroid of pile groupCoordinates of common centre of gravity Eccentricity in x-direction = 0.100 m, ie. 1.09% < 5%, so ok
x = 4.700 m Eccentricity in z-direction = 0.002 m, ie. 0.08% < 5%, so oky = 1.502 m pilecapz = 3.295 m (foundation block) 1.600
mass moment of inertia of system about its own centroidal axis
18.836
97.728 h = length of 2.100
97.453 fixity
centroid of pile group w.r.t originx1 = 4.600 my1 = 1.500 m piles
Origin
3.00
9.20
lxi lyi lzi Wi mi xi yi zi mixi miyi mizi xoi yoi zoi
(mi/12)(lxi2+lyi
2) (mi/12)(lzi2+lyi
2) (mi/12)(lxi2+lzi
2) (x - xi) (y - yi) (z - zi) mi(xoi2+yoi
2) mi(zoi2+yoi
2) mi(xoi2+zoi
2)
(t.s2/m)
fx = t.m.s2
fy = t.m.s3
fz = t.m.s4
Pile group properties 04/22/2023
Pile group properties:
Pile diameter = 0.35 mType of Pile = End BearingPile capacity in compression = 45.0 t Hard Lime/Sand Stone rock considered.
Layout of pilesPile group configeration:No of rows of piles (Y dir.) = 2 @ 2.350 m 2.85 TYP
No of cols. of piles (X dir.) = 4 @ 2.850 m
Total No. of piles = 8.0 o o o oEffective length of pile = 4.5 m 2.35 o o o oTotal Length of pile = 7.0 m ############C. G. of pile group w.r.t. origin as top-left pile ############
4.28 m ############1.18 m ############
############Moment of Inertia of pile group about CG of pile-group: ############
11.045 ############81.225 ############92.270 ###
Calculation for vertical stiffness of a single pile:
End Bearing Pile:W = Load Carried by the Pile = 18.91 t
Self weight of the Pile = 3.20 t
0.17
0.38
71639.88
Vertical Stiffness of a single pile from the calculated Natural frequency is as below.
Vertical stiffness of single pile =
145864 t/m
Calculation of Horizontal stiffness of a single pile:Assuming the pile fixed at top and at base over length h.Length of fixity is assumed as 12.00 times diameter of pilesso, length of fixity h = 4.20 m
Horizontal stiffness of single pile =where,
E= Elasticity of concrete = 2.6E+06
I = 0.0007
310 t/m
XC.G. =
YC.G. =
Ix = m2
Iy = m2
Iz = m2
Wself =
a = Wself / W =Hence,a factor b can be evaluated by the expression
a = b tan bso, b =
Natural frequency of pile, wn
wn2 = b2 / H2 x ( E g / g) = sec-2
Kz = wn2 / g x (1+ a/3) x W
so, vertical stiffness factor for single pile Kz =
Kx = 12 E I / h3
t/m2
M.I. Of pile, p D4/64 = m4
so, Horizontal stiffness of single pile, Kx =
Y
X
Pile group properties 04/22/2023
Calculation of Rotating stiffness of pile group in YZ-plane :
Rotating stiffness of pile group in YZ-plane =(ie. About x axis)
1611065 t.m
Calculation of Rotating stiffness of pile group in XZ-plane :
Rotating stiffness of pile group in XZ-plane =(ie. About y axis)
11847786 t.m
Calculation of Tortional stiffness of pile group in XY-plane :
Tortional stiff. of pile group in XY-plane =(ie. About z axis)
28626 t.m
Mass moment of inertia of the whole system about axis passing thr' common C.G. & Parallel to Y-axis:
97.728Mass moment of inertia of the whole system about Y-axis passing thr' C.G. of base
265.101
0.369
Mass moment of inertia of the whole system about axis passing thr' common C.G. & Parallel to X-axis:
18.836Mass moment of inertia of the whole system about X-axis passing thr' C.G. of base
186.209
0.101
Mass moment of inertia of the whole system about axis passing thr' common C.G. & Parallel to X-axis:
97.453Mass moment of inertia of the whole system about Z-axis passing thr' C.G. of base
97.453
1.000
Vertical stiffness of pile group:
1166910.3 t/m
Horizontal stiffness of pile group:
2482.0 t/m
Kqx = Ix x Kz
so, Kqx =
Kqy = Iy x Kz
so, Kqy =
Ky = Iz x Kx
so, Ky =
fy = t.m.s2
foy = fy + mi.(Z)2
foy = t.m.s2
ay = fy / foy =
fx = t.m.s2
fox = fx + mi.(Z)2
fox = t.m.s2
ax = fx / fox =
fz = t.m.s2
foz = fz
foz = t.m.s2
az = fz / foz =
Tkz = kz x no. of piles
Tkz =
Tkx = kx x no. of piles
Tkx =
natural freq & amp. 04/22/2023
Operating frequency of machines:
1) Pump Speed (Trip Speed) 350 rpm 37 rad/sec2) Pump Speed (Maximum) 1610 rpm 169 rad/sec3) Pump Speed (Minimum) 2100 rpm 220 rad/sec
Unbalanced dynamic forces due to rotating parts:
Unbalanced Dynamic Forces and Couples Supplied by Machine Vendor:
0.202 t 0.130 m from comb. C.G.
0.000 tm 0.013 m from comb. C.G.
1.400 m from comb. C.G.
0.285 t.m
0.309 t.m
0.029 t.m
1) Vertical translation:
The natural frequency in vertical direction,
275.10
0.48
2) Sliding and Rocking motion in XZ-plane:
0.369Limiting Circular frequencies,
44689.63
160.97
Coupled natural circular frequencies,
121502.63
160.60
348.57
12.67
Amplitude of vibration:
Horizontal amplitude in x direction
Rotational amplitude about Y-axis
Unbalanced Force, Pvendor= xe =
Torque Mvendor= ye =
ze =
Mx = Pvendor.ye + Pvendor.ze + Mvendor =
My = Pvendor.xe + Pvendor.ze + Mvendor =
Mz = Pvendor.xe + Pvendor.ye =
wz = SQRT(Tkz / m)
wz = sec-1
Vertical amplitude, az = Pz /( m (wz2 - wm
2) )
az = mm
ay =
wqy2 = (Kqy - W.Z) / foy
wqy2 = sec-2
wx2 = Tkx / m
wx2 = sec-2
wn12 = 1 / (2.ay).[ wqy
2 + wx2 + SQRT ( ( wqy
2 + wx2 )2 - 4.ay.wqy
2.wx2 ) ]
wn22 = 1 / (2.ay).[ wqy
2 + wx2 - SQRT ( ( wqy
2 + wx2 )2 - 4.ay.wqy
2.wx2 ) ]
wn12 = sec-2
wn22 = sec-2
wn1 = sec-1
wn2 = sec-1
ax =
aqy =
natural freq & amp. 04/22/2023
2.14E+11 3.97E+12 5.31E+12
Horizontal Amplitude in x-direction:
1.108E-05 m
11.08
Rotational amplitude about Y-axis:
1.065E-06 rad
Net Horizontal displacement along x-axis of the upper edge of foundation
== 1.152E-05 m= 11.52
3) Sliding and Rocking motion in YZ-plane:
0.1012Limiting Circular frequencies,
8649.25
160.97
Coupled natural circular frequencies,
86938.15
158.31
294.85
12.58
Amplitude of vibration:
Horizontal amplitude in Y direction
Rotational amplitude about x-axis
2.95E+10 4.80E+11 5.40E+11
Horizontal Amplitude in Y-direction:
1.11E-05 m
11.13
f (wm2) = function depending on wm
2
f (wm2) = m.fy.(wn1
2 - wm2).(wn2
2 - wm2)
f (wm2) = for wm1, for wm2, for wm3
ax = ((kqy - WZ + Tkx.Z2 - fy.wm2).Pvendor+ Tkx.Z.My) / f(wm
2)
ax =
ax = mm
aqy = (Tkx.Z.Pvendor + (Tkx - mwm2).My)/ f(wm
2)
aqy =
ax + (H - Z).aqy
mm
ax =
wqx2 = (Kqx - W.Z) / fox
wqx2 = sec-2
wy2 = Tky / m
wy2 = sec-2
wn12 = 1 / (2.ax).[ wqx
2 + wy2 + SQRT ( ( wqx
2 + wy2 )2 - 4.ax.wqx
2.wy2 ) ]
wn22 = 1 / (2.ax).[ wqx
2 + wy2 - SQRT ( ( wqx
2 + wy2 )2 - 4.ax.wqx
2.wy2 ) ]
wn12 = sec-2
wn22 = sec-2
wn1 = sec-1
wn2 = sec-1
ay =
aqx =
f (wm2) = function depending on wm
2
f (wm2) = m.fx.(wn1
2 - wm2).(wn2
2 - wm2)
f (wm2) = for wm1, for wm2, for wm3
ay = ((kqx - WZ + Tky.Z2 - fx.wm2).Pvendor + Tky.Z.Mx) / f(wm
2)
ay =
ay = mm
natural freq & amp. 04/22/2023
Rotational amplitude about Y-axis:
3.898E-07 rad
Net Horizontal displacement along x-axis of the upper edge of foundation
== 1.129E-05 m= 11.29
4) Twisting motion about z-axis:The twisting motion is uncoupled
Natural frequency for twisting mode
17.14
2.821E-07 rad
aqx = (Tky.Z.Pvendor + (Tky - mwm2).Mx)/ f(wm
2)
aqx =
ay + (H - Z).aqx
mm
wy =
ay = Amplitude under the action of twisting moment Mz
wy = SQRT( ky / fz )
ay = 1/(wy2 - wm
2) x { Mz/fz }
wy = sec-1
ay =
Results 04/22/2023
Check for natural frequencies of system:
Machine operating Frequencies:
1) Pump Speed (Minimum) 350 37 rad/sec
2) Pump Speed (Maximum) 1610 169 rad/sec
3) Pump Speed (Trip Speed) 2100 220 rad/sec
frequency margin required (for 1 and 2 above)= 30 % minimum on either side of machine frequencyfrequency margin required (for 3 above)= 20 % minimum on either side of machine frequency
Mode of vibration Notation rad/sec Result
nat. freq. In vertical translation 275.10 0.13 0.61 0.80 ok.
nat. freq. In sliding & rocking in XZ-plane 348.57 0.11 0.48 0.63 ok.
12.67 2.89 13.31 17.36 ok.
nat. freq. In sliding & rocking in YZ-plane 294.85 0.12 0.57 0.75 ok.
12.58 2.91 13.40 17.48 ok.
nat. freq. For twisting motion 17.14 2.14 9.84 12.83 ok.
Check for Amplitudes:
Mode of vibration Allow. Ampl Notation value Result
200.00 0.48 ok.
200.00 11.08 ok.
200.00 11.13 ok.
rpm wm1 =
rpm wm2 =
rpm wm3 =
wm1/w wm2/w wm3/w
wz
wn1
wn2
wn1
wn2
wy
ampl. In vert. Direction, mm az
ampl. In hori. X-direction, mm ax
ampl. In hori Y-direction, mm ay
2033.00 3276.00 2895.00
A1 A2 A3
1511.00
1829.00 1705.90 2065.00 3380.00C D
A4,A5 A6
A,B1905.00
1355.00
555.00645.00
MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC)
1 7.935 0.12603 2 8.255 0.12114 3 9.095 0.10996 4 21.743 0.04599 5 23.855 0.04192 6 26.411 0.03786 7 29.352 0.03407 8 29.628 0.03375 9 46.519 0.02150 10 55.619 0.01798 11 70.757 0.01413 12 75.105 0.01331 13 79.291 0.01261 14 88.040 0.01136
MODE PERIOD(SEC)
1.00 7.94 0.132.00 8.26 0.123.00 9.10 0.114.00 21.74 0.055.00 23.86 0.046.00 26.41 0.047.00 29.35 0.038.00 29.63 0.039.00 46.52 0.02
10.00 55.62 0.0211.00 70.76 0.0112.00 75.11 0.0113.00 79.29 0.0114.00 88.04 0.01
MODE FREQUENCY(CYCLES/SEPERIOD(SEC)
1.00 7.91 0.132.00 8.25 0.123.00 9.09 0.114.00 21.10 0.055.00 23.15 0.046.00 25.69 0.047.00 28.52 0.048.00 28.90 0.03
FREQUENCY(CYCLES/SEC)
9.00 45.38 0.0210.00 54.43 0.0211.00 68.96 0.0112.00 73.09 0.0113.00 77.45 0.0114.00 86.36 0.01
MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC)
1 7.935 0.12603 2 8.255 0.12114 3 9.095 0.10996 4 21.743 0.04599 5 23.855 0.04192 6 26.411 0.03786 7 29.352 0.03407 8 29.628 0.03375 9 46.519 0.02150 10 55.619 0.01798 11 70.757 0.01413 12 75.105 0.01331 13 79.291 0.01261 14 88.040 0.01136
MODE X Y Z SUMM-X SUMM-Y
1.00 0.19 0.00 97.67 0.19 0.002.00 99.72 0.00 0.20 99.91 0.003.00 0.00 0.00 1.28 99.92 0.004.00 0.00 95.83 0.00 99.92 95.835.00 0.07 0.15 0.01 99.99 95.996.00 0.00 0.02 0.83 99.99 96.017.00 0.00 3.55 0.00 100.00 99.568.00 0.00 0.36 0.01 100.00 99.929.00 0.00 0.00 0.00 100.00 99.9210.00 0.00 0.01 0.00 100.00 99.9311.00 0.00 0.00 0.00 100.00 99.9312.00 0.00 0.01 0.00 100.00 99.9413.00 0.00 0.03 0.00 100.00 99.9714.00 0.00 0.00 0.00 100.00 99.97
MODAL WEAL MASS g) IN KN GENERALIZEDMODE X Y Z WEIGHT
1.00 12.08 0.00 6128.10 4013.552.00 6262.55 0.00 12.44 5975.733.00 0.29 0.00 80.21 1482.434.00 0.01 6022.08 0.00 4087.975.00 5.09 10.71 0.58 2213.08
6.00 0.25 1.56 58.76 1957.337.00 0.36 231.25 0.02 1229.568.00 0.01 10.27 0.75 1364.629.00 0.00 0.01 0.02 1756.8710.00 0.28 0.65 0.02 708.9111.00 0.00 0.15 0.00 1743.8912.00 0.00 0.47 0.00 1445.0913.00 0.00 1.93 0.00 497.9614.00 0.00 0.03 0.01 706.08
MODE X Y Z SUMM-X SUMM-Y SUMM-Z
1.00 0.19 0.00 97.57 0.19 0.00 97.572.00 99.71 0.00 0.20 99.90 0.00 97.763.00 0.00 0.00 1.28 99.90 0.00 99.044.00 0.00 95.88 0.00 99.90 95.88 99.045.00 0.08 0.17 0.01 99.99 96.05 99.056.00 0.00 0.02 0.94 99.99 96.07 99.997.00 0.01 3.68 0.00 99.99 99.76 99.998.00 0.00 0.16 0.01 100.00 99.92 100.009.00 0.00 0.00 0.00 100.00 99.92 100.0010.00 0.00 0.01 0.00 100.00 99.93 100.0011.00 0.00 0.00 0.00 100.00 99.93 100.0012.00 0.00 0.01 0.00 100.00 99.94 100.0013.00 0.00 0.03 0.00 100.00 99.97 100.0014.00 0.00 0.00 0.00 100.00 99.97 100.00
SUMM-Z
97.6797.8799.1599.1599.1699.9999.99
100.00100.00100.00100.00100.00100.00100.00