Block Foundation Design
Prepare by Wisit Kawayapanik
Flow Chart for Block Foundation Design Review vender equipment drawing
Review geotechnical data, Calculation seismic force
Preliminary sizing of foundations
Load calculation, Moment calculation, Load combination
Soil bearing capacity check
Dynamics Analysis Mass, Mass moment of inertia, Spring constant, Natural frequency, Damping ratio
Evaluate of Resonance
Evaluate of Displacement
Result of evaluate NG OK END
Basic Terminology Periodic Motion: A motion which repeats itself after equal intervals of time. Frequency: The number of oscillations completed per unit time is known as frequency of the system. Amplitude: The maximum displacement of a vibrating body from its equilibrium position. Natural Frequency: The frequency of free vibration of a system is called Natural Frequency of that particular system. ( fn =
1 2π
k ) m
Damping: The resistance to the motion of a vibrating body is called Damping. In actual practice there is always some damping (e.g., the internal molecular friction, viscous damping, aero dynamical damping, etc.) present in the system which causes the gradual dissipation of vibration energy and results in gradual decay of amplitude of the free vibration. Damping has very little effect on natural frequency of the system, and hence, the calculations for natural frequencies are generally made on the basis of no damping. Damping is of great importance in limiting the amplitude of oscillation at resonance. Fundamental Mode of Vibration: The fundamental mode of vibration of a system is the mode having the lowest natural frequency. Degrees Of Freedom: The minimum number of independent coordinates needed to describe the motion of a system completely, is called the degree-of-freedom of the system. If only one coordinate is required, then the system is called as single degree-of-freedom system. Mechanical System: The system consisting of mass, stiffness and damping are known as mechanical system. Forced vibration: When a dynamic system is subjected to a steady-state harmonic excitation, it is forced to vibrate at the same frequency as that of the excitation. Harmonic excitation is often encountered in engineering systems. It is commonly produced by the unbalance in rotating machinery, forces produced by the reciprocating machines, or the motion of machine itself. Although pure harmonic excitation is less likely to occur than the periodic or other types of excitation, understanding the behavior of a system undergoing harmonic excitation is essential in order to comprehend how the system will respond to more general types of excitation. Harmonic excitation may be in the form of a force or displacement of some point in the system. The harmonic excitation can be given in many ways like with constant frequency and variable frequency or a swept-sine frequency, in which the frequency changes from the initial to final values of frequencies with a given time-rate (i.e., ramp).
Resonance: If the frequency of excitation coincides with one of the natural frequencies of the system, the amplitude of vibration becomes excessively large. This concept is known as resonance.
STEP 1
Review vender equipment drawing • • • • • • • • •
Plan dimension of pump / compressor base frame Height of rotor / shaft center line from the bottom of skid Anchor bolt location, size and embedment depth Weight of machine parts and the rotor parts (pump / compressor rotor and motor rotor) Location of center of gravity both vertically and horizontally Operating speed of machines and power rating of motor (RPM) Magnitude and direction of unbalanced forces. For reciprocating machines both primary and secondary unbalanced forces and couples and respective CG locations needs to be checked. Limit of deflection and vibration amplitudes at center line of rotor.
STEP 2
Review geotechnical data • • • • • •
Soil weight density Poisson's ratio Dynamic shear modulus (G) Shear wave velocity (vs) Dynamic modulus of sub-grade reaction (ks) Allowable soil bearing pressure or pile load carrying capacity for design of foundation
STEP 3
Categorization of rotating machines based on machine speed •
•
•
•
Low Speed machine: The low speed machines operate at a speed range of less than 500 RPM. High tuned foundations, having first natural frequency more than machine's operating speed, should be designed for this type of machines. In this case machine does not pass the resonance during machine start up and coast down condition. Intermediate speed machine: The intermediate speed machines operate at a speed range 500 RPM to 1000 RPM. Foundations should be designed for this type of machines high tuned or low tuned side whichever more practical. If the foundation is low tuned, dynamic amplitude shall be checked during start up and coast down condition. High Speed machine: The high speed machines operate at a speed range of more than 1000 RPM. Low tuned foundations, having first natural frequency less than machine's operating speed, should be designed for this type of machines. In this case machine will pass the resonance during machine start up and coast down condition. Dynamic amplitude shall be checked during start up and coast down condition. You need to ensure that there is no adverse effect to machine operation during the resonant conditions. Variable Speed machine: The variable speed machines operate at a speed range as prescribed by vendor. Foundations should be designed for this type of machines high tuned or low tuned side whichever more practical. A detail dynamic analysis of foundation is required for a range of machine operating speeds to ensure that the dynamic design criteria are met.
STEP 4
Preliminary sizing of foundations • • •
Weight of the block foundation should be at least 4 times the weight of reciprocating machines and 3 times the weight of centrifugal machines. The width of foundation should be at least 1.5 times the vertical distance from the bottom of foundation to the center line of the shaft / rotor. The center of mass of machine foundation (machine foundation system) should coincide with the centroid of the soil foundation or pile group resistance. Horizontal eccentricity should be limited to 5% of the corresponding foundation dimension.
•
For a rigid mat, following criteria to be followed: o
o
Minimum thickness of the mat will be 600 mm or 1/5 th of least foundation dimensions or 1/10 th of largest foundation dimensions, whichever is greater. Maximum thickness of the mat will be 1500 mm
The formula based on Beam on Elastic Foundation Minimum thickness of mat, t = 0.0012 x (ks x (a)4)1/3 ft, ks= soil dynamic modulus of sub-grade reaction, lbs/in3, from soil report, a= maximum cantilever projection (inches), measured from face of block
STEP 5
Requirement for dynamic analysis of foundations Dynamic analysis of concrete foundations is not required for all the foundations supporting rotating equipment. You need to refer your project design criteria for the conditions for dynamic analysis. Following are the general criteria for not performing any dynamic analysis of foundation supporting rotating equipment: • •
Dynamic analysis is not required if the weight of machine is less than 25kN. Dynamic analysis is not required if the power rating of motor is less than 200hp.
If you are not doing any dynamic analysis of concrete block foundation, then follow Step-4 for foundation sizing and put it into 3D model for any interference check if you are doing the dynamic analysis of concrete block, then follow the following steps
STEP 6
Foundation check • •
Calculation foundation weight Check mass ratio Wc/Wm >4 for reciprocating and 3 times the weight of centrifugal
STEP 7
Load calculation • • • •
Structure weight Equipment weight Operating(dynamics load) Seismic load x, y direction
STEP 8
Moment calculation • • • •
Calculation ex,ey for equipment(distance from equipment to C.G of foundation) Calculation ex,ey vertical & horizontal for dynamic load (pump, motor) Summations moment force Calculation moment force from seismic load
STEP 9
Load combination • • • • Case 1 2 3 4 5
Ds1= structure weight Ds2= equipment weight D0 = operating load(dynamic) E = seismic load Load Combination Ds1 + Ds2 + D0 Ds1 + Ds2 + D0 +0.7Ex Ds1 + Ds2 + D0 +0.7Ey 0.9(Ds1 + Ds2 ) +0.7Ex 0.9(Ds1 + Ds2 ) +0.7Ey
STEP 10
Soil bearing capacity check P My P Mx ± ± , Qy= A Zy A Zx
•
Qx=
• •
For long term Qx,Qy < 50% of Qall For short term Qx,Qy < 50% of 1.33xQall
Description Operating weight Operating weight+seismic Operating weight+seismic Empty weight+seismic Empty weight+seismic
Remark Long term Short term
Dynamics Analysis STEP 11
Mass & Mass moment of inertia Wc + Wg 9.81
•
Calculation Mass mt =
•
Calculation mass moment of inertia for rocking
Iψ = Iψ ( machine ) + Iψ ( Foundation ) Σ[mi / 12(ai 2 + bi 2 ) + miki 2 ] = •
Calculation mass moment of inertia for pitching
Iφ = Σ[mi / 12(ai 2 + bi 2 ) + miki 2 ] = I φ ( machine ) + I φ ( Foundation )
STEP 12
Spring constant G .Bz. BL .η z 1− µ
•
Vertical spring
kz =
•
Horizontal spring(x direction)
kx = 2(1 + µ ).G.Bx. BL .η x
•
Horizontal spring(y direction)
ky = 2(1 + µ ).G.By. BL .η y
•
Rocking
kψ =
G .Bψ .BL2 .ηψ 1− µ
•
Pitching
kφ =
G .Bφ .BL2 .ηφ 1− µ
STEP 13
Natural frequency •
Vertical
= ω nz
kz 60 = , fnz .ω nz 2π mt
•
Horizontal x
ω nx =
kx 60 = , fnx .ω nx mt 2π
•
Horizontal y
ω ny =
ky 60 = , fny .ω ny mt 2π
•
Rocking
= ω nψ
kψ 60 = , fnψ .ω nψ 2π Iψ
•
Pitching
= ω nφ
kφ 60 = , fnφ .ω nφ Iφ 2π
STEP 14
Damping ratio • • • • •
Embedment ratio (αi) Mass ratio(Bi) Geometrical ratio(Dig) Internal damping = 0.05(Dii) Dit = Dig+Dii
STEP 15
Resonance frequency check • • • • •
Vertical Horizontal x Horizontal y Rocking Pitching
2xDz2 2xDx2 2xDy2 2xDψ2 2x DФ2
If > 1 resonance not possible, If < 1 resonance can possible check detail again
= fm fn 1 − 2 D 2
fm =
fn 1 − 2D2
for vertical, horizontal for rocking, pitching
Compare between fmachine ± 20%
STEP 16
Amplitude check Magnification factor
• Mz =
1 , rz = (1 − rz 2 ) 2 + (2.Dz.rz ) 2
fo fnz
• Mx =
1 , rx = (1 − rx 2 ) 2 + (2.Dx.rx) 2
fo fnx
• My =
1 , ry = 2 2 (1 − ry ) + (2.Dy.ry ) 2
fo fny
• Mψ = • Mφ =
1 = , rψ 2 2 (1 − rψ ) + (2.Dψ .rψ ) 2 1 = , rφ 2 2 (1 − rφ ) + (2.Dφ .rφ ) 2
fo fnψ fo fnφ
Where fo = frequency of machine
frequency of foundation & machine (vertical) fnx = frequency of foundation & machine (horizontal x) fny = frequency of foundation & machine (horizontal y) fnψ = frequency of foundation & machine (rocking) fnφ = frequency of foundation & machine (pitching) fnz =
STEP 17
Dynamic force Vertical force •
Fz = mixexω 2 Where
mi = rotor weight
e= =
eccentricity of unbalance mass(vender provided, equation, table)
e 1 − ( fo / fc) 2
fo =operating speed fc=critical speed
ω = 2π fo / 60 Horizontal force •
Fy=Fz
Rocking force •
Fψ=Fy x moment arm(cg of machine to base of foundation)
STEP 18
Dynamic displacement • • •
Az = Mz x Fz/kz Ay = My x Fy/ky Aψ = Mψ x Fψ/kψ
STEP 19
Total displacement • •
Azt = e x Aψ+Az Ayt = h x Aψ+Ay Where e = a/2 h = b/2
STEP 20
Amplitude check •
Allowable amplitude(vender provided) > Azt, Ayt
STEP 21
Reinforcement • Minimum reinforcement in block foundation shall be 25 kg/m2 .The minimum size shall be 16 mm diameter and spacing shall be limited to maximum 300 mm. • Minimum cover to reinforcement shall be 75 mm at bottom and 50 mm at top and side faces of the foundation • Arrange 0.5-0.75% reinforcing bar at the opening • The reinforcement shall be extended at least 50 times the rebar diameter from edge of opening • If foundation thickness is over 1 m, shrinkage reinforcement shall be provided at every 600 mm along X,Y&Z direction • Reinforcement shall be used at all faces.
References i. ii. iii.
Samsung Engineering, “Design Manual for Civil Engineering”, October 2011 Samsung Engineering, “Calculation Sheet for 7A30-P03A/b FDN MA’ADEN AMMONA PROJECT”, September 2008 S.Arya, M. O’nell and G. Pincus, “Design of Structures and Foundations for Vibrating Machines”, Gulf Publishing Co., Houston, Texas, May 1981
