Download - Staad Etc Cimbomb
OverviewThis module performs dynamic analysis of a Block Foundation resting on ground and
reports frequencies and amplitudes corresponding to different modes of vibration.
The analysis is based on the method proposed by Barkan [1]. Block Foundation (as shown in Fig. 1) is idealized as a system with six degrees of freedom - three translations along three mutually perpendicular axes x, y and z and three rotations about the same axes. The modes corresponding to translation along the vertical axis (z) and the rotation about the same axis are treated as uncoupled. This is based on the assumption that the common centre of gravity of machine and foundation and the centroid of the base area lie on the same vertical line or within a tolerable limit. On the other hand, the sliding and rocking motions in each of the two vertical planes (xz and yz) passing through the common centre of gravity of machine and foundation are separately coupled.
The effect of damping has been ignored and the supporting soil is modelled by linear weightless springs. Some soil parameters have been introduced to yield the spring stiffness of soil in various modes. These parameters are Coefficient of elastic uniform compression (Cz), Coefficient of elastic non-uniform compression (C), Coefficient of elastic uniform shear (C), and Coefficient of elastic non-uniform shear (C).
The spring stiffnesses of soil (K) for the various modes of vibration are calculated as
For vertical motion Kz= Cz Af
For horizontal (or sliding) motion K = C Af
For rocking motion K = C Ix (or y)
For torsional motion (rotation about vertical axis) Iz
K = C
where,
Af = area of horizontal contact surface between foundation and soilIx (or y) = second moment of contact area about the horizontal axis (x or y)
passing through the centroid of the base and normal to the plane of rocking
Iz = second moment of contact area about the vertical axis passing through the centroid of base area
Vertical Translation (along z axis)
The equation of motion for the undamped, single degree of freedom system is expressed as:
where,
z = displacements along z-axism = mass of the foundationPz(t) = time varying exciting force
along z-axis
The circular natural frequency (z) is
The vertical amplitude (az) under the action of an exicting force Pzsinmt is
Where m is the circular operating frequency of the machine.
[Analysis for the torsional (rotation about z-axis) motion i.e. yawning as shown in Fig.1 is not carried out]
Sliding and Rocking Motion (in xz plane)
The equations of motion for the undamped, two degree of freedom system are expressed as:
For horizontal motion (along x-axis)
For rocking motion (about y-axis)
where,
x = displacement along x-axis y = rotation about y-axis W = weight of the foundationPx(t) = time varying exciting force along x-axis My(t) = time varying exciting moment about y-axisS = height of the centre of gravity of the foundation
from the base
The circular natural frequencies for coupled modes are obtained from the following equation
where, y is the ratio of the mass moment of inertia (y) about the y-axis passing through the centre of gravity to the mass moment of inertia (0y) about a parallel axis through the centre of elasticity of the base support.
The limiting frequencies of the coupled motion are expressed as
and
x and y correspond to the pure sliding along x-axis and pure rocking about y-axis respectively.
The horizontal amplitude (ax) and rotational amplitude (ay) under the action of an exciting force Pxsinwmt and exciting moment Mysinmt are expressed as
and
where,
So the net displacement along the x-axis at top of the foundation is
Sliding and Rocking Motion (in yz plane)
The natural frequencies and the amplitudes are calculated using equations similar to those derived for motion in xz plane with the suffixes x and y interchanged in it.
The output reports the natural frequencies and amplitudes corresponding to the modes as discussed above.
References:
1. Barkan D. D. Dynamics of Bases and Foundations, McGraw-Hill Book Co. Inc., New York 1962
2. Major A. Dynamics in Civil Engineering Analysis and Design, Akade/miai Kiado/ , Budapest 1980
3. Srinivasulu.P and Vaidyanathan.C.V. Handbook of Machine Foundation, Tata McGraw-Hill Publishing Company Ltd., New Delhi 1996
4. Arya C.S., O’Neill W.M. and Pincus G. Design of Structures and Foundations for Vibrating Machines, Gulf Publishing Company, Book Division, Houston 1979.
Machine Data
Input Page 1 of 4 represents Machine Data :
Operating speed of engine(r.p.m)
The operating speed of the engine in r.p.m.The programwill convert it in specific unit system as per requirement
Weight of Machine The weight of machineX Co-ord of CG of machine
X Co-ordinate of Center of Gravity of the Machine
Y Co-ord of CG of machine
Y Co-ordinate of Center of Gravity of the Machine
Z Co-ord of CG of machine
Z Co-ordinate of Center of Gravity of the Machine
Horizontal exciting force along X-axis
Horizontal exciting force along X-axis
Horizontal exciting force along Y-axis
Horizontal exciting force along Y-axis
Exciting Moment about Y-axis
Exciting moment about Y-axis
Exciting Moment about X-axis
Exciting moment about X-axis
Height of foundation Height of foundationHeight of acting point of horz. exciting force from the top of foundation
Height of acting point of horizontal unbalanced force from the top of foundation
Vertical exciting force (along Z-axis)
Vertical Exciting force along Z-axis
Permissible percentage limit for eccentricities in either direction
Permissible limit for checking the eccentricities in either direction
Maximum allowable horizontal amplitude
Maximum allowable horizontal amplitude
Maximum allowable vertical amplitude
Maximum allowable vertical amplitude
Geometry Data
Input Page 2 of 4 represents Block Foundation Plan :
Block No The No. of Block(s)X-Coordinates of CG The X-Coordinate of CG of the
BlockY-Coordinates of CG The Y-Coordinate of CG of the
BlockZ-Coordinates of CG The Z-Coordinate of CG of the
BlockUnit The unit of X,Y &Z Coordinate of
CG of the BlockX-Dim (Block Dimensions)
The Length of the Block in X-direction
Y-Dim (Block Dimensions)
The Length of the Block in Y-direction
Z-Dim (Block Dimensions)
The Length of the Block in Z-direction
Unit The unit of Length of the Block in X,Y&Z direction
Soil Data
Input Page 3 of 4 represents Soil Data :
Unit weight of Soil The unit weight of SoilBearing capacity of Soil The allowable Bearing Capacity of SoilCo-efficient of elastic uniform compression
The Co-efficient of elastic uniform compressionof Soil
Co-efficient of elastic non- The Co-efficient of elastic non uniform
uniform compression compression for rocking mode of SoilCo-efficient of elastic uniform shear
The Co-efficient of elastic uniform shear of Soil
Co-efficient of elastic non-uniform shear
The Co-efficient of elastic non uniform shear ofSoil
Material Properties
Input Page 4 of 4 represents Material Data :
Unit Weight of Concrete
The unit weight of concrete
Output Data
The Output consists of the Analysis Results The results for all the design modules are presented in a grid or spreadsheet format which is compatible with Microsoft ExcelÓ . section.
Analysis Results
Analysis Results reports the natural frequencies and the amplitudes corresponding to the modes as discussed in Overview.