Dynamic analysis of a block foundation supporting a rotary or reciprocating equipment undergo modal and time history analysis which help in determining amplitudes either in terms of displacement, velocity or acceleration.
Required Static and geometric checks are simple and predictable and hence not discussed in this blog.
Modal Analysis
Modal analysis of a block foundation involves extracting the natural frequencies and the mode shapes. Because the block behaves rigidly, under the action of unbalanced forces it undergoes vertical, lateral, longitudinal, rocking, pitching and yawing oscillations.
Six degrees of freedom for a block foundation
The natural frequencies are essential to understand the behaviour of the foundation and also to check their overlap with the machine frequency.
A case study was adopted to understand this behaviour and also extract the amplitude.
The software used is SAP2000.
A block foundation has been modelled and the following unbalanced loads applied on it.
The primary and secondary frequency of the machine are 9.75 and 19.5hz respectively.
The mathematical model in SAP2000 looks somewhat as shown below. Along with the foundation, the machine CG, its axis and the anchor bolt locations have been modelled and connected to each other using rigid links.
Soil springs were computed from Richard and Whitman chart and assigned to base springs.
Mathemaical model of block foundation in SAP2000
The first six mode shapes were extracted and have been presented here.
Mode 1-13.02hz
Mode 2-14.45hz
Mode 3-17.36hz
Mode 4-18.90hz
Mode 5-21.11hz
Mode 6-23.56hz
Some points worth observing are:
Yawing, rocking and pitching behaviour can be observed in the mode shapes.
The natural frequencies are above the primary frequency but are in close vicinity of the secondary frequency.
The displacement amplitude of the following node shall be studied. It is recommended to carry out this study at various locations where the engineer feels is necessary and is also based on the limiting values and locations provided by the vendor.
Node of interest for displacement amplitude
Displacement amplitude for Node of interest (unit-mm)
The vertical displacement amplitudes seem to be the dominant one for this set of foundation and unbalanced forces.
The resultant of these amplitudes shall be generally used for result comparison.
In absence of limiting values one may refer to the following chart taken from IS:2974 part 1.
Amplitude limits of foundation block
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