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1.1. Calculation for Spring Constant and Damping Ratio
1.1.1.
Computation of Equivalent Radius:
Equivalent Foundation Radius for rigid rectangular foundation in
different modes of vibration is follow:
Vertical -----------------------------
LB
Horizontal -----------------------------
LB
Rocking ----------------------------- 43
3
LB
Torsional ----------------------------- 422
6
)(
+ LBLB
1.1.2.Calculation of Coefficients for Embedment for
Stiffness:
The coefficients for embedment to rigid rectangular foundation
in different modes of vibration are follow:
Vertical ----------------------- )(*)1(*6.01o
zr
h +=
Horizontal ----------------------- )(*)2(*55.01o
xr
h +=
Rocking ---
3
*)2(*2.0)(*)1(*2.11
++=
oo r
h
r
h
1.1.3.
Computation of Mass Moment of Inertia
Rocking (I) ----------------------- )(12
1 22 DBg
W+
Torsional (I) ----------------------- )(12
1 22 LBg
W+
1.1.4.Computation of Mass (or Inertia) Ratio:
Equivalent radius for rigid rectangular foundation in different
modes of vibration, are as follow:
Vertical (Bv) -----------------------
34
1
or
W
Horizontal (Bh) -----------------------3)1(32
87
or
W
Rocking (B) ----------------------- 58
)1(3
o
r
r
I
Torsional (B) ----------------------- 5or
I
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1.1.5.Calculation of Coefficients for Embedment for Damping:
Vertical -----------------------
z
o
z
r
h
)(*)1(*9.11 +
=
Horizontal -----------------------x
ox r
h
)(*)2(*9.11 +
=
Rocking ---
3
*)2(*6.0)(*)1(*7.01
++
= oo r
h
r
h
1.1.6.
Computation of Spring Constant:
Equivalent spring constants for rigid rectangular foundation in
different modes of vibration are
follow:
Vertical (Kv) ----------------------- zz LBG
*1
Horizontal (Kh) ----------------------- xx LBG + *)1(2
Rocking (K) -----------------------
2*
1LB
G
Torsional (K) -----------------------3
162
orG
1.1.7.
Computation of Damping Ratio:
Damping Ratios for rigid rectangular foundation in different
modes of vibration is are follow:
Vertical (Dv) ----------------------- zvB
425.0
Horizontal (Dh) ----------------------- xhB
288.0
Rocking (D) -----------------------
rr BnBnI )(
15.0
+
Torsional (D) -----------------------)2(
5.0
BI+
1.2. Computation of Fundamental Mode Frequency in Hz:
As the equivalent spring constants (K) for different modes of
vibrations are already computed in sectio6 so the fundamental
frequency (Fn) at different modes are as follow:
Vertical (Fnv) -----------------------M
Kv
2
1
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Horizontal (Fnh) -----------------------M
Kh
2
1
Rocking (Fn) -----------------------
I
K
2
1
Torsional (Fn) -----------------------
I
K
2
1
1.3. Checking for Resonant Frequency:
Resonance in a damped vibrating system is only possible when the
damping ratio (D) is low i.e. D
within the range of, 0 < D
