REFERENCES
193
(b) This monotower is subjected to a simple wave as described in Table 6.1.
Dérivé the explicit équations for the two major components of the wave-induced
moment A/(t): the moment on the uniform leg, and the moment on the caisson.
HINTS* For the leg moment, use q of Example Problem 4-4> integrate q over
the leg height to calculate the total horizontal wave load on the leg, compute
the centroid of this load from point 0, and form the product of the last two
quantities to give the first component of the moment. The second component
of the moment, that on the caisson, was derived in Example Problem 4.3. Carry
through those calculations, expressed symbolically by équation (4.22).
(c) Based on the results of part (b), dérivé the équation for the transfer
function G(cu) corresponding to the total wave-induced moment M(t) on the
whole structure.
7.9 Assume that the wave field imposed on the monotower described by
Problem 7.8 is stationary and ergodic.
(a) By comparing the symbols in the équation (7.27) to the équation of
motion for rotation 6 given in Problem 7.8, deduce without calculation the
explicit forms of Sg(w) and
(b) For the quantities
G (ai). Se(a>), and crj corresponding to rotational
motion, write down a consistent set of units, first in the traditional English
System, and then in the SI System.
7.10 The purpose of this problem is to obtain numerical results for the
responses of the concrète monotower, for which the theoretical results were
obtained in Problems 7.8 and 7.9. The System parameters for this tower are
summarized in Table 5.1, which also lists two values for the free, undamped
rocking frequency wo based on two soil foundation stiffnesses.
(a) Based on the weaker soil foundation for which Gs — 10 MPa and
w = w0 = 1.41 rad/s, compute the soil foundation parameters kg and ce using équations (2.78) and (2.79).
_____
(b) Compute the foundation damping factor £ = ce/yjAkgJo. This damping
factor is analogous to C = c-Jy/Akim, the damping factor for équation (7.27).
(c) The monotower is subjected to steady, unidirectional waves with a significant wave height Hs of 15 m and with a distribution .S’n|*) given by the
Pierson-Moskowitz spectrum, équation (7.60). With this spectrum, the numerical results of part (a), and the équation previously derived in Problem 7.9 for
the variance, compute Og by numerical intégration.
(d) Based on the ±3
overturning moment for this 180 m high monotower.
REFERENCES
Bryson, A. E., and Hu, Y. C., Applied Optimal Control: Opttmuatum, Estimation,
and Control, Wiley, New York, 1975.
193
(b) This monotower is subjected to a simple wave as described in Table 6.1.
Dérivé the explicit équations for the two major components of the wave-induced
moment A/(t): the moment on the uniform leg, and the moment on the caisson.
HINTS* For the leg moment, use q of Example Problem 4-4> integrate q over
the leg height to calculate the total horizontal wave load on the leg, compute
the centroid of this load from point 0, and form the product of the last two
quantities to give the first component of the moment. The second component
of the moment, that on the caisson, was derived in Example Problem 4.3. Carry
through those calculations, expressed symbolically by équation (4.22).
(c) Based on the results of part (b), dérivé the équation for the transfer
function G(cu) corresponding to the total wave-induced moment M(t) on the
whole structure.
7.9 Assume that the wave field imposed on the monotower described by
Problem 7.8 is stationary and ergodic.
(a) By comparing the symbols in the équation (7.27) to the équation of
motion for rotation 6 given in Problem 7.8, deduce without calculation the
explicit forms of Sg(w) and
(b) For the quantities
G (ai). Se(a>), and crj corresponding to rotational
motion, write down a consistent set of units, first in the traditional English
System, and then in the SI System.
7.10 The purpose of this problem is to obtain numerical results for the
responses of the concrète monotower, for which the theoretical results were
obtained in Problems 7.8 and 7.9. The System parameters for this tower are
summarized in Table 5.1, which also lists two values for the free, undamped
rocking frequency wo based on two soil foundation stiffnesses.
(a) Based on the weaker soil foundation for which Gs — 10 MPa and
w = w0 = 1.41 rad/s, compute the soil foundation parameters kg and ce using équations (2.78) and (2.79).
_____
(b) Compute the foundation damping factor £ = ce/yjAkgJo. This damping
factor is analogous to C = c-Jy/Akim, the damping factor for équation (7.27).
(c) The monotower is subjected to steady, unidirectional waves with a significant wave height Hs of 15 m and with a distribution .S’n|*) given by the
Pierson-Moskowitz spectrum, équation (7.60). With this spectrum, the numerical results of part (a), and the équation previously derived in Problem 7.9 for
the variance, compute Og by numerical intégration.
(d) Based on the ±3
overturning moment for this 180 m high monotower.
REFERENCES
Bryson, A. E., and Hu, Y. C., Applied Optimal Control: Opttmuatum, Estimation,
and Control, Wiley, New York, 1975.