2
Structure-Environmental
Force Interactions
James F. Wilson
This chapter has three main objectives: (1) to discuss basic ideas, limitations,
and physical laws involved in modeling complex offshore structures as single
degree of freedom Systems; (2) to quantify the important environmental forces,
except for wave action, that occur offshore and show how these forces interact
with structures (discussions of wave action are in Chapters 3 and 4); and (3) to
illustrate the modeling of structural mass, stiffness, and the structural restraint
forces of guy lines and soil foundations. Emphasized in this chapter is the first
step in dynamic engineering analysis: the formulation of the structural équations
of motion. Solutions for structural motion, both deterministic and stochastic,
are presented in later chapters.
2.1 SINGLE DEGREE OF FREEDOM STRUCTURES
Before the motion of an offshore structure can be calculated, an analytical représentation is needed for the structure (or part of the structure), together with
the loadings and restraints. This représentation, called the mathematical model,
has two parts: a simplified schematic diagram or free body sketch of the structure, and the associated équations of motion. The free body sketch shows a
typical dynamic position or mode shape of the structure, relative to its static
equilibrium position; it describes the necessary and sufficient independent coordinates, equal in number to the degrees of freedom needed to describe motion
uniquely; and it shows as arrows four classes of generalized forces, which include
moments. These forces are: (1) self-weight; (2) externally applied environmental forces mentioned briefly in Chapter 1; (3) reaction forces (due to System
restraints) that tend to restore the structure to its static equilibrium position;
and (4) damping forces that mitigate motion. Based on the free body sketch, the
équations of motion are formulated in a straightforward manner, using either
Newton’s second law, as is done in this chapter, or Lagrange’s energy methods, as is done in Chapter 8. Although these two methods may be employed
17
Structure-Environmental
Force Interactions
James F. Wilson
This chapter has three main objectives: (1) to discuss basic ideas, limitations,
and physical laws involved in modeling complex offshore structures as single
degree of freedom Systems; (2) to quantify the important environmental forces,
except for wave action, that occur offshore and show how these forces interact
with structures (discussions of wave action are in Chapters 3 and 4); and (3) to
illustrate the modeling of structural mass, stiffness, and the structural restraint
forces of guy lines and soil foundations. Emphasized in this chapter is the first
step in dynamic engineering analysis: the formulation of the structural équations
of motion. Solutions for structural motion, both deterministic and stochastic,
are presented in later chapters.
2.1 SINGLE DEGREE OF FREEDOM STRUCTURES
Before the motion of an offshore structure can be calculated, an analytical représentation is needed for the structure (or part of the structure), together with
the loadings and restraints. This représentation, called the mathematical model,
has two parts: a simplified schematic diagram or free body sketch of the structure, and the associated équations of motion. The free body sketch shows a
typical dynamic position or mode shape of the structure, relative to its static
equilibrium position; it describes the necessary and sufficient independent coordinates, equal in number to the degrees of freedom needed to describe motion
uniquely; and it shows as arrows four classes of generalized forces, which include
moments. These forces are: (1) self-weight; (2) externally applied environmental forces mentioned briefly in Chapter 1; (3) reaction forces (due to System
restraints) that tend to restore the structure to its static equilibrium position;
and (4) damping forces that mitigate motion. Based on the free body sketch, the
équations of motion are formulated in a straightforward manner, using either
Newton’s second law, as is done in this chapter, or Lagrange’s energy methods, as is done in Chapter 8. Although these two methods may be employed
17