Tmr 4195Design of Offshore Structures

NTNU

Department of Marine Technology / EXERCISE 9

TMR 4195DESIGN OF OFFSHORE STRUCTURES

Distr. Date / Sign: Q. Chen / Voluntary Exercise

PROBLEM 1Re-evaluation of Platform

Safety of existing platform must be re-evaluated, e.g. when

The use of the platform is changed
The service life of the platform should be extended
Damage is detected

Such a re-evaluation would normally include inspection of the platforms to decide which condition they are in, calculation of loads and the strength as well as design check where possible new knowledge about load and strength should be taken into account. In this problem the re-evaluation should be calculated for an existing jacket in about 70-meter deep water in the North Sea. The platform is made up of circular tubes.

The platform was originally designed by using steel with specified yield stress of 240 MPa and geometry as illustrated in Figure 1. The platform was originally designed for a service life of T0 = 20 years.

The collapse resistance (ultimate strength) of braces/legs and joints was determined on the basis of functional and natural loads that the platform is subjected to in operation and installation condition. Fatigue life for typical tubular joints is given in Table 1.

Horizontal and inclined braces of the truss work are designed to comply exactly with the NPD’s failure criteria of the loads that the platform is subjected to in operation condition. While there are other conditions relating to installation which influence the dimensions (diameter, plate thickness) of the legs, only 50% strength utilised in operation condition.

The legs were about to be made up of steel as assumed (yield stress of 240 MPa), but steel with yield stress of 320 MPa was used because of a problem with delivering tubes with the small dimensions used in braces.

TABLE 1Fatigue Life (years)

Location / Joint
Level / K- (brace) / KT - (leg/brace)
2
3
4
5 / 120
150
210
220 / 100
120
200
300

FIGURE 1Existing Jacket Platform in the North Sea

a)Which aspects associated with the structural safety of the platform should be included in the condition check? Which inspection methods should be applied in the condition check?

b)Consider the inclined brace between level 2 and 3 in Figure 1b, calculate how much ‘residual strength’ is due to ‘upgraded’ yield stress under fabrication of the inclined braces, which is subjected to axial tension or compression force. Assume that the buckling length is 80% of the length of the brace. Refer to the given NORSOK N-004 code.

Comment on how the collapse resistance of the platform will change by increasing

Live/dead load on deck
Wave/current load

c)Assume that the service life of the platform is to be extended from 20 to 50 years. Will NPD fatigue criteria be fulfilled for a service life of 50 years? State your reasons. How can the fatigue life for an existing welded connection (tubular joint) possibly be increased?

To which extent will the fulfilment of the ULS criteria be influenced by the extension of service life?

Given

The fatigue damage D in a time period T0 can be calculated by a simple expression in this case:

where

K, m-parameters which describe the SN-curve

s0-stress range exceeded by a probability of 1/N0 in the period T0

N0-number of stress cycles in the period T0

( )-Gamma function

PROBLEM 2Wave, Current and Wind Effect

Figure 2 shows a platform consisting of a deck, buoyancy body, a truss work which is pinned-jointed at the sea floor (A).

The structure is considered to be rigid, rotating about point A.

Other data are given in Figure 2b.

FIGURE 2Articulated Tower

a)Consider the constant wind-force FW = 25 MN acting at z = 380 m and a constant current force FC = 13 MN at z = 320 m, and a concentrated mass w1, as well as distributed mass w and buoyancy B.

Determine the angle of rotation  and the vertical and horizontal forces on the joint A for the load case: selfweight (w1 and w), buoyancy (B) and forces FW and FC. (Assume that sin = , cos = 1).

b)Assume that the platform is subjected to a wave with a resultant force acting at z = 350 m. (Vertical wave forces neglected).

Establish the dynamic equation of equilibrium for the platform for small , considering

Wave excitation force,
Inertia forces (prop. with acceleration)
Elastic or restoring forces due to buoyancy and “weight” of the structure (prop. with relevant “displacement”)

“Equivalent” hydrodynamic (or added) mass is supposed to amount to 70 000 tons, with a centre of gravity at the buoyancy centre, B. Write the equation as

(2.1a)

(2.1b)

Where  is the rotation and u0 = 390 is the horizontal displacement (in meters) of the deck mass w1. and are generalized mass and stiffness, respectively.

Determine the eigenfrequency of the platform.

c)The complete dynamic equilibrium equation for moment about point A may be written as:

(2.2)

where zwa = 350 m is the centre of the resultant horizontal force.

Determine the maximum angle of rotation  and the shear force and bending moment along the tower from z = 0 to 280 m, when the structure is subjected to a regular wave with frequency rad/s and load amplitude MN. The eigenfrequency of the platform is 0.1 rad/s and the damping ratio .

See the given information below.

Density of water:

Solution of Equation 2.2:

(2.3)

where

(damping ratio)

: generalized mass: generalized stiffness

d)Assume that the resultant forces in the tower at level z = 240 m are

Axial force, N
Shear force, Q
Bending moment, M

Find the axial forces in the members (legs and braces) of the truss work at this level, expressed by N, Q and/or M.

e)Assume that one of the vertical diagonal braces is damaged (See Figure 3). What could cause this damage?

What is now the axial force due to M, N and Q in the damaged member, compared to what is was for the intact structure?

Assume that the damage corresponds to dent depth and the permanent deflection corresponds to . What is strength reduction when the member is subjected to an axial load – which is tensile and compressive, respectively?

Which criterion – ULS or ALS (with reference to the damage case given above) do you expect to be most critical (governing the design)?

FIGURE 3Damaged Braces

Given information

Ultimate load vs. dent depth for simply supported tubes are presented in below curves [1].

-reduced slenderness,

lk-effective buckling length of the member, assume member original length 45 m.

r-radius of gyration, (r = 0.335 D for thin-walled circular cylinder)

y-yield stress, assume 360 N/mm^2

E-Young’s modulus, 2.1E+05 N/mm^2

t-Plate thickness, assume 25 mm.

PP-the fully plastic axial load,

Dd-depth of dent

Dm-diameter of member

The critical buckling stress for tubular columns can be estimated by the following equations (AISC, API).

[1]J. Taby and T. Moan (1985): Collapse and Residual Strength of Damaged Tubular Members, BOSS ’85, The Netherlands.