Krzywe Nośności Granicznej dla Cienkościennego Rurociągu Poddanego Ciśnieniu Wewnętrznemu i Zginaniu

Limit was of a thin-walled pipeline under internal pressure p and bending moment Mq, is analyses; possible presence of a longitudinal force is taken into consideration by introducing an appropriate coefficient ϕ (2.5).
In Ref. [3] one of the present authors determined a certain statically admissible stress field described by Fig. 2 and Eqs. (2.1) and (2.6). He gave also a preliminary form of the equation of the limit load curve m = m (q, ϕ), Eq. (2.8). It involves an unknown parameter ϕ0 describing the discontinuity of the axial stress σz. In the present paper the limit curve is determined first by means of power series. Assuming ϕ0 =0 a power expansion is obtained determining the influence of the internal pressure on the load-carrying capacity of the pipe under bending (3.2). Assuming ϕ0 = -π/2 an expansion is obtained determining the influence of bending on the load-carrying capacity of the pipe line under the action of a pressure and a longitudinal force (3.7) and (3.8).
Next, Hermitian approximation is used taking into consideration the compatibility conditions at the edges of the interval. The equation of the limit load curve is approximated by polynomials of the third and fourth degree, (4.1). In the case of ϕ = 1/2 (a pipe having bottoms at both ends) the limit curve is approximated by means of an ellipse (5.1). Examples of limit load curves are given in Fig, 3 for various values of . It is seen that a tension force up to ϕ 1/2, improves considerably, the load-carrying capacity of the pipe.