1. Pipe Stress
1.1. Purpose
The stress timeseries are calculated from timeseries of effective tension (\(T_{e}\)) and moment from the dynamic analysis. The external diameter (\(OD\)), wall thickness (\(t\)), Youngâ€™s modulus (\(E\)), internal pressure (\(P_{i}\)), and external pressure (\(P_{e}\)) is given by the user. It is important that the input corresponds with input given in the model so that the resulting axial and bending stiffness is identical, otherwise the stresses may be under or overestimated. The user may also select if stresses are to be calculated at the inner or outer wall of the pipe and specify number of points for calculating stresses.
1.2. Input
The effective tension and bending moment will in general be timeseries from a dynamic analysis. The stress timeseries will in general be generated for all elements where both bending moment components (\(M_{y},M_{z}\)), and Tension is present. The first stress timeseries is generated at the local yaxis of the element, and subsequent results are generated for points at increments \(d\theta\) = \(2\pi/N\) around the crosssection, where N is number of points for stress calculations given in input.
The moment conventions are as follows:

\(\theta\) is a positive rotation from the local yaxis

Positive \(M_{y}\) results in max compression for \(\theta=90^\circ\) and max tension for \(\theta=270^\circ\)

Positive \(M_{z}\) results in max compression for \(\theta=0^\circ\) and max tension for \(\theta=180^\circ\)
1.3. Output
The following timeseries may be calculated:
Axial bending stress \( \sigma_{ab} = \frac{M\times r}{I} \)
True wall axial stress \( \sigma_{tw} = \frac{T_{tw}}{A} \)
Resultant axial stress \( \sigma_{as} = \sigma_{tw}+\sigma_{ab} \)
von Misesâ€™ stress \( \sigma_{vm} = \sqrt{(\sigma_{le}\sigma_{ab})^2 3 * \tau^2} \)
where
\( M \) = Resultant moment at point in cross tension where stress is calculated
\( I \) = \(\pi\times\frac{r_{e}^4  r_{i}^4}{4}\)
\( r \) = Radius to point in crosssection (outer or inner radius)
\( T_{tw} \) = \(T_e +(p_i A_ip_e A_e)\) = True wall tension
\( \sigma_{le} \) = \(\frac{T_{e}}{A}\) = Effective stress
\( p_{int} \) = Internal pressure
\( p_{o} \) = External pressure