The Study of Limit Load and Plastic Collapse Load Under Combined Loads

  • Ying ZhangEmail author
  • Bin Zheng
  • Liping Zhang
  • Zhenyu Liu
  • Juan Du
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 75)


In the process of mechanical analysis for equipment and pipe of reactor coolant system (RCS), due to the severe load condition, the stress analysis cannot satisfy the evaluation criteria at times, the limit analysis and plastic analysis is necessary. This paper focus on the limit load and the plastic collapse load of the straight pipe and three-way pipe of reactor coolant system (such as the nozzle of main equipment and the pipe of main system) under combined loads, the analytical method and the finite element (FE) method are adopted in this paper. Get the limit load curve and the plastic collapse load curve of straight pipe and three-way pipe under combined loads, the effect of load history and structure size is analyzed. Tangent intersection criterion (TI) and Plastic work-tangent criterion (PWT) are adopted to study the plastic collapse load curve of straight pipe under combined load of pressure and bending moment. Get the theoretical equation of the limit load and plastic collapse curve of straight pipe under combined loads; get the theoretical equation of the limit load surface of straight pipe under combined load of pressure, bending moment and torque. The effect of many factors is analyzed on three-way pipe.


Limit load Plastic collapse load Limit load curve Plastic collapse load curve Limit load surface 


\( P_{L} \)

Limit load for pure pressure

\( M_{L} \)

Limit load for pure bending

\( T_{L} \)

Limit load for pure torsion

\( P_{P} \)

Plastic collapse load for pure pressure

\( M_{P} \)

Plastic collapse load for pure bending

\( W^{p} \)

Plastic work

\( \sigma_{y} \)

Yield strength

\( \sigma_{e} \)

Von Mises equivalent stress

\( \varepsilon_{p} \)

Plastic strain

\( E \)

Elastic modulus

\( \nu \)

Poisson ratio

\( r_{m} \)

Mean pipe radius

\( V \)

Single element volume of FE model

\( n \)

Total element number of FE model

\( t \)

Thickness of pipe

\( Z \)

Plastic section modulus for bending

\( D \)

Outside diameter of pipe

\( d \)

Inside diameter of pipe

\( l \)

Length of pipe

\( \lambda \)

Radius-thickness ratio


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Ying Zhang
    • 1
    Email author
  • Bin Zheng
    • 1
  • Liping Zhang
    • 1
  • Zhenyu Liu
    • 1
  • Juan Du
    • 1
  1. 1.State Key Laboratory of Reactor System Design TechnologyNuclear Power Institute of ChinaChengduChina

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