分类： 论文专利 |

Ultimate load of cylindrically curved panels under uniform compression at straight edge and the influence of curvature

**
Hui** **
G****uo ^{1,
2}**

**,**

**Zhibin Zeng**

^{1, 2}**,**

**Xiaoguang**

**L**

**iu**

^{1, 2}**,**

**Xiaochen Ju**

^{1, 2}**,**

**Xinxin Zhao**

^{1, 2}^{
1}*Railway
Engineering Research Institute**,*
*
China Academy of Railway Sciences, Beijing, China*

^{2}*State
Key Laboratory for Track Technology of High-speed Railway, Beijing,
China*

**
Contact:** **
superhugo@163.com**

# Abstract

**
Keywords:**
curved panel; stability; steel pylon of cable-stayed bridge;
elasto-plastic buckling; full-scale model test; ultimate load;
curvature; reduction factor; empirical formula.

# 1
Introduction

^{1}. It appeared that the behavior of cylindrically curved panels usually depended on its curvature, its slenderness and its imperfection

^{1}. Martins et al. also studied the ultimate load of simply supported cylindrically curved panels subjected to pure compression and in-plane bending by numerical method. Results showed that the ultimate behavior of cylindrically curved panels was similar to flat plates (similar curves)

^{2}. Xu et al. derived approximate solutions by shallow shell theory and Galerkin method for buckling stress of curved web plate of a steel bridge under wheel compression. Solutions of straight plate as the special case were then proved to be reasonable compared to the calculated value from Japan’s structural stability handbook

^{3}. Research group from Institute of Mechanics, China Academy of Sciences had carried out theoretical study and test on buckling of stiffened cylindrical shells under external pressure. Model tests for stiffened cylindrical shells subjected to external pressure by gas cell were conducted and it revealed that the ultimate load of test was accord with the calculated value from membrane theory under the boundary condition of simply support at the straight edge with longitudinal restrictions and sliding simply support at curved edge. Test results also influenced by additional bending moment at the loading end, initial imperfections and movement of boundary at the straight edge

^{4, 5}.

*(a)
Cylindrically curved panel under uniform axial
compression*

*(b) Cylindrically curved panel under
uniform external compression*

*(c) Cylindrically curved panel under
uniform compression at straight edge*

Figure 1. Cylindrically curved panel under uniform compression in different directions

# 2
Design case of curved pylon

Figure 2. Rendering of Beijing Yongding River Bridge

Figure

*3*

*.*

*Local structural design of curved plate at the top of curved pylon (higher pylon)*

#
3
Buckling of cylindrically curved panels under uniform compression
at straight edge

**3.1**
Validation of numerical model

(a) Mode1
(b)
Mode2

*
(c) Mode3
(d)
Mode4*

*(e)
Mode5*

*Figure*
*4**.* *First five
modes of elastic buckling*

Table 1. Comparison of critical stress of elastic buckling obtained by numerical model and theory

(1) |

*k* was the
elasto-plastic buckling coefficient which could be expressed
by *E*
equalled to 2.1e5 MPa and*k* had the
value of 0.693. *D* was the flexural rigidity of plate’s unit
width. And *t* equalled to 32mm, *b* had the value of
700mm, and

*Figure*
*5**.* *Verification of
numerical model for elasto-plastic buckling by model
test*

## 3.2
Model test of curved panels

*(a) Curved plate S2 at the
outmost panels with smaller radius of curvature of the
pylon*

*(b) Curved plate S3 at the outmost panels with
larger radius of curvature of the pylon*

*Figure*
*6**.* *Curved panels
for ultimate load test*

*Figure*
*7**.* *Buckling test
equipment for curved panels with simply support at four
edges*

*(a) Longitudinal and vertical displacement of curved plate S2*

*Figure*
*8**.* *Displacement of
curved panels obtained by model test*

*(a) Load-longitudinal displacement curve at
loading edge of S2 panel*

*(b) Load-* *longitudinal displacement curve at loading edge
of S3 panel*

*Figure*
*9**.* *Comparison of
load-displacement curves between model test and numerical
model*

*(a)
Load-displacement curve of S2 (numerical)*

*(b)
Load-displacement curve of S3 (numerical)*

*Figure*
*10**.* *Total
displacement (USUM) distribution of curved panels under the
ultimate load*

## 3.3
Influence of curvature on ultimate load

*Figure* *11**.*
*Influence of curvature on
load-longitudinal displacement curve and ultimate load*

^{6, 7, 8}. *k* for curved
panels. Result was obtained and given in Figure 12. Conclusions
could be made that reduction factor 𝜌 decreased as the curvature increased.
It conformed to a linear correlation. Correlation between
reduction
factor *k* of the sub-panel of
the curved pylon of Yongding River Bridge could be expressed as
follows.

*Figure*
*12**.* *Relationship
between the reduction factor of local stability*
*𝜌* *and curvature
k*

# 4
Conclusions

# 5
Acknowledgements

# 6
References

*Journal of Constructional Steel Research*

*.*2012;

**69**(1):30-38.

[2] *Thin-Walled Structures*.
2014;
**77**(4): 36-47.

[3]

[4] *Mechanical
Bulletin*. 1976; (3): 30-37.

[5] *Mechanical
Bulletin*. 1976; (3): 37-42.

[6]

[7] *Journal of
Fuzhou University (Natural Science Edition)*. 2014; 42(1):
123-127.

[8]

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