考慮初始變形的鋼管腳手架穩定性分析*

趙元一¹，徐佳²，趙成成²

(1.同濟大學浙江學院，浙江 嘉興 314051； 2.浙江上嘉建設有限公司，浙江 嘉興 314001)

［摘要］以結構力學的能量方程為基礎，采用結構變分和歐拉(Euler) 方程，對既定邊界條件的受壓桿件進行駐值求解?；诘谝活惽€積分，以一階近似泰勒級數結合壓桿軸向變形的解析表達式，推導出多項式及三角級數的半解析方程，經實例驗證，其結果與理論解一致?？紤]桿件初始變形后，以常規臨界壓力為基礎，結合已有全微分方程，得出軸力作用下桿件的撓度方程，以材料屈服應力為控制標準，歸納出桿件的初始撓度與臨界壓力關系。通過實際算例的對比分析可知，多項式級數的半解析臨界壓力與已有結果較一致且能根據計算精度自行選擇，初始變形對桿件臨界壓力影響較大，是影響壓桿承載力的主要因素。

［關鍵詞］腳手架；穩定性；最小勢能原理；半解析解

［中圖分類號］TU731.2         ［文獻標識碼］A         ［文章編號］2097-0897(2021)23-0132-04

Stability Analysis of Steel Tube Scaffold Considering Initial Deformation

ZHAO Yuanyi¹, XU Jia², ZHAO Chengcheng²

(1.Tongji Zhejiang College, Jiaxing，Zhejiang 314051, China；2.Zhejiang Shangjia Construction Co., Ltd., Jiaxing, Zhejiang 314001, China)

Abstract:The semi-analytical solution for minimum energy point of given boundary, which is based on energy equation of structural mechanics and Euler formula, can be derived form Taylor series in the form of first curve integral. This solution, classified by trigonometric or polynomial series, has been proved essentially correct. Once the formula takes initial deformation into account, this paper presents the relationship between initial deflection and critical compressive force. Compared with engineering examples, the result fits the exact solution well and reviews that the initial deformation is the main factor to affect the stability of steel scaffolds.

Keywords: scaffolds;stability;minimum potential energy;semi-analytical solution

*“一環四路”外立面改造項目可借鑒及可推廣性項目（20SJJSS－02）

［作者簡介］趙元一，博士，講師，Email：258421300@qq.com

［通信作者］趙成成，高級工程師，Email：14564266@qq.com