A Method for Calculating the Length of the Vertical Rods of Steel Pipe Fully-Supported Frames with Fasteners

This paper studied the method of calculating the length of the vertical rods of steel pipe fully-supported frames with fasteners in construction. The linear interpolation method for calculating the length coefficient in the current specification:according to Appendix D of Technical Standard for Safety of Steel Tubular Scaffold with Couplers in Construction (T/CECS 699—2020), the step length h of the fully-supported frame or the length a of the vertical rod extending from the center line of the top horizontal rod to the support point increased with a fixed step length, and the initial calculated lengthL_C of the vertical pole section was taken as an independent variable, firstly, the calculated length coefficient (μ₁ or μ₂) of the vertical bar of the fully-supported frame was calculated by linear insertion method, and then the calculated lengthL_L of the corresponding vertical rod segment was calculated. The newly proposed direct linear interpolation method for calculating length was as follows:the length coefficient (μ₁ or μ₂ based on theoretical and experimental results) was calculated according to the specific parameters given in Appendix D of T/CECS 699—2020 (step distance h, distance between vertical poles, length a from the center line of the vertical rod extending out of the top horizontal rod to the support point), firstly, the mechanical calculation lengthL_L of the vertical rod section under specific parameters was calculated, and then the step distance h of the fully-supported frame or the length a (or h+2a) of the vertical pole extending from the center line of the top horizontal rod to the support point was increased by a fixed step, and the initial calculated length L_C (h+2a orh) of the vertical rod section was taken as the independent variable, then, the corresponding mechanical length L_L of the vertical rod segment was calculated by linear insertion method. By analyzing the scatter plots and fitting functions of the mechanical calculation length L_L of the vertical rod segment and the initial calculation length L_C(a or h+2a, h) of the above two insertion methods, it was found that the calculation results of the linear interpolation method of the calculation length coefficient in the current specification violated the basic principle of linear interpolation (the interpolated dependent variable exceeded the scope of the interpolated dependent variable). Further analysis showed: the initial calculation lengthL_C and mechanical calculation length L_L in Appendix D of T/CECS 699—2020 were fitted according to linear function with sufficient accuracy, and could be regarded as linear relations; the calculated length L₀, the slenderness ratio λ, the stability coefficient φ and the stability bearing capacity were all linear; in the current specification, the function which was actually a concave L_C-μ quadratic term or power was wrongly regarded as a linear function, which led to the reason that the calculated lengthL_L (or bearing capacity) of the vertical rod segment violated the basic principle of linear interpolation. Based on the measured results and finite element analysis of the stable bearing capacity in relevant literatures, and referring to the calculation method in the current British standard BS 5975[DK]∶2019, a method of directly calculating the length of the vertical rod with linear insert fasteners was proposed, taking the initial calculation length L_C (h+2a orh) as the independent variable.