Article Figures & Data
Figures
- Figure 1.
Measured branches: a) branch no. 1; b) branch no. 2; c) branch no. 3; d) branch no 4.
- Figure 2.
Measurement setup: markers at the neutral axis, direction of loading, and inclinometer location.
- Figure 3.
FE model of branch no. 2, non-deformed and in vertical displacement: SEC1…8 number of cross-section, uy is vertical displacement [m], ux is horizontal displacement, ϴ0 is rotation of branch anchorage, and F is applied force.
- Figure 4.
The variability of deflections along branches during loading: the mean value of deflection with minimum and maximum values along the branch during the loading phase.
- Figure 5.
The calculated MOE : MOEvar_L1..4 is variable MOE along branch no. 1 to 4; MOEx_L1..4 is average value of the modulus of elasticity without extreme values for branch no. 1 to 4.
- Figure 6.
Comparison of deflection obtained experimentally and numerically: Model_Ex is model with average E, Model_Evar is model with variable E along the branch length; a) branch no. 1; b) branch no. 2; c) branch no. 3; d) branch no 4.
- Figure 7.
The correlation between the input and output parameters—Analysis I. (Spearman correlation coefficients, p = 0.05).
- Figure 8.
The correlations between the input and output parameters—Analysis II. (Spearman correlation coefficients, p = 0.05).
Tables
- Table 1.
General branch parameters: dbasell is branch base diameter in the direction of pulling, dbase_ is branch base diameter vertically to the direction of pulling, α is the angle of branch attachment.
Lime dbaseII dbase_ tapering α cross-section shape 1 51 cm 36 cm 0.2 0° ellipse convex 2 28 cm 29 cm 0.1 - circle concave 3 21 cm 23 cm 0.05 33° circle slightly concave 4 21 cm 15 cm 0.03 45° ellipse slightly concave - Table 2.
The input and output parameters of sensitivity analysis: ymax is maximum deflection, y1…5 are deflections at the points, θ3,5 are rotations at the points 3 and 5.
Description Analysis I Analysis II Input parameters Extension Output parameters Input parameters Extension Output parameters branch length L 2-4 m ymax L 2-2.5 m y1 base diameter dbase_ 10-50 cm θ3 dbase_ 20-26 cm y2 tapering dtop dtop = 1 dbase_ – 1/2 dbase_ θ5 dtop dtop = 1 dbase_ – 1/2 dbase_ y3 ellipse e 1 dbase_ – 2 dbase_ e 1 dbase_ – 1.6 dbase_ y4 curvature R 1-1000 m R 2-1000 m y5 attachment angle α 0-60° α 0-30° θ3 elastic moduli E 8e9 ± 30% E 8e9 ± 30% θ5 anchorage rotation θ0 0-0.1° θ0 0-0.06° - Table 3.
Experiment result: Fmax is the maximum force, ymax is the maximum deflection, θ1_2 is the inclination between point 1 and 2 (branch base), d_2II is the diameter at point 2 (with the elimination of branch collar), MOEx is the average MOE value.
Lime Fmax ymax θ1_2 d_2II MOEx 1 2023 N 12.6 mm 0.057° 30 cm 2.98 GPa 2 350 N 25.2 mm 0.13° 13 cm 7.69 GPa 3 231 N 33.7 mm 0.35° 11 cm 7.85 GPa 4 1193 N 18.55 mm 0.23° 21 cm 6.51 GPa - Table 4.
Mean relative errors of simulation: Ex is model with mean E, Evar is model with variable E along branch.
Lime Ex RE [%] Ex RE [%] Evar 1 2.98 GPa −24 −26 2 7.69 GPa −11 −19 3 7.85 GPa 16 −0.5 4 6.51 GPa −4 −7
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