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How to model non-circular pile sections in Repute 1.x

Repute 1's calculation engine is designed to analyse piles with circular cross-sections. However, piles with other cross-sections can be simulated by idealising them as solid circular piles with equivalent:

• Cross-sectional area (A)
• Axial rigidity (EA)
• Bending rigidity (EI)

Cross-sectional area

The pile's internal diameter should be set to zero and its external diameter chosen so that the pile's cross-sectional area matches that of the non-circular pile:

πD_ext²/4 = A_actual

» D_int = 0 and D_ext = √(4A_actual / π) ...[eq'n 1]

Axial rigidity

The pile's axial Young's modulus should be chosen so that its axial rigidity matches that of the non-circular pile:

E_axialA = E_axialπD_ext²/4 = (EA)_actual

» E_axial = 4(EA)_actual / πD_ext² ...[eq'n 2]

Bending rigidity

The pile's lateral Young's modulus should be chosen so that its bending rigidity matches that of the non-circular pile:

E_lateralI = E_lateralπD_ext⁴/64 = (EI)_actual

» E_lateral = 64(EI)_actual / πD_ext⁴ ...[eq'n 3]

Example 1 - square pile

Consider a 0.6m x 0.6m square section pile (A = B², I = B⁴/12) made out of concrete (E = 35 GPa):

A_actual = 0.6 x 0.6 = 0.36 m² = 3600 cm²
(EA)_actual = 35 x 0.36 = 12.6 GN = 12600 MN
(EI)_actual = 35 x 0.6⁴/12 = 378 MNm²

The equivalent circular pile to enter into Repute is:

D_int = 0
D_ext = √(4 x 0.36 / π) = 0.677 m
E_axial = (4 x 12.6) / (π x 0.677²) = 35.0 GPa
E_lateral = (64 x 378) / (π x 0.677⁴) = 36.47 GPa

Example 2 - H-section pile

Consider a 254 x 254 x 63 universal (H-section) bearing pile (A = 79.7 cm²; I_xx = 8775 cm⁴) made out of steel (E = 200 GPa).

The relevant cross-sectional area for equation [1] is the gross enclosed area of the pile (A_gross = B²), but for equation [2], based on axial rigidity, it is the actual cross-sectional area of the pile (A_actual = 79.7 cm²), so:

A_gross = 0.254 x 0.254 = 0.0645 m²
(EA)_actual = 200 x 0.00797 = 1.59 GN
(EI)_actual = 200 x 0.00008775 = 17.55 MNm²

The equivalent circular pile to enter into Repute is:

D_int = 0
D_ext = √(4 x 0.0645 / π) = 0.287 m
E_axial = (4 x 1.59) / (π x 0.287²) = 24.6 GPa
E_lateral = (64 x 17.55) / (π x 0.287⁴) = 52.7 GPa