This paper investigates the higher order geometrical effects on the deflections of a helical armour wire when the pipe is subjected to uniform bending and is away from any end effects from its remaining fittings (end fittings), and the effect on the subsequent bending stresses. Due to its complexity in both geometrical shape and loading conditions, the approaches found in the literature are often to assume either a bent helix or geodesic as its deflected configuration with linearized mathematical expressions for simplification. The bending stresses are then calculated based on the geometrical difference between the assumed deflection and the original helical shape. The effect of the wire cross-section characteristics, for example the width and thickness ratio, over its deflection are often ignored. This paper presents an analytical strain energy model to quantify the influence of the wire width and thickness ratio over its final deflection. The higher order geometrical effects are fully considered in determining the wire deflection by using the exact mathematical expressions, and in the subsequent wire deformation and stress calculations. The paper also discusses briefly the structural coupling behavior between the pipe axial and bending deformations raised by using the exact expressions. The analytical results are validated by finite element simulation of an identical structure. The results are shown in good agreement in both deflection and the bi-normal bending stress. The results also show desirable conservatism in the normal and the total bending stresses. The presented analytical approach is demonstrated as an efficient and conservative way for investigating the behaviour of such a helical wire.

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