Machine Design
Two closely coiled helical springs with stiffness k₁ and k₂ respectively are connected in series. The stiffness of an equivalent spring is given by

(k₁ k₂)/ (k₁ + k₂)
(k₁ - k₂)/ (k₁ k₂)
(k₁ - k₂)/ (k₁ + k₂)
(k₁ + k₂)/ (k₁ k₂)

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Machine Design
In case of thick cylinders, the tangential stress across the thickness of cylinder is

Maximum at the outer surface and zero at the inner surface
Maximum at the outer surface and minimum at the inner surface
Maximum at the inner surface and zero at the outer surface
Maximum at the inner surface and minimum at the outer surface

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