The spring constant of a helical spring under axial load is...

The spring constant of a helical spring under axial load is given by $$ k=\frac{G d^{4}}{8 N D^{3}} $$ where $G$ is the shear modulus, $d$ is the wire diameter, $D$ is the coil diameter, and $N$ is the number of turns. Find the spring constant and the weight of a helical spring made of steel for the following data: $D=0.2 \mathrm{~m}, d=0.005 \mathrm{~m}, N=10$.

The spring constant of a helical spring under axial load is given by
$$
k=\frac{G d^{4}}{8 N D^{3}}
$$
where $G$ is the shear modulus, $d$ is the wire diameter, $D$ is the coil diameter, and $N$ is the number of turns. Find the spring constant and the weight of a helical spring made of steel for the following data: $D=0.2 \mathrm{~m}, d=0.005 \mathrm{~m}, N=10$.

Key Concepts

Helical Spring Mechanics

Helical springs are mechanical components that store energy through deformation when a load is applied along their axis. Their behavior is typically defined by the relationship between the applied load and the resulting deflection, governed by principles of elasticity and material science.

Spring Constant

The spring constant is a measure of a spring's stiffness, representing the force required to produce a unit displacement. It is derived from the material's properties and the spring's geometry, and it plays a crucial role in determining the system's response under axial loading.

Shear Modulus

The shear modulus is a material property that quantifies the stiffness of a material against shear deformation. In the context of helical springs, it directly influences the spring constant as it determines how the material resists twisting and deformation under load.

Geometric Parameters

The geometric parameters of a spring, including the wire diameter, coil diameter, and number of turns, critically affect both the spring constant and the overall performance of the spring. These dimensions determine the distribution of stresses and the effective material volume contributing to the spring's mechanical behavior.

Weight Calculation

The weight of a helical spring made from a given material is determined by its volume and the density of the material. Calculating the volume involves understanding the geometry of the spring (wire diameter and coil length), which, when multiplied by the material density, yields the mass and consequently the weight.

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