# helical spring

## Problem 01 | Stress in Helical Spring

**Situation**

The helical spring shown is axially loaded with a compression force *P* equal to 5 kN. The mean diameter of the spring is 100 mm and the wire used is 10 mm as indicated in the figure.

- What is the shear stress at
*A*? - What is the shear stress at
*B*? - On diameter
*AB*, locate the point of zero stress measured from*C*.

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## Solution to Problem 350 | Helical Springs

**Problem 350**

As shown in Fig. P-350, a homogeneous 50-kg rigid block is suspended by the three springs whose lower ends were originally at the same level. Each steel spring has 24 turns of 10-mm-diameter on a mean diameter of 100 mm, and *G* = 83 GPa. The bronze spring has 48 turns of 20-mm-diameter wire on a mean diameter of 150 mm, and *G* = 42 GPa. Compute the maximum shearing stress in each spring using Eq. (3-9).

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## Solution to Problem 349 | Helical Springs

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## Solution to Problem 347 | Helical Springs

**Problem 347**

Two steel springs arranged in series as shown in Fig. P-347 supports a load P. The upper spring has 12 turns of 25-mm-diameter wire on a mean radius of 100 mm. The lower spring consists of 10 turns of 20-mm diameter wire on a mean radius of 75 mm. If the maximum shearing stress in either spring must not exceed 200 MPa, compute the maximum value of P and the total elongation of the assembly. Use Eq. (3-10) and G = 83 GPa. Compute the equivalent spring constant by dividing the load by the total elongation.

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## Solution to Problem 346 | Helical Springs

**Problem 346**

Compute the maximum shearing stress developed in a phosphor bronze spring having mean diameter of 200 mm and consisting of 24 turns of 20-mm diameter wire when the spring is stretched 100 mm. Use Eq. (3-10) and G = 42 GPa.

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## Solution to Problem 345 | Helical Springs

**Problem 345**

A helical spring is fabricated by wrapping wire 3/4 in. in diameter around a forming cylinder 8 in. in diameter. Compute the number of turns required to permit an elongation of 4 in. without exceeding a shearing stress of 18 ksi. Use Eq. (3-9) and G = 12 × 10^{6} psi.

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## Solution to Problem 344 | Helical Springs

**Problem 344**

Determine the maximum shearing stress and elongation in a bronze helical spring composed of 20 turns of 1.0-in.-diameter wire on a mean radius of 4 in. when the spring is supporting a load of 500 lb. Use Eq. (3-10) and G = 6 × 10^{6} psi.

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## Solution to Problem 343 | Helical Springs

**Problem 343**

Determine the maximum shearing stress and elongation in a helical steel spring composed of 20 turns of 20-mm-diameter wire on a mean radius of 90 mm when the spring is supporting a load of 1.5 kN. Use Eq. (3-10) and G = 83 GPa.

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## Helical Springs

When close-coiled helical spring, composed of a wire of round rod of diameter *d* wound into a helix of mean radius *R* with *n* number of turns, is subjected to an axial load *P* produces the following stresses and elongation:

The maximum shearing stress is the sum of the direct shearing stress τ_{1} = *P*/*A* and the torsional shearing stress τ_{2} = *Tr*/*J*, with *T* = *PR*.

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