Chapter 3:

TorsionChapter 5:

Stresses

In beams

Chapter 4:

Shear and

Moment

Diagram

Helical SpringsAre analyzed with the combined effects of

simple shearing stress and torsional shearing stressP

P

P

P

P

RR

P

P

P

PR

d

PP

PRPR

The derived formulas are:

Where:

– Torsional Shearing Stress

P - Axial Force Applied

R – Mean Radius

d – Wire Diameter

The derived formulas are:

Where:

P - Axial Force Applied

R – Mean Radius

d – Wire Diameter

n – Number of Turns

Example : Two steel springs arranged in series

support a load P. The upper string has 12turns of 25 mm diameter wire on a meanradius of 10omm. The lower spring consistsof 10 turns of 20 mm diameter wire on amean radius of 75 mm. If the maximumshearing stress in either spring must notexceed 200 MPa, compute the maximumvalue of P and the total elongation of theassembly. Use G = 83 GPa.

P

Example : A helical spring is made by wrapping steel wire

20 mm in diameter around forming a cylinder 150mm in diameter. Compute the number of turnsrequired to permit an elongation of 100 mm withoutexceeding a shearing stress of 140 MPa. Use G = 83GPa.

Example : A rigid bar, hinged at one end, is supported by

two springs as shown. The first spring consists of 20turns of 20 mm diameter wire on a mean diameter of150 mm. The second spring has 30 turns of 20 mmdiameter wire on a mean diameter of 200 mm.Compute the maximum shearing stress in thesprings. Neglect the mass of the rigid bar.

A

2m 1m1 m

15kg

Example : A rigid plate of negligible mass rests on a central

spring which is 20 mm higher than thesymmetrically located outer springs. Each of theouter springs consists of 18 turns of 10 mm wire on amean diameter of 100 mm. The central spring has 24turns of 20mm wire on a mean diameter of 150 mm.If a load P = 5 kN is now applied to the plate, useG=83 GPa. (a) Determine the carried by the centralspring (b) Shearing Stress of each spring.

Example : A rigid bar, hinged at one end, is supported by

two springs as shown. The first spring consists of 20turns of 20 mm diameter wire on a mean diameter of150 mm. The second spring has 30 turns of 20 mmdiameter wire on a mean diameter of 200 mm.Compute the maximum shearing stress in thesprings. Neglect the mass of the rigid bar.

A

1.5 m 1m1 m

10kg

Example : A load P is supported by two concentric steel

springs arranged as shown. The inner spring consistsof 30 turns of 20 mm diameter wire on a meandiameter of 150 mm. The outer spring has 20 turnsof 30 mm diameter wire on a mean diameter of 200mm. Compute the maximum load P that will notexceed as shearing stress of 140 MPa in either spring.Use G = 83 GPa. P

Example : A homogeneous 50 kg rigid block is suspended

by three springs whose lower ends were originally atthe same level. Each steel spring has 24 turns of 10mm diameter wire on a mean diameter of 100 mm, G= 83 GPa. The bronze spring has 48 turns of 20 mmdiameter wire on a mean diameter of 150 mm, and G= 42 GPa. Compute the maximum shearing stress ineach spring if the allowable stress in steel is 40 MPa.

2m1 m

Steel

Bronze

50 kg