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the Stresses In Helical Spring Of Circular Wire

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Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of UK Essays.

Published: Mon, 5 Dec 2016


A Spring Is Defined As An Elastic Whose Function Is To Disort When Loaded And To Recover Its Original Shape When The Load Is Removed.

Helical Spring

The Helical springs are made up of wire coiled in the form of helix and is primarily intended for compressive or tensile loads. The cross section of wire from which the spring is made it may be either circular or squared. The two forms of helical springs are compression and tension helical spring. These springs are said to be “Closely Coiled” when the spring is coiled so close that the plane containing each turn is nearly at right angle to the axis of helix and wire is subjected to tension. In closely coiled helical spring the helix angle is very small it is usually less than 10 degrees. The major stress produced in helical springs is shear stresses due to twisting. The load applied is either parallel or along spring. In “Open Coiled” helical springs the spring wire is coiled in such a way that there is gap between 2 consecutive turns, as a result of which the helix angle is large.

Advantages Of Springs:

  • Easy to mfg.
  • Available in wide range.
  • Reliable.
  • Constant spring constant.
  • Performance is accurate.
  • Characteristics can be varied by changing dimensions.

Applications Of Springs:

  • Absorbs energy due to shock or vibration.
  • To apply force in brake, clutches, spring loaded values.
  • To measure forces in spring balance and engine indicators.
  • To store energy.

Material For Helical Springs

The material of spring should have high fatigue strength, high ductility, high resistance and it should be creep resistance. It largely depends upon the service for which they are used.

Severe Service

Rapid continuous loading where ratio of minimum and maximum load is half an automotive valve spring.

Average Service

Includes same stresses range as in severe service but with only intermittent operation as in engine governor spring.

Light Service

It is subjected to loads that are static or very infrequently varied as in safety valve springs. Actually springs are made from oil tempered carbon steel wires containing 0.6% to 0.7% carbon and 0/6% to 1% manganese.

Soild Length

When the compression spring is compressed until the coils comes in contact with each other, then the spring is said to be solid. The solid length of a spring is the product of total number of coils and the diameter of wire.

Ls = n’d.

N’ = total number of coils.

d = dia of wire.

Free Length

The free length of compression spring is the maximum length of spring in free condition. It is equal to solid length. Plus the maximum deflection of spring and clearance adj to two coils.

Lf = solid+max compression+clr b/w adj coils

= n’d+$ max+0.15 $ max.

Spring Index

The spring index is defined as the ratio of the mean diameter of the coil to the dia of wire.

C = D/d.

D = Mean dia of the coil.

D = Dia of the wire.

Spring Rate

The spring rate is defined as load required per unit deflection of the spring.

K = W/£.

W = Load.

£ = Deflection of the spring.


The pitch of the coil is defined as axial distance between adjacent coils in uncompressed state.

P = Free Length/ N’-1.

Stresses In Helical Spring Of Circular Wire

Consider a helical compression spring made of circular wire and subjected to an axial load “W”.

D = Mean dia of spring coil.

d = Dia of spring wire.

N = number of active coils.

G = Modulus of rigidity for spring material.

W = Axial load on spring.

T = Max shear stresses induced in wire.

P = Pitch of the coils.

£ = Deflection of the spring.

Now consider a part of the compression spring. The load “W” tends to rotate the wire due to the twisting moment (T) set up in the wire. Thus torsion shear stress is induced.

A little consideration will show that part of the spring is in equilibrium under the action of two forces “W” and twisting moment (T)

T = W * D/2 = π/16 * T1 * d3.

T1 = 8WD/Πd3.

The Torsional

Shear Stress Is Given By:-

1. Direct shear stress due to load “W”.

2. Stress due to curvature of the wire.

T2 = Load/ Cross sectional area of wire.

The resultant shear stress induced in wire is given by

T = t1+t2= 8WD/πd3 + 4W/πd2.

The positive sign is used for inner edge of wire and negative sign is for outer edge.

Maximum shear induced in wire is given by

= Torsional shear stress + Direct shear stress

Ks = shear stress factor = 1+1/2c.

In order to consider the effects of both direct shear as well as curvature of the wire, a Wahl’s stress factor (K) introduced


The force of resistance offered by a body against the deformation is called as “STRESS”. The external force acting on body is called as “LOAD”. The load is applied on the body while the stress is induced in the material of the body.

Types Of Stress

A rod of uniform sectional area ‘A’ and subjected to axial loads ‘P’ at the ends of A & B.

Consider a section XX normal to the longitudinal axis of the member. Let the member be taken to consist of two parts C & D into which it is divided by section XX.

Let us consider the equilibrium part C. This part is subjected to the external load P at the end A. In order to keep in equilibrium, the part D offers a resistance R at the section XX. Similarly the part D is subjected to external load P at end B.

The resistance R is equal and opposite to load. If the resistance offered by resistance by section against the deformation be assumed to be uniform across the section, the intensity of the resistance per unit area of section is called as intensity of stress.

Intensity of stress = P = R/A = P/A.

Let due to application of the load the length of material changes from L to L+dl. The ratio of change in length to original length is called as strain.

Strain = e = dl/l.

  • TENSILE STRESS: – When section offered by section of member against an increase in length the section is said to offer a tensile stress.

o P = R/A = P/A.

  • COMPRESSIVE STRESS: – If the bar is subjected to axial loads a resistance is set up by any section such as XX against decrease in length. This resistance is called as compressive resistance.

o Compressive strain = decrease in length/original length

  • SHEAR STRESS: – Let the bottom face of the block be fixed to surface EF. Let a force P be applied tangentially along top face of the block. Such force acting is called as shear force.

For the equilibrium of the force of the block, the surface EF will offer a tangential reaction P equal and opposite to the force applied on P. let the block consists of two blocks G & H to which it is divided by section XX.

In order the part G may not move from left to right, the part H will offer resistance R along the section XX such that R=P.

Considering the equilibrium part of H we find that part G will offer resistance R along the section XX such that R=P.

The resistance R along section XX is called as shear resistance.

A failure of section XX is called as tangential forces acting on top and bottom faces of the block. This type of failure is called as shear failure. In this the two parts which it is separated, slides over each other.

The intensity of the shear resistance along section XX is called as shear stress.

SHEAR STRESS = q = R/P = R/L*1 = P/L*1.

Shear deformation shows a rectangular block subjected to shear forces P on its top and bottom faces.

When the block does not fail in shear, a shear deformation occurs. If the face of the block be fixed, it can be realized that the block has deformed to position A1B1CD. Or we can say that, face ABCD has been distorted to positions A1B1CD through the angle BCB1=Ø.

Let us now imagine that the block consists of a number of horizontal layers. These layers have under gone horizontal displacement by different amounts with respect of the bottom face. We can say that it is proportional to its distance from bottom face of the block.


= Dx/x.

The Knee And The Ligaments:-

The evidence accumulated in the various phases of this study strongly suggests that the deep-squat exercise, especially as done in weight-training and as used in athletic or other physical conditioning programs, should be discouraged because of its deleterious effect on the ligamentous structures of the knee.

If the ligaments are the first line of defense against knee injury and function in unison with the muscles to maintain stability, then the deep-squat exercise is not a specific exercise suitable to build up strength of the knees since deep-squatting tends to weaken the ligaments and hence make the knee more vulnerable to injury.

Also of significance in later life are the implications of the knee instability so created? After the completion of school when physical activity decreases, general muscle tone and strength decrease, and the stability of the ligaments becomes increasingly important. If the ligaments have been weakened and stretched in school athletics, then abnormal movement is possible within the joint throughout life with the result that internal derangements, osteo-arthritis, and the like, may be more frequent.

There are other exercises similar to full-squat that has a comparable effect on the knee ligaments if carried out in conditioning practices. These include the duck-waddle, squat-jump, and deep-knee bends. These have been used in athletic conditioning in past years but are gradually being eliminated from the programs of the more astute coaches and trainers.

We suggest that the squat exercise used in weight-training and in athletics and conditioning programs be modified so that this exercise is done with the feet straight ahead and the squat limited to a half (thigh parallel) knee bend. This will strengthen the muscles but not place abnormal stresses on the ligamentous structures of the joint.

Guitar Tuning:-

  • Just tune the 5th A string to the A reference note above. If your string has lower pitch, tighten it, if it has higher pitch, first loosen it quite enough and then tighten it to make it correspond to the reference note. Once you have a good a, go ahead to tune the 6th string:
  • Press down on the 6th string at the 5th fret. Strike the 6th string, 5th fret and an open 5th string. Compare their pitch. Both strings should be exactly the same. If not, the 5th string must be adjusted. Once you have your 6th string tuned, go ahead to tune the 4th string:
  • Press down on the 5th string at the 5th fret. Strike the 5th string, 5th fret and an open 4th string. Compare their pitch. Both strings should be exactly the same. If not, the 4th string must be adjusted. Once you have your 4th string tuned, go ahead to tune the 3rd string:
  • Press down on the 4th string at the 5th fret. Strike the 4th string, 5th fret and an open 4th string. Compare their pitch. Both strings should be exactly the same. If not, the 4th string must be adjusted. Once you have your 4th string tuned, go ahead to tune the 3rd string:
  • Press down on the 4th string at the 5th fret. Strike the 4th string, 5th fret and an open 3rd string. Compare their pitch. Both strings should be exactly the same. If not, the 3rd string must be adjusted. Once you have your 3rd string tuned, go ahead to tune the 2nd string:
  • Press down on the 3rd string at the 4th fret. Strike the 2nd string, 4th fret and an open 2nd string. Compare their pitch. Both strings should be exactly the same. If not, the 2nd string must be adjusted. Once you have your 2nd string tuned, go ahead to tune the 1st string:
  • Press down on the 2nd string at the 5th fret. Strike the 2nd string, 5th fret and an open 1st string. Compare their pitch. Both strings

Stress Terms:-

A material being loaded in

1) Compression,

2) Tension,

3) Shear.

Uniaxial Stress Is Expressed By:-

Where F is the force (N) acting on an area A (m^2). The area can be the unreformed area or the deformed area, depending on whether engineering stress or true stress is used.

Compressive stress (or compression) is the stress state when the material (compression member) tends to compact. A simple case of compression is the uniaxial compression induced by the action of opposite, pushing forces. Compressive strength for materials is generally higher than that of tensile stress, but geometry is very important in the analysis, as compressive stress can lead to buckling.

Tensile stress is a loading that tends to produce stretching of a material by the application of axially directed pulling forces. Any material which falls into the “elastic” category can generally tolerate mild tensile stresses while materials such as ceramics and brittle alloys are very susceptible to failure under the same conditions. If a material is stressed beyond its limits, it will fail. The failure mode, either ductile or brittle, is based mostly on the microstructure of the material. Some Steel alloys are examples of materials with high tensile strength.

Shear stress is caused when a force is applied to produce a sliding failure of a material along a plane that is parallel to the direction of the applied force. An example is cutting paper with scissors.

Stress can cause headaches, irritable bowel syndrome, eating disorder, allergies, insomnia, backaches, frequent cold and fatigue to diseases such as hypertension, asthma, diabetes, heart ailments and even cancer. In fact, Sanjay Chug, a leading Indian psychologist, says that 70 per cent to 90 per cent of adults visit primary care physicians for stress-related problems. Scary enough. But where do we err?

Just about everybody—men, women, children and even fetuses—suffer from stress. Relationship demands, chronic health problems, pressure at workplaces, traffic snarls, and meeting deadlines, growing-up tensions or a sudden bearish trend in the bourse can trigger stress conditions. People react to it in their own ways. In some people, stress-induced adverse feelings and anxieties tend to persist and intensify. Learning to understand and manage stress can prevent the counter effects of stress.

Methods of coping with stress are aplenty. The most significant or sensible way out is a change in lifestyle. Relaxation techniques such as meditation, physical exercises, listening to soothing music, deep breathing, various natural and alternative methods, personal growth techniques, visualization and massage are some of the most effective of the known non-invasive stress busters.

Dynamic Of Stress

In a challenging situation the brain prepares the body for defensive action—the fight or flight response by releasing stress hormones, namely, cortisone and adrenaline. These hormones raise the blood pressure and the body prepares to react to the situation. With a concrete defensive action (fight response) the stress hormones in the blood get used up, entailing reduced stress effects and symptoms of anxiety.

When we fail to counter a stress situation (flight response) the hormones and chemicals remain unreleased in the blood stream for a long period of time. It results in stress related physical symptoms such as tense muscles, unfocused anxiety, dizziness and rapid heartbeats. We all encounter various stressors (causes of stress) in everyday life, which can accumulate, if not released. Subsequently, it compels the mind and body to be in an almost constant alarm-state in preparation to fight or flee. This state of accumulated stress can increase the risk of both acute and chronic psychosomatic illnesses and weaken the immune system of the human


The word ‘stress’ is defined by the Oxford Dictionary as “a state of affair involving demand on physical or mental energy” . A condition or circumstance which can disturb the normal physical and mental health of an individual. In medical parlance ‘stress’ is defined as a perturbation of the body’s homeostasis. This demand on mind-body occurs when it tries to cope with incessant changes in life. A ‘stress’ condition seems ‘relative’ in nature. Extreme stress conditions, psychologists say, are detrimental to human health but in moderation stress is normal and, in many cases, proves useful. Stress, nonetheless, is synonymous with negative conditions. Today, with the rapid diversification of human activity, we come face to face with numerous causes of stress and the symptoms of stress and depression.

At one point or the other everybody suffers from stress. Relationship demands, physical as well as mental health problems, pressure at workplaces, traffic snarls, meeting deadlines, growing-up tensions—all of these conditions and situations are valid causes of stress. People have their own methods of stress management. In some people, stress-induced adverse feelings and anxieties tend to persist and intensify. Learning to understand and master stress management techniques can help prevent the counter effects of this urban malaise.

Stress Can Be Positive:-

The words ‘positive’ and ‘stress’ may not often go together. But, there are innumerable instances of athletes rising to the challenge of stress and achieving the unachievable, scientists stressing themselves out over a point to bring into light the most unthinkable secrets of the phenomenal world, and likewise a painter, a composer or a writer producing the best paintings, the most lilting of tunes or the most appealing piece of writing by pushing themselves to the limit. Psychologists second the opinion that some ‘stress’ situations can actually boost our inner potential and can be creatively helpful. Sudha Chandra, an Indian danseus, lost both of her legs in an accident. But, the physical and social inadequacies gave her more impetus to carry on with her dance performances with the help of prosthetic legs rather than deter her spirits.

Experts tell us that stress, in moderate doses, are necessary in our life. Stress responses are one of our body’s best defense systems against outer and inner dangers. In a risky situation (in case of accidents or a sudden attack on life et al), body releases stress hormones that instantly make us more alert and our senses become more focused. The body is also prepared to act with increased strength and speed in a pressure situation. It is supposed to keep us sharp and ready for action.

Research suggests that stress can actually increase our performance. Instead of wilting under stress, one can use it as an impetus to achieve success. Stress can stimulate one’s faculties to delve deep into and discover one’s true potential. Under stress the brain is emotionally and biochemically stimulated to sharpen its performance.

A working class mother in down town California, Erin Brokovich, accomplished an extraordinary feat in the 1990s when she took up a challenge against the giant industrial house Pacific Gas & Electric. The unit was polluting the drinking water of the area with chromium effluents. Once into it, Brokovich had to work under tremendous stress taking on the bigwigs of the society. By her own account, she had to study as many as 120 research articles to find if chromium 6 was carcinogenic. Going from door to door, Erin signed up over 600 plaintiffs, and with attorney Ed Masry went on to receive the largest court settlement, for the town people, ever paid in a direct action lawsuit in the U.S. history—$333 million. It’s an example of an ordinary individual triumphing over insurmountable odds under pressure. If handled positively stress can induce people to discover their inherent talents.

Stress is, perhaps, necessary to occasionally clear cobwebs from our thinking. If approached positively, stress can help us evolve as a person by letting go of unwanted thoughts and principle in our life. Very often, at various crossroads of life, stress may remind you of the transitory nature of your experiences, and may prod you to look for the true happiness of life.

Stress Through Evolution

Stress has existed throughout the evolution. About 4 billion years ago, violent collision of rock and ice along with dust and gas, led to the formation of a new planet. The planet survives more than 100 million years of meltdown to give birth to microscopic life. These first organisms endured the harshest of conditions—lack of oxygen, exposure to sun’s UV rays and other inhospitable elements, to hang on to their dear life. Roughly 300,000 years ago, the Neanderthals learnt to use fire in a controlled way, to survive the Glacial Age. And around 30,000 years, Homo sapiens with their dominant gene constitutions and better coping skills, won the game of survival. Each step of evolution a test of survival, and survival, a matter of coping with the stress of changing conditions.

Millions of trials and errors in the life process have brought men to this stage. Coping with events to survive has led men to invent extraordinary technologies, beginning with a piece of sharpened stone.

From the viewpoint of microevolution, stress induction of transpositions is a powerful factor, generating new genetic variations in populations under stressful environmental conditions. Passing through a ‘bottleneck’, a population can rapidly and significantly alters its population norm and become the founder of new, evolved forms.

Gene transposition through Transposable Elements (TE)—’jumping genes’, is a major source of genetic change, including the creation of novel genes, the alteration of gene expression in development, and the genesis of major genomic rearrangements. In a research on ‘the significance of responses of the genome to challenges,’ the Nobel Prize winning scientist Barbara McClintock, characterized these genetic phenomena as ‘genomic shock’.This occurs due to recombinational events between TE insertions (high and low insertion polymorphism) and host genome. But, as a rule TEs remain immobilized until some stress factor (temperature, irradiation, DNA damage, the introduction of foreign chromatin, viruses, etc.) activates their elements.

The moral remains that we can work a stress condition to our advantage or protect ourselves from its untoward follow-throughs subject to how we handle a stress situation. The choice is between becoming a slave to the stressful situations of life or using them to our advantage.

Strength Terms:-

Yield strength is the lowest stress that gives permanent deformation in a material. In some materials, like aluminum alloys, the point of yielding is hard to define, thus it is usually given as the stress required causing 0.2% plastic strain.

Compressive strength is a limit state of compressive stress that leads to compressive failure in the manner of ductile failure (infinite theoretical yield) or in the manner of brittle failure (rupture as the result of crack propagation, or sliding along a weak plane – see shear strength).

Tensile strength or ultimate tensile strength is a limit state of tensile stress that leads to tensile failure in the manner of ductile failure (yield as the first stage of failure, some hardening in the second stage and break after a possible “neck” formation) or in the manner of brittle failure (sudden breaking in two or more pieces with a low stress state). Tensile strength can be given as either true stress or engineering stress.

Fatigue strength is a measure of the strength of a material or a component under cyclic loading, and is usually more difficult to assess than the static strength measures. Fatigue strength is given as stress amplitude or stress range (Δσ = σmax − σmin), usually at zero mean stress, along with the number of cycles to failure.

Impact strength, it is the capability of the material in withstanding by the suddenly applied loads in terms of energy. Often measured with the Izod impact strength test or Charpy impact test, both of which measure the impact energy required to fracture a sample.

Strain (Deformation)


Deformation of the material is the change in geometry when stress is applied (in the form of force loading, gravitational field, acceleration, thermal expansion, etc.). Deformation is expressed by the displacement field of the material.

Strain or reduced deformation is a mathematical term to express the trend of the deformation change among the material field. For Uniaxial loading – displacements of a specimen (for example a bar element) it is expressed as the quotient of the displacement and the length of the specimen. For 3D displacement fields it is expressed as derivatives of displacement functions in terms of a second order tensor (with 6 independent elements).

Stress-Strain Relation:-

Elasticity is the ability of a material to return to its previous shape after stress is released. In many materials, the relation between applied stress and the resulting strain is directly proportional (up to a certain limit), and a graph representing those two quantities is a straight line.

The slope of this line is known as Young’s Modulus, or the “Modulus of Elasticity.” The Modulus of Elasticity can be used to determine stress-strain relationships in the linear-elastic portion of the stress-strain curve. The linear-elastic region is taken to be between 0 and 0.2% strain, and is defined as the region of strain in which no yielding (permanent deformation) occurs.

Plasticity or plastic deformation is the opposite of elastic deformation and is accepted as unrecoverable strain. Plastic deformation is retained even after the relaxation of the applied stress. Most materials in the linear-elastic category are usually capable of plastic deformation. Brittle materials, like ceramics, do not experience any plastic deformation and will fracture under relatively low stress. Materials such as metals usually experience a small amount of plastic deformation before failure while soft or ductile polymers will plastically deform much more. Consider the difference between a fresh carrot and chewed bubble gum. The carrot will stretch very little before breaking, but nevertheless will still stretch. The chewed bubble gum, on the other hand, will plastically deform enormously before finally breaking.

Stress/Strain Curve

A stress-strain curve is a graph derived from measuring load (stress – σ) versus extension (strain – ε) for a sample of a material. The nature of the curve varies from material to material. The following diagrams illustrate the stress-strain behavior of typical materials in terms of the engineering stress and engineering strain where the stress and strain are calculated based on the original dimensions of the sample and not the instantaneous values. In each case the samples are loaded in tension although in many cases similar behavior is observed in compression.

Ductile Materials

1. Ultimate Strength

2. Yield Strength

3. Rupture

4. Strain hardening region

5. Necking region.

Steel generally exhibits a very linear stress-strain relationship up to a well defined yield point (figure 1). The linear portion of the curve is the elastic region and the slope is the modulus of elasticity or Young’s Modulus. After the yield point the curve typically decreases slightly due to dislocations escaping from Cottrell atmospheres. As deformation continues the stress increases due to strain hardening until it reaches the ultimate strength. Until this point the cross-sectional area decreases uniformly due to Poisson contractions. However, beyond this point a neck forms where the local cross-sectional area decreases more quickly than the rest of the sample resulting in an increase in the true stress. On an engineering stress-strain curve this is seen as a decrease in the stress. Conversely, if the curve is plotted in terms of true stress and true strain the stress will continue to rise until failure. Eventually the neck becomes unstable and the specimen ruptures (fractures).

Less ductile materials such as aluminum and medium to high carbon steels don’t have a well-defined yield point. For these materials the yield strength is typically determined by the “offset yield method”, by which a line is drawn parallel to the linear elastic portion of the curve and intersecting the abscissa at some arbitrary value (most commonly .2%). The intersection of this line and the stress-strain curve is reported as the yield point.

Brittle Materials:-

Brittle materials such as ceramics do not have a yield point. For these materials the rupture strength and the ultimate strength are the same, therefore the stress-strain curve would consist of only the elastic region, followed by a failure of the material.


The area underneath the stress-strain curve is the toughness of the material—the energy the material can absorb prior to rupture.

The resilience of the material is the triangular area underneath the elastic region of the curve.

Design Terms:-

Ultimate strength is an attribute directly related to a material, rather than just specific specimen of the material, and as such is quoted force per unit of cross section area (N/m²). For example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440 MN/m². In general, the SI unit of stress is the Pascal, where 1 Pa = 1 N/m². In Imperial units, the unit of stress is given as lbf/in² or pounds-force per square inch. This unit is often abbreviated as psi. One thousand psi is abbreviated ksi.

Factor of safety is a design constraint that an engineered component or structure must achieve. FS = UTS / R, where FS: the Factor of Safety, R: The applied stress, and UTS: the Ultimate force (or stress).

Margin of Safety is also sometimes used to as design constraint. It is defined MS=Factor of safety – 1

For example to achieve a factor of safety of 4, the allowable stress in an AISI 1018 steel component can be worked out as R = UTS / FS = 440/4 = 110 MPa, or R = 110×106 N/m².

The Knee And The Ligaments:-

The evidence accumulated in the various phases of this study strongly suggests that the deep-squat exercise, especially as done in weight-training and as used in athletic or other physical conditioning programs, should be discouraged because of its deleterious effect on the ligamentous structures of the knee.

If the ligaments are the first line of defense against knee injury and function in unison with the muscles to maintain stability, then the deep-squat exercise is not a specific exercise suitable to build up strength of the knees since deep-squatting tends to weaken the ligaments and hence m

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