wire rope calculation formula free sample

Wire rope is also known by many other names, such as: wire, multi-strand wire, flexible wire, cable, cord, steelcord, etc. but it is essentially a collection of small filaments wound around each other in a manner that largely retains its shape when bent, crushed and/or tensioned.

It is a system for significantly increasing the strength and flexibility of steel wire and is used in almost every important application we see around us. For example: suspension bridges, tyres, brake and accelerator cables (in cars), high-pressure flexible pipes, lifting and rigging cables, electrical conductors, etc. and it comes in many different forms. Fig 2 shows just a very small sample of available designs.

With minor variations, the generally accepted method for designating a wire rope construction in the industry is by describing it numerically. For example:

Whilst "IWRC" wire ropes offer a slightly greater tensile capacity (≈7%) than those with fabric or polymer fillers, the additional strength does not come from the tensile capacity of the core filaments but from improved dimensional stability under load. And whilst they are also much more resistant to crushing, they are stiffer than fibre core ropes and therefore not recommended for applications where tension occurs under bending.

Warrington (Fig 1) is a parallel lay construction with an outer layer comprising wires of alternating large and small diameters, each outer layer having twice the number of wires as the layer immediately beneath. The benefit of this design is to increase packing and therefore strength density, however, unless the different diameter filaments are of the same strength (unlikely), this construction is limited by the strength of the weakest filaments.

Seale (Figs 1 & 2 6x36) is also a parallel lay construction but with the same number of wires in each wire layer. All the wires in any layer are the same diameter. This is an alternative to the Warrington construction, with similar benefits and disadvantages.

Regular lay constructions are used much more widely (than Lang lay) because they have excellent structural stability and less tendency to unwrap under tension (see Rotating vs Non-Rotating below). However, because it has a knobbly (undulating) surface it will wear both itself and any surface over which it is run much more quickly than Lang lay wire rope.

Lang lay constructions have a flatter surface than regular lay constructions giving them better resistance to wear and bending fatigue, especially when made from flattened (elliptical) filaments. They are, however, much less structurally stable and subject to birdcaging if the wire rope is over-bent or twisted against its wrapped direction.

"Regular Lay", multi-strand constructions are normally subject to slightly less rotation under tension (than Lang lay) due to the opposite helical direction of the filaments (within the strands) and the strands (within the rope), however, you can improve their rotation characteristics still further by;

Fillers (Fig 2) may be fabric, polymer or even smaller diameter filaments (e.g. 6x36). Whilst they contribute little to the tensile strength of wire rope, they can significantly; improve performance under bending (fabric and polymer cores only), reduce axial growth, reduce rotation in rotation-resistant constructions, improve structural stability and increase fatigue life.

This filler material should not be included in strength (tensile capacity) calculations, but must be included in those for axial stiffness (extension). If it is ignored, your calculations will reveal excessive extension as the wire rope collapses.

Suspension bridges tend to be constructed from densely packed, single strand plain "Wire Rope" constructions using large diameter galvanised filaments. Little heed is paid to rotational resistance as strength is paramount and once tensioned, they should remain in that loading condition for their design life.

Lifting & winching normally require wire ropes of good flexibility and fatigue resistance. Therefore they tend to be similar to 6x36 but with fibre core instead of the IWRC in Fig 2

Remote operating cables such as hand-brakes and accelerators on cars normally only work in tension so they need to be strong but not necessarily stiff (as they are fully contained in reinforced outer sheaths). These tend to be manufactured from large diameter "TyreCord" or small diameter single-strand "Wire Rope".

Wire rope does not obey Hooke"s law. Therefore, you cannot accurately predict how much it will stretch for any specified force. This unpredictability applies to any section removed from the same manufactured length of cord and even between cords produced to the same specification but by different manufacturers.

CalQlata has decided that the accuracy of axial stiffness (EA) of wire rope falls outside its own levels of acceptability and therefore does not include it in the wire rope calculator. The extension calculated in the Wire Rope calculator (δLᵀ) is based upon the effect of axial tension on packing density. It is therefore important that core material is not ignored when using the calculator to evaluate this characteristic.

Wire rope does not obey Hooke"s law. Therefore, you cannot accurately predict how much it will twist for any specified torque. This unpredictability applies to any section removed from the same manufactured length of cord and even between cords produced to the same specification but by different manufacturers.

CalQlata has decided that the accuracy of torsional stiffness (GJ) of wire rope falls outside its own levels of acceptability and therefore does not include it in the wire rope calculator.

1) No wire rope calculator, whether dedicated or generic, will accurately predict the properties of any single construction under a wide range of loading conditions

2) No wire rope calculator, whether dedicated or generic, will accurately predict any single property for a range of constructions under a wide range of loading conditions

The only wire rope that can be reliably analysed is that which is used for suspension bridges, because; it comprises a single strand, is very densely packed, has negligible twist, contains filaments of only one diameter, is never subjected to minimum bending and every filament is individually tensioned.

There is a very good reason why manufacturers do not present calculated performance data for construction or design proposals, because even they cannot accurately predict such properties and quite rightly rely on, and publish, test data.

During his time working in the industry, the wire rope calculator"s creator has seen, created and abandoned numerous mathematical models both simple and complex. He has gradually developed his own simplified calculation principle based upon his own experience that still provides him with consistently reliable results of reasonable accuracy.

The purpose of CalQlata"s wire rope calculator is to provide its user with the ability to obtain a reasonable approximation for a generic construction, after which, accurate test data should be sought from the manufacturer for the user"s preferred construction.

The calculation principle in the wire rope calculator is based upon changes in the properties of the wire rope that occur with variations in packing density under tension

Bearing in mind the above limitations CalQlata can provide the following assistance when generating (manipulating) the wire rope calculator"s input data and interpreting its output

Alternatively, for wire rope with multiple filament diameters, you need to find an equivalent diameter with the following proviso; you must enter the minimum filament yield stress (SMYS)

It is expected that apart from fillers, all the material in the wire rope will be identical and therefore have the same density, i.e. using different materials will result in less than "best" performance. However, if such a construction is proposed, you can calculate an equivalent density as follows:

It is expected that apart from fillers, all the material in the wire rope will be identical and therefore have the same tensile modulus, i.e. using different materials will result in less than "best" performance. However, if such a construction is proposed, you should enter the highest tensile modulus.

The wire rope calculator simply adds together the total area of all the filaments and multiplies them by the SMYS entered, which represents a theoretical maximum breaking load that would exist if this load is equally shared across all of the filaments and the lay angles have been arranged to eliminate localised (point) loads between adjacent filaments.

If the wire rope has been properly constructed it is likely that its actual break load will be greater than 80% of this theoretical value. However, given the vagaries of wire rope construction, the actual break load can vary considerably dependent upon a number of factors. CalQlata suggest that the following factors may be used to define the anticipated break load of any given construction:

The axial stiffness and strain under load will be affected by this value, hence the reason why the most reliable (predictable) constructions tend to be minimum [number of] strands and single filament diameter. The Warrington and Seale constructions and combinations thereof tend to provide the highest packing density (but lowest flexibility) and there is little to be gained from using these constructions in more than single stranded wire rope as the benefit of high-packing density will be lost with no gain in flexibility.

The anticipated second moment of area of the wire rope at tension "T" due to deformation but insignificant flattening as it is assumed the wire rope will be bent over a formed (shaped) sheave or roller.

The anticipated tensile modulus of the wire rope at tension "T" due to deformation but insignificant flattening as it is assumed the wire rope will be bent over a formed (shaped) sheave or roller.

It is not advisable to induce this bend radius in operation due to uncertainties associated with wire rope construction, especially for dynamic applications. CalQlata suggests that a similar approach to that used for the break load (Fb) above also be applied here, i.e.:

A change in diameter will occur in all wire rope, irrespective of construction, until packing density has reached a limiting value. The value provided in the wire rope calculator is that which would be expected if the construction remains intact at the applied tension "T"

Unreliability of this value increases with complexity in wire rope due to its longitudinal variability and the increased likelihood of premature failure.

The accuracy of this data will range from about ±1% for wire rope with a single strand and a single filament diameter, up to about ±15% for constructions of similar complexity to OTR cord

A change in length of any wire rope will occur due to the fact that the packing density increases with tension. This is not, however, a linear relationship.

This can be an unreliable value as illustrated by tests carried out (by the author) on two pieces of wire rope supplied by the same well-known manufacturer both of which were cut from the same length, varied in tensile capacity by only 1.5%, but the tensile modulus (and strain at break) varied by 34%. Whilst this was an extreme case, significant variations have been seen in wire rope manufactured by a number of manufacturers.

Whilst the wire rope calculator does not calculate axial stiffness (see Calculation Limitations 9) above), CalQlata can suggest the following rule-of-thumb that will provide reasonable results for most constructions at the applied tension "T":

Whilst the wire rope calculator does not calculate bending stiffness (see Calculation Limitations 8) above), CalQlata can suggest the following rule-of-thumb that will provide reasonable results for most constructions at the applied tension "T":

Low complexity means single strand and single wire diameter. Medium complexity means multi-strand and single wire diameter. High complexity means multi-strand and multiple wire diameters.

Wire ropes are essential for safety purposes on construction sites and industrial workplaces. They are used to secure and transport extremely heavy pieces of equipment – so they must be strong enough to withstand substantial loads. This is why the wire rope safety factor is crucial.

You may have heard that it is always recommended to use wire ropes or slings with a higher breaking strength than the actual load. For instance, say that you need to move 50,000 lbs. with an overhead crane. You should generally use equipment with a working load limit that is rated for weight at least five times higher – or 250,000 lbs. in this case.

This recommendation is all thanks to the wire rope safety factor. This calculation is designed to help you determine important numbers, such as the minimum breaking strength and the working load limit of a wire rope.

The safety factor is a measurement of how strong of a force a wire rope can withstand before it breaks. It is commonly stated as a ratio, such as 5:1. This means that the wire rope can hold five times their Safe Work Load (SWL) before it will break.

So, if a 5:1 wire rope’s SWL is 10,000 lbs., the safety factor is 50,000 lbs. However, you would never want to place a load near 50,000 lbs. for wire rope safety reasons.

The safety factor rating of a wire rope is the calculation of the Minimum Break Strength (MBS) or the Minimum Breaking Load (MBL) compared to the highest absolute maximum load limit. It is crucial to use a wire rope with a high ratio to account for factors that could influence the weight of the load.

The Safe Working Load (SWL) is a measurement that is required by law to be clearly marked on all lifting devices – including hoists, lifting machines, and tackles. However, this is not visibly listed on wire ropes, so it is important to understand what this term means and how to calculate it.

The safe working load will change depending on the diameter of the wire rope and its weight per foot. Of course, the smaller the wire rope is, the lower its SWL will be. The SWL also changes depending on the safety factor ratio.

The margin of safety for wire ropes accounts for any unexpected extra loads to ensure the utmost safety for everyone involved. Every year there aredue to overhead crane accidents. Many of these deaths occur when a heavy load is dropped because the weight load limit was not properly calculated and the wire rope broke or slipped.

The margin of safety is a hazard control calculation that essentially accounts for worst-case scenarios. For instance, what if a strong gust of wind were to blow while a crane was lifting a load? Or what if the brakes slipped and the load dropped several feet unexpectedly? This is certainly a wire rope safety factor that must be considered.

Themargin of safety(also referred to as the factor of safety) measures the ultimate load or stress divided by theallowablestress. This helps to account for the applied tensile forces and stress thatcouldbe applied to the rope, causing it to inch closer to the breaking strength limit.

A proof test must be conducted on a wire rope or any other piece of rigging equipment before it is used for the first time.that a sample of a wire rope must be tested to ensure that it can safely hold one-fifth of the breaking load limit. The proof test ensures that the wire rope is not defective and can withstand the minimum weight load limit.

First, the wire rope and other lifting accessories (such as hooks or slings) are set up as needed for the particular task. Then weight or force is slowly added until it reaches the maximum allowable working load limit.

Some wire rope distributors will conduct proof loading tests before you purchase them. Be sure to investigate the criteria of these tests before purchasing, as some testing factors may need to be changed depending on your requirements.

When purchasing wire ropes for overhead lifting or other heavy-duty applications, understanding the safety dynamics and limits is critical. These terms can get confusing, but all of thesefactors serve an important purpose.

Our company has served as a wire rope distributor and industrial hardware supplier for many years. We know all there is to know about safety factors. We will help you find the exact wire ropes that will meet your requirements, no matter what project you have in mind.

Wire ropes are largely used in marine environment or for rigging purposes. They receive considerable loads and thus suffer a great deal of mechanical damage throughout their service life. Moreover, research has shown that the major cause of wire rope failure is excessive deterioration and corrosion, lack of maintenance and inspection, and wrong usage resulting in early discarding, reduced safety and replacement cost increase.

Sometimes damage can be easily detected, while in other cases fractured wires may occur on the inside. Hence, wire ropes should be inspected and maintained by the right person (competent person assigned by the company), to assure they’re in perfect condition. Regular inspectionsensure high rope performance, long service lifetime , safety of personnel and equipment, and reduced operating costs.

All ropes (synthetic, high modulus and wire ropes) should be inspected before and after an operation. This guideline ensures maximum safety for both a ship’s personnel and equipment. Even though it’s difficult to determine the exact service life span of ropes, there is a way to have a more precise estimation about their efficient lifecycle. Calculating the exact time ropes have been in use (e.g mooring time, mooring conditions, weather and tidal conditions) is the answer. All in all, rope inspections should occur at least once a year.

Inspecting wire ropes in particular, comes with great responsibility. Inspection results should be recorded, and any defects noticed have to be reported and addressed properly. Some defects can be repaired, while in some cases replacing a wire rope is inevitable.

Periodical inspections ofvessel deck equipment is also crucial for maintaining the good condition of wire ropes. The condition of the drum, chocks, bitts, rollers, sheaves, cable clamps and other end fittings, affect the rope’s performance, threads and cords. Make sure to mark these parts during your overall inspection.

In order to help marine officers and staff conduct successful wire rope inspections – and keep an up-to-date record of them – we have created an inspection solution that helps in maintaining and monitoring a ship’s ropes and deck equipment.Learn more about Katradis inspection Neptune Solution

When calculating mass using F = Minimum Breaking Force, according to the wire rope’s diameter, you can determine the Minimum Breaking Massand therefore the wire’s max strength. When calculating mass using F = Safe Load according to the wire rope’s diameter, you can determine the Safe Load Mass,which is the advised load for this rope diameter.

The strands of a wire rope absorb the majority of the tensile force applied on the rope. Their design and manufacturing standards affect the level of fatigue resistance and resistance to abrasion. An easy way to understand which rope design is suitable for each purpose, is the wire rope classification.

Wire ropes are classified according to the number of strands in each construction and the number of wires in each strand. For example, a classification of 6X19 means that a wire rope of this type always has six strands, but its wires could be 15-26 per strand. This is because 19 is not the exact number of wires, but the classification of a wire number range.

Visual inspections are a common and fast way to assess wire rope condition. Both the standard and rotation resistant wire rope inspectionprocesscomply with the same four steps of examination. A ship’s crew can perform them as follows:

Steel wire rope distortion is obvious in most cases and can easily be identified by the inspector or the ship‘s crew. It usually occurs if load is suddenly applied or abruptly released (shock loading), or even if swift torque is forcefully induced.

Although not all of these deformations make the rope absolutely dangerous to use, they all may cause ropes to wear unevenly in time. This means inspections should take place more often, and distorted ropes should be handled with caution.

The rag and visual inspection is a good method for regular inspection intervals. The inspector pulls a rag along the rope trying to find broken wire cords. If the rug gets snagged by the rope, the inspector has to stop and assess the wire rope’s condition. Extreme caution should be exercised during the visual inspection, and under no circumstances should this method be the only one used to inspect wire ropes.

Tip: When you encounter a protruding wire end, bend it back and forth manually, until it separates from the wire. This will protect neighboring wires from wearing out.

Diameter reduction is a critical factor in steel wire rope wear and if not properly taken care of, it can result in rope breakage. Excessive abrasion, loss of core mass, corrosion or inner wire failure are all factors that contribute to diameter reduction.

To get an accurate measurement of the rope’s diameter, measure the rope at three different points at least 5 feet apart. Take the average of these three measurements to determine the true diameter.

Any measurements showing a reduction of ⅓ or more, indicate that a replacement should follow without delay. A diameter reduction of less than 1/3 still requires attention, and the inspector or the ship’s crew should be on guard in the next scheduled wire rope inspection.

Failure from abrasion or corrosion is a result of deficient deck equipment inspection or insufficient wire rope lubrication respectively. Internal corrosive damage is more difficult to identify than any other types of degradation. In most cases, the damage has progressed more than the external signs suggest.

Wire rope storage plays a significant role in the rope’s operation life.Wire rope corrosion and pitting can be avoided if ropes are safely stored in a clean, cool, dry and well-ventilated place. Steel wire ropes should not by any means rest on the floor, and should be protected from water, dust or any chemical fumes. Long term storage requires periodic greasing, turning the reel upside down for preventing grease dripping and possibly re-winding to another reel with larger inner tube diameter.

Wire ropes should be maintained with periodical lubrication. In order to prevent internal corrosion, a pressure lubricator is suggested to be used. In this case, a small amount of grease is used to lubricate the rope internally, while the deck stays grease-clean. Pressure lubricators clean the rope before they grease it so that the new grease enters a clean rope. The type of grease used is very important for maximum protection and greasing efficiency.

Steel wire ropes exposed to dirt, grime and other contaminants, have to be cleaned with a wire brush and petroleum (unless a pressure lubricator is used). Optimal cleaning of wire ropes can extend their service life and guarantee safe operations.

The reeling process is of high importance for the longevity of wire ropes. To protect them from being damaged, it is important that the surface of the drum is clean, smooth and dry. Improper reeling may cause wire-rope strands to spread or get flattened, when in contact with one another, as successive layers are being spooled and upper layers apply pressure on the lower ones.

Katradis S.A. offers a wide range of top quality wire ropes for shipping (mooring and hoisting operations), fishing and construction purposes. Our wire ropes have greater resistance to fatigue, and they distribute tension force equally among the rope strands. They are less likely to kink, providing higher staff safety and assuring operation success.Choose your new wire ropes

Structural Stretch is the lengthening of the lay in the construction of cable and wire rope as the individual wires adjust under load. Structural Stretch in Loos & Co., Inc. products is less than 1% of the total cable length. This form of stretch can be completely removed by applying a cable or wire rope prestretching operation prior to shipment.

Elastic Stretch is the actual physical elongation of the individual wires under load. The elastic stretch can be calculated by using the following formula*:

Enter the diameter of the wire rope, in mm, into the calculator to determine the safe working load (SWL). This calculator is for education purposes only, follow manufacturing guidelines for true SWL values.

A safe working load of a wire rope is a measure of the total load or weight that a wire rope can safely support during operation. Values greater than the SWL could result in a failure of the rope.

We can see in the illustration below that the force, F, needed to lift the object is equal to the weight, W, of the object. This idea is the fundamental concept that underlies our tension force formula. Also shown below is the free-body diagram of the object which shows the tension forces, T, acting in the string. As you can see, the tension forces come in pairs and in opposite directions:

where weight, W, becomes negative since it is directed downwards. By transposing W to the other side of the equation, we can now see that the tension force in the rope is equal to the weight of the object it carries, as also shown above.

If we use more ropes to lift the object, the total tension force gets divided up into the ropes. The tension force in each rope depends on their angles with respect to the direction of the force it opposes. To further understand this, let us consider another free-body diagram of an object suspended by two ropes, as shown below:

Now all you need to know are the angles of the tension ropes with respect to the horizontal. If an angle from the vertical is given, just subtract this angle from 90°. Doing so will provide you with the angle from the horizontal. However, if you are given other values of angles that may be greater than 90° or even 180°, you might want to check out our reference angle calculator to help you determine the angle you need. After determining the values for the variables in our tension force formulas, we can now solve for the tension forces.

The main goal of this book is to present the methods used to calculate the most important parameters for ropes, and to explain how they are applied on the basis of numerous sample calculations. The book, based on the most important chapters of the German book DRAHTSEILE, has been updated to reflect the latest developments, with the new edition especially focusing on computational methods for wire ropes. Many new calculations and examples have also been added to facilitate the dimensioning and calculation of mechanical characteristics of wire ropes.

This book offers a valuable resource for all those working with wire ropes, including construction engineers, operators and supervisors of machines and installations involving wire ropes.