# What is the Breaking Stress of Steel Ropes for Lifting Heavy Loads?

• karmatic
In summary, the problem is that the max stress of 714MPa is much higher than the actual stress being applied to the ropes, which is a problem because the option with the smallest diameter is being used and the calculations are based on the maximum mass for the lift.
karmatic

## Homework Statement

Select a suitable steel rope to suspend a lift from a winch. The weight of the lift is variable as is the weight and diameter of the ropes the lift is suspended from. As an example, I'll use 13mm for the ropes diameter and 0.63kg/m for the rope mass, the total length of the rope at its longest is 37m. The lift mass will be 11,563.1646 kg. I must use at least 3 ropes to suspend the lift. The maximum breaking stress of the ropes is given as 714MPa and I must use a safety factor of 10!

## Homework Equations

P=F/A or P=M/A
Area of a circle=Pie x R2

## The Attempt at a Solution

First I want to know the total weight of the lift plus ropes to calculate the force acting on the rope.

37 x 3 x 0.63 = 69.93kg

69.93kg + 11,563.1646kg = 11,633.0946kg total weight of lift and ropes.

Next I need to divide the mass by the cross sectional area of the ropes. Now I am unsure of whether to use the area of one rope or to multiply by 3 for the total number of ropes. Either way, the cross sectional area of a single rope is given by

0.0065m x 0.0065m x 3.14 = 1.32665m2

Now to calculate the total pressure acting over that area I divide the total mass by the area.

P=M/A
P=11,633.0946/1.32665
P=8768.774432Pa

Now I multiply that answer by 10 to calculate the final answer after applying the safety factor of 10 and I get 87,687.774432Pa.

Assuming this is all mostly correct, the problem I am having is that the max stress of 714MPa is way way way higher than the actual stress being applied to the ropes. This is a problem because I am using the rope option with the smallest diameter listed in my problem description, and calculating the total stress using the maximum mass for the lift that I have worked out. So I am assuming I have made a simple mistake in the calculations along the way...

But where is it?!

You forgot to multiply the mass by g to get the force in Newtons (you are using mass units instead of weight units).

what does G represent, force due to gravity?

the 'g' represents the acceleration of gravity, 9.81m/s^2 in SI units, on the surface of the earth. An oject of mass m, in kilograms, has weight on Earth of _____, in units of Newtons.

thanks a lot for that, i think i have it worked out now =)

## 1. What is the definition of steel rope breaking stress?

The breaking stress of a steel rope refers to the maximum amount of tensile stress that the rope can withstand before it breaks. It is a measure of the strength and durability of the rope.

## 2. How is the breaking stress of steel rope determined?

The breaking stress of steel rope is determined through standardized tests where the rope is subjected to increasing tension until it breaks. The resulting force at the point of breakage is then recorded as the breaking stress.

## 3. What factors affect the breaking stress of steel rope?

The breaking stress of steel rope can be influenced by various factors, including the type and quality of the steel used, the manufacturing process, the diameter and length of the rope, and the environmental conditions in which it is used.

## 4. Can the breaking stress of steel rope be increased?

Yes, the breaking stress of steel rope can be increased through the use of higher quality steel, improved manufacturing techniques, and proper maintenance and care. Additionally, using thicker and shorter ropes can also increase their breaking stress.

## 5. What are the consequences of exceeding the breaking stress of steel rope?

If the breaking stress of steel rope is exceeded, it can lead to the rope snapping or breaking, which can cause serious injuries or accidents. It can also result in costly repairs or replacements and downtime for equipment that relies on the rope.

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