Sags & Tensions of Span Attachments

Now that we understand how a material will respond to changes in loads and temperature, we need to use this to determine the Sags and Tension values we are looking for. The first question then should be "What are you looking for"? Code requirements of the NESC and CSA will identify some design requirements that you need to meet, but can be less specific on how to calculate them. Each code set will specify certain load cases and require that the design requirements of the standard be tested against all possible conditions (for that requirement). The end result is that just one calculation for sag and tension of a wire or cable is always inadequate. Several values must be calculated for evaluation against the various code requirements. For instance, maximum sag never occurs under the same load conditions as maximum tension.

One thing you should note from the Material discussion is that finding the worst load condition (as seen from the material's perspective) is highly important as that helps define the "Final after Load" conditions for the wire or cable. The extent that the material experiences the plastic region of the Initial Curve has a significant impact on Final after Load values. The higher it goes on the curve, the more permanent stretch there will be. The temperature and load experienced under every-day conditions (assumed to be 10°C for most cases), defines the "Final after Creep" values.

So we have three different curves (Initial, Final after Load and Final after Creep) for how this material behaves. Which one should we use? The answer is all three, as the design requirement is to meet the code requirements under all expected conditions. Load conditions plus material conditions. Let's review each of these expected conditions in the material:

1. Initial. The day after a wire or cable is strung; it could experience any of the expected load conditions, from no loading to maximum loading.
2. Final after Load. The wire or cable may have experienced a maximum loading condition already. Some permanent stretching has occurred.
3. Final after Creep. The wire or cable may have never experienced a significant loading event in its lifetime, but has existed for several years undergoing some amount of creep. The actual amount of creep could be anywhere from none (which follows the Initial curves) to a maximum predicted value, dependent on the length of time since it was first installed.

As you can see, you must calculate sag and tension values using all three curves and then test the worst value against the code requirements for all load conditions. This is because the wire or cable could be in any one of these states or some variation of the three. To meet code requirements you must test against all expected conditions in the material and these three curves are the major variations recognized in the Industry all over the world. Determining values using each curve individually establishes the maximum values for that scenario. Since actual wires could be in a state that is a mixture of these scenarios, using the three curves ensures that the worst case condition is always used for testing against code requirements. It also ensures that your design will be compliant with today's code not just for today, but for the expected lifetime of the structure . Since the actual occurrence of specific load conditions are not predictable (since weather is involved), this approach ensures that all realistic scenarios are included when testing against code requirements.

To determine the Creep curve, you must know the stress value expected on the Initial curve under everyday loads (no wind or ice, 10°C; for example). Find this spot on the Initial curve. Then use the creep polynomials to estimate the amount of strain after creep. This will be either equal to (low probability) or greater than the strain value from the Initial curve. Now draw a line through this point that parallels the Final Load curve. The slope of both of these lines is equal to the Final Modulus value for that material, which is provided by the manufacturer. For any load condition expected on the Creep curve that is higher than the point where it intersects the Initial curve, the Initial curve is expected to be followed.

After now establishing the three curves (Initial, Final after Load, Final after Creep), we can now proceed to answer any of the code requirements that we have. Remember, for each requirement we must use the worst value expected of all real load and material conditions. For an example, what is the maximum sag for the wire we evaluated? This would typically be for ground clearance requirements. In essence you need to test all possible load conditions required for code compliance, plus any other you feel are warranted. For this requirement there are a few conditions that are typically the most significant:

1. Thermal conditions – the maximum sag at the thermal temperature for the wire of any of the three curves. Often the thermal temperature is 50C, 80C or 100C with no wind or ice. The sag value required is the maximum value obtained from any of the three curves.
2. Maximum Sag with Ice at the highest temperature – this is most often a condition where ice is formed on the wire, the wind is low or zero and the temperature is as high as can be expected with the ice still attached. The circulating air temperature can be higher than the wire, but it is the wire's temperature, not the air, which determines the thermal elongation of the wire. In many locations this is 0° C, no wind and maximum ice. The sag value required is the maximum value obtained from any of the three curves.
3. The codes will specify exact temperatures to evaluate some of the requirements, such as mid-span separations of attachments on the same line or crossing over/under others. These may vary based on the type of wire or cable. The same process would be applied for those temperatures and load conditions, looking for the maximum/worst value from all three curves. Although in these examples we were interested in the resulting sag values, the same process and rationale is used when looking for maximum tensions for assumed structural loads.