## Non-Linear Response

The focus of these tests are to ensure that non-linearities that are important to the structural analysis of poles and pole lines are thoroughly addressed. How well are the Non-linear Analysis methodologies applied:

- Material Non-linearity of Wire attachments (Non-linear Sags & Tensions)
- Material Non-linearity of Guy attachments (Stretching of guy wires under load)
- Non-linearity/flexibility of attachment supports.
- Non-linearity of member reactions due to structure deflection (Geometric Non-linearity)
- Non-linearity of loads due to structure deflection (Attachment Load Non-linearity).

Non-Linear Sags and Tensions have already been addressed in the Sags & Tension section. The most accurate and expected results will always include the Material Non-Linearity effects of the span attachments.

Guy wire attachments are not normally considered for their material non-linearities in the Structural Analysis of Pole Structures. Guy wires are typically made of steel, which has very small material non-linearity. Also with their typically short length, it is generally considered not significant nor important to include them.

Flexibility of attachment supports such as insulator strings can be important for Transmission Line Structures. Their ability to swing can impact the Sags and tensions of the attached wires, which will change the loads applied to the pole. However, since Quick Pole is focussed on addressing Distribution Pole Lines, this aspect will not be covered here.

### Geometric Non-linearity

This Non-linear methodology is the one most often referred to in Codes. It was developed initially to better assess poles with heavy equipment. However, it was found that all structures are better assessed when this Non-linear analysis method is used. The tests are broken down into those structures without guying first, followed by those that include guying. Without guying, this non-linearity is essentially the familiar P-Delta effect. For Geometric Non-linearity with guys attached to the structures, the change in angle and length of any attached guying is also considered as the pole deflects.

The following non-guyed structure tests are suggested. The loads were carefully chosen to be much less than the buckling capacity of the poles so that geometric effects are measured and not the software's ability to deal with "near-unstable" conditions.

- Use 40ft, 50ft and 60ft poles; classes 4 and 1. Pole Species to be Red Pine with CSA rating for Modulus of Elasticity (8894 MPa).
- Apply a 20,000N vertical load at 2 feet from the top of the pole for the 40ft pole, 15,000N for the 50ft pole and 10,000N for the 60ft pole.. Also place a 1000 Newton horizontal load to help start the reaction.
- Perform a P-Delta Non-linear analysis and note the pole top deflection and the Groundline stresses and moments.
- Repeat these tests using NESC ratings for Modulus of Elasticity and physical dimensions.
- On the 40ft class 4 pole, add one guy at the vertical load attachment height that is at 90 degrees to the horizontal load at a lead of 5.0 meters.
- Note the guy component forces and the Groundline stresses and moments.
- No wind or storm loads.
- No overload factors.

The first set of tests are used to validate the P-Delta like scenarios for both CSA and NESC rated poles.

The second tests are to validate that the software tool does guying non-linearity, which is required to be able to say that the tool performs a full Geometric Non-Linear Analysis. If the tool does not implement this feature, it will only support loads in its original direction plus generate vertical loads. Here is a template file that can be used to collect results.

### Attachment Load Non-Linearity

This Non-linear method captures the changes in the magnitude and angle of the applied loads as the pole deflects. In accordance with popular codes, all other poles are assumed to remain stationary. There are two main scenarios where this additional methodology greatly helps to model the structures more accurately:

- The balancing of inline tensions. Very common in scenarios where the span length on one side of the pole is much different than the other.
- The recognition that wire attachments can also handle some loads that the pole does not need to address all by itself. A common scenario is where two relatively balanced lines attached to a pole cross each other at 90 degrees and the wires can be shown to help support the lateral wind load.

This is an improvement over just doing a Geometric Non-linear analysis as it more completely models how the pole would actually behave with the attached wires. If a software tool cannot address Attachment Load Non-linearity, they should note this in the compliance matrix.

The following tests are suggested to assess the Inline Tension situation:

- Use 40 foot class 4 and 1 poles
- Attach one medium size wire at two feet from the top of the pole.
- Assume the span lengths are 40 meters and 60 meters.
- Calculate the final tensions of the wires on both sides of the pole, plus the pole top deflection and Groundline stresses.
- No storm loads

The following tests are suggested to assess the Wire Attachment carrying load situation:

- Use 40 foot class 4 and 1 poles
- Attach one medium size wire at two feet from the top of the pole with an average span length of 60 meters.
- Place another wire attachment at the same height and crossing the previous at 90 degrees.
- Apply horizontal load in the direction of the crossed wire with a magnitude of 3000 Newtons to simulate wind load.
- Calculate the final tensions of the wires in all directions, plus the pole top deflections.
- ½" ice and -20C storm loads, no wind