The guy wire pretension can have a big impact on the behavior of the guy wire supported system. The guy wires help resist the lateral loads (Wind, seismic) applied to the stack.
A guy wire is on an incline, and so any tension in the guy wire creates a Horizontal and Vertical force component. The horizontal force component is desirable, because that is what is helping resist the lateral loads. The vertical component is not very desirable, it doesn't really provide any benefit to the system it only adds to the vertical compressive load on the stack and increases the foundation loads.
Thermal Expansion:
Many stacks contain gases which are at a temperature greater than the ambient temperature. When the stack is exposed to a temperature it will experience thermal expansion. If the stack is tall, and the temperature is significant, then this thermal expansion can be significant. When the stack has guy wires the thermal expansion is being resisted by those guy wires. This will increase the vertical component of the guy wire forces and the stack loadings.
This effect can be significant and can be further impacted by the following factors:
- Deadman Radius -When the deadman radius is decreased, it causes the vertical component of the cable tension to be higher due to trigonometry. Since the vertical component is larger, the horizontal component is smaller. That means we have less resistance to the lateral loads, which is the whole purpose of the guy wires. A rule of thumb is that the deadman radius should be 0.7 multiplied by the stack height.
- Guy Wire Material - Generally there are two types of guy wires, Wire Rope and Structural Bridge Strand. Wire rope is relatively flexible, while Structural Bridge strand is very stiff. The modulus of elasticity of wire rope is about 1/2 of structural bridge strand. While the structural bridge strand can be desirable because it is very strong and helps reduce lateral deflection of the stack, the negative consequence is that it increases the tension due to thermal expansion and it increases the undesirable vertical component of the cable tension.
As stated previously the main purpose of the guy wires is to help resist lateral loadings on the stack. That means that the guy wires also help reduce the lateral deflection of the stack due to those lateral loads. To be most effective we want the horizontal component of the cable tension to be greater, and the vertical component to be lessor. Just as with thermal expansion, a deadman radius that is too small will negatively impact the lateral deflection of the stack under later loads. In addition, a guy wire that is stiffer will help to reduce lateral deflection of the stack. The cable stiffness can be increased by the use of a stiffer material, such as by using structural bridge strand. The stiffness can also be increased by increasing the area of the cable. While increasing stiffness will help to reduce lateral deflections, both will negatively impact the response of the stack to thermal expansion by making the vertical component of the guy wire load greater.
Deflection Limits:
A guy wire supported stack is very tall and slender, and it is important that you use a realistic deflection limit in trying to limit your lateral deflection. Meca recommends H/100 (12 inches per 100 ft), and have seen this used on many stacks with great success. Many specifications give a standard deflection limit of H/200 (6 inches per 100 ft) for stack design, and then they just blindly apply that same criteria to guy wire supported stacks. The believe they are being "conservative", but they are really only hurting themselves. The guy wires must be made very stiff in order to keep the deflection limit that low, and the pretension may be higher also. If the stack is hot, these stiff cables are now introducing a huge vertical component into the guy wire loading. These vertical components are going to be introduced to the deadman design as well as the stack foundation design, and it's going to present a major challenge to the designer of those two components of the system.
Realistic Temperature:
When designing the stack we consider a "design temperature", which is generally a conservative estimate of the maximum temperature that the stack will experience. Material properties decrease as temperature increases and so it is important to consider this temperature in the design. Most engineers understand the decrease in material properties, but they don't usually consider the negative effect the design temperature is going to have on their guy wires and foundation. Stacks are usually controlled by design wind speed, which can be an extremely high wind that has a low probability of occurring. When it does occur there will be significant cooling of the stack shell due to the high wind velocities. In many cases it is probably not realistic to think that the steel temperature is going to be at the design temperature during this extreme wind event. While it is definitely conservative to consider the design wind and design temperature occurring at the same time, it just may not always be a realistic assumption. If you have a high design temperature and are having problems balancing the requirements, you might consider the design temperature and whether it is realistic.
Non-Linear guy behavior:
Guy wires are not linear due to the sag that is in the cable. As the guy becomes more taut and the sag is reduced then they start behaving more linearly. The transition from non-linear to linear typically happens at a tension of around 10% of the breaking strength. This can be a factor if trying to balance between reducing lateral displacement and minimizing vertical loads. As you increase pretension you are getting closer to this linear transition where the cable is going to effectively be "stiffer".
Pretension:
Selecting guy wire pretension can be difficult because we are balancing these competing interests. Most guy wire pretensions fall in the 6% to 12% of breaking strength, with the majority falling in the 6% to 8% range. There are exceptions that may cause you to go outside of this range, but it is rare. The only times we have seen designers go below 6% is when they have a very tall hot stack. In this case they might use a large diameter cable to help control lateral deflection and then lower the pretension so that the vertical components were not excessive. If a stack has a relatively low design temperature and you are trying to reduce lateral deflection, then you might go to the upper end of the range for pretension. This allows you to get into the linear range of the guy wire and maximize the stiffness of the cable for a give diameter.