The answer is, Yes. Poorly designed Eavestroughing systems can be the reason for the ice damming.
Properly designed Eavestroughing will flow equal amounts of water from every corner of the house. Faster the water exists the roof, less ice there will be.
Downspouts should be installed every 25 feet. Anything longer than 25 feet will force the eavestrough to move away from the Fascia due to the weight of the water/ice. Installing downspouts away from the driveway is also a must to prevent slippery pavement.
Downspouts should be extended minimum 5 feet away from your foundation. If there is a negative Slope, Slope should be graded properly to keep water going away from the house.
There are preventive measures you can take to minimize ice damming if it’s an issue. Heating cables work if installed properly. Plug it in from the beginning of January to March 15 to be safe. I’m not sure how much electricity it will use to stay energized, but either that or you call a professional roofing contractor to remove the ice.
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