I don't think it ever put a major strain on the marriage- they were very devoted to each other, their's was one of the greatest royal love stories.
Maybe it wasn't how he wished things, but I don't think he ever felt resentment or strain about it, so there wasn't any strain major or minor. Nicholas simply went along with circumstances, and what was part of that, his wife's emotional and physical condition, and Rasputin, etc. He famously said '' Better one Rasputin than ten fits of hysterics a day''. I think he just wanted to avoid trouble, so he never felt any negative emotions towards Alexandra. He was very devoted to her- some might say blindly in matters regarding her health, and her son's health, and thus Rasputin. With lesser marriages, and perhaps most, there might have been a strain, but not with this one.