Most people don't climb long enough to wear out their back muscles. But they do get a workout when climbing steep roads, as the lower back muscles are used when climbing.
If you haven't experienced this, go out and do a 2-hour climb seated. Your back will be tight.
I make a point of standing every few minutes on a climb, or whenever I feel my back start to tighten up. It helps immensely.
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Ride, Rest, Repeat. ROUVY:
terrymorse