In Spain (or at least where I live) "escaleras" means stairs, and "escalera" means both depending on context. "Escalera de mano" is the ladder-specific word.
"Voy por la escalera" sounds fine to me if you're taking the stairs.
EDIT. Another example: when a building is divided in two stairs (left and right) we mark it as "Escalera Izquierda" and "Escalera Derecha".
"Voy por la escalera" sounds fine to me if you're taking the stairs.
EDIT. Another example: when a building is divided in two stairs (left and right) we mark it as "Escalera Izquierda" and "Escalera Derecha".