Stair Climbing Benefits. Strengthening the muscles around the knee will decrease the stress or strain on the joint itself. These muscles include the quadriceps at the front of the thigh and the hamstrings at the back of the thigh.tair Climbing Benefits. Strengthening the muscles around the knee will decrease the stress or strain on the joint itself. These muscles include the quadriceps at the front of the thigh and the hamstrings at the back of the thigh.