How to increase your strength without lifting more weight
On the face of it, it seems obvious; if you want to build your strength you just need to increase the weight you are lifting and do more reps. It's not the only way to strength build though. Here are some tips that just require tweaking your technique and will bring fantastic results.
Vary your range of motion
From the squatting position, push up all the way to the point where your elbows lock out and spread your shoulders wide. With pull-ups, try to pull the chest as far as you can to the bar rather than stopping at the chin. You won't be able to as many reps pushing yourself this way but it'll be building your strength up brilliantly.
Change the leverage
Think about doing a push-up from your feet being on an elevated position compared to a starting position on the ground. From the ground, much more weight is exerted on the chest, shoulders and arms. Just by changing the leverage, the challenge increases and this builds up your strength more effectively.
By rushing through reps it's easy to get sloppy as you strive to just increase the number. Quality is definitely more important than quantity and by slowing down the reps you maximise the resistance out of each rep and increase the tension which activates the muscles far more.
The secret to strength building is not simply about doing more or lifting more, it's about doing it better. Improving your technique by varying your motion, changing and manipulating your leverage and slowing down your reps will push the body more and build your strength more effectively.