What is a good exercise for upper body strength/arm strength without weight machines?

I do allot of exercises everyday, push-ups being an example. I do 30-35 a day in sets of 3. I increase this number every week but is this alone good enough for upper body strength or arm strength? I don`t have the luxuries of going to a gym or buying a dum-bell/weight machine set because I am not rich. Is there ANY other exercise I can add on to my day that would give me upper body strength without buying anything? The reason I ask this in military is because I would like to join the AF one day. Answers are appreciated