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It's not either-or. Low-rep (1-5) high weight is for strength. High-rep (8-12) with lower weight is for muscle endurance, but we would never suggest more than 10 reps for any powerlift set.
A typical powerlift sequence is a warm up set with very light weight, then 4-5 working sets advancing to your day's target. For example, lately I have been doing, say, with deadlift (most important exercise, I feel), warm-up set of 5 at about 100, 5 reps at 155, 5 reps at about 180, 1 rep at 200 and another rep around 225. Like I say, I am not a big strong guy. Everybody is different. My one-rep max is probably 245, but I don;t know for sure. My goal is 300.
Many fitness people do a week of high rep every month or two. "Lower weight" is around 60-70% of your one rep max. "Higher weight" is around 80-90% of your one rep max.
As always, there are exceptions, mainly for accessory exercises. For example, for curls or tricep cable push-downs, 10-20 is fine to keep those things "toned".
My take on heavy weights: Pull-ups are heavy weight. Push-ups are just calisthenics. If you can do 20 pullups bravo to you and put some weights on you to be more efficient. I won't do barbell bench or barbell squats without trainer or partner. Without those, I'll do dumbbell bench and kettlebell lunges or squats instead. If no weight station is free, I'll do kettlebell deadlifts or trap bar instead of regular. It's all good as long as it is HARD and makes you want to cry or spout 4-letter words.
Since I only do half of my powerlifts one day, and half of them another day (not ideal for strength but ok for fitness), I fill in my weights hours with accessory lifts to get a full workout. But to be more precise, I also do pullups twice/wk and one day of dumbell bench and another day barbell bench because I want to focus on those right now. There's only so much time to fit in weights, calis, and plain cardio. If a week had 8 days, I'd do another day of weights. It doesn't fatigue you like calis, but it kicks your ass and kicks your mind.
If I could make a suggestion for your deadlift routine, I would try:
100 x 5 (why not 135?)
155 x 3
185 x 2
205 x 1
225 x 5
The work set is what drives the strength increase. A one rep work set is not enough stress to disrupt homeostasis and trigger an adaptation. The warm-up sets are just that, a warm-up to the work set. They don't build strength and you don't want to do too many reps before the work set or the fatigue will interfere with the work set.
Agree! The sets between the warmup and the set or sets at 85/90% of 1RM aren't for building strength. They are to (1) prep you for the heavy set(s) and (2) help you dial in the weight for your heavy set(s) for the day. Doing too many reps only fatigues you - if your only goal is strength.
On the other hand, a strict 5x5 type progression can be useful if conditioning is a goal as well, i.e. being strong when you are already fatigued.
OK, I've dished out some crap in the past, but here's the "beer summit" version:
You've gotta have a face to face with the man in the mirror and ask yourself "What's my goal?" NOTE: I said "goal" as singular, not plural. If you want some secondary goals, that's ok. But keep it to a few, keep them simple and remember that any secondary goals will detract from you reaching your main goal.
Are you looking to get stronger? better conditioned? less fat? OK, define what these terms mean to you - metrics (numbers) are good, i.e. "I want to DL 300#" or "I want to be able to sprint 400m in 90s and repeat that three more times within 20 minutes" or "I want my body fat to be 12%"
If you don't measure it, you won't do it.
Sometimes - especially as you get older - it's better to work on goal #1 first. Once you reach goal #1, do maintenance work for #1 while working on goal #2, etc.
Having a goal is great, but (like RJP said) you also need a plan - a concrete plan with sets, reps, rest intervals, intensity (%RM), days per week, periodization, etc. - not "I'll do heavy deadlifts two days a week and cardio two days a week"
I do high reps on dips (Monday was 17,13,11,9,7 reps) and on assisted pullups--1/5 my body weight as an assist for reps of 10, 10, 7, 7 and 6. At my body weight (200) the dips count as "resistance" exercise.
When moving steel, I do 2 warmup sets and 3 work sets. Last time out on the bench press I did 20 reps at 95 pounds, 11 at 135 pounds and 2 sets of 5 and 1 set of 3 at 170. And yeah, I used a spotter.
For deadlifts I did 20 reps at 135, 8 reps at 225 and the 5,4,3 reps at 265.
Higher rep sets allegedly increase the vascular system, which I figure might be useful in a situation where you are doing something like filling sandbags to stop a flood, or shifting debris to get people out of a collapsed building after a tornado.
Or just shoving 6 or 8 inches of global warming off the driveway.
William O. B'Livion
Dips are an awesome exercise. If you are doing almost 60 reps of shoulder-below-elbow back up to full lockout movements, that's impressive. Ever think about getting a weight belt to make them a bit more challenging and building more strength?
Deadlift for a set of 20? You're a masochist.
If filling sandbags or lifting debris off people is a concern, consider gaining more strength. Each individual sandbag will feel lighter so you can fill more of them and with a 405 deadlift, you'll be able to pull heavier objects off a victim.
I basically follow the Starting Strength regimen. Warm up sets that are not too taxing and then 3x5 for the work sets. I also read a lot on the MusclePhd website. He suggests that since all muscle are made of a fast and slow twitch component that you should vary your workouts by doing both low reps and high reps to target both types of muscle. So, I mix it up. Heavy lower reps for 3 or 4 weeks and switching to higher lighter reps for a couple weeks.
Well, unfortunately the fast twitch muscles we are born with are the ones we have all our lives. Their performance just can't be trained much, being limited by genetics. That's why the standing vertical jump is such a good indicator of athletic success. You can't train it (not much anyway, especially when compared to strength) so it is what it is.