Assuming you complete a vocal warmup, I'm wondering how you know when you've overdone it and should stop singing.
Is it normal to feel a bit of strain in the vocal chords? How much strain should you feel?
If you are feeling strain, then you're doing it wrong.
Since starting with a vocal instructor, I can sing 30 minutes-60 minutes without feeling strain. A feeling of strain used to onset within 5 minutes of singing.
I'm going to try to describe what I learned, but this should only serve as motivation to get a vocal instructor to teach you. Really it comes down to sounding your vocal chords, without involving other muscles of the throat. But you will never get it unless you sit there with a piano and an instructor and she listens to how you sound and corrects you and tells you what you're doing wrong.
You probably cannot learn how to sing without a teacher to show you. Even if you can, getting an instructor will greatly accelerate your learning.
Yes they are expensive. But if you want to sing, you really need one.
My advice in selecting a vocal coach:
First, I've been a professional musician, but I'm not a professional singer - nonetheless, I've recently started working with a teacher that has made a huge difference in my singing, and the lessons are fresh in my mind.
The trick, I believe, is learning to tell the difference between your voice being tired vs. strained. If you are straining, you are tense, you are not getting "good exercise", and pushing more may damage things - you'll have hoarseness the next day, or worse. But if you are simply tired, your voice will recover fully after a good night's sleep, and you will have taken yourself far enough past your to be strengthen it in the long run.
So how do you tell? For me, the sensations are similar, but very distinct. For one thing, strain comes on much more quickly. And I can usually think back about how I have been singing that would lead to stress. And if I've been rehearsing for hours, and the rest of my body is fatigued (good voice teachers will tell you that your whole body is your instrument), well, that's a clue. So just deciding that you are going to learn to tell the difference between the two sensations is a huge step.
A good trick for checking your tension is to put one palm on either cheek, and drag them downwards, caressing your jaw and throat, feeling the tenseness drop out of your face and neck.
In the end, I've been told by several professionals that a good warm-up is the best protection against strain. And then there's all that business about "support" and so forth that I'm working on with my teacher...