Intimidation by strength doesn't make much sense, since a character's strength score isn't the main determinant of someone's ability to beat you up in DnD. Certainly a 10th level fighter could kick a 1st level barbarian's butt. Would the barbarian's 18 strength really allow him to cow a fighter with strength 10. I think not, since the fighter could easily avoid the barbarian's blows, and could probably put on a display of prowess with his weapons that would make bending an iron bar seem really unimpressive.
What about a wizard? Meteor Swarm makes the barbarian's strength look pretty pathetic. Should the wizard get a bonus because of that?
Intimadation is the ability to cow someone, and bring them under your sway with force of will alone. This is related to being scared of physical force, but certainly not the same. If someone intimidates you, then you would listen to them even if they can't kill you, because their charisma has overwhelmed your natural ability to rationally assess threats. If you are scared of physical danger, and back down from a situation, that is different because you are still making fully rational decisions based on a threat assessment.
I think maybe a better example of intimadation would be comparing Worf and Captain Picard. Actually not, because Worf is pretty charismatic too, but I think Picard is a great example of someone who is intimidating without being a huge physical specimen. If you had a phaser pointed at Picard, he could probably stare you down, and threaten you, and make you think the best thing you can do is give him that phaser. Worf is a pretty scary guy, but you'd probably just end up trying to shoot him.