Super Strength/Analysis

Required Secondary Powers
Many characters with super-strength also have super anchoring abilities. This keeps them from being shoved into the ground when they lift up something remarkably heavy, like buildings or land masses. An ability to fly such as Superman's - the ability to support and move your own body in empty space as you wish - could do the trick, as you wouldn't need the ground to support you. A common subversion is a hero that lacks this anchoring ability, thereby heavily restricting what they can lift without sending themselves up to their waist in the ground.

Also, characters that are super-strong but not explicitly Nigh Invulnerable have some level of enhanced resistance in their bones. If their super-powerful muscles were anchored by normal bones, the bones would repeatedly be broken apart by the muscles' exertion (or just constantly pulled off the anchor points, resulting in rather horrific sprains).

To use super strength effectively also requires the ability to strengthen objects by touching them (Unless the object is made of some advanced material, of course). Otherwise, holding up (for example) an airplane with one hand would simply result in a hand-shaped hole in the still-plummeting airplane. This was addressed in the second episode of The Big Bang Theory, as the characters discuss a scene from the original Christopher Reeve Superman movie: "Sheldon: Lois Lane is falling, accelerating at an initial rate of 32 feet per second per second... Superman swoops down to save her by reaching out two arms of steel... Miss Lane who is now traveling at approximately 120 miles an hour hits them and is immediately sliced into three equal pieces...Frankly, if he really loved her, he'd let her hit the pavement - it'd be a more merciful death."

If however he matched her velocity, grabbed her, then started decreasing his rate of descent, she would be OK. The Post-Crisis explanation is given in The DCU that Superman's body emits a "field" that hovers 1-2 millimeters above his skin. Anything within that "field" his superpowers treat it as if it were his skin. Thus his costume (but not his cape, which takes frequent damage) is just as invulnerable as he is, and the field can partially extend its effects into things or people he touches. Perhaps this is how he is able to catch Lois Lane without hurting her, or how he manages to carry her while moving at speeds that would cause her clothes or skin to rip off by the time they reached their destination. Effectively, he provides her with Inertial Dampening. Who knows how many super-strong characters have an undetected version of this?