Armies containing a steamroller or sledgehammer unit like to deploy said unit in a position whereby it is able to see most combat and exert maximum influence. And what better place than right in the centre of the army? Classic strong center units are units like a squad of 4 termies, and a termi chaplain in a Landraider. This squad will pretty much eat anything in the game, but tends to be a serious point expenditure so you want it in the thick of the action. Strong center units do not always need to be hth though. They can also be groups of units like 2 demolishers driving up the middle or with chaos, a unit of bikes turbo boosting into your opponents deployment zone and summoning in a bunch of daemons, aka Deamon Bomb.
A souped-up unit, variously known as a steamroller or sledgehammer tends to cost a lot of points, so a player would naturally have big plans for it. This usually involves being in the forefront of the assault, leading the rest of the army in breaking through the enemy lines. The best place for this is usually in the centre of the line, which leads to the Strong Centre formations.
Strong Centre. The cream of the units are in the middle, the weaker ones play a supporting role from the wings.
Drive a Wedge. The classic attack, breaking through the centre and then turning to roll the line in either direction.
The strong center formation maximizes the potential of your expensive units by placing them where the enemy is least able to avoid confronting them. The spearhead need not be in the exact middle of your line, indeed, it is more commonly slightly off-centre. If timed well the Spear head rolls over much of the army as your opponent is helpless to react to your charge. This form of attack can lead to spectacular victories or disastrous slaughters. Once the enemy centre collapses, he will always be facing an uphill task to hold his army together.
The Empty Centre deployment or Cannae tactic can be employed successfully to counter the central advance. Or if the enemy has strong units (or tarpits) holding his centre (or Lady Luck turns her back on you), you may not achieve the fast breakthrough required, and your spearhead runs the risk of being trapped in and pinched off leaving your supporting units out matched on the flanks and left to die a less than glorious death.
There are not many variations for this formation. It's usually a straightforward frontal assault. You may sometimes decide to vary your choice of which part of the enemy line to target, but beyond that the basic concept is CHARGE!!!! or blood for the blood God etc…
Off-centre Attack. Same principle as Drive a Wedge, but with the spearhead pointed at a slanted angle to catch a weak point in the enemy line.
Held! The Spearhead fails to penetrate and is stranded in no man's land as the rest of the enemy army advance to cut off the supporting units.
The strong center is a simple formation that doesn't require much tactical genius, yet brutally effective. In 3rd ed, the strong centers was the bread and butter of the rhino rush army. In 4th ed, a strong center formation is still a very viable option but is much less effective due to dumbed down vehicle rules and an increase in special movements. A strong center attack does you no good if they teleport in behind your Spearhead and pin you down.