Like the title says....stuck case at the range today,  ended my day right then.

How do I get the damn thing out without causing any damage?

Push it out with a cleaning rod?

This is an excellent example why sectional USGI rods - while not being the best cleaning tool - are a good thing to have on hand.  And broken shell extractors.

yep...works like a champ. Recommend a one piece rod

Lemme guess....Wolf?

I tried a cleaning rod...a cheap one...it bent and I put some pretty good pressure on it.
Tapped it on the ground

Yes WOLF, polymer coated....first problem in 500 rounds or so....

I'll have to get a stronger rod and try tapping it out.

Just use a GI M-16 Cleaning rod, and push it through. If you use a regular cleaning rod it will bend and possibly break.
 

I find holding the rod off the case a quarter of an inch or so then giving it little more than a tap with pop the case right out

you can go to lowe's or home depot  and get a solid brass rod , i keep one in the truck  they work great.

get a USGI rod and tap it out. then use the chamber brush from the same kit















 

If you still have trouble, I know people use a dowel rod to knock them out.  It won't ding up your barrel and shouldn't break if you use the biggest one you can find that still slides down easy.

Worse case scenario I have had to correct.
1. Remove most of the broken and jammed bits of various rod material owner used and broke while trying to tap case out.
2. Remove barrel from upper, drill out bottom of damaged and punched through case head, carefully insert a screw extractor and use a BFH to whack on Tap Handle and drive the remains of the case free of the chamber.
3. Remove rest of material jammed into barrel bore, clean and scour bore and chamber, lap barrel to reduce scratches left by materials jammed into barrel bore.
4. Reassemble everything and test fire.

Best case scenario
1. Stand upper muzzle up and fill bore with a good penetrating oil, about 2 ounces of oil is all that is needed, I like KROIL Oil for this, let soak for about 20 minutes.
2. Insert solid brass rod turned to .224 diameter into bore
3. Tap rod sharply, hydraulic pressure of the oil forces the stuck case out.
4. This won't work if you have punched through the bottom of the case trying to drive it out with a too small rod plus if you do drive the case out it sometimes becomes hopelessly stuck on the rod.

Best prevention method.
Keep a one piece rod and oil in your shooting kit.
If a case becomes stuck at the range, drizzle a bit of oil down the muzzle and use the rod to tap the case free.
Stuck cases are usually much easier to pop free while the rifle is still hot and the metals are expanded.
Once the rifle chamber walls and the cartridge case cool and contract they tend to stick to each other like high quality glue.HTH

This, in spades.

I have a collection of "oops, I lost a section" range pick ups, plus a handle section.  It's in my range bag for just such a purpose.  I have yet to see a shell come apart and leave anything in the gun, but I can see that happening-I may be buying a broken shell extractor for the range bag with my next Midway order.

spray some penetrating oil on it from the chamber and down the barrel (liberally).   let it soak.

put your cleaning rod in (preferably the thicker, HD kind) or a similar wooden dowel - $0.50 at the depot stores).

Tap with hammer until case pops out.

for really stubborn ones, You can heat the steel casing with a propane torch for a short period (to get the case hot) - it will expand and contract at different rates than the chamber, then repeat with penetrating oil and cleaning rod.   Your gas tub can get so hot it glows, think about how hot the barrel gets at the chamber and the aluminum upper adjacent to it; mild heat is no big deal here.  

Go slow, think about it, and be patient.   It will come out.

After I got home from work today I went out to the shop and cut a length of stainless rod, not sure the diameter but less than .250 and more than .187.

Sprayed some Deep Creep down the barrel and a couple light taps and it popped right out....the edge of the shell at the extractor was broken off.

You are probably very careful but I would not use a steel rod in the barrel.  Get a brass rod from Lowe's.