Here is a close up of the leaves.

This is the side that is dead.

It could be this one - or not. There are over 700 varieties of eucalyptus trees. If you're near a reputable nursery, take a piece of limb w/leaves in and see what they say.

Welcome to the forum! We've just been having a discussion about trees, including the very negative characteristics of eucs. I would definitely cut that dead limb off **but** I'd call out a good arborist for advice on 'pruning' the rest of the tree. Looks like it really needs some growth taken off. However, you'll find many people here who think your best bet is to take the whole thing down. Those trees really are too big for urban yards. I've learned that the hard way.

Here is a link that might be useful: eucalyptus radiata

Thank you for the welcome and advice!

It is a big tree but love it for the shade, however it is VERY messy.

This is a guess, but I think this may be Eucalyptus camadulensis also called Red River Gum. It could also be Eucalyptus rudis or Eucalyptus erthrocorys. When it blooms you'll be able to narrow it down by flower color.

Your tree's leaves look chlorotic (yellowing tissue with green veins) so try using a little chelated iron. Chelated refers to the product being water soluble. It's usually available in liquid form that you dilute and apply to the soil at the drip line and not next to the trunk.

As far as the dying/dead branch - I would take it off where it intersects with the main trunk. You'll need to follow proper pruning techniques and not cut too close to the trunk or leave a stub. Wait until fall to do this - it's just too blasted hot right now and the reflected heat and light from your sea of gravel can sunburn other parts of the tree.

NEVER top a tree. I causes multiple shoots to grow where you made the cut in sort of a Medusa style that compounds the weight of the branch. Plus these adventitious shoots are weakly attached and can break easily in the wind.

After pruning your tree will eventually fill in the void left by removing the dead branch.

These trees like deep, infrequent irrigation. This time of year water once every two or three weeks to a depth of 2 - 3 feet. If you use a hose, place it on the ground at the drip line (edge of branches) and let it trickle overnight. You'll probably need to move it to another side of the tree and repeat on the next night, and perhaps even a third night. Water going through a hose slowly during the day is too hot so wait till after sunset.

Here is a link that might be useful: Pruning, Planting and Care

aztreelvr thank you very much for all the useful info!

It looks a lot like the one I still have which is e. rudis. At least one half of it is. I'm curious; do you know how old it is?

tomatofreak, I am not sure how old it is. We have only been in this house for about 4 years and it was big when we moved in. It will flower yellow....does e. rudis have yellow flowers? Do you know how old your tree is and how big?