Gauging the strength of an old tree

The ~60 year old mulberry tree in my back yard has developed two large dead limbs. It's clear the tree will have to come out eventually, but it still yields useful shade, so I'd like to keep it as long as possible.
Simply cutting off the limbs will badly unbalance the tree and so long as they're not rotten they'll still provide support to the branches cabled together. Tapping on the buttress roots and the trunks suggests the is mostly solid, with a decayed core.
Are there any accepted tests for stability (pulling on lines to the crown, or pushing on jacks applied to the trunk, for example) that can be used to gauge the stability of the tree as a whole? Obviously, if a tug on the crown tips the base of the trunk, it has to come out now. If a pull or push on the upper part of the tree doesn't disturb the root crown there's some hope of another year or two of shade.
A set of photos is at http://www.zefox.net/~bp/mulberry/ The images can be laid out something like
westlimb eastlimb crown trunks base to get an overall view if you're curious.
I had the cables installed in 2009 and the tree grew vigorously until the middle of this summer. Even now, the surviving limbs are well-leafed and seem healthy, thus my desire to save what I can as long as I can.
Thanks for reading
bob prohaska
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On 28/08/18 00:38, bob prohaska wrote:

Are those power cables the east limb overhangs? And do any of the affected branches overhang the building shown in mulberry_base? If so, what damage would be done if the limbs broke and fell?
Have you considered replacing (or at least planting nearby) with eucalyptus? They are very fast growing and will give decent shade all year round if you want it as they are evergreen.
--

Jeff

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Yes, but they're only 240 volt feeding only my house.

With the present cabling no limbs can reach the house. If the affected limbs are removed entirely that'll remove the protective cabling. Cutting the limbs off above the cables might be an option, if they're still sound. Thus my question about gauging the soundness of the tree's structure.

Eucalyptus is out of favor in this area (southern Sacramento Valley), and I'd prefer deciduous trees for shade in summer and sun in winter.
Successor trees are already growing, started about ten years ago. Once the mulberry is out I'll just have to wait for the replacements to grow. It'll be about ten years before they reach useful size, given normal rain. Any extension in the useful life of the mulberry would be helpful, but I know it has to go away before I do 8-)
Thanks for reading,
bob prohaska
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On 8/27/2018 4:38 PM, bob prohaska wrote:

A decayed core means your tree is already seriously compromised. I would have it removed immediately.
--
David E. Ross
Climate: California Mediterranean, see
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On 8/28/2018 4:51 PM, David E. Ross wrote:

I would remove it too. Since it threatens the power lines the power company may do it gratis. Just happened to a friend but power company would not remove it until it fell since it would be cheaper. It was in his next door neighbors yard and hit by lightening knocked part but did not cause outage. It damaged my friends fence. The power company removed all of the tree and fixed the fence.
Also sometimes an insurance company will have it removed if it might cause more damage than it costs them to remove it.
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