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I already stalked you and found the pictures you posted of your deck a while back... Unfortunately I don't have enough clearance to run a beam under the joists otherwise I would definetly do it this way.
Regarding oak posts, I found a few places selling oak posts cut to 4x4 in actually, but they don't look like the best quality timbers, and I'd have to drive out to collect them so am debating using PT stuff with post savers. Didn't know concrete was an option so will investigate that.
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Ah yes, did wonder about your clearances.
These are the concrete posts, we didn't use them as would have to get them at the right level, which we couldn't be bothered to do! http://www.chilterntimber.co.uk/product/decking-concrete-deck-post-100-x-100mm/
If you like I can send you the plans for our deck which were done by a professional. we used 6 x 2 for the framing and instead of using noggins we ran the cross beams underneath the main beams, as apparently this gives more strength, but does depend on the clearance you have.
As with all decking the point of weakness will be the posts into the ground, there are a few options you can use to help this
We went with upgrading the wood, and got oak sleepers which we got ripped in half down to 4x4 and then also pot postsavers on them as well for belt and braces.