Embedded tube support in concrete slab

First suggestion is ACI app. D type analysis.

Is this an accurate depiction of the condition, where the embedded steel element serves as an extension of the slab to a support?


If so I see the force transfer requiring internal development of compression bearing stresses to form the couple required to have the steel act as an extension of the slab. A Strut-and-Tie approach may be appropriate in this case.

Yes, this is the case. Basically it is solved like a simply supported beam with a cantilever part. Then reinforcement to hang the tube to the slab reinforcement designed for the support reactions of the notational beam. The end, but...


... I dislike couple of things in the design flow:
- thickness of the slab doesn't matter, but it should;
- concrete grade doesn't play any role, it seems to me strange;
- length of the embedded part may be long, but actual lever arm should be limited to some extend;
- seems to me thickness of the slab is too narrow relatively to the tube to use anchor analogy;
- how distance to edge or existence of holes near the tube affects capacity.

That is why I am trying to find something scientific

This is typical connection detail to avoid thermal bridges for cold climates ..I know similar detail for balcony slabs and stair landings.

You may develop STM in this case as Mr CELT83 pointed out..

Regarding your concerns, concrete grade, thickness of slab, length of embedment are important factors..
When you develop STM you will see..

The following is excerpt from ( Structural connections for precast concrete buildings FIB -CEB Bulletin 43)











Tim was so learned that he could name a
horse in nine languages: so ignorant that he bought a cow to ride on.
(BENJAMIN FRANKLIN )

This is indeed a balcony slab connection.

Yes, sure. SnT definitely is going to be a nice 1st step for assessment of the connection capacity. But if the connection has been used in masses, SnT shall be supported at least by testing.

I have thought about a truss model 1st, but stuck in some places. Will try to present it

1. The slab is missing stirrups, thus "classic" distributions of load when each strut hanged by a stirrup is impossible. So I have assumed 2 fan shape struts from top to bottom corners.


2. If to look from top compression stresses should flow to the tubes. Have taken the 33.7 degrees angle of the strut inclination from Eurocode recommendations for anchorage zone of post-tensioned tendons. Somehow need to hang bottom reinforcement of the slab to the tubes.


3. Something like that as a local model. It seems to me the edge should fail similarly to punching failure. Dimensions of the cone are unclear. Seems to me the top rebar passing through the edge U-rebars should be massive or many rebars with small step. Somehow to check that the block straight above the tube will not fail with vertical edges (the failure cone will be formed). Maybe need to make direct contact of the top rebar to the tube to avoid transfer of compression by the concrete in-between.