Property Line Conc. Foundation Shear Capacity

[RareBugTX]

Does anybody know the shear capacity of a continuous spread footing at the distance "d" from the inside face of the foundation wall.
The foundation is on line with the lot line, hence, there is only one projection at the bottom of the footing (to the inside) i.e. my footing is an "L" not an inverted "T"
I don't remember in Concrete Design classes anything mentioned about it, and am looking at an example in Leet's and Bernal "Reinforced concrete design" page 335, third edition, for a continous footing with projections to both sides. Their formula is as follows:

phi(Vc)= 0.85(2) (f'c)^0.5 (bw)d


Specific question, does that "2" in the formula correspond to the two planes when you are checking an inverted "T" footing.

Thanks for the patience.

RareBug

 

[UcfSE]

2sqrt(f'c) is the allowable concrete shear stress for beam shear, one-way shear. That would be the shear generated by the factored soil pressure on the bottom of the footing beyond the critical section. You treat the design for shear strength bascially the same as with an inverted "T". If you take a look at your example you will see the factored soil pressure and the design shear force will be found different for the "L" than for the inverted "T".

 

[JAE]

Just to further clarify UcfSE's post - the 2 does not correspond to the two planes...it is as UcfSE said - the base maximum shear stress for factored shear design. The b and d represent the "area" used to determine the maximum shear of whatever shape, sections, or elements you are checking.

 

[RareBugTX]

OK, I get that, now let's forget about formulas and only consider in "areas". Does an "inverted T Shape footing" has the same area as an "L" shaped footing. Don't we have less area to count on? It sounds to me that an Inverted T is in double shear and the L foundation has only single shear capacity. How do I get that concept in my calculations. Would I just have to multiply phi(Vc) X 0.5 ??? Thanks!!!

 

[JAE]

When you check a "T" type footing - there are two shear planes to consider. One on each side.

Each shear plane resists a shear force at a distance d from the face of the wall (ACI318-99 11.1.3.1). At this distance from the face of the wall, there is a length of footing beyond that point towards the outside edge. This length has soil bearing pushing up on it.

Thus, the shear force applied at d from the face is the shear created by that upward bearing on the outer length of footing.

For an "L" type footing/wall condition, you still have that same width of footing beyond d-from-the-face on one side only and that should be checked just like the "T" condition. Each side only takes its applicable load.

 

[UcfSE]

You don't modify the capacity. You simply have a different shear force acting on the section. You could think of it as the "T" is in double shear if you want, as long as you realize that you check the thickness using the shear on a given shear plane at the critical location as defined by the ACI. Because you have 2 shear planes, your shear area (b*d) is double what it would be for a similar "L" footing. The "L" footing has one shear plane. In effect you don't have half the capacity, you have more force.

 

[cap4000]

The 2 comes from many lab tests performed on beams. Its "Empirically" arrived at, with applied moments and shears on beams. Cracks then develop and thus the formula corresponds to the results. ACI has committees with many refernces on this issue.