Doubly Reinforced Cantilever Retaining Wall Example 4

[VVang]

Hello, I am struggling to find an example of how to design a doubly reinforced retaining wall. I tried analyzing the structure as a 1' wide beam but due to the 12" thickness of the wall I keep getting a very small As required and a very small a. Trying to use the doubly reinforced design method for beams, this causes my compressive strain to go in the negative because my d' is larger than c. Does anyone have any tips or recommendations?
Basically, I want to design a doubly reinforced retaining wall that is 12" thick. From my analysis I can use #5 @ 12" and it will satisfy, but I want to to analyze if I can use a lower rebar size (like #4@12") if I reinforced it on both sides. Trying to find out how to properly analyze that. Any help is appreciated, thank you.

 

[hokie66]

The bars on the compression face will barely contribute to resisting flexure. For design purposes in bending, neglect them.

 

[Lomarandil]

For small bars and large cover distances, you can get up to a ~15% boost in flexural capacity by considering the "compression face bars". Is that worth the extra effort? Many designers (including hokie) will say no.

Most doubly-reinforced examples in textbooks assume large bars and small covers such that the "compression face bars" are just that, in compression. When strain compatibility indicates that the compression face bars are in fact in tension (d' > c), you can treat them just like the other flexural bars, except that the stress in those bars is strain*E, usually not reaching yield.

One old example I have of SMath calculations which will handle the strains (whatever they may be) is here.

https://github.com/open-struct-engineer/SMath_Studio/tree/master/03-Concrete

This version requires some iterative guess-and-check using an "alpha factor" to converge on the actual strain solution. It can also be programmed in using a loop for those so inclined.

 

[Celt83]

If you go with the accurate strain compatibility approach and utilize the tension in the front face bars be aware of the impact to the section shear strength, the way ACI defines d used for shear as the center of the tension reinforcement you may take a significant reduction in capacity using the front face bars.

 

[Forgot2Yield]

I've ran into this before as well trying to design doubly reinforced thick sections. You end up getting both steel layers in tension because the concrete section is much thicker than needed for flexure and the area of concrete being utilized on the compression side is super small (i.e. c is less than d'). In this case I would second hokie. The compression face bars in the stem should just be designed as temperature and shrinkage steel. Design the tension face bars neglecting that temp steel in the other face.

 

[Lomarandil]

Technically true Celt, but I recently found a section in the ACI commentary (R22.5.5.1) which allows one to neglect steel within 1/3 of the total depth to the compression fiber for the reinforcing ratio used in shear capacity.

Between that and AASHTOs lower limit of shear depth as 0.72h (also ACI R22.5.2.1 for prestressed members), I don't worry about the letter of the law in this instance.

(edited to correct reference)