Effective width for a concentrated load applied on a wall corner and how to design it

[Sandychan]

Hello everyone,
I am doing a design of a precast concrete wall with a point load from a beam reaction at its left corner. Besides the point load, the wall only have it own weight. There is a recommendation in old Swedish concrete code suggested that the effective width of the wall under a concentrated load at the corner is:
be = bo+(h/6)
where bo is a bearing width and h is the height of the wall

The thing is that the code only told how to calculate the effective width but not how to design it. I am wondering if I use that effective section, do I still need to consider eccentricity between the load and the center of the effective section? Or can I just think that the point load is concentric? Please see the picture for the sketch of the case I work with. Thank you all so much in advance.

 

[hardbutmild]

I think this is a provision very similar to the one for masonry walls subjected to concentrated loads in Eurocode 6. There, the check is done at the middle of the wall along the height with angle of the load spread of 60°. This would amount to be = bo+(0,29*h), so your proposal gives an even steeper angle (of about 72°) which should be safe. See the picture below for an explanation (it's taken from EN 1996-1-1)

In accordance with that I don't think you need to take the moment into account other than to calculate the horizontal steel on the top (look at the mechanism below). For the concentrated force in the middle of the wall (along the length) no horizontal steel is needed. The bottom force is resisted simply by the "volume" of the wall.

EDIT: So I'd just check it for crushing and potential out of plane buckling (that's why the middle of the height). Also, note how you used the 0,5 P / fy for the area of bursting steel. That would coincide with the angle of about 63° (but this is the angle of the dashed green line on my drawing, whereas the previously mentioned angle was the outer, thick green line angle. The dashed line will have a steeper angle obviously) if you were talking about horizontal steel (if you just calculate the upper red force on my drawing, it amounts to 0,5 of the blue force if the angle of the dashed green line is 63° to the horizontal). If you were talking about a steel at some angle, you'd need to check the force at that particular angle.

 

[Sandychan]

@Hardbutmild

Thanks for explaining the mechanism for my problem. I would like to ask a few more questions to make sure I understand you right:

1. If I have the steel calculated from the top force, I don't need to consider in plane moment due to eccentricity, e right?

2. What would be the suggestion for the length of the steel? Does it have to anchor pass a certain point or make a U-turn down the base of the wall?

3. For the bottom force, do you refer to the force with the red arrow pointing in the opposite direction to the steel force? If that force shall be taken care by the volume of the the wall, could you please explain how to check if we have sufficient volume of the wall? Should we look at it as shear force and check that against the remaining length of the wall?

Thank you again for further explanation.

 

[Tomfh]

If you are bearing right on the edge can you embed a cast in angle or bearing plate, to protect the corner? Like is done on corbels:

 

[hardbutmild]

1. If I have the steel calculated from the top force, I don't need to consider in plane moment due to eccentricity, e right?

I would say yes, because you already took the moment with that top steel.

2. What would be the suggestion for the length of the steel? Does it have to anchor pass a certain point or make a U-turn down the base of the wall?

I'd do as a drew below (hope you can get it from this)

3. For the bottom force, do you refer to the force with the red arrow pointing in the opposite direction to the steel force? If that force shall be taken care by the volume of the the wall, could you please explain how to check if we have sufficient volume of the wall?

Yes, I referred to the red force. I was imagining something like this picture.

Should we look at it as shear force and check that against the remaining length of the wall?

I would do this as well, but considering your specific case, I presume it'll be satisfied easily.

Also, I agree with what Tomfh said, that's a good point.

 

[r13]

do I still need to consider eccentricity between the load and the center of the effective section?

Yes. Design as an eccentrically loaded compression member.

 

[Sandychan]

@Tomfh Thanks for examples of some failure cases.
@Hardbutmild Thanks for more details. I understand a lot better and I believe a good direction now.

 

[Sandychan]

@r13
Do you think if I have enough horizontal reinforcement right under the load according to @hardbutmild´s suggestion, we can just design this effective section as a compression member under a concentric point load?

 

[r13]

1) Do you think if I have enough horizontal reinforcement right under the load according to @hardbutmild´s suggestion, 2) we can just design this effective section as a compression member under a concentric point load?

1) He treats the entire wall as a deep beam, solving use strut and tie method. If you chose this approach, you shall analyze the whole wall consistently (use the same method).
2) My approach is the traditional nut-and-bolt method, design and stiffen the element that subjects to the concentrate force, and ignore the rest parts that do not directly involve/affect by the action.

Both methods are valid, you have to make your own choice.

 

[Sandychan]

@r13
Thank you for clarifications. It is very nice to have multiple solutions for a problem and explanation behind them as well.

 

[r13]

You are welcome.

 

[Tomfh]

I would say yes, because you already took the moment with that top steel.

If you get the load inside of the top steel then I think you’re good. It’s just a bit tricky when you’re bearing right on the edge. The edge can give way before your steel has a chance to engage.