Basement Wall Analysis (take 2) 2

[PSUengineer1]

I am re-posting a question from a few days ago in the hope that some fresh thoughts from the group are generated. Thank you to all who have replied to the previous post.

The stresses created in basement walls by earth pressures against their exterior faces are resisted by bending of the walls in horizontal and vertical spans. The distribution of the total lateral load between the vertical and horizontal span depends on the height and length of the wall, and its stiffness in the spans. The lateral load on a basement wall will be carried entirely in the vertical span when the length of the wall between supports approaches three and a half to four times the height.

Question: can someone explain where the 3.5 to 4.0 times the height comes from? Either explain the theory or please point me to a code reference (explanation of theory preferred).

Thank you.

 

[BAretired]

Explanation of the theory is not possible in a forum of this kind. If you want to delve deeper into theory, I suggest you obtain a copy of "Plates and Shells" by Timoshenko and Woinowsky-Krieger. A fourth order differential equation of a simply supported rectangular plate under sinusoidal loading is the basis of the theory. This is extended to cover other types of load and other boundary conditions. Several tables for uniform and hydrostatic load are included along with various boundary conditions such as fixed, simple or free edges.

Your value of 3.5 to 4.0 may be a reasonable guide for some situations but it is by no means representative of all. It seems intuitively obvious that when the length of wall becomes large relative to height, the central part of the wall will tend to span vertically, not horizontally. But even in very long walls, the region around the corners is affected by continuity with the wall around the corner. A yield line analysis can be used to approximate the wall's behavior.

BA

 

[hokie66]

3.5 or 4.0 are just arbitrary. The load is carried in the two directions in proportion to stiffness. You should take the time to learn about and understand two way action of slabs.

 

[shin25]

As hokie said, the load will be distributed based on the proportion of the stiffness. If you know how to calculate the beam stiffness (hint: may consider slightly stiffer than simple span beam in each direction)then the distribution factor for flexure for each direction beam can be calculated. When the beam span in the horizontal direction may be 3.5 to 4 times the vertical span, you may find that the moment that will be shared by the horizontal span is low and can be neglected.

 

[shin25]

Correction: I meant to say distribution factor for load NOT moment.

 

[JLNJ]

There are many, many, tables for moment and shear distribution for a whole variety of wall configurations. The tables are produced for a wide range of support conditions and loading. The various support conditions (fixed, free, supported) are all idealized and do not quite act as idealized in real life. The loading may be more of less uniform or vary in one manner or other by the height. Each of the different tables is given for each different geometry, support condition, and loading variation. The type of load applied varies by the soil type and state and its interaction with the wall. The material of which the wall is made and how it acts plays a significant role as well.

Foundation walls are a beautifully complicated system.

 

[amecENG]

The 3.5 or 4 are just a rule of thumb that is derived from empirical data. In general it has been found that at this aspect ratio the edge effects are minimal. You can try it yourself with a FEM model and vary the lenght and height of the wall. Of course, as others have said it is a rule of thumb and will vary based on the stiffness.

A good resource would be "Rectangular Concrete Tanks" by the Portland Cement Association. The book provides a number of tables with different edge restraints and varying aspect ratios. It explains how these tables were created and you can see the progession of the moment coefficients to the vertical axis as the wall length increases.

 

[BAretired]

The usual practice is to design basement walls to span vertically irrespective of the length/height ratio and to provide nominal horizontal steel. That practice seems to work out pretty well.

BA