Concept of "Strong Band" 1

[ZAP]

Can anyone please explain to me what is the concept of "Strong Band" in reinforced/post tensioned concrete?

Is it possible to design a beam which has the same thickness as the slab it is supporting? What should the width of the beam be?

 

[dlew]

Zap,

For reinforced concrete two-way slabs, that would be the "column strip". See Chapter 13 of the ACI 318.
Essentially, the column strip is a beam of the same thickness than the rest of the slab.

The width of the column strip is 1/4 of the span (L1 or L2, whichever is less), on each side of the column line.

 

[Ingenuity]

zap,

Depending on where you are located in the world and the nomenclature you are more familiar with will depend on what you define as "strong band". In my experience the "strong band" is a method of concrete analysis and design, and most often referred to as "strip design" method. It is a pretty old technique and is a lower-bound method, as opposed to a upper-bound method such as yield-line method. The lower-bound methods are also refereed to as "safe" designs because it gives a lower-bound estimate of the flexural slab capacity.

In the "strip method" the slab is divided up into strips which carry the loads placed upon them. Some strips may be selected that are orthogonal to each other and so span in two directions representing the 2-way action of the slab. The bending moments are calculated from the structural system spanning in one direction for each strip, as either simply supported or continuous. Twisting moments and shear forces between adjacent strip are disregarded.

The division of load which is to be carried by the strips in each direction is somewhat arbitrary and so is the choice of the strip width. However, to minimize slab deflection and control cracking, the ratio of reinforcement placed in each direction should be consistent with the stiffness of the slab in that direction. If you screw up or deviate from the more "correct" placement of rebar in your design, you will have to crack the concrete and rely upon moment redistribution to get the load across to where you have provided the reinforcement.

The magnitude of the bending moment calculated in the chosen strip is an averaged one across the strip which basically violates the principles of elasticity of a 2D state of equilibrium but provided the strip width is not excessive for the application it will work well in practice.

It works well and is intuitive for say triangular slabs supported on walls, or maybe perimeter loads on a slab edge, or point loads, or especially around dominant openings (e.g. stairs) where no beams are provided. You can also visualize the behavior and see the load path, and is handy when some more traditional 2D elastic analysis techniques are cumbersome for unusual slab panels or loadings.

Some RC texts will probably cover this topic - i think James MacGregor's "RC Mechanics and Design" text covers it. The reinforcement i refer to above can be mild steel or P-T strand. With P-T you have to be a little more careful because the reinforcement is "active" as the tendon curvature provides uplift and also downward forces (not loads) to the slabs. Some may argue with me on this, but i think that the USA practice of banded/uniform PT tendons in a flat plate is really a "strip design" method with the banded PT tendons really forming a "support strip" for the orthogonal uniform direction - only problem is that using the "strip design" method, the width used should not be the full panel width, which is commonly used in banded/uniform flat plates.

HTH