Analysis and Design of Slabs

A slab supported primarily on two opposite edges is treated as a one-way slab. For a rectangular panel supported on all four sides, the familiar aspect-ratio screening rule is based on the longer clear span $L$ and shorter clear span $S$: panels with $L/S > 2$ are commonly treated as one-way, while panels with $L/S \le 2$ develop significant two-way action.

The aspect-ratio rule is not a substitute for understanding supports. A nominally square slab supported only on two opposite sides is still one-way, while a four-side-supported panel near the $L/S=2$ boundary should be modeled consistently with the adopted design method and actual stiffness of beams, walls, columns, and slab regions.

For ordinary uniform loading, a one-way slab is conveniently analyzed as a representative $1\text{-m}$-wide strip spanning in the direction of one-way action. The strip is designed for the factored bending and shear actions associated with that width, and the resulting reinforcement is reported per meter of slab width.

Main flexural reinforcement runs in the spanning direction. Reinforcement perpendicular to that direction provides shrinkage and temperature crack control and also assists load distribution and tying; it is not a substitute for the primary flexural steel.

For the material grades used in this lesson, the minimum gross-section ratios for shrinkage and temperature reinforcement are $0.0020$ for Grade 280 or 350 deformed bars and $0.0018$ for Grade 420 deformed bars or welded wire reinforcement. For a $1\text{-m}$ strip, the gross concrete area is $1000h$ in $\text{mm}^2$.

The distributed reinforcement spacing used in this lesson is limited to the smaller of $5h$ and $450\text{ mm}$. Flexural-bar spacing, crack-control requirements, cover, and detailing may impose tighter limits and must be checked separately under the adopted design provisions.

After a trial thickness is selected, recompute slab self-weight from that thickness and combine it with the other applicable loads using the governing structural load combinations. The worked design example uses $1.2D+1.6L$ only for its stated dead-load/live-load case; other actions and governing combinations must be included when applicable.

For a simply supported strip under uniform factored load, $M_u=w_uL^2/8$. Flexural reinforcement is then selected so that $\phi M_n\ge M_u$. For the singly reinforced rectangular section used in the worked example,

One-way shear is a separate strength check near the support. The required critical section, concrete contribution, strength-reduction factor, and any permitted shear reinforcement must follow the adopted code edition. Thin slabs are commonly proportioned so concrete shear resistance is adequate rather than assuming that beam-style stirrups can simply be inserted into any slab.

Common two-way systems include slabs supported by beams on four sides, flat plates of essentially uniform thickness supported directly by columns, flat slabs with drops or column capitals, and two-way joist or waffle systems. Beamless systems are particularly sensitive to slab-column connection behavior and punching shear.

For two-way moment distribution, a design panel is commonly divided into column strips centered on column lines and middle strips between them. These are design regions used to distribute calculated panel moments; they are not independent physical beams. The applicable strip definitions and moment fractions depend on the selected analysis method and governing provisions.

Using virtual work on an assumed admissible mechanism gives a collapse load associated with that mechanism. In classical yield-line analysis, this is an upper-bound result: an assumed mechanism can predict a collapse load that is at or above the true collapse load under the idealized plastic assumptions. The mechanism is therefore not automatically the exact physical failure pattern. Competing plausible mechanisms should be examined, and the lowest admissible upper-bound result governs among those investigated.

Yield-line analysis concerns ultimate plastic mechanism capacity. It does not replace service-load deflection analysis, punching-shear checks, brittle shear limits, anchorage/detailing requirements, or a suitable elastic analysis where those are required.

Beamless two-way slabs require special attention at columns because large reactions are transferred through limited slab depth and critical perimeter. For the interior rectangular-column geometry used in this lesson, a critical perimeter taken at $d/2$ from the column faces has perimeter $b_o=2(c_1+d)+2(c_2+d)$.

Edge and corner supports have reduced available critical perimeters, and unbalanced moments at slab-column connections can increase the demand. Drops, column capitals, increased slab thickness, or properly designed shear reinforcement may improve resistance, but the actual strength calculation must follow the governing punching-shear provisions.

Openings interrupt flexural reinforcement and can reduce punching-shear perimeter when placed near columns. Reinforcement cut by an opening must be properly replaced and anchored around it, while the punching-shear model must account for any ineffective portions of the critical perimeter as required by the governing provision.

Serviceability remains a separate design obligation. Thickness, reinforcement ratio and spacing, cracking, long-term deflection, load duration, continuity, and construction sequence can all affect slab performance even when strength checks pass. Support labels such as “simply supported” or “continuous” should describe the actual rotational restraint and continuity assumed in analysis and detailing rather than being selected merely to obtain a thinner prescriptive value.