Analysis and Design of Slabs

A slab supported mainly on two opposite sides behaves one-way even if it is square. For a rectangular panel supported on all four sides, the familiar screen uses the longer span $L$ and shorter span $S$: $L/S>2$ generally indicates predominantly one-way action, while $L/S\le2$ permits significant two-way action.

That ratio is not a universal classifier. Wall supports, beams, column stiffness, discontinuous edges, openings, drops, and actual continuity determine the load path.

For the nonprestressed solid one-way slab teaching case, the Grade 420 basic screening values are $L/20$ simply supported, $L/24$ one end continuous, $L/28$ both ends continuous, and $L/10$ for a cantilever. For another $f_y$ represented by this rule:

This is a serviceability screening rule, not an analytical proof of deflection and not a strength design. If a thinner slab is selected, perform the explicit serviceability analysis required by the governing code. Even a slab that passes the screen still requires strength, cracking, durability, fire, vibration, and detailing checks.

After selecting a trial thickness:

1. Recompute slab self-weight from that thickness and form the governing load combinations.
2. Establish effective depth $d$ from actual cover, bar diameter, and reinforcement layer.
3. Calculate factored flexural demand for the actual support/continuity model.
4. Solve for required flexural steel and enforce the applicable slab minimum reinforcement.
5. Select a constructible bar diameter and spacing and verify provided $A_s$.
6. Check one-way shear at the code-defined critical section.
7. Provide shrinkage-temperature reinforcement perpendicular to primary span action.
8. Check flexural and distributed-steel spacing limits separately.
9. Check serviceability and then detail continuity, anchorage, laps, cutoffs, and cover.

For the grade set used by this lesson, the gross-section shrinkage-temperature ratios are $0.0020$ for Grade 280 or 350 deformed bars and $0.0018$ for Grade 420 deformed bars. For a one-meter strip:

The distributed reinforcement spacing in this lesson is limited to the smaller of $5h$ and $450\text{ mm}$. The main flexural reinforcement spacing is checked separately using the applicable flexural slab limit; the design laboratory uses the smaller of $3h$ and $450\text{ mm}$ for the represented one-way case.

For the ordinary normal-weight, nonprestressed teaching state represented by the simulator, concrete one-way shear is evaluated at the required critical section and compared using the shear strength-reduction factor. Thin slabs are normally proportioned so concrete shear resistance is adequate; do not assume beam-style stirrups can simply be inserted into any slab without satisfying slab-specific detailing and minimum-depth requirements.

• Beam-supported two-way slab: slab panels frame into beams or walls on the support lines.
• Flat plate: essentially uniform slab thickness supported directly by columns; simple geometry but often punching-shear-sensitive.
• Flat slab: beamless two-way slab with drops and/or column capitals that increase local depth or bearing region.
• Waffle/two-way joist slab: orthogonal ribs reduce self-weight while creating a two-way ribbed system; solid regions are normally required where slab-column punching and force transfer demand them.
• Column strip: design region centered on a column line where support-related moments are concentrated.
• Middle strip: design region between adjacent column strips receiving the remainder of the panel moment distribution.

Column and middle strips are analysis/design regions, not literal hidden beams.

Use DDM only when all applicable limits pass. The principal limits represented in the simulator are:

• at least three continuous spans in each direction;
• successive span lengths differ by no more than one-third of the longer span;
• rectangular panels have long/short centerline span ratio not exceeding 2;
• column offset does not exceed 10% of the span in the direction of offset;
• loads are gravity only and uniformly distributed over the entire panel;
• unfactored live load does not exceed two times unfactored dead load;
• when beams are present on all sides, the additional beam/slab stiffness condition must also satisfy the code.

Failure of any required DDM criterion is not a small penalty factor. It means the DDM permission is not available for that system.

For the qualifying interior beamless panel represented by the simulator, the total static moment is split into 65% negative and 35% positive. The represented strip distribution then assigns 75% of the negative moment and 60% of the positive moment to the column strip, with the remainder to the middle strip.

These fractions are not universal values for every exterior span, beam stiffness, edge condition, or analysis method. Select the correct code distribution for the actual slab system.

EFM can treat a broader range of gravity slab systems than DDM because it analyzes an equivalent frame instead of relying entirely on DDM coefficients. However, EFM still requires code-consistent member stiffness, cracking assumptions, torsional members, boundary conditions, and load cases.

Major geometric irregularity, large or irregular openings, transfer behavior, nonuniform loading, significant diaphragm or lateral-force participation, or systems that do not fit the equivalent-frame idealization require a validated general structural analysis. A plate/shell model is appropriate only when its mesh, stiffness, support conditions, loading, cracking assumptions, extraction regions, and equilibrium are verified; this lesson does not fabricate finite-element output.

For an interior rectangular column, the basic critical perimeter at $d/2$ from the faces is

An edge connection loses the portion outside the slab boundary and a corner connection loses two sides; therefore equal column size and slab depth do not produce the same $b_o$ at interior, edge, and corner locations. The factored punching demand is the column reaction minus the factored slab load acting inside the critical perimeter.

For the normal-weight, nonprestressed, no-shear-reinforcement teaching state, the nominal concrete stress is the least of the applicable ACI expressions represented by the simulator:

Here $\beta$ is the long-to-short column-side ratio and $\alpha_s$ reflects interior, edge, or corner location. The design comparison uses $\phi V_c$ with the adopted shear strength-reduction factor. Unbalanced moment transfer, prestressing, shear reinforcement, seismic connection requirements, and other special cases require their own provisions.

An opening close enough to a slab-column connection can remove part of the effective punching perimeter and interrupt flexural reinforcement. The ineffective perimeter must be determined using the governing geometric rule, not guessed from opening area. Reinforcement cut by the opening must be replaced and anchored around it, and moment transfer across the slab-column region must remain viable.

The punching simulator therefore asks for the already determined ineffective-perimeter fraction and visualizes that reduction instead of pretending to be an arbitrary-opening finite-element solver.

A slab analysis is not complete until its moment regions are translated into a buildable reinforcement layout:

• place top reinforcement over supports for negative moment and bottom reinforcement in span regions for positive moment;
• maintain required continuity through column strips and across critical slab-column regions;
• respect main-bar and distribution-bar spacing, cover, development, splice, and cutoff provisions;
• replace and anchor reinforcement interrupted by openings;
• keep column-strip and middle-strip reinforcement consistent with the moment distribution used in design;
• provide required integrity reinforcement and edge detailing;
• coordinate drops, capitals, openings, sleeves, and MEP penetrations before finalizing punching perimeters.

Slab serviceability depends on short- and long-term deflection, cracking, reinforcement ratio and distribution, load duration, creep and shrinkage, continuity, construction sequence, vibration sensitivity, and nonstructural finishes. Prescriptive thickness can permit omission of a detailed deflection calculation only within its stated limits; it does not guarantee satisfactory vibration or crack performance for every occupancy.

• American Concrete Institute — ACI 318-14, Building Code Requirements for Structural Concrete and Commentary
• American Concrete Institute — ACI 318 standards and code resources
• Association of Structural Engineers of the Philippines — NSCP publisher/organization information