How a flat slab on columns is designed with the STATIX flat slab calculator on the SANS 10100-1 route: the equivalent frame, pattern loading, column and middle strips, the edge and corner columns, and punching with shear links.
1. Learning outcomes
After this lesson you can:
set up the equivalent frames of a flat slab in both directions;
explain pattern loading and the design hogging moment at hc/2;
share the frame moments between column and middle strips and design the steel;
check the moment an edge or corner column can take;
design punching links at interior, edge and corner columns.
2. Before you start
RC Design 1: bending and steel (lesson 1), two-way slabs (lesson 6) and punching (lesson 7).
Why flat slabs. A flat slab sits directly on its columns. It is quick to build and leaves a flat soffit, but the whole floor load gathers into a small area at each column, so punching shear and the moments next to the columns decide the design. RC Design 1 lesson 7 introduced punching; this lesson designs the whole slab.The equivalent frame. Each line of columns and the slab panel width around it (l2, from mid-panel to mid-panel) is analysed as a continuous beam on the columns, first in one direction, then in the other. The calculator takes the columns above and below as rotational springs fixed at their far ends; set the storey heights to 0 for knife-edge supports.Pattern loading. The imposed load may be on some spans and not others. The calculator runs every combination with the imposed load on all spans, odd spans, even spans and each pair of adjacent spans, and keeps the worst moment at each section. Two loaded neighbours give the largest hogging at the column between them.The design hogging moment. The peak moment over the column centre is not used: SANS 10100-1 takes the support moment at hc/2 from the column centre, hc being the diameter of a circle of the same area as the column (or its effective head). The calculator does this at every column, and reports the moment at each.
4. Strips and steel
Column and middle strips. The frame moment is shared between a column strip, half the smaller span wide and centred on the columns, and the middle strips beside it. The column strip is stiffer and takes more: 75 % of the hogging and 55 % of the sagging in the calculator (the distribution of BS 8110-1 Table 3.18, which SANS 10100-1 follows). Steel is then designed per metre of each strip.Placing the top steel. Over the columns the moment is highest close to the column, so two thirds of the column-strip top steel go in the central half of the strip. The calculator gives the steel per metre and reminds you of this rule.Edge and corner columns. A flat slab can only pass a limited moment into a column at its edge, through a narrow width be around the column. SANS 10100-1 4.6.5.3 caps it at Mt,max; any excess goes back into the end span. The calculator also designs the edge frames along the slab edges on their own.
5. Punching and deflection
Punching perimeters. SANS 10100-1 checks the shear stress on perimeters around the column, the first at 1.5d from the face, then further out at 0.75d steps until the stress falls to vc. The factor β allows for the moment the column takes: 1.15 at an interior column, 1.4 at an edge and 1.25 at a corner, as preset in the calculator.Shear links for punching. Up to twice vc, links on each failing perimeter can carry the excess; beyond it the slab is too thin. Each perimeter needs its own area, never less than the minimum, so the outer perimeters often need more steel than the first. The calculator lists the perimeters, the area and a leg layout.Deflection by span/d. A flat slab deflects more than a slab on beams, so the basic span/d ratio is cut by 0.9 for the longer span, then raised by the tension-steel modification factor as in RC Design 1. Lesson 6 of this course calculates deflection where span/d is not enough.Drops, heads and openings, in outline. A drop or a column head thickens the slab where the shear and hogging are highest; an opening near a column cuts the punching perimeter. The calculator takes drops, heads, openings and cantilever edges; this lesson works the plain slab on the SANS route and leaves them as options to try.
6. Example A: an office floor, the interior frame
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7. Example B: the edge and corner columns
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8. Do it in STATIX
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9. Common mistakes
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10. Exercises
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11. Self-check quiz
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12. Lesson 1 on one page
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Next: Lesson 2, post-tensioned slabsTendon profiles, load balancing, losses and stresses with the PT slab calculator. Go to lesson 2
A worked example for learning, not a design. Check every value against the current code and your own project, and have the design checked and signed by a registered professional engineer.
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