CivilReinforced ConcreteeasyCourseworkPE / Advanced

Design Moment in a Continuous One-Way Slab

A continuous one-way slab carries a factored load of $w_u = 12\ \text{kN/m}^2$ and has a clear span of $l_n = 4.0\ \text{m}$ .

Using the ACI approximate moment coefficient for the positive moment in an interior span, $M_u = w_u l_n^2 / 16$ , find the design moment per metre width of slab.

Given

wu	12 kN/m^2	Factored load
ln	4 m	Clear span

Hint 1

Slab design is done on a 1 m wide strip, which turns kN/m² into kN/m.

Hint 2

Use the coefficient given, with the clear span.

Hint 3

M_u = w_u·l_n²/16.

Worked solution — try the problem first

Design a 1 m wide strip of slab. The load on that strip is $12\ \text{kN/m}^2 \times 1\ \text{m} = 12\ \text{kN/m}$ — numerically unchanged, but now a line load.

$M_u = \frac{w_u l_n^2}{16} = \frac{12 \times 4.0^2}{16} = \frac{12 \times 16}{16} = 12\ \text{kN·m/m}$

$\boxed{M_u = 12\ \text{kN·m per metre width}}$

Why 1/16 and not 1/8? The $wl^2/8$ result is for a simply supported span. Continuity over the supports transfers moment to the supports and reduces the mid-span positive moment. The ACI coefficients (1/14, 1/16, 1/11, 1/9, ...) are tabulated approximations that let you skip a full indeterminate analysis, provided the geometry and loading conditions for their use are satisfied.

Note the coefficients use the clear span $l_n$ , face to face of supports, not the centre-to-centre span.

Concepts:One-way slabsACI moment coefficientsContinuous beams

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