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Hollowcore slab design to SANS 10100

A hollowcore unit is a precast slab with long cores to save weight, pre-tensioned by strands in the bottom (sometimes a few on top). The strands are stressed before casting and released once the concrete is strong: they squeeze the bottom of the unit and lift it into a camber. The design checks the stresses at release and in service, the strength at ultimate, the shear near the supports (where the strands are still bonding in), and the deflection. Every number below comes from the free STATIX hollowcore slab calculator with the inputs in step 1.

1. The problem

Input	Value
Design code	SANS 10100-1
Unit	Topfloor 200
Wiring pattern	D
Depth h	200 mm
Width b	1197 mm
Span	8 m
Bearing	100 mm
Other dead	1.5 kN/m²
Imposed Qk	2.5 kN/m²
Grade fcu	50 MPa
Class	2 — limited tension

2. The section

The cores are taken out of the gross section. Area, centroid height and second moment of area give the section moduli used for the stresses; the webs between the cores carry the shear.

A = 140,710 mm², y_b = 99.1 mm I = 631.9 × 10⁶ mm⁴ Z_bottom = 6.37, Z_top = 6.26 × 10⁶ mm³ web width (total) = 484 mm Topfloor 200 mm, pattern D

3. Prestress and losses

The strands are stressed to a percentage of their strength. Elastic shortening at release, then shrinkage, creep and relaxation over time reduce the force. The effective force after losses is what acts in service.

A_ps = 411 mm² at e = 66.6 mm below the centroid jacking 70 % of f_pu, total loss 14.2 % effective stress f_pe = 1,079 MPa

4. Stresses at transfer and in service

At release the full force acts with only the self-weight: the bottom is squeezed hard and the top may go into tension. In service the force is lower and the full load acts: the bottom compression drops and may turn into tension. Each face stress is checked against its limit.

transfer: top 2.53, bottom 4.63 MPa compression: 4.63 ≤ 10.50 MPa OK service: top 8.86, bottom −2.46 MPa compression: 8.86 ≤ 16.50 MPa OK tension limit 3.18 MPa

5. Ultimate moment

At ultimate the strands reach a stress close to their strength; the compression block sits in the top flange. The resistance must exceed the factored moment.

M_u / M_resistance: 88.0 ≤ 99.5 kNm OK

6. Shear near the supports

Near a support the strands are still transferring their force by bond, so the prestress is only partly there. The shear resistance of the uncracked webs (or of the cracked section) is checked at the worst point.

worst at 1,304 mm from the end (cracked Vcr) V / V_c: 29.6 ≤ 58.3 kN OK

7. Camber and deflection

The prestress lifts the unit (camber), the loads push it down, and creep makes both grow with time. The net movement after the finishes and partitions must stay within the limits.

net final 12.7 mm down (limit 32.0 mm down) after partitions: 17.5 ≤ 20.0 mm OK

8. Bearing and fire

The unit needs enough bearing length on its support, and enough cover and depth for the fire rating.

Bearing width at each end (dry bearing on insitu): [SANS 10100-1 cl.6.2.4.4-6.2.4.6, figure 27 (p.144-147)] net = max(40, V/(L_eff f_b)) = max(40, 44.923 kN/(600 x 12)) = 40 mm; L_eff = least of b 1197, b/2 + 100, 600; f_b = 0.4 x 30 (weaker surface); support edge concrete grade 30: 15 mm; unit end (strands exposed at the end) nil; inaccuracy 39.5 mm (25 or 5 mm/m of 7.9 m between faces) -> nominal 94.5 mm vs 100 mm given 95 ≤ 100 mm OK Fire resistance: [SANS 10100-1 cl.5.9.3.2 table 38 (p.136); cl.7.3 table 46 (p.168)] NOT CHECKED - give the fire rating (h) from the building regulations (SANS 10400-T). NOT CHECKED

Open the load-span curve under the drawing to see how the longest span changes with the load, for this unit or your own.

Run this example yourselfOpen the free STATIX hollowcore slab calculator and press Load the example (Topfloor 200, pattern D, 8 m) under "How it is calculated". Change any value and every step updates, with a calc sheet.
Open the hollowcore slab calculator

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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