## Simply supported oneway slab simple version

This calculation is intended to show a typical hand calculation.

A 175 mm thick slab is required to support screed, finishes, an office variable action of 2.5 kN / m2 and demountable partitions (@ 2 kN / m). The slab is supported on load-bearing block walls. /ck = 30, /yk = 500. Assume a 50-year design life and a requirement for 1 hour resistance to fire.

Figure 3.1

Simply supported slab (simple version)

Figure 3.1

Simply supported slab (simple version)

3.2.1 Actions

Permanent

Self-weight 0.175 x 25 50 mm screed Finishes, services gk

Variable

Offices, general use B1 Movable partitions @ 2.0 kN / m kN / m2

3.2.2 Cover

Nominal cover, c where

where cminb = minimum cover due to bond = diameter of bar Assume 12 mm main bars cmindur = minimum cover due to environmental conditions

Assuming XCI and using C30 / 37 concrete, cmin.dur = 15 mm Acdev = allowance in design for deviation.

Assuming no measurement of cover

Fire

Check adequacy of section for 1 hour fire resistance (i.e. REI 60) Thickness, hsmin = 80 mm cf. 175 mm proposed

Axis distance, amin = 20 mm cf. 25 + p / 2 = 31 i.e. not critical

Acdev — 10 mm cnom — 15 + 10 — 25 mm cnom — 25 mm

By inspection, BS EN 1990 Exp. (6.10b) governs <Fig. 2. 5>

n = 1.25 x 5.9 + 1.5 x 3.3 = 12.3 kN / m2 <BS EN 1990 Exp. (6.10b)>

3.2.4 Analysis

Design moment

3.2.5 Flexural design

Flexure in span

K = MEd / bdf = 35.4 x 106 / (1000 x 1442 x 30) =0.057

<Fig. 3.5> <Appendix A.1> <Concise Table 15.5>

As = MEd / fydz = 35.4 x 106 / (137 x 500 / 1.15) = 594 mm2 / m

3.2.6 Deflection

Check span-to-effective-depth ratio

Basic span-to-effective-depth ratio for p = 0.41% = 20

Max. span = 20 x 1.08 x 144 = 3110 mm i.e. < 4800 mm

Consider in more detail:

N = 25.6 (p= 0.41%, fck = 30) K = 1.0 (simply supported)

F1 = 1.0 (beff / bw = 1.0) F2 = 1.0 (span < 7.0 m) F3 = 310 / <rs where

where

<ren « 242 MPa (From Concise Figure 15.3 and gk / qk = 1.79, W2 = 0.3, yt = 1.25) S= redistribution ratio = 1.0 . (Ts « 242 x 594 / 645 = 222 . F3 = 310 / 222 = 1.40

<7.4.2, Concise Sec. 15.7> <Concise Table 15.10> <Concise Table 15.11> <Concise Table 15.12> <Concise Table 15.13>

Allowable I / d = 25.6 x 1.40 = 35.8 Actual I / d = 4800 / 144 = 33.3

3.2.7 Shear

By Inspection, OK

However, if considered critical

VEd= 29.5 - 0.14 x 12.3 = 27.8 kN / m vEd = 27.8 x 103 / 144 x 103 = 0.19 MPa vRd.c =0.53 MPa

No shear reinforcement required

3.2.8 Summary of design

Figure 3.2

Simply supported slab: summary Note

It Is presumed that the detaller would take this design and detail the slab to normal best practice, e.g. to SMDSC[21]. This would usually Include dimensioning and detailing curtailment, laps, U-bars and also undertaking the other checks detailed in Section 3.2.9.

Figure 3.2

Simply supported slab: summary Note

It Is presumed that the detaller would take this design and detail the slab to normal best practice, e.g. to SMDSC[21]. This would usually Include dimensioning and detailing curtailment, laps, U-bars and also undertaking the other checks detailed in Section 3.2.9.

3.2.9 Other design/detailing checks

Minimum area of reinforcement

As.min = 0.26 (ftm / fyk) M > 0.0013 btd where bt

: width of tension zone

fctm = 0.30 x fck0666 As,min = 0.26 x 0.30 x 300666 x 1000 x 144 / 500 = 216 mm2 / m

Crack control

OK by inspection <Table 7.2N & NA>

Curtailment main bars

Curtail main bars 50 mm from or at face of support. <SMDSC[21] Fig. 6.4; How to,

Detailing>

At supports

50% of As to be anchored from face of support <9.3.1.2.(1)>

Use H12 @ 350 B1 T1 U-bars In accordance with SM DSC[21] detail MS3 lap U-ba rs 500 mm with main steel, curtail T1 leg of U-bar 0.1I (= say 500 mm) from face of support.

Maximum spacing of bars

Secondary reinforcement

20% Asre, = 0.2 x 645 = 129 mm2 / m <9.3.1.1.(2)>

Edges: effects of assuming partial fixity along edge

Top steel required = 0.25 x 594 = 149 mm2 / m <9.3.1.2.(2)>

Use H10 @ 350 (224) T2 B2 as U bars extending 960 mm into slab*

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### Responses

• teodros dahlak
How to design a simply supported concrete slab?
8 years ago