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. 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. 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 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 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* Greener Homes for You

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Responses

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