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ETABS MANUAL

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Table of Contents

1.0 Slab modeling .......................................................................................................... 4

1.1 Assumptions ............................................................................................................. 4

1.2 Initial step before run the analysis ........................................................................... 4

2.0 Calculation of ultimate moments ............................................................................. 5

3.0 Design of slab according to Eurocode 2 .................................................................. 7

4.0 Example 1: Analysis and design of RC slab using ETABS................................... 11

4.1 Ultimate moments results ...................................................................................... 12

4.1.1 Maximum hogging and Sagging moment at Longitudinal direction Ly............. 12

4.1.2 Maximum hogging and Sagging moment at Transverse direction Lx ................ 12

4.1.3 Hand calculation results ...................................................................................... 13

4.1.4 Hand calculation Results..................................................................................... 14

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1.0 Slab modeling

1.1 Assumptions

In preparing this document a number of assumptions have been made to avoid overcomplication; the assumptions and their implications are as follows.

a) Element type : SHELLb) Meshing (Sizing of element) : Size= min{Lmax/10 or l000mm}c) Element shape : Ratio= Lmax/Lmin= 1 !ratio !2d) Acceptable error : 20%

1.2 Initial step before run the analysis

a) Sketch out by hand the expected results before carrying out the analysis.b) Calculate by hand the total applied loads and compare these with the sum of

the reactions from the model results.

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2.0 Calculation of ultimate moments

Maximum moments of two-way slabs

If ly/lx< 2: Design as a Two-way slab

If lx/ly> 2: Deisgn as a One-way slab

!"#$% lx is the longer spanly is the shorter span

Msx= asxnlx2in

direction of span lx

n:is the ultimate load m2

Msy= asynlx2in

direction of span ly


Bending moment coefficient for simply supported slab

ly/lx 1.0 1.1 1.2 1.3 1.4 1.5 1.75 2.0

asx 0.062 0.074 0.084 0.093 0.099 0.104 0.113 0.118

asy 0.062 0.061 0.059 0.055 0.051 0.046 0.037 0.029

Maximum moment of Simply supported (pinned) two-way slab

Maximum moment of Restrained supported (fixed) two-way slab

Msx= asxnlx2in

direction of span lx


Msy= asynlx2in

direction of span ly


Bending moment coefficient for two way rectangular slab supported by beams

(Manual of EC2 ,Table 5.3)

Type of panel and moment

considered

Short span coefficient for value of Ly/Lx Long-span coefficients for all

values of Ly/Lx1.0 1.25 1.5 1.75 2.0

Interior panels

Negative moment at continuous edge 0.031 0.044 0.053 0.059 0.063 0.032

Positive moment at midspan 0.024 0.034 0.040 0.044 0.048 0.024

One short edge discontinuous



One long edge discontinuous



Two adjacent edges discontinuous



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L: is the effective span

Maximum moments of one-way slabs

If ly/lx< 2: Design as a Two-way slab

If lx/ly> 2: Deisgn as a One-way slab

Note: lxis the longer span

lyis the shorter span

MEd= 0.086FL

F:is the total ultimate

load =1.35Gk+1.5QkL:is the effective span

Note: Allowance has been made in the coefficients in

Table 5.2 for 20% redistribution of moments.

Maximum moment of Simply supported (pinned)

one-way slab

(Manual of EC2, Table 5.2)

Maximum moment of continuous supported one-

way slab


Uniformly distributed loads

End support condition MomentEnd support support MEd=-0.040FL

End span MEd=0.075FL

Penultimate support MEd= -0.086FL

Interior spans MEd=0.063FL

Interior supports MEd=-0.063FL

!' total design ultimate load on span

L:is the effective span

Note: Allowance has been made in the coefficients in

Table 5.2 for 20% redistribution of moments.

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3.0 Design of slab according to Eurocode 2

Determine design yield strength of reinforcement

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!!

FLEXURAL DESIGN

(EN1992-1-1,cl. 6.1)

Determine K from:

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KK (then compression reinforcement required

not recommended for typical slab)

Obtain lever armz: ! !!

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!=1.0 for no redistribution

!=0.85 for 15% redistribution

!=0.7 for 30% redistribution

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Area of steel reinforcement required:

One way solid slab Two way solid slab

For slabs, provide group of bars with area As.prov per meter widthSpacing of bars (mm)

75 100 125 150 175 200 225 250 275 300

Bar

Diameter

(mm)

8 670 503 402 335 287 251 223 201 183 168

10 1047 785 628 524 449 393 349 314 286 262

12 1508 1131 905 754 646 565 503 452 411 377

16 2681 2011 1608 1340 1149 1005 894 804 731 670

20 4189 3142 2513 2094 1795 1571 1396 1257 1142 1047

25 6545 4909 3927 3272 2805 2454 2182 1963 1785 1636

32 10723 8042 6434 5362 4596 4021 3574 3217 2925 2681

For beams, provide group of bars with area As. provNumber of bars

1 2 3 4 5 6 7 8 9 10

Bar

Diameter

(mm)

8 50 101 151 201 251 302 352 402 452 503

10 79 157 236 314 393 471 550 628 707 785

12 113 226 339 452 565 679 792 905 1018 1131

16 201 402 603 804 1005 1206 1407 1608 1810 2011

20 314 628 942 1257 1571 1885 2199 2513 2827 3142

25 491 982 1473 1963 2454 2945 3436 3927 4418 4909

32 804 1608 2413 3217 4021 4825 5630 6434 7238 8042

Check of the amount of reinforcement provided above the minimum/maximum amount ofreinforcement limit

(CYS NA EN1992-1-1, cl. NA 2.49(1)(3))

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SHEAR FORCE DESIGN

(EN1992-1-1,cl 6.2)

MEd= 0.4F

F:is the total ultimate

load =1.35Gk+1.5Qk

Maximum moment of Simply supported (pinned)

one-way slab

(Manual of EC2, Table 5.2)

Maximum shear force of continuous supported

one-way slab


Uniformly distributed loads

End support condition MomentEnd support support MEd=0.046FPenultimate support MEd= 0.6F

Interior supports MEd=0.5F

!' total desi n ultimate load on s an

Determine design shear stress, vEd

vEd=VEd/bd

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Design shear resistance

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Alternative value of design shear resistance, VRd.c (Concrete centre) ("#a)

!I=As/(bd)

Effective depth, d(mm)

"200 225 250 275 300 350 400 450 500 600 750

0.25% 0.54 0.52 0.50 0.48 0.47 0.45 0.43 0.41 0.40 0.38 0.36

0.50% 0.59 0.57 0.56 0.55 0.54 0.52 0.51 0.49 0.48 0.47 0.45

0.75% 0.68 0.66 0.64 0.63 0.62 0.59 0.58 0.56 0.55 0.53 0.51

1.00% 0.75 0.72 0.71 0.69 0.68 0.65 0.64 0.62 0.61 0.59 0.57

1.25% 0.80 0.78 0.76 0.74 0.73 0.71 0.69 0.67 0.66 0.63 0.61

1.50% 0.85 0.83 0.81 0.79 0.78 0.75 0.73 0.71 0.70 0.67 0.65

1.75% 0.90 0.87 0.85 0.83 0.82 0.79 0.77 0.75 0.73 0.71 0.68

#2.00% 0.94 0.91 0.89 0.87 0.85 0.82 0.80 0.78 0.77 0.74 0.71

k 2.000 1.943 1.894 1.853 1.816 1.756 1.707 1.667 1.632 1.577 1.516

Table derived from: vRd.c=0.12k(100!Ifck)1/3#0.035k1.5fck

0.5

where k=1+(200/d)0.5"0.02

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DESIGN FOR CRACKING(EN1992-1-1,cl.7.3)

Asmin

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DESIGN FOR DEFLECTION

(EN1992-1-1,cl.7.4)

Simplified Calculation approach

Span/effective depth ratio(EN1992-1-1, Eq. 7.16a and 7.16b)

The effect of cracking complicacies the deflection calculations of the RC member under

service load. To avoid such complicate calculations, a limit placed upon the span/effective

depth ration.

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! !"! ! !!Note:The span-to-depth ratios should ensure that deflection is limited to span/250

Structural system modification factor

(CY NA EN1992-1-1,NA. table 7.4N)

The values of K may be reduced to account for long span as follow:

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4.0 Example 1: Analysis and design of RC slab using ETABS

1. Dimensions:

Depth of slab, h: h=150mm

Length in longitudinal direction, Ly: Ly=6m

Length in transverse direction, Lx: Lx=5m

Number of slab panels: N=3

2. Loads:

Dead load:Self weight, gk.s: gk.s=3.75kN/m

2

Extra dead load, gk.e: gk.e=1.00kN/m2

Total dead load, Gk: Gk=4.75kN/m2

Live load:Live load, qk: gk=2.00kN/m2

Total live load, Qk: Qk=2.00kN/m2

3. Load combination:

Total load on slab: 1.35Gk+1.5Qk=

COMB1: 1.35*4.75+1.5*2.00=9.1kN/m2

4. Layout of model:

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4.1 Ultimate moments results

4.1.1 Maximum hogging and Sagging moment at Longitudinal direction Ly

4.1.2 Maximum hogging and Sagging moment at Transverse direction Lx

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4.1.3 Hand calculation results

Program results

Ultimate moment at longitudinal direction Ly

Mid-span

GL1-GL2

(kNm)

GL2

(kNm)

Mid-span

GL2-GL3

(kNm)

GL3 Mid-span

GL3-GL4

(kNm)

ETABS Results 10.43 11.54 7.68 11.54 10.40

Hand calculation

results 110.20 13.60 8.00 10.70 10.20

Error percentage 2,20% 15.14% 4.00% 7.30% 1.92%

1Hand calculation are based on moment coefficient of Manual to Eurocode 2

Institutional of Structural Engineers, 2006 (Table 5.2).

Program results

Ultimate moment at longitudinal direction Lx

Mid-span

GL1-GL2

(kNm)

Mid-span

GL2-GL3

(kNm)

Mid-span

GL3-GL4

(kNm)

ETABS Results 13.5 13.5 13.5

Hand calculation

results 113.2 13.2 13.2

Error percentage 2.20% 2.20% 2.20%

1Hand calculation are based on moment coefficient of Manual to Eurocode 2

Institutional of Structural Engineers, 2006 (Table 5.2).

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4.1.4 Hand calculation Results

Analysis and design of Interior slab panel (GL1-GL2)

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