ETABS MANUAL  

 

Part-­‐II:  Model  Analysis  &  Design  of  Slabs    

 

According  to  Eurocode  2

AUTHOR:  VALENTINOS  NEOPHYTOU  BEng  (Hons),  MSc   REVISION  1:  April,  2013

 

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ABOUT  THIS  DOCUMENT  

 

This  document  presents  an  example  of  analysis  design  of  slab  using  ETABS.  This  example  examines  a  simple  single  story  building,  which  is  regular  in  plan  and  elevation.  It  is  examining  and  compares  the  calculated  ultimate  moment  from   ETABS   with   hand   calculation.     Moment   coefficients   were   used   to  calculate   the  ultimate  moment.  However   it   is  good  practice   that   such  hand  analysis   methods   are   used   to   verify   the   output   of   more   sophisticated  methods.  

Also,   this   document   contains   simple   procedure   (step-­‐by-­‐step)   of   how   to  design  solid  slab  according  to  Eurocode  2.  The  process  of  designing  elements  will  not  be  revolutionised  as  a  result  of  using  Eurocode  2.  

Due   to   time   constraints   and   knowledge,   I   may   not   be   able   to   address   the  whole  issues.  

Please   send   me   your   suggestions   for   improvement.   Anyone   interested   to  share  his/her  knowledge  or  willing  to  contribute  either  totally  a  new  section  about  ETABS  or  within  this  section  is  encouraged.  

For  further  details:  

 

My  LinkedIn  Profile:  http://www.linkedin.com/profile/view?id=125833097&trk=hb_tab_pro_top  

 

Email:  valentinos_n@hotmail.com  

Slideshare  Account: http://www.slideshare.net/ValentinosNeophytou  

 

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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 over complication; the assumptions and their implications are as follows.

a) Element type : SHELL

b) Meshing (Sizing of element) : Size= min{Lmax/10 or l000mm}

c) Element shape : Ratio= Lmax/Lmin = 1 ≤ ratio ≤ 2

d) 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 Note:  lx is the longer span ly is the shorter span    

 Msx= asxnlx

2 in direction of span lx

n: is the ultimate load m2

Msy= asynlx2 in

direction of span ly n: is the ultimate load m2

 

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= asxnlx

2 in direction of span lx

n: is the ultimate load m2

Msy= asynlx2 in

direction of span ly n: is the ultimate load m2

 

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/Lx 1.0 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 Negative moment at continuous edge 0.039 0.050 0.058 0.063 0.067 0.037 Positive moment at midspan 0.029 0.038 0.043 0.047 0.050 0.028

One long edge discontinuous Negative moment at continuous edge 0.039 0.059 0.073 0.083 0.089 0.037 Positive moment at midspan 0.030 0.045 0.055 0.062 0.067 0.028

Two adjacent edges discontinuous Negative moment at continuous edge 0.047 0.066 0.078 0.087 0.093 0.045 Positive moment at midspan 0.036 0.049 0.059 0.065 0.070 0.034

 

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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: lx is the longer span ly is the shorter span  

 

MEd= 0.086FL F: is the total ultimate load =1.35Gk+1.5Qk L: 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

(Manual of EC2 ,Table 5.2)

 Uniformly distributed loads

End support condition Moment End 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

F:  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

𝑓!" =𝑓!"𝛾!

 

FLEXURAL DESIGN (EN1992-1-1,cl. 6.1)

Determine K from:

𝐾 =𝑀!"

𝑏𝑑!𝑓!"

𝐾 ′ = 0.6𝛿 − 0.18𝛿! − 0.21  

K<K′ (no compression reinforcement required)

Obtain lever arm z: 𝑧 = !

!!1 + √1 − 3.53𝐾! ≤ 0.95𝑑

 

K>K′ (then compression reinforcement required – not recommended for typical slab)

Obtain lever arm z: 𝑧 = !

!!1 + √1 − 3.53𝐾 ′! ≤ 0.95𝑑

 

δ=1.0 for no redistribution δ=0.85 for 15% redistribution δ=0.7 for 30% redistribution  

𝐴!.!"# =𝑀!"

𝑓!"𝑧  

 

𝐴!".!"# =𝑀!",!"

𝑓!"𝑧        

 𝐴!".!"# =𝑀!",!"

𝑓!"𝑧  

 

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 width

Spacing 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. prov

Number 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 of reinforcement “ limit

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

𝐴!,!"# =0.26𝑓!"#𝑏𝑑

𝑓!"≥ 0.0013𝑏𝑑   ≤        𝐴!,!"#$              ≤ 𝐴!,!"# = 0.04𝐴!  

 

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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

(Manual of EC2 ,Table 5.2)

 Uniformly distributed loads

End support condition Moment End support support MEd =0.046F Penultimate support MEd= 0.6F

Interior supports MEd =0.5F F:  total design ultimate load on span

Determine design shear stress, vEd vEd=VEd/b·d

 

Reinforcement  ratio,  ρ1    (EN1992-­‐1-­‐1,  cl  6.2.2(1))  ρ1=As/b·d  

   

Design shear resistance

𝑘 = 1 +!200𝑑

≤ 2,0  with  𝑑  in  mm

𝑉!".! = !0.18𝛾!

𝑘(100𝜌!𝑓!")!! + 𝑘!  𝜎!"! 𝑏𝑑

𝑉!".!.!"# = !0.0035!𝑓!"𝑘!.! + 𝑘!  𝜎!"!𝑏𝑑

Alternative value of design shear resistance, VRd.c (Concrete centre) (ΜΡa) ρI =

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 ρI fck)1/3≥0.035k1.5fck

0.5 where k=1+(200/d)0.5≤0.02

 

If  VRdc≥VEd≥VRdc.min,  Concrete  strut  is  adequate  in  resisting  shear  stress  

Shear  reinforcement  is  not  required  in  slabs      

 

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

Asmin<As.prov  

Minimum area of reinforcement steel within tensile zone

(EN1992-1-1,Eq. 7.1)

𝐴!.!!" =𝑘  𝑘!𝑓!",!""𝐴!"

𝜎!

 

Chart to calculate unmodified steel stress σsu (Concrete Centre - www.concretecentre.com)

 

Crack widths have an influence on the durability of the RC member. Maximum crack width sizes can be determined from the table below (knowing σs, bar diameter, and spacing).

Maximum bar diameter and maximum spacing to limit crack widths (EN1992-1-1,table7.2N&7.3N)

σs

(N/mm2) Maximum bar diameter and spacing for

maximum crack width of: 0.2mm 0.3mm 0.4mm

160 25 200 32 300 40 300 200 16 150 25 250 32 300 240 12 100 16 200 20 250 280 8 50 12 150 16 200 300 6 - 10 100 12 150

Note. The table demonstrates that cracks widths can be reduced if; • σs  is  reduced  • Bar  diameter  is  reduced.  This  mean  that  spacing  is  reduced  if  As.prov    is  to  be  the  

same.  • Spacing  is  reduced  

 

kc=0.4 for bending k=1 for web width < 300mm or k=0.65for web > 800mm fct,eff= fctm = tensile strength after 28 days Act=Area of concrete in tension=b (h-(2.5(d-z))) σs=max stress in steel immediately after crack initiation

𝜎! = 𝜎!" !!!.!"#!!.!"#$

!!! or 𝜎! = 0.62 ! !!.!"#

!!.!"#$𝑓!"!

 

 

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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.

𝑙𝑑= 𝐾 !11 + 1.5!𝑓!"

𝜌!𝜌+ 3.2!𝑓!" !

𝜌!𝜌− 1!

!.!!  𝑖𝑓  𝜌 ≤ 𝜌!

𝑙𝑑= 𝐾 !11 + 1.5!𝑓!"

𝜌!𝜌 − 𝜌′

+112!

𝑓!"!𝜌,

𝜌!!  𝑖𝑓  𝜌 > 𝜌!

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:

• In  beams  and  slabs  where  the  span>7.0m,  multiply  by  leff/7  

Type of member K Cantilever 0.4 Flat slab 1.2

Simply supported 1.0 Continuous end

span 1.3

Continuous interior span

1.5

   

Reference reinforcement ratio

(EN1992-1-1,cl. 7.4.2(2))

𝜌! = 0.001!𝑓!"  

Tension reinforcement ratio (EN1992-1-1,cl. 7.4.2(2))

𝜌 =𝐴!.!"#𝑏𝑑

 

 

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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/m2 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 1 10.20 13.60 8.00 10.70 10.20

Error percentage 2,20% 15.14% 4.00% 7.30% 1.92% 1 Hand 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 1 13.2 13.2 13.2

Error percentage 2.20% 2.20% 2.20% 1 Hand 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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Analysis and design of Interior slab panel (GL2-GL3)

 

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Analysis and design of Interior slab panel (GL3-GL4)