etabsmodeling-designofslab-130416153345-phpapp02.pdf

January 19, 2018 | Author: Robert Giuga | Category: Bending, Structural Load, Strength Of Materials, Fracture, Concrete
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ETABS MANUAL    

Part-­‐II:  Model  Analysis  &  Design  of  Slabs       According  to  Eurocode  2

AUTHOR:  VALENTINOS  NEOPHYTOU  BEng  (Hons),  MSc  

REVISION  1:  April,  2013

 

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:  [email protected]  

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

 

3  

  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.

 

4  

  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                   Maximum moment of Simply supported (pinned) two-way slab         Bending moment coefficient for simply supported slab   Msx= asxnlx2 in n: is the ultimate load m2   lx direction of span ly/lx 1.0 1.1 1.2 1.3 1.4 1.5 1.75 2.0 2   Msy= asynlx in n: is the ultimate load m2 asx 0.062 0.074 0.084 0.093 0.099 0.104 0.113 0.118 direction of span   ly asy 0.062 0.061 0.059 0.055 0.051 0.046 0.037 0.029           Maximum moment of Restrained supported (fixed) two-way slab           Msx= asxnlx2 in n: is the ultimate load m2 direction of span lx   Msy= asynlx2 in n: is the ultimate load m2   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 Short span coefficient for value of Ly/Lx Long-span coefficients for all considered 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   at midspan Positive moment 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   at midspan Positive moment 0.030 0.045 0.055 0.062 0.067 0.028   Two adjacent edges discontinuous Negative moment at continuous edge Positive moment at midspan

 

0.047 0.036

0.066 0.049

0.078 0.059

0.087 0.065

0.093 0.070

0.045 0.034

5  

                       

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

 

Maximum moment of Simply supported (pinned) one-way slab (Manual of EC2, Table 5.2) L: is the effective span   F: is the total ultimate MEd= 0.086FL 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 continuous supported oneway 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.

 

6  

  3.0 Design of slab according to Eurocode 2 FLEXURAL DESIGN (EN1992-1-1,cl. 6.1) Determine design yield strength of reinforcement 𝑓!" 𝑓!" = 𝛾!

 

Determine K from: 𝑀!" 𝐾= ! 𝑏𝑑 𝑓!" 𝐾 ′ = 0.6𝛿 − 0.18𝛿 ! − 0.21

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

 

 

KK′ (then compression reinforcement required – not recommended for typical slab) !

Obtain lever arm z: 𝑧 = !1 + √1 − 3.53𝐾 ′ ! ≤ 0.95𝑑 !

 

 

Area of steel reinforcement required: One way solid slab Two way solid slab

  𝐴!.!"# =

 

𝑀!"   𝑓!" 𝑧

𝑀!",!"         𝑓!" 𝑧 𝑀!",!" =   𝑓!" 𝑧

𝐴!".!"# =  𝐴!".!"#

 

For slabs, provide group of bars with area A s.prov per meter width Spacing of bars (mm)

Bar Diameter (mm)

8 10 12 16 20 25 32

75 670 1047 1508 2681 4189 6545 10723

100 503 785 1131 2011 3142 4909 8042

125 402 628 905 1608 2513 3927 6434

150 335 524 754 1340 2094 3272 5362

175 287 449 646 1149 1795 2805 4596

200 251 393 565 1005 1571 2454 4021

225 223 349 503 894 1396 2182 3574

250 201 314 452 804 1257 1963 3217

275 183 286 411 731 1142 1785 2925

300 168 262 377 670 1047 1636 2681

8 402 628 905 1608 2513 3927 6434

9 452 707 1018 1810 2827 4418 7238

10 503 785 1131 2011 3142 4909 8042

For beams, provide group of bars with area As. prov Number of bars

Bar Diameter (mm)

8 10 12 16 20 25 32

1 50 79 113 201 314 491 804

2 101 157 226 402 628 982 1608

3 151 236 339 603 942 1473 2413

4 201 314 452 804 1257 1963 3217

5 251 393 565 1005 1571 2454 4021

6 302 471 679 1206 1885 2945 4825

7 352 550 792 1407 2199 3436 5630

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

7  

 

SHEAR FORCE DESIGN (EN1992-1-1,cl 6.2)

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)

 

MEd= 0.4F

 

F: is the total ultimate load =1.35Gk+1.5Qk

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+!

𝑉!".! = !

200 ≤ 2,0  with  𝑑  in  mm 𝑑

! 0.18 𝑘(100𝜌! 𝑓!" )! + 𝑘!  𝜎!" ! 𝑏𝑑 𝛾!

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 0.25% 0.54 0.52 0.50 0.48 0.47 0.45 0.50% 0.59 0.57 0.56 0.55 0.54 0.52 0.75% 0.68 0.66 0.64 0.63 0.62 0.59 1.00% 0.75 0.72 0.71 0.69 0.68 0.65 1.25% 0.80 0.78 0.76 0.74 0.73 0.71 1.50% 0.85 0.83 0.81 0.79 0.78 0.75 1.75% 0.90 0.87 0.85 0.83 0.82 0.79 ≥2.00% 0.94 0.91 0.89 0.87 0.85 0.82 k 2.000 1.943 1.894 1.853 1.816 1.756 1/3 1.5 0.5 Table derived from: vRd.c=0.12k(100 ρI fck) ≥0.035k fck where k=1+(200/d)0.5≤0.02  

400 0.43 0.51 0.58 0.64 0.69 0.73 0.77 0.80 1.707

450 0.41 0.49 0.56 0.62 0.67 0.71 0.75 0.78 1.667

500 600 0.40 0.38 0.48 0.47 0.55 0.53 0.61 0.59 0.66 0.63 0.70 0.67 0.73 0.71 0.77 0.74 1.632 1.577

750 0.36 0.45 0.51 0.57 0.61 0.65 0.68 0.71 1.516

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

 

Shear  reinforcement  is  not  required  in  slabs      

8  

 

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

Minimum area of reinforcement steel within tensile zone (EN1992-1-1,Eq. 7.1) 𝐴!.!!" =

 

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

𝑘  𝑘! 𝑓!",!"" 𝐴!" 𝜎!

𝜎! = 𝜎!" !

 

!!.!"# ! !!.!"#$ !

!

or

𝜎! = 0.62 !

!!.!"# 𝑓 ! !!.!"#$ !"

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

 

 

Asmin 𝜌! ′ 𝑑 𝜌 − 𝜌 12 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  w here  the  span>7.0m,  multiply  by   leff/7   Type of member Cantilever Flat slab Simply supported Continuous end span Continuous interior span  

K 0.4 1.2 1.0 1.3 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

10  

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

Dimensions:

Depth of slab, h: Length in longitudinal direction, Ly: Length in transverse direction, Lx: Number of slab panels: 2.

Loads:

Dead load: Self weight, gk.s: Extra dead load, gk.e: Total dead load, Gk: Live load: Live load, qk: Total live load, Qk: 3.

h=150mm Ly=6m Lx=5m N=3

gk.s=3.75kN/m2 gk.e=1.00kN/m2 Gk=4.75kN/m2 gk=2.00kN/m2 Qk=2.00kN/m2

Load combination:

Total load on slab: 1.35Gk+1.5Qk= COMB1: 4.

 

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

Layout of model:

11  

  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

 

12  

  4.1.3 Hand calculation results Ultimate moment at longitudinal direction Ly Program results

ETABS Results Hand calculation results 1 Error percentage

Mid-span GL1-GL2 (kNm)

GL2 (kNm)

Mid-span GL2-GL3 (kNm)

GL3

Mid-span GL3-GL4 (kNm)

10.43

11.54

7.68

11.54

10.40

10.20

13.60

8.00

10.70

10.20

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)”.

Ultimate moment at longitudinal direction Lx Program results

ETABS Results Hand calculation results 1 Error percentage

Mid-span GL1-GL2 (kNm)

Mid-span GL2-GL3 (kNm)

Mid-span GL3-GL4 (kNm)

13.5

13.5

13.5

13.2

13.2

13.2

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)”.

 

13  

  4.1.4 Hand calculation Results Analysis and design of Interior slab panel (GL1-GL2)

 

14  

  Analysis and design of Interior slab panel (GL2-GL3)

 

15  

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

 

16  

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