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:
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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 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
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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.
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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
K
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 !
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!"
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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
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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
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
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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. !.! 𝑙 𝜌! 𝜌! = 𝐾 !11 + 1.5!𝑓!" + 3.2!𝑓!" ! − 1! ! 𝑖𝑓 𝜌 ≤ 𝜌! 𝑑 𝜌 𝜌 𝑙 𝜌! 1 𝜌, = 𝐾 !11 + 1.5!𝑓!" + !𝑓!" ! ! 𝑖𝑓 𝜌 > 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
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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:
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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 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%
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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)”.
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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)
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