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CSI ETABS & SAFE MANUAL: Slab Analysis and Design to EC2


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 CSI ETABS & SAFE 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.

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CSI ETABS & SAFE MANUAL: Slab Analysis and Design to EC2

  1. 1. CSI ETABS & SAFE MANUAL Part‐III: Model Analysis & Design of Slabs According to Eurocode 2 AUTHOR: VALENTINOS NEOPHYTOU BEng (Hons), MSc REVISION 2: August, 2014
  2. 2. 2 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 CSI ETABS & SAFE 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
  3. 3. 3 TABLE OF CONTENTS 1. SLAB MODELING .................................................................................... 4 2. THEORETICAL CALCULATION OF ULTIMATE MOMENTS ......... 5 3. DESIGN OF SLAB ACCORDING TO EUROCODE 2 ........................... 7 4. WORKED EXAMPLE : ANALYSIS AND DESIGN OF RC SLAB USING CSI ETABS AND SAFE .............................................................. 11 5. ANALYSIS RESULTS ............................................................................. 17 6. DESIGN THE SLAB FOR FLEXURAL USING MOMENT CAPACITY VALUES .................................................................................................... 19 ANNEX A - EXAMPLE OF HOW TO DETERMINE THE DESIGN BENDING MOMENT USING MOMENT COEFFICIENTS...…………………….22 ANNEX B - EXAMPLE OF HOW TO DETERMINE THE MOMENT CAPACITY OF RC SLAB………………………………………………………..…….28 ANNEX C - EXAMPLE OF DESIGN SLAB PANEL WITH TWO DISCONTINUOUS EDGES…………..…..………………………..…….32 ANNEX D - EXAMPLE OF DESIGN SLAB PANEL WITH ONE DISCONTINUOUS EDGES………………………………………..…….48 ANNEX E - EXAMPLE OF DESIGN INTERIOR PANEL SLAB..…………..…….65
  4. 4. 4 1. 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.
  5. 5. 5 2. THEORETICAL 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 2 in Msx= asxnlx direction of span lx Maximum moment of Simply supported (pinned) two-way slab n: is the ultimate load m2 2 in Msy= asynlx 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 Restrained supported (fixed) two-way slab 2 in Msx= asxnlx direction of span lx n: is the ultimate load m2 2 in Msy= asynlx 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 1.0 1.25 1.5 1.75 2.0 values of Ly/Lx 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
  6. 6. 6 Maximum moment of Simply supported (pinned) one-way slab (Manual of EC2, Table 5.2) 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+1.5Qk 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 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.
  7. 7. Check of the amount of reinforcement provided above the “minimum/maximum amount of 7 3. DESIGN OF SLAB ACCORDING TO EUROCODE 2 FLEXURAL DESIGN (EN1992-1-1,cl. 6.1) Determine design yield strength of reinforcement 푓푦푑 = 푓푦푘 훾푠 Determine K from: 퐾 = 푀퐸푑 푏푑2푓푐푘 퐾′ = 0.6훿 − 0.18훿2 − 0.21 K<K′ (no compression reinforcement required) Obtain lever arm z:푧 = 푑 2 1 + 1 − 3.53퐾 ≤ 0.95푑 K>K′(then compression reinforcement required – not recommended for typical slab) Obtain lever arm z:푧 = 푑 2 1 + 1 − 3.53퐾′ ≤ 0.95푑 δ=1.0 for no redistribution δ=0.85 for 15% redistribution δ=0.7 for 30% redistribution 퐴푠.푟푒푞 = 푀퐸푑 푓푦푑 푧 퐴푠푥 .푟푒푞 = 푀퐸푑 ,푠푥 푓푦푑 푧 퐴푠푦 .푟푒푞 = 푀퐸푑 ,푠푦 푓푦푑 푧 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 퐴푠,푚푖푛 = (CYS NA EN1992-1-1, cl. NA 2.49(1)(3)) 0.26푓푐푡푚 푏푑 푓푦푘 reinforcement “limit ≥ 0.0013푏푑 ≤ 퐴푠,푝푟표푣 ≤ 퐴푠,푚푎푥 = 0.04퐴푐
  8. 8. 8 SHEAR FORCE DESIGN (EN1992-1-1,cl 6.2) Maximum moment of Simply supported (pinned) (Manual of EC2, Table 5.2) MEd= 0.4F one-way slab F: is the total ultimate load =1.35Gk+1.5Qk 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 푘 = 1 + 200 푑 Design shear resistance ≤ 2,0with 푑 in mm 푉푅푑 .푐 = 0.18 훾푐 푘 100휌1푓푐푘 1 3 + 푘1휎푐푝 푏푑 푉푅푑 .푐 .푚푖푛 = 0.0035 푓푐푘 푘1.5 + 푘1휎푐푝 푏푑 Alternative value of design shear resistance, VRd.c (Concrete centre) (ΜΡa) ρI = Effective depth, d (mm) As/(bd) ≤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(100ρIfck)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
  9. 9. 9 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) 퐴푠.푚푖푛 = 푘푘푐 푓푐푡 ,푒푓푓 퐴푐푡 휎푠 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.provis 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 휎푠 = 휎푠푢 퐴푠.푟푒푞 퐴푠.푝푟표푣 1 훿 or 휎푠 = 0.62 퐴푠.푟푒푞 퐴푠.푝푟표푣 푓푦푘
  10. 10. 10 DESIGN FOR DEFLECTION (EN1992-1-1,cl.7.4) Simplified Calculation approach 푙 푑 = 퐾 11 + 1.5 푓푐푘 휌0 휌 + 3.2 푓푐푘 휌0 휌 − 1 1.5 푖푓휌 ≤ 휌0 푙 푑 = 퐾 11 + 1.5 푓푐푘 휌0 휌 − 휌′ + 1 12 푓푐푘 휌, 휌0 푖푓휌 > 휌0 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. 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)) 휌0 = 0.001 푓푐푘 Tension reinforcement ratio (EN1992-1-1,cl. 7.4.2(2)) 휌 = 퐴푠.푟푒푞 푏푑
  11. 11. 11 4. WORKED EXAMPLE : ANALYSIS AND DESIGN OF RC SLAB USING CSI ETABS AND SAFE 4.1 DIMENSIONS: Depth of slab, h: h=170mm Length in longitudinal direction, Ly: Ly=5m Length in transverse direction, Lx: Lx=5m Number of slab panels: N=3x3 4.2 LOADS: Dead load: Self weight, gk.s: gk.s=4.25kN/m2 Extra dead load, gk.e: gk.e=2.00kN/m2 Total dead load, Gk: Gk=6.25kN/m2 Live load: Live load, qk: gk=2.00kN/m2 Total live load, Qk: Qk=2.00kN/m2 4.3 LOAD COMBINATION: Total load on slab: 1.35Gk+1.5Qk= ULS: 1.35*6.25+1.5*2.00=11.4kN/m2 Total load on slab: 1.35Gk+1.5Qk= SLS: 1.00*6.25+1.00*2.00=8.25kN/m2
  12. 12. 12 4.4 LAYOUT OF MODEL: Figure 1: Layout of the model
  13. 13. 13 4.5 PROCEDURE FOR EXPORTING ETABS MODEL TO SAFE A very useful and powerful way to start a model in SAFE is to import the model from ETABS. Floor slabs or basemats that have been modeled in ETABS can be exported from ETABS. From that form, the appropriate floor load option can be selected, along with the desired load cases. After the model has been exported as an .f2k text file, the same file can then be imported into SAFE using the File menu > Import command. Using the export and import steps will complete the transfer of the slab geometry, section properties, and loading for the selected load cases. The design strips need to be added to the imported model since design strips are not defined as part of the ETABS model. ETABS: File > Export > Storey as SAFE Text File commands saves the specified story level as a SAFE.f2k text input file. You can later import this file/model into SAFE. Figure 2: Load to Export to SAFE Notes: Model must be analyzed and locked to export. The export floor loads only option is for individual floor plate design. The export floor loads and loads from above is used to design foundation. The export floor loads plus Column and Wall Distortions is necessary only when displacement compatibility could govern and needs to be checked floor slab design.(Effects punching shear and flexural reinforcement design).
  14. 14. 14 Figure 3: Load cases selection Figure 4: Load combination selection
  15. 15. 15 4.6 DRAW DESIGN STRIPS Use the Draw menu > Draw Design Strips command to add design strips to the model. Design strips are drawn as lines, but have a width associated with them. Design strips are typically drawn over support locations (e.g., columns), with a width equal to the distance between midspan in the transverse direction. Design strips determine how reinforcing will be calculated and positioned in the slab. Forces are integrated across the design strips and used to calculate the required reinforcing. Typically design strips are positioned in two principal directions: Layer A and Layer B. Select the Auto option. The added design strips will automatically adjust their width to align with adjacent strips. Figure 5: Design strip for x direction
  16. 16. 16 Figure 6: Design strip for y direction Figure 7: Model after drawing design strip
  17. 17. 17 5. ANALYSIS RESULTS Figure 8: Maximum hogging and Sagging moment at Short span direction Lx Figure 9: Maximum Shear Force at Short span direction Lx
  18. 18. Figure 10: Maximum hogging and Sagging moment at Long span direction 18 Ly Figure 11: Maximum Shear Force at Short span direction Ly
  19. 19. 6. DESIGN THE SLAB FOR FLEXURAL USING MOMENT CAPACITY 19 VALUES SAFE: Display > Show slab forces/stresses
  20. 20. 20 Figure 12: Bending moment for M11 (Mx – direction) contours displayed The figure above indicates that the proposed bending reinforcements are adequate to resist the design moment (hogging & sagging moments).
  21. 21. 21 Figure13: Bending moment for M22 (My – direction) contours displayed The figure above indicates that the proposed bending reinforcements are adequate to resist the design moment (hogging & sagging moments).
  22. 22. ANNEX A - EXAMPLE OF HOW TO DETERMINE THE DESIGN 22 BENDING MOMENT USING MOMENT COEFFICIENTS
  23. 23. CALUCLATIION SHEET BEAM FLEXURAL AND SHEAR CAPACITY CHECK Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK BENDING MOMENT COEFFICIENTS FOR TWO-WAY SPANNING RECTANGULAR SLABS (Table 5.3, Manual to EC2 - IStrucTE) GEOMETRICAL DATA: Shorter effective span of panel (clear span): lx  5000mm Longer effective span of panel: ly  5000mm Type of panel and moment considered: Slab_type:= "Interior panel" Slab_type:= "One short edge discontinuous" Slab_type:= "One long edge discontinuous" Slab_type:= "Two adjacent edges discontinuous" Slab_type  "Two adjacent edges discontinuous" Ratio of Ly/Lx: Ratio ly lx   1 LOADINGS: Characteistic permanent action: Gk 6.25kN m 2   Characteistic variable action: Qk 2kN m 2   PARTIAL FACTOR FOR LOADS: Permanent action (dead load) - Ultimate limit state (ULS): γGk.ULS  1.35 Variable action (live load) - Ultimate limit state (ULS): γQk.ULS  1.50 Permanent action (dead load) - Ultimate limit state (SLS): γGk.SLS  1.00 Variable action (live load) - Ultimate limit state (SLS): γQk.SLS  1.00 DESIGN LOADS: Ultimate design load (ULS): FEd.ULS γGk.ULSGk  γQk.ULSQk 11.438 kN m 2     Ultimate design load (SLS): FEd.SLS γGk.SLSGk  γQk.SLSQk 8.25 kN m 2     MOMENT COEFFICIENT: Short span - Bending moment coefficient for negative moment (hogging moment) at continuous edge SEISMIC ASSESSMENT OF EXISTING RC BUILDING Page 23 of 27
  24. 24. CALUCLATIION SHEET BEAM FLEXURAL AND SHEAR CAPACITY CHECK Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK βsx.support 0.031 lx ly if  1.0  Slab_type = "Interior panel" 0.044 1.0 ly lx if   1.25  Slab_type = "Interior panel" 0.053 1.25 ly lx if   1.50  Slab_type = "Interior panel" 0.059 1.5 ly lx if   1.75  Slab_type = "Interior panel" 0.063 1.75 ly lx if   2.00  Slab_type = "Interior panel" 0.039 lx ly if  1.0  Slab_type = "One short edge discontinuous" 0.050 1.0 ly lx if   1.25  Slab_type = "One short edge discontinuous" 0.058 1.25 ly lx if   1.50  Slab_type = "One short edge discontinuous" 0.063 1.5 ly lx if   1.75  Slab_type = "One short edge discontinuous" 0.067 1.75 ly lx if   2.00  Slab_type = "One short edge discontinuous" 0.039 lx ly if  1.0  Slab_type = "One long edge discontinuous" 0.059 1.0 ly lx if   1.25  Slab_type = "One long edge discontinuous" 0.073 1.25 ly lx if   1.50  Slab_type = "One long edge discontinuous" 0.082 1.5 ly lx if   1.75  Slab_type = "One long edge discontinuous" 0.089 1.75 ly lx if   2.00  Slab_type = "One long edge discontinuous" 0.047 lx ly if  1.0  Slab_type = "Two adjacent edges discontinuous" 0.066 1.0 ly lx if   1.25  Slab_type = "Two adjacent edges discontinuous" l  SEISMIC ASSESSMENT OF EXISTING RC BUILDING Page 24 of 27
  25. 25. CALUCLATIION SHEET BEAM FLEXURAL AND SHEAR CAPACITY CHECK Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK 0.078 1.25 ly lx if   1.50  Slab_type = "Two adjacent edges discontinuous" 0.087 1.5 ly lx if   1.75  Slab_type = "Two adjacent edges discontinuous" 0.093 1.75 ly lx if   2.00  Slab_type = "Two adjacent edges discontinuous" Short span - Bending moment coefficient for positive moment (sagging moment) at continuous edge βsx.midspan 0.024 lx ly if  1.0  Slab_type = "Interior panel" 0.034 1.0 ly lx if   1.25  Slab_type = "Interior panel" 0.040 1.25 ly lx if   1.50  Slab_type = "Interior panel" 0.044 1.5 ly lx if   1.75  Slab_type = "Interior panel" 0.048 1.75 ly lx if   2.00  Slab_type = "Interior panel" 0.029 lx ly if  1.0  Slab_type = "One short edge discontinuous" 0.038 1.0 ly lx if   1.25  Slab_type = "One short edge discontinuous" 0.043 1.25 ly lx if   1.50  Slab_type = "One short edge discontinuous" 0.047 1.5 ly lx if   1.75  Slab_type = "One short edge discontinuous" 0.050 1.75 ly lx if   2.00  Slab_type = "One short edge discontinuous" 0.030 lx ly if  1.0  Slab_type = "One long edge discontinuous" 0.045 1.0 ly lx if   1.25  Slab_type = "One long edge discontinuous" 0.055 1.25 ly lx if   1.50  Slab_type = "One long edge discontinuous" l  SEISMIC ASSESSMENT OF EXISTING RC BUILDING Page 25 of 27
  26. 26. CALUCLATIION SHEET BEAM FLEXURAL AND SHEAR CAPACITY CHECK Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK 0.062 1.5 ly lx if   1.75  Slab_type = "One long edge discontinuous" 0.067 1.75 ly lx if   2.00  Slab_type = "One long edge discontinuous" 0.036 lx ly if  1.0  Slab_type = "Two adjacent edges discontinuous" 0.049 1.0 ly lx if   1.25  Slab_type = "Two adjacent edges discontinuous" 0.059 1.25 ly lx if   1.50  Slab_type = "Two adjacent edges discontinuous" 0.065 1.5 ly lx if   1.75  Slab_type = "Two adjacent edges discontinuous" 0.070 1.75 ly lx if   2.00  Slab_type = "Two adjacent edges discontinuous" Long span - Bending moment coefficient for negative moment (hogging moment) at continuous edge βsy.support 0.032 if Slab_type = "Interior panel" 0.037 if Slab_type = "One short edge discontinuous" 0.037 if Slab_type = "One long edge discontinuous" 0.045 if Slab_type = "Two adjacent edges discontinuous"  Long span - Bending moment coefficient for positive moment (sagging moment) at continuous edge βsy.midspan 0.024 if Slab_type = "Interior panel" 0.028 if Slab_type = "One short edge discontinuous" 0.028 if Slab_type = "One long edge discontinuous" 0.034 if Slab_type = "Two adjacent edges discontinuous"  Summary of moment coefficient: Short span - Moment coefficient - support: βsx.support  0.047 Short span - Moment coefficient - midspan: βsx.midspan  0.036 Long span - Moment coefficient - support: βsy.support  0.045 Long span - Moment coefficient - midspan: βsy.midspan  0.034 SEISMIC ASSESSMENT OF EXISTING RC BUILDING Page 26 of 27
  27. 27. CALUCLATIION SHEET BEAM FLEXURAL AND SHEAR CAPACITY CHECK Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK BENDING MOMENT RESULTS: Note: Bending moment per unit width. Short span - Bending moment at support: MEd.sx.sup βsx.supportFEd.ULS lx   2  13.439kN   2  10.294kN Short span - Bending moment at midspan: MEd.sx.mid βsx.midspanFEd.ULS lx   2  12.867kN Long span - Bending moment at support: MEd.sy.sup βsy.supportFEd.ULS lx   2  9.722kN Long span - Bending moment at midspan: MEd.sy.mid βsy.midspanFEd.ULS lx SEISMIC ASSESSMENT OF EXISTING RC BUILDING Page 27 of 27
  28. 28. ANNEX B - EXAMPLE OF HOW TO DETERMINE THE MOMENT 28 CAPACITY OF RC SLAB
  29. 29. CALUCLATIION SHEET BEAM FLEXURAL CAPACITY CHECK Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Note: The following colour key is a guide to using the full calculation page. INPUT DTATA COMPUTED OUTPUT DATA TO BE CHECKED STANDARD DATA Figure 1: Analysis of rectangular section - stress strain ASSUMPTIONS: GEOMETRICAL DATA: Concrete cover: cnom  25mm Breadth of the section (assumed 1m strip): b  1m Depth of the section: h  170mm Longitudinal diameter (tension zone - bottom): dt  10mm Longitudinal diameter (compression zone - top): dc  12mm Spacing of steel reinforcement: sp  200mm    392.699mm2 Area of steel reinforcement provided: As.prov.t π 2 4 dt  m sp    565.487mm2 Area of steel reinforcement provided: As.prov.c π 2 4 dc  m sp Effective depth of the section. d: d h  cnom dt 2    140mm Effective depth of the section. d2: d2 cnom dc 2    31mm MATERIAL PROPERTIES: Mean characteristic compressive SLAB DESIGN TO EUROCODE 2 Page 29 of 31
  30. 30. CALUCLATIION SHEET BEAM FLEXURAL CAPACITY CHECK Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN cylinder strength of concrete (Laboratory results): fck 30N mm 2   Characteristic yield strength of steel reinforcement: fyk 500N mm 2   PARTIAL SAFETY FACTOR (CYS NA EN1992-1-1,Table 2.1): Partial factor for reinforcement steel (NA CYS EN 1992-1-1:2004, Table 2.1)): γs  1.15 Partial factor for concrete (NA CYS EN 1992-1-1:2004, Table 2.1)): γc  1.5 DESIGN STRENGTHS OF MATERIAL(EN1992-1-1,cl.3.1.6): Design yield strength of reinforcement (EN1992-1-1,Fig.3.8): fyd fyk γs 434.783 N mm 2     Coefficient value for compressive strength (NA CYS EN 1992-1-1:2004, cl. NA 2.8): αcc  1 Design value of concrete compressive strength fcd (EN 1992-1-1:2004, Equation 3.15): αccfck γc 20 N mm 2     RECTANGULAR STRESS BLOCK FACTORS: Factor, λ λ  0.8 if fck  50MPa  0.8 (EN1992-1-1,Eq.3.19&3.20) 0.8 fck  50MPa 400MPa    if fck  50MPa Factor, η η  1.0 if fck  50MPa  1 (EN1992-1-1,Eq.3.21&3.22) 1.0 fck  50MPa 200MPa    if fck  50MPa BENDING MOMENT CAPACITY (AT MIDSPAN) FOR A SINGLY REINFORCED SECTION Figure 2: Detail of reinforcement slab at midspan For equilibrium, the ultimate design moment, must be balanced by the moment of resistance of the section (figure 1): Fc  Fst Fst  fydAs.prov.t  170.739kN Fc  fcdbλx  kN Therefore depth of stress block is: SLAB DESIGN TO EUROCODE 2 Page 30 of 31
  31. 31. CALUCLATIION SHEET BEAM FLEXURAL CAPACITY CHECK Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN s fydAs.prov.t fcdb   8.537mm x s   10.671mm λ To ensure rotation of the plastic hinge with sufficient yielding of the tension steel and also to allow for other factors such as the strain hardening of the steel, EC2 limit the depth of neutral axis to: Check  if (x  0.45d"PASS" "FAIL" )  "PASS" z d s 2    135.732mm Moment capacity: MRd  fydAs.prov.tz  23.175kNm BENDING CAPACITY (AT SUPPORTS) OF SECTION WITH COMPRESSION REINFORCEMENT AT ULTIMATE LIMIT STATE Figure 3: Detail of reinforcement slab at support For equilibrium, the ultimate design moment, must be balanced by the moment of resistance of the section (figure 1): Fst  Fc  Fsc Fsc  fydAs.prov.c  245.864kN Fst  fydAs.prov.t  170.739kN Fc  fcdbλx Therefore depth of stress block is: s fydAs.prov.c  As.prov.t   3.756mm fcdb x s   10.671mm λ Check  if (x  0.45d"PASS" "FAIL" )  "PASS" To ensure rotation of the plastic hinge with sufficient yielding of the tension steel and also to allow for other factors such as the strain hardening of the steel, EC2 limit the depth of neutral axis to: Moment capacity: MRd. fcdbs d s 2       fydAs.prov.cd  d2  37.176kNm SLAB DESIGN TO EUROCODE 2 Page 31 of 31
  32. 32. 32 ANNEX C - EXAMPLE OF DESIGN SLAB PANEL WITH TWO DISCONTINUOUS EDGES
  33. 33. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Note: The following colour key is a guide to using the full calculation page. INPUT DTATA ASSUMPTIONS: 1. Fire resistance 1hour (REI 60). 2. Exposure class of concrete XC1. 3. No redistribution of bending moment made. COMPUTED OUTPUT DATA TO BE CHECKED STANDARD DATA GEOMETRICAL DATA: Structural_system:= "Simply supported" "End span of continuous slab" "Interior span" "Flat slab" "Cantilever" Structural system: Structural_system  "End span of continous slab" Depth of slab: h  170mm Strip width: b  1000mm Shorter effective span of panel (clear span): lx  5000mm Longer effective span of panel: ly  5000mm Type of slab: Type_slab "Two way slab" ly lx  if  2.0  "Two way slab" "One way slab" ly lx if  2.0 ANALYSIS & LOADING RESULTS: TWO DISCONTINOUS EDGE Page 33 of 48
  34. 34. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Figure 1: Bending moment diagram for x - direction Figure 2: Bending moment diagram for y - direction TWO DISCONTINOUS EDGE Page 34 of 48
  35. 35. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Figure 3: Shear force diagram for x - direction TWO DISCONTINOUS EDGE Page 35 of 48
  36. 36. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Figure 4: Shear force diagram for y - direction Loads: Characteistic permanent action: Gk 6.25kN m 2   Characteistic variable action: Qk 2kN m 2   Quasi-permanent value of variable action: ψ2  0.3 Short span: Design bending moment at short span - continuous support: Mx.1  21.14kNm Design bending moment at short span - middle: Mx.m  12.35kNm Design shear force at short span - continous support: Vx.1  21kN Design shear force at short span - discontinous support: Vx.2  13kN Long span: Design bending moment at long span - continous support: My.1  10.52kNm Design bending moment at long span - middle: My.m  11.86kNm Design shear force at long span - continous support: Vy.1  18kN TWO DISCONTINOUS EDGE Page 36 of 48
  37. 37. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Design shear force at long span - discontinous support: Vy.2  13kN STEEL REINFORCEMENT PROPERTIES: Bars diameter for short/long span-midspan: ϕy.p  10mm Characteristic yield strength of steel reinforcement: fyk 500N mm 2    CONCRETE PROPERTIES: Characteristic compressive cylinder strength of concrete: fck 30N mm 2    Mean value of compressive sylinder strength (EN 1992-1-1:2004, table 3.1): fctm 0.3 fck MPa   0.667    MPa 2.9 N mm 2     PARTIAL SAFETY FACTORS: Partial factor for reinforcement steel (NA CYS EN 1992-1-1:2004, Table 2.1)): γs  1.15 Partial factor for concrete (NA CYS EN 1992-1-1:2004, Table 2.1)): γc  1.5 DESIGN STRENGTHS OF MATERIAL(EN1992-1-1,cl.3.1.6): Design yield strength of reinforcement (EN1992-1-1,Fig.3.8): fyd fyk γs 434.783 N mm 2     Coefficient value for compressive strength (NA CYS EN 1992-1-1:2004, cl. NA 2.8): αcc  1 Design value of concrete compressive strength fcd (EN 1992-1-1:2004, Equation 3.15): αccfck γc 20 N mm 2     CONCRETE COVER TO REINFORCEMENT: Allowance in design for deviation (Assuming no measurement of cover) (EN1992-1-1,cl.4.4.1.3(3): Δcdev  10mm Minimum cover due to bond (Diameter of bar) (EN1992-1-1,Table 4.2): cmin.b  ϕy.p  10mm Minimum cover due to environmental condition (Condition :XC1) ("How to design to Eurocode 2",Table 8): cmin.dur  15mm Minimum concrete cover (EN1992-1-1,Eq.4.2): cmin  maxcmin.bcmin.dur10mm  15mm Nominal cover (EN1992-1-1,Eq.4.1): cnom  cmin  Δcdev  25mm TWO DISCONTINOUS EDGE Page 37 of 48
  38. 38. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK FIRE DESIGN CHECK: Minimum slab thickness (EN1992-1-2,Table 5.8): hs.min  80mm Fire_resistance  if h  hs.min"OK" "NOT OK"   "OK" Axis distance to top and bottom reinforcement, a (EN1992-1-2,Table 5.8): amin  20mm Minimum distance to top and bottom reinforcement: aprov cnom ϕy.p 2    30mm Fire_resistance  if aprov  amin"OK" "NOT OK"   "OK" REINFORCEMENT DESIGN AT MID-SPAN IN SHORT SPAN DIRECTION: Actual bar size: ϕx.m  10mm Actual bar spacing: sx.m  200mm    392.699mm2 Area of reinforcement provided: Asx.m π 2 4 ϕx.m  m sx.m dx.m h  cnom ϕx.m 2    140mm Values for Klim (Assumed no redistribution): K Mx.m b dx.m   0.021 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dx.m 2 1  1  3.53K   0.95dx.m     133mm Area of reinforcement required for bending: Asx.p.m Mx.m fydz   213.571mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdx.m0.0013bdx.m     211.102m Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdx.m 5.6 10   3mm2 Check_steel_1  if Asx.p.m  Asx.m  As.min  Asx.m  As.max"OK" "NOT OK"   "OK" Ratio_1 maxAs.minAsx.p.m   0.544 Asx.m Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asx.p.m Asx.m 1      141.617 N mm 2     TWO DISCONTINOUS EDGE Page 38 of 48
  39. 39. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   300mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  300mm Spacing_1  if sx.m  smax."OK" "NOT OK"   "OK" Ratio_s_1 sx.m smax   0.667 REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT IN SHORT SPAN DIRECTION: Actual bar size: ϕx.1  12mm Actual bar spacing: sx.1  200mm    565.487mm2 Area of reinforcement provided: Asx.1 π 2 4 ϕx.1  m sx.1 dx.1 h  cnom ϕx.1 2    139mm Values for Klim (Assumed no redistribution): K Mx.1 b dx.1   0.036 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dx.1 2 1  1  3.53K   0.95dx.1     132.05mm Area of reinforcement required for bending: Asx.n.1 Mx.1 fydz   368.209mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdx.10.0013bdx.1     209.594mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdx.1 5.56 10   3mm2 TWO DISCONTINOUS EDGE Page 39 of 48
  40. 40. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Check_steel_2  if Asx.n.1  Asx.1  As.min  Asx.1  As.max"OK" "NOT OK"   "OK" Ratio_2 maxAs.minAsx.n.1   0.651 Asx.1 Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asx.n.1 Asx.1 1      169.552 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   275mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  275mm Spacing_2  if sx.1  smax."OK" "NOT OK"   "OK" Ratio_s_2 sx.1 smax   0.727 REINFORCEMENT DESIGN AT MID-SPAN IN LONG SPAN DIRECTION: Actual bar size: ϕy.m  10mm Actual bar spacing: sy.m  200mm    392.699mm2 Area of reinforcement provided: Asy.m π 2 4 ϕy.m  m sy.m dy.m h  cnom ϕy.m 2    140mm Values for Klim (Assumed no redistribution): K My.m b dy.m   0.02 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" TWO DISCONTINOUS EDGE Page 40 of 48
  41. 41. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Level arm: z min dy.m 2 1  1  3.53K   0.95dy.m     133mm Area of reinforcement required for bending: Asy.p.m My.m fydz   205.098mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdy.m0.0013bdy.m     211.102mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdy.m 5.6 10   3mm2 Check_steel_3  if Asy.p.m  Asy.m  As.min  Asy.m  As.max"OK" "NOT OK"   "OK" Ratio_3 maxAs.minAsy.p.m   0.538 Asy.m Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asy.p.m Asy.m 1      135.998 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   0.3m 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  300mm Spacing_3  if sy.m  smax."OK" "NOT OK"   "OK" Ratio_s_3 sy.m smax   0.667 REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT IN LONG SPAN DIRECTION: Actual bar size: ϕy.1  10mm Actual bar spacing: sy.1  200mm    392.699mm2 Area of reinforcement provided: Asy.1 π 2 4 ϕy.1  m sy.1 TWO DISCONTINOUS EDGE Page 41 of 48
  42. 42. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK dy.1 h  cnom ϕy.1 2    140mm Values for Klim (Assumed no redistribution): K My.1 b dy.1   0.018 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dy.1 2 1  1  3.53K   0.95dy.1     133mm Area of reinforcement required for bending: Asy.n.1 My.1 fydz   181.925mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdy.10.0013bdy.1     211.102mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdy.1 5.6 10   3mm2 Check_steel_4  if Asy.n.1  Asy.1  As.min  Asy.1  As.max"OK" "NOT OK"   "OK" Ratio_4 maxAs.minAsy.n.1   0.538 Asy.1 Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asy.n.1 Asy.1 1      120.632 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   300mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  300mm Spacing_4  if sx.1  smax."OK" "NOT OK"   "OK" Ratio_s_4 sy.m smax   0.667 TWO DISCONTINOUS EDGE Page 42 of 48
  43. 43. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK SHEAR CAPACITY CHECK AT SHORT SPAN CONTINUOUS SUPPORT: Effective depth factor (EN1992-1-1,cl.6.2.2): k min 2.0 1 200mm dx.1   0.5       2 Reinforcement ratio: ρ1 min 0.02 Asx.1 bdx.1    4.068 10 3    Minimum shear resistance (EN1992-1-1,Eq.6.3N &6.2b): VRd.c.min 0.035k fck MPa   0.5    bdx.1   N mm 2    53.293kN Shear resistance (EN1992-1-1, Eq.6.2a): VRd.c.x.1 max VRd.c.min 0.18MPa γc   k 100ρ1 fck MPa      0.333   bdx.1     76.743k Shear_1  if Vx.1  VRd.c.x.1"NO SHEAR REQUIRED" "SHEAR REQUIRED"  Shear_1  "NO SHEAR REQUIRED" Ratio1 Vx.1 VRd.c.x.1   0.274 SHEAR CAPACITY CHECK AT SHORT SPAN DISCONTINUOUS SUPPORT: Flexural reinforcement at As.req  Asx.m0.25  98.175mm2 discontinuous support EN1992-1-1,cl.9.3.1.2(2): Actual bar size: ϕx.2  8mm Bar spacing: sx.2  sx.m  200mm    251.327mm2 Area of reinforcement provided: Asx.2 π 2 4 ϕx.2  m sx.2 Effective depth: dx.2 h  cnom ϕx.2 2    141mm Effective depth factor (EN1992-1-1,cl.6.2.2): k min 2.0 1 200mm dx.2   0.5       2 Reinforcement ratio: ρ1 min 0.02 Asx.2 bdx.2    1.782 10 3    Minimum shear resistance (EN1992-1-1,Eq.6.3N &6.2b): VRd.c.min 0.035k fck MPa   0.5    bdx.2   N mm 2    54.06kN Shear resistance (EN1992-1-1, Eq.6.2a): VRd.c.x.2 max VRd.c.min 0.18MPa γc   k 100ρ1 fck MPa      0.333   bdx.2     59.143k Shear_2  if Vx.2  VRd.c.x.2"NO SHEAR REQUIRED" "SHEAR REQUIRED"  Shear_2  "NO SHEAR REQUIRED" TWO DISCONTINOUS EDGE Page 43 of 48
  44. 44. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Ratio2 Vx.2 VRd.c.x.2   0.22 SHEAR CAPACITY CHECK AT LONG SPAN CONTINUOUS SUPPORT: Effective depth factor (EN1992-1-1,cl.6.2.2): k min 2.0 1 200mm dy.1   0.5       2 Reinforcement ratio: ρ1 min 0.02 Asy.1 bdy.1    2.805 10 3    Minimum shear resistance (EN1992-1-1,Eq.6.3N &6.2b): VRd.c.min 0.035k fck MPa   0.5    bdy.1   N mm 2    53.677kN Shear resistance (EN1992-1-1, Eq.6.2a): VRd.c.y.1 max VRd.c.min 0.18MPa γc   k 100ρ1 fck MPa      0.333   bdy.1     68.294kN Shear_3  if Vy.1  VRd.c.y.1"NO SHEAR REQUIRED" "SHEAR REQUIRED"  Shear_3  "NO SHEAR REQUIRED" Ratio3 Vy.1 VRd.c.y.1   0.264 SHEAR CAPACITY CHECK AT LONG SPAN DISCONTINUOUS SUPPORT: Flexural reinforcement at As.req  Asy.m0.25  98.175mm2 discontinuous support EN1992-1-1,cl.9.3.1.2(2): Actual bar size: ϕy.2  8mm Bar spacing: sy.2  sy.m  200mm    251.327mm2 Area of reinforcement provided: Asy.2 π 2 4 ϕy.2  m sy.2 Effective depth: dy.2 h  cnom ϕy.2 2    141mm Effective depth factor (EN1992-1-1,cl.6.2.2): k min 2.0 1 200mm dy.2   0.5       2 Reinforcement ratio: ρ1 min 0.02 Asy.2 bdy.2    1.782 10 3    Minimum shear resistance (EN1992-1-1,Eq.6.3N &6.2b): VRd.c.min 0.035k fck MPa   0.5    bdy.2   N mm 2    54.06kN Shear resistance (EN1992-1-1, Eq.6.2a): VRd.c.y.2 max VRd.c.min 0.18MPa γc   k 100ρ1 fck MPa      0.333   bdy.2     59.143kN TWO DISCONTINOUS EDGE Page 44 of 48
  45. 45. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Shear_4  if Vy.2  VRd.c.y.2"NO SHEAR REQUIRED" "SHEAR REQUIRED"  Shear_4  "NO SHEAR REQUIRED" Ratio4 Vy.2 VRd.c.y.2   0.22 BASIC SPAN-TO-DEPTH DEFLECTION RATIO CHECK: Reference reinforcement ratio: ρo 0.001 fck MPa   0.5  5.477 10 3    Required compression reinforcement (at mid-span - short span): ρc  0 Required tension reinforcement (at mid-span - short span): ρt max 0.0035 Asx.m bdx.m    3.5 10 3    Structural system factor (EN1992-1-1,Table 7.4N): Kδ 1.0 if Structural_system = "Simply supported"   1.3 1.3 if Structural_system = "End span of continous slab" 1.5 if Structural_system = "Interior span" 1.2 if Structural_system = "Flat slab" 0.4 if Structural_system = "Cantilever" Basic limit span-to-depth ratio (EN1992-1-1,Eq.7.16a&7.16b):  Limx.bas Kδ 11 1.5 fck MPa   0.5    40.689 ρo ρt   3.2 fck MPa   0.5  ρo ρt  1   1.5     ρt ρo  if Kδ 11 1.5 fck MPa   0.5  ρo ρt  ρc   1 12 fck MPa   0.5  ρc ρo        if ρt  ρo Actual span to effective depth ratio: Ratioact lx dx.m   35.714 Deflection  if Ratioact  Limx.bas"OK" "NOT OK"   "OK" Ratio Ratioact Limx.bas   0.878 CALCULATION SUMMARY RESULTS: Short span - Bending capacity: PASS/FAIL: Ratio: Check bending capacity at midspan: Check_steel_1  "OK" Ratio_1  0.544 Spacing at midspan reinforcement: Spacing_1  "OK" Ratio_s_1  0.667 Check bending capacity at support 1: Check_steel_2  "OK" Ratio_2  0.651 Spacing at support 1 reinforcement: Spacing_2  "OK" Ratio_s_2  0.727 TWO DISCONTINOUS EDGE Page 45 of 48
  46. 46. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Long span - Bending capacity: PASS/FAIL: Ratio: Check bending capacity at midspan: Check_steel_3  "OK" Ratio_3  0.538 Spacing at midspan reinforcement: Spacing_3  "OK" Ratio_s_3  0.667 Check bending capacity at support 1: Check_steel_4  "OK" Ratio_4  0.538 Spacing at support 1 reinforcement: Spacing_4  "OK" Ratio_s_4  0.667 Short span - Shear capacity: PASS/FAIL: Ratio: Check shear capacity at support 1: Shear_1  "NO SHEAR REQUIRED" Ratio1  0.274 Check shear capacity at support 2: Shear_2  "NO SHEAR REQUIRED" Ratio2  0.22 Long span - Shear capacity: PASS/FAIL: Ratio: Check shear capacity at support 1: Shear_3  "NO SHEAR REQUIRED" Ratio3  0.264 Check shear capacity at support 2: Shear_4  "NO SHEAR REQUIRED" Ratio4  0.22 Deflection: PASS/FAIL: Ratio: Check deflection of panel: Deflection  "OK" Ratio  0.878 RENFORCEMENT SUMMARY: Short span: Midspan in short span direction: ϕx.m  10mm at C/C sx.m  200mm Continuous support 1 in short span direction: ϕx.1  12mm at C/C sx.1  200mm Discontinuous support 2 in short span direction: ϕx.2  8mm at C/C sx.2  200mm Long span: Midspan in short span direction: ϕy.m  10mm at C/C sy.m  200mm Continuous support 1 in long span direction: ϕy.1  10mm at C/C sy.1  200mm Discontinuous support 2 in long span direction: ϕy.2  8mm at C/C sy.2  200mm TWO DISCONTINOUS EDGE Page 46 of 48
  47. 47. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK ϕy.2  8mmsy.2  200mm ϕx.2  8mmsx.2  200mm ϕx.1  12mmsx.1  200mm ϕx.m  10mmsx.m  200mm ϕy.m  10mm sy.m  200mm ϕy.1  10mmsy.1  200mm TWO DISCONTINOUS EDGE Page 47 of 48
  48. 48. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK mm2 TWO DISCONTINOUS EDGE Page 48 of 48
  49. 49. 48 ANNEX D - EXAMPLE OF DESIGN SLAB PANEL WITH ONE DISCONTINUOUS EDGES
  50. 50. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Note: The following colour key is a guide to using the full calculation page. INPUT DTATA ASSUMPTIONS: 1. Fire resistance 1hour (REI 60). 2. Exposure class of concrete XC1. 3. No redistribution of bending moment made. COMPUTED OUTPUT DATA TO BE CHECKED STANDARD DATA GEOMETRICAL DATA: Structural_system:= "Simply supported" "End span of continuous slab" "Interior span" "Flat slab" "Cantilever" Structural system: Structural_system  "End span of continous slab" Depth of slab: h  170mm Strip width: b  1000mm Shorter effective span of panel (clear span): lx  5000mm Longer effective span of panel: ly  5000mm Type of slab: Type_slab "Two way slab" ly lx  if  2.0  "Two way slab" "One way slab" ly lx if  2.0 ANALYSIS & LOADING RESULTS: ONE DISCONTINUOUS EDGE Page 49 of 64
  51. 51. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Figure 1: Bending moment diagram for x - direction Figure 2: Bending moment diagram for y - direction ONE DISCONTINUOUS EDGE Page 50 of 64
  52. 52. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Figure 3: Shear force diagram for x - direction ONE DISCONTINUOUS EDGE Page 51 of 64
  53. 53. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Figure 4: Shear force diagram for y - direction Loads: Characteistic permanent action: Gk 6.25kN m 2   Characteistic variable action: Qk 2kN m 2   Quasi-permanent value of variable action: ψ2  0.3 Short span: Design bending moment at short span - continuous support: Mx.1  21kNm Design bending moment at short span - middle: Mx.m  7kNm Design bending moment at short span - continuous support: Mx.2  21kNm Design shear force at short span - continous support: Vx.1  22kN Design shear force at short span - continous support: Vx.2  18kN Long span: Design bending moment at long span - continous support: My.1  20kNm Design bending moment at long span - middle: My.m  12kNm ONE DISCONTINUOUS EDGE Page 52 of 64
  54. 54. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Design shear force at long span - continous support: Vy.1  21kN Design shear force at long span - discontinous support: Vy.2  13kN STEEL REINFORCEMENT PROPERTIES: Bars diameter for short/long span-midspan: ϕy.p  10mm Characteristic yield strength of steel reinforcement: fyk 500N mm 2    CONCRETE PROPERTIES: Characteristic compressive cylinder strength of concrete: fck 30N mm 2    Mean value of compressive sylinder strength (EN 1992-1-1:2004, table 3.1): fctm 0.3 fck MPa   0.667    MPa 2.9 N mm 2     PARTIAL SAFETY FACTORS: Partial factor for reinforcement steel (NA CYS EN 1992-1-1:2004, Table 2.1)): γs  1.15 Partial factor for concrete (NA CYS EN 1992-1-1:2004, Table 2.1)): γc  1.5 DESIGN STRENGTHS OF MATERIAL(EN1992-1-1,cl.3.1.6): Design yield strength of reinforcement (EN1992-1-1,Fig.3.8): fyd fyk γs 434.783 N mm 2     Coefficient value for compressive strength (NA CYS EN 1992-1-1:2004, cl. NA 2.8): αcc  1 Design value of concrete compressive strength fcd (EN 1992-1-1:2004, Equation 3.15): αccfck γc 20 N mm 2     CONCRETE COVER TO REINFORCEMENT: Allowance in design for deviation (Assuming no measurement of cover) (EN1992-1-1,cl.4.4.1.3(3): Δcdev  10mm Minimum cover due to bond (Diameter of bar) (EN1992-1-1,Table 4.2): cmin.b  ϕy.p  10mm Minimum cover due to environmental condition (Condition :XC1) ("How to design to Eurocode 2",Table 8): cmin.dur  15mm Minimum concrete cover (EN1992-1-1,Eq.4.2): cmin  maxcmin.bcmin.dur10mm  15mm ONE DISCONTINUOUS EDGE Page 53 of 64
  55. 55. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Nominal cover (EN1992-1-1,Eq.4.1): cnom  cmin  Δcdev  25mm FIRE DESIGN CHECK: Minimum slab thickness (EN1992-1-2,Table 5.8): hs.min  80mm Fire_resistance  if h  hs.min"OK" "NOT OK"   "OK" Axis distance to top and bottom reinforcement, a (EN1992-1-2,Table 5.8): amin  20mm Minimum distance to top and bottom reinforcement: aprov cnom ϕy.p 2    30mm Fire_resistance  if aprov  amin"OK" "NOT OK"   "OK" REINFORCEMENT DESIGN AT MID-SPAN IN SHORT SPAN DIRECTION: Actual bar size: ϕx.m  10mm Actual bar spacing: sx.m  200mm    392.699mm2 Area of reinforcement provided: Asx.m π 2 4 ϕx.m  m sx.m dx.m h  cnom ϕx.m 2    140mm Values for Klim (Assumed no redistribution): K Mx.m b dx.m   0.012 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dx.m 2 1  1  3.53K   0.95dx.m     133mm Area of reinforcement required for bending: Asx.p.m Mx.m fydz   121.053mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdx.m0.0013bdx.m     211.102mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdx.m 5.6 10   3mm2 Check_steel_1  if Asx.p.m  Asx.m  As.min  Asx.m  As.max"OK" "NOT OK"   "OK" Ratio_1 maxAs.minAsx.p.m   0.538 Asx.m ONE DISCONTINUOUS EDGE Page 54 of 64
  56. 56. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asx.p.m Asx.m 1      80.269 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   300mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  300mm Spacing_1  if sx.m  smax."OK" "NOT OK"   "OK" Ratio_s_1 sx.m smax   0.667 REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT 1 IN SHORT SPAN DIRECTION: Actual bar size: ϕx.1  12mm Actual bar spacing: sx.1  200mm    565.487mm2 Area of reinforcement provided: Asx.1 π 2 4 ϕx.1  m sx.1 dx.1 h  cnom ϕx.1 2    139mm Values for Klim (Assumed no redistribution): K Mx.1 b dx.1   0.036 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dx.1 2 1  1  3.53K   0.95dx.1     132.05mm Area of reinforcement required for bending: Asx.n.1 Mx.1 fydz   365.771mm2 ONE DISCONTINUOUS EDGE Page 55 of 64
  57. 57. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdx.10.0013bdx.1     209.594mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdx.1 5.56 10   3mm2 Check_steel_2  if Asx.n.1  Asx.1  As.min  Asx.1  As.max"OK" "NOT OK"   "OK" Ratio_2 maxAs.minAsx.n.1   0.647 Asx.1 Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asx.n.1 Asx.1 1      168.429 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   275mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  275mm Spacing_2  if sx.1  smax."OK" "NOT OK"   "OK" Ratio_s_2 sx.1 smax   0.727 REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT 2 IN SHORT SPAN DIRECTION: Actual bar size: ϕx.2  12mm Actual bar spacing: sx.2  200mm    565.487mm2 Area of reinforcement provided: Asx.2 π 2 4 ϕx.2  m sx.2 ONE DISCONTINUOUS EDGE Page 56 of 64
  58. 58. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK dx.2 h  cnom ϕx.2 2    139mm Values for Klim (Assumed no redistribution): K Mx.2 b dx.2   0.036 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dx.2 2 1  1  3.53K   0.95dx.2     132.05mm Area of reinforcement required for bending: Asx.n.2 Mx.2 fydz   365.771mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdx.20.0013bdx.2     209.594mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdx.2 5.56 10   3mm2 Check_steel_3  if Asx.n.2  Asx.2  As.min  Asx.2  As.max"OK" "NOT OK"   "OK" Ratio_3 maxAs.minAsx.n.2   0.647 Asx.2 Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asx.n.2 Asx.2 1      168.429 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   275mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  275mm Spacing_3  if sx.2  smax."OK" "NOT OK"   "OK" Ratio_s_3 sx.2 smax   0.727 ONE DISCONTINUOUS EDGE Page 57 of 64
  59. 59. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK REINFORCEMENT DESIGN AT MID-SPAN IN LONG SPAN DIRECTION: Actual bar size: ϕy.m  10mm Actual bar spacing: sy.m  200mm    392.699mm2 Area of reinforcement provided: Asy.m π 2 4 ϕy.m  m sy.m dy.m h  cnom ϕy.m 2    140mm Values for Klim (Assumed no redistribution): K My.m b dy.m   0.02 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dy.m 2 1  1  3.53K   0.95dy.m     133mm Area of reinforcement required for bending: Asy.p.m My.m fydz   207.519mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdy.m0.0013bdy.m     211.102mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdy.m 5.6 10   3mm2 Check_steel_4  if Asy.p.m  Asy.m  As.min  Asy.m  As.max"OK" "NOT OK"   "OK" Ratio_4 maxAs.minAsy.p.m   0.538 Asy.m Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asy.p.m Asy.m 1      137.603 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   0.3m 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa ONE DISCONTINUOUS EDGE Page 58 of 64
  60. 60. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  300mm Spacing_4  if sy.m  smax."OK" "NOT OK"   "OK" Ratio_s_4 sy.m smax   0.667 REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT IN LONG SPAN DIRECTION: Actual bar size: ϕy.1  12mm Actual bar spacing: sy.1  200mm    565.487mm2 Area of reinforcement provided: Asy.1 π 2 4 ϕy.1  m sy.1 dy.1 h  cnom ϕy.1 2    139mm Values for Klim (Assumed no redistribution): K My.1 b dy.1   0.035 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dy.1 2 1  1  3.53K   0.95dy.1     132.05mm Area of reinforcement required for bending: Asy.n.1 My.1 fydz   348.353mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdy.10.0013bdy.1     209.594mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdy.1 5.56 10   3mm2 Check_steel_5  if Asy.n.1  Asy.1  As.min  Asy.1  As.max"OK" "NOT OK"   "OK" Ratio_5 maxAs.minAsy.n.1   0.616 Asy.1 Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asy.n.1 Asy.1 1      160.409 N mm 2     ONE DISCONTINUOUS EDGE Page 59 of 64
  61. 61. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   275mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  275mm Spacing_5  if sy.1  smax."OK" "NOT OK"   "OK" Ratio_s_5 sy.1 smax   0.727 SHEAR CAPACITY CHECK AT SHORT SPAN CONTINUOUS SUPPORT 1: Effective depth factor (EN1992-1-1,cl.6.2.2): k min 2.0 1 200mm dx.1   0.5       2 Reinforcement ratio: ρ1 min 0.02 Asx.1 bdx.1    4.068 10 3    Minimum shear resistance (EN1992-1-1,Eq.6.3N &6.2b): VRd.c.min 0.035k fck MPa   0.5    bdx.1   N mm 2    53.293kN Shear resistance (EN1992-1-1, Eq.6.2a): VRd.c.x.1 max VRd.c.min 0.18MPa γc  k 100ρ1 fck MPa      0.333   bdx.1     76.743k Shear_1  if Vx.1  VRd.c.x.1"NO SHEAR REQUIRED" "SHEAR REQUIRED"  Shear_1  "NO SHEAR REQUIRED" Ratio1 Vx.1 VRd.c.x.1   0.287 SHEAR CAPACITY CHECK AT SHORT SPAN CONTINUOUS SUPPORT 2: Effective depth factor (EN1992-1-1,cl.6.2.2): k min 2.0 1 200mm dx.2   0.5       2 ONE DISCONTINUOUS EDGE Page 60 of 64
  62. 62. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Reinforcement ratio: ρ1 min 0.02 Asx.2 bdx.2    4.068 10 3    Minimum shear resistance (EN1992-1-1,Eq.6.3N &6.2b): VRd.c.min 0.035k fck MPa   0.5    bdx.2   N mm 2    53.293kN Shear resistance (EN1992-1-1, Eq.6.2a): VRd.c.x.2 max VRd.c.min 0.18MPa γc   k 100ρ1 fck MPa      0.333   bdx.2     76.743k Shear_2  if Vx.2  VRd.c.x.2"NO SHEAR REQUIRED" "SHEAR REQUIRED"  Shear_2  "NO SHEAR REQUIRED" Ratio2 Vx.2 VRd.c.x.2   0.235 SHEAR CAPACITY CHECK AT LONG SPAN CONTINUOUS SUPPORT: Effective depth factor (EN1992-1-1,cl.6.2.2): k min 2.0 1 200mm dy.1   0.5       2 Reinforcement ratio: ρ1 min 0.02 Asy.1 bdy.1    4.068 10 3    Minimum shear resistance (EN1992-1-1,Eq.6.3N &6.2b): VRd.c.min 0.035k fck MPa   0.5    bdy.1   N mm 2    53.293kN Shear resistance (EN1992-1-1, Eq.6.2a): VRd.c.y.1 max VRd.c.min 0.18MPa γc   k 100ρ1 fck MPa      0.333   bdy.1     76.743kN Shear_3  if Vy.1  VRd.c.y.1"NO SHEAR REQUIRED" "SHEAR REQUIRED"  Shear_3  "NO SHEAR REQUIRED" Ratio3 Vy.1 VRd.c.y.1   0.274 SHEAR CAPACITY CHECK AT LONG SPAN DISCONTINUOUS SUPPORT: Flexural reinforcement at As.req  Asy.m0.25  98.175mm2 discontinuous support EN1992-1-1,cl.9.3.1.2(2): Actual bar size: ϕy.2  8mm Bar spacing: sy.2  sy.m  200mm    251.327mm2 Area of reinforcement provided: Asy.2 π 2 4 ϕy.2  m sy.2 Effective depth: dy.2 h  cnom ϕy.2 2    141mm ONE DISCONTINUOUS EDGE Page 61 of 64
  63. 63. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Effective depth factor (EN1992-1-1,cl.6.2.2): k min 2.0 1 200mm dy.2   0.5       2 Reinforcement ratio: ρ1 min 0.02 Asy.2 bdy.2    1.782 10 3    Minimum shear resistance (EN1992-1-1,Eq.6.3N &6.2b): VRd.c.min 0.035k fck MPa   0.5    bdy.2   N mm 2    54.06kN Shear resistance (EN1992-1-1, Eq.6.2a): VRd.c.y.2 max VRd.c.min 0.18MPa γc   k 100ρ1 fck MPa      0.333   bdy.2     59.143kN Shear_4  if Vy.2  VRd.c.y.2"NO SHEAR REQUIRED" "SHEAR REQUIRED"  Shear_4  "NO SHEAR REQUIRED" Ratio4 Vy.2 VRd.c.y.2   0.22 BASIC SPAN-TO-DEPTH DEFLECTION RATIO CHECK: Reference reinforcement ratio: ρo 0.001 fck MPa   0.5  5.477 10 3    Required compression reinforcement (at mid-span - short span): ρc  0 Required tension reinforcement (at mid-span - short span): ρt max 0.0035 Asx.m bdx.m    3.5 10 3    Structural system factor (EN1992-1-1,Table 7.4N): Kδ 1.0 if Structural_system = "Simply supported"   1.3 1.3 if Structural_system = "End span of continous slab" 1.5 if Structural_system = "Interior span" 1.2 if Structural_system = "Flat slab" 0.4 if Structural_system = "Cantilever" Basic limit span-to-depth ratio (EN1992-1-1,Eq.7.16a&7.16b): Limx.bas Kδ 11 1.5 fck MPa   0.5    40.689 ρo ρt   3.2 fck MPa   0.5  ρo ρt  1   1.5        if ρt  ρo Kδ 11 1.5 fck MPa   0.5  ρo ρt  ρc   1 12 fck MPa   0.5  ρc ρo        if ρt  ρo Actual span to effective depth ratio: Ratioact lx dx.m   35.714 Deflection  if Ratioact  Limx.bas"OK" "NOT OK"   "OK" ONE DISCONTINUOUS EDGE Page 62 of 64
  64. 64. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Ratio Ratioact Limx.bas   0.878 CALCULATION SUMMARY RESULTS: Short span - Bending capacity: PASS/FAIL: Ratio: Check bending capacity at midspan: Check_steel_1  "OK" Ratio_1  0.538 Spacing at midspan reinforcement: Spacing_1  "OK" Ratio_s_1  0.667 Check bending capacity at support 1: Check_steel_2  "OK" Ratio_2  0.647 Spacing at support 1 reinforcement: Spacing_2  "OK" Ratio_s_2  0.727 Check bending capacity at support 2: Check_steel_3  "OK" Ratio_3  0.647 Spacing at support 2 reinforcement: Spacing_3  "OK" Ratio_s_3  0.727 Long span - Bending capacity: PASS/FAIL: Ratio: Check bending capacity at midspan: Check_steel_4  "OK" Ratio_4  0.538 Spacing at midspan reinforcement: Spacing_4  "OK" Ratio_s_4  0.667 Check bending capacity at support 1: Check_steel_5  "OK" Ratio_5  0.616 Spacing at support 1 reinforcement: Spacing_5  "OK" Ratio_s_5  0.727 Short span - Shear capacity: PASS/FAIL: Ratio: Check shear capacity at support 1: Shear_1  "NO SHEAR REQUIRED" Ratio1  0.287 Check shear capacity at support 2: Shear_2  "NO SHEAR REQUIRED" Ratio2  0.235 Long span - Shear capacity: PASS/FAIL: Ratio: Check shear capacity at support 1: Shear_3  "NO SHEAR REQUIRED" Ratio3  0.274 Check shear capacity at support 2: Shear_4  "NO SHEAR REQUIRED" Ratio4  0.22 Deflection: PASS/FAIL: Ratio: Check deflection of panel: Deflection  "OK" Ratio  0.878 RENFORCEMENT SUMMARY: Short span: Midspan in short span direction: ϕx.m  10mm at C/C sx.m  200mm Continuous support 1 in short span direction: ϕx.1  12mm at C/C sx.1  200mm Discontinuous support 2 in short span direction: ϕx.2  12mm at C/C sx.2  200mm Long span: Midspan in short span direction: ϕy.m  10mm at C/C sy.m  200mm ONE DISCONTINUOUS EDGE Page 63 of 64
  65. 65. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:IK Continuous support 1 in long span direction: ϕy.1  12mm at C/C sy.1  200mm Discontinuous support 2 in long span direction: ϕy.2  8mm at C/C sy.2  200mm ϕy.2  8mmsy.2  200mm ϕx.2  12mmsx.2  200mm ϕx.1  12mmsx.1  200mm ϕx.m  10mmsx.m  200mm ϕy.m  10mm sy.m  200mm ϕy.1  12mmsy.1  200mm ONE DISCONTINUOUS EDGE Page 64 of 64
  66. 66. 65 ANNEX E - EXAMPLE OF DESIGN INTERIOR PANEL SLAB
  67. 67. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Note: The following colour key is a guide to using the full calculation page. INPUT DTATA ASSUMPTIONS: 1. Fire resistance 1hour (REI 60). 2. Exposure class of concrete XC1. 3. No redistribution of bending moment made. COMPUTED OUTPUT DATA TO BE CHECKED STANDARD DATA GEOMETRICAL DATA: Structural_system:= "Simply supported" "End span of continuous slab" "Interior span" "Flat slab" "Cantilever" Structural system: Structural_system  "Interior span" Depth of slab: h  170mm Strip width: b  1000mm Shorter effective span of panel (clear span): lx  5000mm Longer effective span of panel: ly  5000mm Type of slab: Type_slab "Two way slab" ly lx  if  2.0  "Two way slab" "One way slab" ly lx if  2.0 ANALYSIS & LOADING RESULTS: INTERIOR PANEL Page 66 of 82
  68. 68. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN Figure 1: Bending moment diagram for x - direction Figure 2: Bending moment diagram for y - direction INTERIOR PANEL Page 67 of 82
  69. 69. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN Figure 3: Shear force diagram for x - direction Figure 4: Shear force diagram for y - direction INTERIOR PANEL Page 68 of 82
  70. 70. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN Loads: Characteistic permanent action: Gk 6.25kN m 2   Characteistic variable action: Qk 2kN m 2   Quasi-permanent value of variable action: ψ2  0.3 Short span: Design bending moment at short span - continuous support: Mx.1  21kNm Design bending moment at short span - middle: Mx.m  6kNm Design bending moment at short span - continuous support: Mx.2  21kNm Design shear force at short span - continous support: Vx.1  21kN Design shear force at short span - discontinous support: Vx.2  21kN Long span: Design bending moment at long span - continous support: My.1  21kNm Design bending moment at long span - middle: My.m  6kNm Design bending moment at long span - continous support: My.2  21kNm Design shear force at long span - continous support: Vy.1  21kN Design shear force at long span - discontinous support: Vy.2  21kN STEEL REINFORCEMENT PROPERTIES: Bars diameter for short/long span-midspan: ϕy.p  10mm Characteristic yield strength of steel reinforcement: fyk 500N mm 2    CONCRETE PROPERTIES: Characteristic compressive cylinder strength of concrete: fck 30N mm 2    Mean value of compressive sylinder strength (EN 1992-1-1:2004, table 3.1): fctm 0.3 fck MPa   0.667    MPa 2.9 N mm 2     PARTIAL SAFETY FACTORS: INTERIOR PANEL Page 69 of 82
  71. 71. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN Partial factor for reinforcement steel (NA CYS EN 1992-1-1:2004, Table 2.1)): γs  1.15 Partial factor for concrete (NA CYS EN 1992-1-1:2004, Table 2.1)): γc  1.5 DESIGN STRENGTHS OF MATERIAL(EN1992-1-1,cl.3.1.6): Design yield strength of reinforcement (EN1992-1-1,Fig.3.8): fyd fyk γs 434.783 N mm 2     Coefficient value for compressive strength (NA CYS EN 1992-1-1:2004, cl. NA 2.8): αcc  1 Design value of concrete compressive strength fcd (EN 1992-1-1:2004, Equation 3.15): αccfck γc 20 N mm 2     CONCRETE COVER TO REINFORCEMENT: Allowance in design for deviation (Assuming no measurement of cover) (EN1992-1-1,cl.4.4.1.3(3): Δcdev  10mm Minimum cover due to bond (Diameter of bar) (EN1992-1-1,Table 4.2): cmin.b  ϕy.p  10mm Minimum cover due to environmental condition (Condition :XC1) ("How to design to Eurocode 2",Table 8): cmin.dur  15mm Minimum concrete cover (EN1992-1-1,Eq.4.2): cmin  maxcmin.bcmin.dur10mm  15mm Nominal cover (EN1992-1-1,Eq.4.1): cnom  cmin  Δcdev  25mm FIRE DESIGN CHECK: Minimum slab thickness (EN1992-1-2,Table 5.8): hs.min  80mm Fire_resistance  if h  hs.min"OK" "NOT OK"   "OK" Axis distance to top and bottom reinforcement, a (EN1992-1-2,Table 5.8): amin  20mm Minimum distance to top and bottom reinforcement: aprov cnom ϕy.p 2    30mm Fire_resistance  if aprov  amin"OK" "NOT OK"   "OK" REINFORCEMENT DESIGN AT MID-SPAN IN SHORT SPAN DIRECTION: Actual bar size: ϕx.m  10mm INTERIOR PANEL Page 70 of 82
  72. 72. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN Actual bar spacing: sx.m  200mm    392.699mm2 Area of reinforcement provided: Asx.m π 2 4 ϕx.m  m sx.m dx.m h  cnom ϕx.m 2    140mm Values for Klim (Assumed no redistribution): K Mx.m b dx.m   0.01 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dx.m 2 1  1  3.53K   0.95dx.m     133mm Area of reinforcement required for bending: Asx.p.m Mx.m fydz   103.759mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdx.m0.0013bdx.m     211.102mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdx.m 5.6 10   3mm2 Check_steel_1  if Asx.p.m  Asx.m  As.min  Asx.m  As.max"OK" "NOT OK"   "OK" Ratio_1 maxAs.minAsx.p.m   0.538 Asx.m Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asx.p.m Asx.m 1      68.802 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   300mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  300mm INTERIOR PANEL Page 71 of 82
  73. 73. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN Spacing_1  if sx.m  smax."OK" "NOT OK"   "OK" Ratio_s_1 sx.m smax   0.667 REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT 1 IN SHORT SPAN DIRECTION: Actual bar size: ϕx.1  12mm Actual bar spacing: sx.1  200mm    565.487mm2 Area of reinforcement provided: Asx.1 π 2 4 ϕx.1  m sx.1 dx.1 h  cnom ϕx.1 2    139mm Values for Klim (Assumed no redistribution): K Mx.1 b dx.1   0.036 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dx.1 2 1  1  3.53K   0.95dx.1     132.05mm Area of reinforcement required for bending: Asx.n.1 Mx.1 fydz   365.771mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdx.10.0013bdx.1     209.594mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdx.1 5.56 10   3mm2 Check_steel_2  if Asx.n.1  Asx.1  As.min  Asx.1  As.max"OK" "NOT OK"   "OK" Ratio_2 maxAs.minAsx.n.1   0.647 Asx.1 Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asx.n.1 Asx.1 1      168.429 N mm 2     INTERIOR PANEL Page 72 of 82
  74. 74. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   275mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  275mm Spacing_2  if sx.1  smax."OK" "NOT OK"   "OK" Ratio_s_2 sx.1 smax   0.727 REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT 2 IN SHORT SPAN DIRECTION: Actual bar size: ϕx.2  12mm Actual bar spacing: sx.2  200mm    565.487mm2 Area of reinforcement provided: Asx.2 π 2 4 ϕx.2  m sx.2 dx.2 h  cnom ϕx.2 2    139mm Values for Klim (Assumed no redistribution): K Mx.2 b dx.2   0.036 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dx.2 2 1  1  3.53K   0.95dx.2     132.05mm Area of reinforcement required for bending: Asx.n.2 Mx.2 fydz   365.771mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdx.20.0013bdx.2     209.594mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdx.2 5.56 10   3mm2 INTERIOR PANEL Page 73 of 82
  75. 75. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN Check_steel_3  if Asx.n.2  Asx.2  As.min  Asx.2  As.max"OK" "NOT OK"   "OK" Ratio_3 maxAs.minAsx.n.2   0.647 Asx.2 Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asx.n.2 Asx.2 1      168.429 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   275mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  275mm Spacing_3  if sx.2  smax."OK" "NOT OK"   "OK" Ratio_s_3 sx.2 smax   0.727 REINFORCEMENT DESIGN AT MID-SPAN IN LONG SPAN DIRECTION: Actual bar size: ϕy.m  10mm Actual bar spacing: sy.m  200mm    392.699mm2 Area of reinforcement provided: Asy.m π 2 4 ϕy.m  m sy.m dy.m h  cnom ϕy.m 2    140mm Values for Klim (Assumed no redistribution): K My.m b dy.m   0.01 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" INTERIOR PANEL Page 74 of 82
  76. 76. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN Level arm: z min dy.m 2 1  1  3.53K   0.95dy.m     133mm Area of reinforcement required for bending: Asy.p.m My.m fydz   103.759mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdy.m0.0013bdy.m     211.102mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdy.m 5.6 10   3mm2 Check_steel_4  if Asy.p.m  Asy.m  As.min  Asy.m  As.max"OK" "NOT OK"   "OK" Ratio_4 maxAs.minAsy.p.m   0.538 Asy.m Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asy.p.m Asy.m 1      68.802 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   0.3m 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  300mm Spacing_4  if sy.m  smax."OK" "NOT OK"   "OK" Ratio_s_4 sy.m smax   0.667 REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT 1 IN LONG SPAN DIRECTION: Actual bar size: ϕy.1  12mm Actual bar spacing: sy.1  200mm    565.487mm2 Area of reinforcement provided: Asy.1 π 2 4 ϕy.1  m sy.1 INTERIOR PANEL Page 75 of 82
  77. 77. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN dy.1 h  cnom ϕy.1 2    139mm Values for Klim (Assumed no redistribution): K My.1 b dy.1   0.036 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dy.1 2 1  1  3.53K   0.95dy.1     132.05mm Area of reinforcement required for bending: Asy.n.1 My.1 fydz   365.771mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdy.10.0013bdy.1     209.594mm Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdy.1 5.56 10   3mm2 Check_steel_5  if Asy.n.1  Asy.1  As.min  Asy.1  As.max"OK" "NOT OK"   "OK" Ratio_5 maxAs.minAsy.n.1   0.647 Asy.1 Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asy.n.1 Asy.1 1      168.429 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   275mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa Maximum spacing of bars (EN1992-1-1,cl.9.3.1.1(3): smax.  min3h400mmsmax  275mm Spacing_5  if sx.1  smax."OK" "NOT OK"   "OK" Ratio_s_5 sy.1 smax   0.727 INTERIOR PANEL Page 76 of 82
  78. 78. CALUCLATIION SHEET REINFORCED CONCRETE SOLID SLAB DESIGN TO EUROCODE 2 Date:01/09/2014 Rev:B Calculated by:VN Checked by:VN REINFORCEMENT DESIGN AT CONTINUOUS SUPPORT 2 IN LONG SPAN DIRECTION: Actual bar size: ϕy.2  12mm Actual bar spacing: sy.2  200mm    565.487mm2 Area of reinforcement provided: Asy.2 π 2 4 ϕy.2  m sy.2 dy.2 h  cnom ϕy.2 2    139mm Values for Klim (Assumed no redistribution): K My.2 b dy.2   0.036 Klim  0.22  2 f ck Compression  if K  Klim"NOT REQUIRED" "REQUIRED"   "NOT REQUIRED" Level arm: z min dy.2 2 1  1  3.53K   0.95dy.2     132.05mm Area of reinforcement required for bending: Asy.n.2 My.2 fydz   365.771mm2 Minimum reinforcement (EN1992-1-1,Eq.9.1N) : As.min max 0.26 fctm fyk  bdy.20.0013bdy.2     209.594mm2 Maximum reinforcement (EN1992-1-1,cl.9.2.1.1(3)): As.max 0.04bdy.2 5.56 10   3mm2 Check_steel_6  if Asy.n.2  Asy.2  As.min  Asy.2  As.max"OK" "NOT OK"   "OK" Ratio_6 maxAs.minAsy.n.2   0.647 Asy.2 Stress in the reinforcement (IStrucTE EC2 Manual) σs fyk γs   ψ2Qk  Gk 1.5Qk  1.35Gk    min Asy.n.2 Asy.2 1      168.429 N mm 2     Maximum spacing (for wk=0.3mm) (EN1992-1-1,Table 7.3N: smax 300mm if σs  160MPa   275mm 275mm if 160MPa  σs  180MPa 250mm if 180MPa  σs  200MPa 225mm if 200MPa  σs  220MPa 200mm if 220MPa  σs  240MPa 175mm if 240MPa  σs  260MPa 150mm if 260MPa  σs  280MPa 125mm if 280MPa  σs  300MPa 100mm if 300MPa  σs  320MPa 75mm if 320MPa  σs  340MPa 50mm if 340MPa  σs  360MPa INTERIOR PANEL Page 77 of 82

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