sachpazis: flat slab design to bs8110 part 1-1997

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Flat Slab Analysis & Design, (In accordance with BS8110:PART 1:1997).

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  • 1.Job Ref.Flat Slab Analysis & Design, In accordance with BS8110:PART 1:1997 Project:SectionSheet no./rev. 1Civil & Geotechnical EngineeringGEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures.DateCalc. byDr. C. SachpazisTel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.infoChk'd by Date18/01/2014App'd byDateFLAT SLAB DESIGN TO BS8110:PART 1:1997 Slab geometry Span of slab in x-direction;Spanx = 7200 mmSpan of slab in y-direction;Spany = 7200 mmColumn dimension in x-direction;lx = 400 mmColumn dimension in y-direction;ly = 400 mmExternal column dimension in x-direction;lx1 = 250 mmExternal column dimension in y-direction;ly1 = 250 mmEdge dimension in x-direction;ex = lx1 / 2 = 125 mmEdge dimension in y-direction;ey = ly1 / 2 = 125 mmEffective span of internal bay in x direction;Lx = Spanx lx = 6800 mmEffective span of internal bay in y direction;Ly = Spany ly = 6800 mmEffective span of end bay in x direction;Lx1 = Spanx lx / 2 = 7000 mmEffective span of end bay in y direction;Ly1 = Spany ly / 2 = 7000 mmexBCSpan xSpan xlxey 1Alxl y1Sp anylx1 lySp any2ly3hSlab details Depth of slab;h = 250 mm 1

2. Job Ref.Flat Slab Analysis & Design, In accordance with BS8110:PART 1:1997 Project:Section Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures.Sheet no./rev. 1Civil & Geotechnical EngineeringGEODOMISI Ltd. - Dr. Costas SachpazisCalc. byTel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.infoDr. C. SachpazisDateChk'd by Date18/01/2014App'd byDate2Characteristic strength of concrete;fcu = 35 N/mmCharacteristic strength of reinforcement;fy = 500 N/mmCharacteristic strength of shear reinforcement;fyv = 500 N/mmMaterial safety factor;m = 1.152 2Cover to bottom reinforcement;c = 20 mmCover to top reinforcement;c = 20 mmLoading details 2Characteristic dead load;Gk = 7.000 kN/mCharacteristic imposed load;Qk = 5.000 kN/m2Dead load factor;G = 1.4Imposed load factor;Q = 1.6Total ultimate load;Nult = (Gk G) + (Qk Q) = 17.800 kN/mMoment redistribution ratio;b = 1.0Ratio of support moments to span moments;i = 1.02DESIGN SLAB IN THE X-DIRECTION SAGGING MOMENTS End bay A-B Effective span;L = 7000 mmDepth of reinforcement;d = 200 mmMidspan moment;m = (Nult L ) / (2 (1 + (1 + i)) ) = 74.823 kNm/mSupport moment;m = i m = 74.823 kNm/m22Design reinforcement Lever arm;2K = 0.402 (b 0.4) 0.18 (b 0.4) = 0.176 2K = m / (d fcu) = 0.053 Compression reinforcement is not required z = min((0.5 + (0.25 (K / 0.9))), 0.95) d = 187.3 mm Area of reinforcement designed;2As_des = m / (z fy / m) = 919 mm /m 2Minimum area of reinforcement required;As_min = 0.0013 h = 325 mm /mArea of reinforcement required;As_req = max(As_des, As_min) = 919 mm /m2Provide 20 dia bars @ 150 centres Area of reinforcement provided;22As_prov = D / (4 s) = 2094 mm /m PASS - Span reinforcement is OKCheck deflection Design service stress;fs = 2 fy As_req / (3 As_prov b) = 146 N/mm 222 2Modification factor;k1 = min(0.55+(477N/mm -fs)/(120(0.9N/mm +(m/d ))),2) = 1.545Allowable span to depth ratio;0.9 26 k1 = 36.151Actual span to depth ratio;L / d = 35.000 2 3. Job Ref.Flat Slab Analysis & Design, In accordance with BS8110:PART 1:1997 Project:Section Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures.Sheet no./rev. 1Civil & Geotechnical EngineeringGEODOMISI Ltd. - Dr. Costas SachpazisCalc. byTel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.infoDr. C. SachpazisDateChk'd by Date18/01/2014App'd byDatePASS - Span to depth ratio is OK Internal bay B-C Effective span;L = 6800 mmDepth of reinforcement;d = 202 mmMidspan moment;m = (Nult L ) / (2 ((1 + i) + (1 + i)) ) = 51.442 kNm/mSupport moment;m = i m = 51.442 kNm/m22Design reinforcement Lever arm;2K = 0.402 (b 0.4) 0.18 (b 0.4) = 0.176 2K = m / (d fcu) = 0.036 Compression reinforcement is not required z = min((0.5 + (0.25 (K / 0.9))), 0.95) d = 191.9 mm 2Area of reinforcement designed;As_des = m / (z fy / m) = 617 mm /mMinimum area of reinforcement required;As_min = 0.0013 h = 325 mm /mArea of reinforcement required;As_req = max(As_des, As_min) = 617 mm /m22Provide 16 dia bars @ 200 centres Area of reinforcement provided;22As_prov = D / (4 s) = 1005 mm /m PASS - Span reinforcement is OKCheck deflection 2Design service stress;fs = 2 fy As_req / (3 As_prov b) = 204 N/mmModification factor;k1 = min(0.55+(477N/mm -fs)/(120(0.9N/mm +(m/d ))),2) = 1.601Allowable span to depth ratio;0.9 26 k1 = 37.469Actual span to depth ratio;L / d = 33.663222PASS - Span to depth ratio is OK HOGGING MOMENTS INTERNAL STRIP Penultimate column B3 Consider the reinforcement concentrated in half width strip over the support Depth of reinforcement; d = 200 mm Support moment;m = 2 i m = 149.646 kNm/mLever arm;K = 0.402 (b 0.4) 0.18 (b 0.4) = 0.17622K = m / (d fcu) = 0.107 Compression reinforcement is not required z = min((0.5 + (0.25 (K / 0.9))), 0.95) d = 172.5 mm Area of reinforcement required;2As_des = m / (z fy / m) = 1996 mm /m 2Minimum area of reinforcement required;As_min = 0.0013 h = 325 mm /mArea of reinforcement required;As_req = max(As_des, As_min) = 1996 mm /m2Provide 20 dia bars @ 150 centres Area of reinforcement provided;22As_prov = D / (4 s) = 2094 mm /m PASS - Support reinforcement is OK 3 4. Job Ref.Flat Slab Analysis & Design, In accordance with BS8110:PART 1:1997 Project:Section Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures.Sheet no./rev. 1Civil & Geotechnical EngineeringGEODOMISI Ltd. - Dr. Costas SachpazisCalc. byTel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.infoDr. C. SachpazisDateChk'd by Date18/01/2014App'd byDateInternal column C3 Consider the reinforcement concentrated in half width strip over the support Depth of reinforcement; d = 200 mm Support moment;m = 2 i m = 102.884 kNm/mLever arm;K = 0.402 (b 0.4) 0.18 (b 0.4) = 0.17622K = m / (d fcu) = 0.073 Compression reinforcement is not required z = min((0.5 + (0.25 (K / 0.9))), 0.95) d = 182.1 mm 2Area of reinforcement required;As_des = m / (z fy / m) = 1300 mm /mMinimum area of reinforcement required;As_min = 0.0013 h = 325 mm /mArea of reinforcement required;As_req = max(As_des, As_min) = 1300 mm /m22Provide 20 dia bars @ 200 centres Area of reinforcement provided;22As_prov = D / (4 s) = 1571 mm /m PASS - Support reinforcement is OKHOGGING MOMENTS EXTERNAL STRIP Penultimate column B1, B2 Consider one and a half bays of negative moment being resisted over the edge and penultimate column Width of span;B = 7200 mmEdge distance;e = 125 mmDepth of reinforcement;d = 200 mmSupport moment;m = m i (e + B + B / 2) / ((0.5 B) + (0.2 B) + e) = 158.265kNm/m Lever arm;2K = 0.402 (b 0.4) 0.18 (b 0.4) = 0.176 2K = m / (d fcu) = 0.113 Compression reinforcement is not required z = min((0.5 + (0.25 (K / 0.9))), 0.95) d = 170.5 mm Area of reinforcement required;2As_des = m / (z fy / m) = 2134 mm /m 2Minimum area of reinforcement required;As_min = 0.0013 h = 325 mm /mArea of reinforcement required;As_req = max(As_des, As_min) = 2134 mm /m2Provide 20 dia bars @ 125 centres Area of reinforcement provided;22As_prov = D / (4 s) = 2513 mm /m PASS - Support reinforcement is OKInternal column C1, C2 Consider one and a half bays of negative moment being resisted over the edge and penultimate column Width of span;B = 7200 mmEdge distance;e = 125 mmDepth of reinforcement;d = 200 mmSupport moment;m = m i (e + B + B / 2) / ((0.5 B) + (0.2 B) + e) = 108.810kNm/m 4 5. Job Ref.Flat Slab Analysis & Design, In accordance with BS8110:PART 1:1997 Project:Section Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.infoSheet no./rev. 1Civil & Geotechnical EngineeringGEODOMISI Ltd. - Dr. Costas SachpazisCalc. byDr. C. SachpazisLever arm;DateChk'd by Date18/01/2014App'd byDate2K = 0.402 (b 0.4) 0.18 (b 0.4) = 0.176 2K = m / (d fcu) = 0.078 Compression reinforcement is not required z = min((0.5 + (0.25 (K / 0.9))), 0.95) d = 180.9 mm 2Area of reinforcement required;As_des = m / (z fy / m) = 1383 mm /mMinimum area of reinforcement required;As_min = 0.0013 h = 325 mm /mArea of reinforcement required;As_req = max(As_des, As_min) = 1383 mm /m22Provide 20 dia bars @ 200 centres Area of reinforcement provided;22As_prov = D / (4 s) = 1571 mm /m PASS - Support reinforcement is OKCorner column A1 Depth of reinforcement;d = 206 mmTotal load on column;S = ((Spanx / 2) + ex) ((Spany / 2) + ey) Nult = 247 kNArea of column head;A = lx ly1 = 0.100 mSupport moment;m = S (1 (Nult A / S) ) / 2 = 99.639 kNm/mLever arm;K = 0.402 (b 0.4) 0.18 (b 0.4) = 0.1762 1/322K = m / (d fcu) = 0.067 Compression reinforcement is not required z = min((0.5 + (0.25 (K / 0.9))), 0.95) d = 189.3 mm 2Area of reinforcement required;As_des = m / (z fy / m) = 1211 mm /mMinimum area of reinforcement required;As_min = 0.0013 h = 325 mm /mArea of reinforcement required;As_req = max(As_des, As_min) = 1211 mm /m22Provide 16 dia bars @ 150 centres Area of reinforceme

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