Hollowcore Worked Example Chris Poland Associate Clendon Burns & Park
Hollowcore Floor Example • Wealth of background information in ‘Purple Book’ • More detailed example calculations provided in Appendix
Hollowcore Floor Example – Parameters • Ductile frame building with 200 deep hollowcore floors • Beam span = 8 m • Beam depth = 800 mm • Topping = 65mm • Seating = 50mm • 665 mesh • D12-300 starter bars (600 lap) • Elastic drift = 0.6% ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – Required checks Scenarios to check: A. Unit adjacent corner columns • Check using unrestrained hinge (U) B. Unit adjacent elongating beam, away from corners • Check using restrained hinge (R) C. Internal unites away from elongating beam • Check using starter bar elongation ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – Required checks Checks for each scenario: 1. Loss of support (unseating) 2. Negative moment 3. Positive moment ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 1. Loss of support • Unit “A” adjacent corner column Elongation + • Initial seating 50 mm Rotation • Construction tolerance -20 mm HOLLOW CORE UNIT • Initial spalling -15 mm Drift related spalling • Min bearing -5 mm (example) • Residual seating = 10 mm Initial spalling Construction (example) tolerance (portion of) Through iteration 10mm of seating is SUPPORT BEAM exceeded at a total inter-storey drift of 1.15% ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 1. Loss of support • Additional spalling = 3 mm Additional spalling due to rotation Initial spalling ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 1. Loss of support Beam elongation: • Plastic storey drift col = θ p 1.15% - 0.6% = 0.55% plastic drift • Plastic beam rotation col * L / (L - h col - L p ) θ p = θ p = 0.55%*8000/(8000-800-335) = 0.6% col θ p θ p • Beam elongation (Unrestrained) δ el = 2.6 * θ p /2 * (d - d’) ≤ 0.036h b (h col + L p )/2 = 2.6*0.006/2*(800-65*2) L = 5 mm ≥ 0.005h b ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 1. Loss of support Beam rotation: • Support rotation θ = 1.15% δ r1 = (h b /2 – h L )*θ = (800/2-(200+65))*0.0115 = 2 mm Note that unit elongation + rotation δ r2 should also be checked to ensure that this mechanism does not govern ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 1. Loss of support Through iteration 10mm of seating is exceeded at a total inter-storey drift of 1.15% • Additional spalling + 3 mm • Beam elongation + 5 mm (Construction tolerance = 0) • Beam rotation + 2 mm 10 mm LOS = 1.85% ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Two loading conditions: i. Yielding of starter bars placing unit into axial tension eccentric about section centroid ii. Rotation of seating inducing moment into unit ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Loading condition ii: • Determine whether the critical section occurs at the support or whether it occurs within the span (at the end of the starter bars). • This may be done by calculating the maximum demand at the end of the starter bars based on the overstrength moment capacity at the support ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Loading condition ii: • Overstrength moment at support M o = 46 kNm • Gravity moment at end of starter bars M* G = 11 kNm • Moment demand at end of starter bars M* = 46*(7500-600)/7500 – 11 = 31 kNm ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Loading condition ii: Moment capacity within span • Starters 46kNm => 0 kNm • Prestress contribution = 10 kNm Moment capacity (kNm) • Mesh contribution = 23 kNm Mn = 33kNm Starters M* = 31kNm • Total moment capacity: 10 + 23 = 33 kNm Mesh M n_span (33kNm) > M* span (31kNm) Prestress Therefore negative moment failure will not occur within span under this loading Distance (m) ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Loading condition ii: • But, changing the starter bar length to 300mm results in failure Moment capacity (kNm) Mesh Prestress Starters Distance (m) ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Loading condition ii: • But, changing the starter bar length to 300mm results in failure Starters • Or keeping the length at 600mm but Moment capacity (kNm) increasing starter bars to D16-300: Alteration to length and strength affects susceptibility to failure Mesh Prestress Distance (m) ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Loading condition i: N = A s f o = 113*1.25*324*1200/300* 10 -3 = 183 kN M* N = N.e Moment capacity M* N = A s f o e = 183 * [(265-140-65/2]* 10 -3 = 17 kNm 600mm M* G = (4+0.5)*1200*600/2*(7500-600)* 10 -9 Moment demand = M* G - M* N = 11 kNm M* = 17 - 11 = 6kNm ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Loading condition i: Moment capacity within span 600mm • Axial load contribution = -22 kNm Mn = 12kNm • Prestress contribution = 11 kNm Moment capacity (kNm) • Mesh contribution = 23 kNm M* = 6kNm • Total moment capacity = -22 + 11 + 23 = 12 kNm M n_span (12kNm) > M* span (6kNm) Therefore negative moment failure will not occur within span under this loading Distance (m) ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Loading condition i: Note when calculating moment capacity: • Plane sections do not remain plane with brittle mesh • Need to modify mesh strain by strain concentration factor Scf = 2.8 for h = 265mm ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Loading condition i: f ypm Note when calculating moment capacity: • Plane sections do not remain plane with brittle mesh ε ym • Need to modify mesh strain by stress-strain for brittle mesh strain concentration factor ε ym = 0.002 + 600MPa/200,000MPa = 0.005 ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment Loading condition i: Using a spreadsheet or section 663 Mesh analysis software: av = ε ym /S cf = 0.18% • Taking ε ym 600 MPa • And solving for ‘c’ to get: 925 MPa = 0.02% • Change in prestress strain - ε p 17 MPa = 0.06% 7- ⌀ 12.5mm strands • And elastic concrete strain - ε c • Provides the moment capacity beyond the starter bars ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 2. Negative moment If negative moment failure was found to occur the limiting drift would be 1%, and would therefore be the governing mechanism in this example. ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 3. Positive moment Three checks required: 1. Transverse cracking near support 2. Web splitting due to frame-floor deformation incompatibility 3. Web splitting due to torsion ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 3. Positive moment 3.1. Transverse cracking near support: • Compare max crack width with crack demand due to support rotation + elongation • Max crack width = strand dia. = 12.5 mm Through iteration max crack is exceeded at a total inter-storey drift of 1.7% • Beam elongation = 11 mm • Beam rotation = 2 mm 13 mm ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 3. Positive moment 3.1. Transverse cracking near support: Beam elongation: • Plastic beam rotation col * L / (L - h col - L p ) θ p = θ p = (1.7-0.6)*8000/(8000-800-335) = 1.3% • Beam elongation δ el = 2.6 * θ p /2 * (d - d’) = 2.6*0.013/2*(800-65*2) = 11 mm ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 3. Positive moment 3.1. Transverse cracking near support: Beam rotation: • Support rotation θ = 1.7% δ r1 = (h b /2 – h L )*θ = (800/2-(200+65))*0.017 = 2 mm ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 3. Positive moment 3.1. Transverse cracking near support: Through iteration max crack is exceeded at a total inter-storey drift of 1.7% • Critical crack width = 13 mm • Beam elongation = 11 mm • Beam rotation = 2 mm 13 mm ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
Hollowcore Floor Example – 3. Positive moment 3.2. Frame-floor deformation incompatibility: Through iteration web splitting occurs at a total inter-storey drift of 1.8% • Permitted differential displacement δ v ≤ 8 mm ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS
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