Hollowcore Worked Example Chris Poland Associate Clendon Burns - - PowerPoint PPT Presentation

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
• Initial seating

50 mm

• Construction tolerance
• 20 mm
• Initial spalling
• 15 mm
• Min bearing
• 5 mm
• Residual seating

= 10 mm Through iteration 10mm of seating is exceeded at a total inter-storey drift of 1.15%

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Construction tolerance (portion of) Drift related spalling (example) Elongation + Rotation

HOLLOW CORE UNIT SUPPORT BEAM

Initial spalling (example)

Hollowcore Floor Example – 1. Loss of support

• Additional spalling = 3 mm

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Additional spalling due to rotation Initial spalling

Hollowcore Floor Example – 1. Loss of support

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Beam elongation:

• Plastic storey drift

θp

col =

1.15% - 0.6% = 0.55% plastic drift

• Plastic beam rotation

θp = θp

col * L / (L - hcol - Lp)

= 0.55%*8000/(8000-800-335) = 0.6%

• Beam elongation (Unrestrained)

δel = 2.6 * θp/2 * (d - d’) ≤ 0.036hb = 2.6*0.006/2*(800-65*2) = 5 mm ≥ 0.005hb

θp

col

θp (hcol + Lp)/2 L

Hollowcore Floor Example – 1. Loss of support

Beam rotation:

• Support rotation

θ = 1.15% δr1 = (hb/2 – hL)*θ = (800/2-(200+65))*0.0115 = 2 mm Note that unit elongation + rotation δr2 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

• Beam rotation

+ 2 mm 10 mm

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

LOS = 1.85% (Construction tolerance = 0)

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

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Loading condition ii:

• Determine whether the critical section
• ccurs at the support or whether it
• ccurs 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

Hollowcore Floor Example – 2. Negative moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Loading condition ii:

• Overstrength moment at support

Mo = 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

Hollowcore Floor Example – 2. Negative moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Loading condition ii: Moment capacity within span

• Starters 46kNm => 0 kNm
• Prestress contribution = 10 kNm
• Mesh contribution

= 23 kNm

• Total moment capacity:

10 + 23 = 33 kNm Mn_span (33kNm) > M*span (31kNm) Therefore negative moment failure will not

• ccur within span under this loading

Prestress Moment capacity (kNm) Distance (m) Mesh Starters Mn = 33kNm M* = 31kNm

Hollowcore Floor Example – 2. Negative moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Loading condition ii:

• But, changing the starter bar length

to 300mm results in failure

Moment capacity (kNm) Distance (m) Prestress Mesh Starters

Hollowcore Floor Example – 2. Negative moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Loading condition ii:

• But, changing the starter bar length

to 300mm results in failure

• Or keeping the length at 600mm but

increasing starter bars to D16-300: Alteration to length and strength affects susceptibility to failure

Moment capacity (kNm) Distance (m) Prestress Mesh Starters

Hollowcore Floor Example – 2. Negative moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Loading condition i: N = Asfo = 113*1.25*324*1200/300* 10-3 = 183 kN M*N= N.e = 183 * [(265-140-65/2]* 10-3 = 17 kNm M*G= (4+0.5)*1200*600/2*(7500-600)* 10-9 = 11 kNm M* = 17 - 11 = 6kNm

Moment capacity Moment demand = M*G - M*N M*N = Asfoe 600mm

Hollowcore Floor Example – 2. Negative moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Loading condition i: Moment capacity within span

• Axial load contribution = -22 kNm
• Prestress contribution = 11 kNm
• Mesh contribution

= 23 kNm

• Total moment capacity =
• 22 + 11 + 23 = 12 kNm

Mn_span (12kNm) > M*span (6kNm) Therefore negative moment failure will not

• ccur within span under this loading

600mm

Moment capacity (kNm) Distance (m) Mn = 12kNm M* = 6kNm

Hollowcore Floor Example – 2. Negative moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

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

Hollowcore Floor Example – 2. Negative moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

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 εym = 0.002 + 600MPa/200,000MPa = 0.005

stress-strain for brittle mesh εym fypm

663 Mesh 7-⌀12.5mm strands

Hollowcore Floor Example – 2. Negative moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Loading condition i: Using a spreadsheet or section analysis software:

• Taking εym

av = εym/Scf

• And solving for ‘c’ to get:
• Change in prestress strain - εp
• And elastic concrete strain - εc
• Provides the moment capacity

beyond the starter bars

= 0.18% = 0.02% = 0.06% 600 MPa 925 MPa 17 MPa

Hollowcore Floor Example – 2. Negative moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

If negative moment failure was found to

• ccur the limiting drift would be 1%, and

would therefore be the governing mechanism in this example.

Hollowcore Floor Example – 3. Positive moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Three checks required:

• 1. Transverse cracking near support
• 2. Web splitting due to frame-floor

deformation incompatibility

• 3. Web splitting due to torsion

Hollowcore Floor Example – 3. Positive moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

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

Hollowcore Floor Example – 3. Positive moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

3.1. Transverse cracking near support: Beam elongation:

• Plastic beam rotation

θp = θp

col * L / (L - hcol - Lp)

= (1.7-0.6)*8000/(8000-800-335) = 1.3%

• Beam elongation

δel = 2.6 * θp/2 * (d - d’) = 2.6*0.013/2*(800-65*2) = 11 mm

Hollowcore Floor Example – 3. Positive moment

3.1. Transverse cracking near support: Beam rotation:

• Support rotation

θ = 1.7% δr1 = (hb/2 – hL)*θ = (800/2-(200+65))*0.017 = 2 mm

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Hollowcore Floor Example – 3. Positive moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

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

Hollowcore Floor Example – 3. Positive moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

3.2. Frame-floor deformation incompatibility: Through iteration web splitting occurs at a total inter-storey drift of 1.8%

• Permitted differential displacement

δv ≤ 8 mm

Hollowcore Floor Example – 3. Positive moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

3.2. Frame-floor deformation incompatibility:

• Hollowcore displacement

δr =

• .
• =
• .∗
• =

4 mm

Hollowcore Floor Example – 3. Positive moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

3.2. Frame-floor deformation incompatibility:

• Beam displacement
• From Table C5G.1:

hc/hb = 1.0 L/hb = 10

1.8% 1.5%

Hollowcore Floor Example – 3. Positive moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

3.2. Frame-floor deformation incompatibility:

• Beam displacement

δb = 1.5% * 800 mm = 12 mm

• Differential displacement

δd = δb - δr = 12 – 4 = 8 mm = δv @ 1.8% drift

• This is higher than transverse cracking @

1.7% drift -> not critical

Hollowcore Floor Example – 3. Positive moment

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

3.3. Torsion:

• At 1.7% drift (previously assessed for

transverse cracking) it can be shown that the maximum torsion which can be tolerated will permit 7mm of differential movement along the unit

• Based on using an equivalent thin tube

analogy together with the tensile strength

• f concrete

7mm

Hollowcore Floor Example – Summary

ASSESSMENT OF EXISTING PRECAST CONCRETE FLOORS

Checks for each scenario: 1. Loss of support @ 1.15% drift 2. Negative moment does not govern (default is 1% when activated) 3. Positive moment @ 1.7% drift due to transverse cracking Therefore the floor %NBS may be evaluated at the limiting building drift of 1.15% as a result of loss of support due to inadequate seating

Questions?