armadillo-500r calculation note
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ARMADILLO ™ 500R
CALCULATION NOTE
Designed by www.cresco-group.com
For more information: www.armadillo-system.com
CHRISTCHURCH BUILDERS LTD
Street
Christchurch
Attention:
►
Christchurch, the 30th of July 2014
CALCULATION REPORT NO. 1326_A
Christchurch
# 001
Subject:
Geotechnical investigation (Project number: ) - 31th December 2013
PO Box 9200 Addington 8149 (Christchurch)T +64.27.838.8338 www.cresco-group.com
Cresco Engineers New Zealand Ltd was requested by xxxxxx to undertake the structural design of a new foundation for a
residential building.
In accordance with the Client Briefing, in order to better fulfill the purposes of safety and quality, we have decided to use the
ARMADILLO™ Foundation System which is a voided biaxial re-levellable reinforced concrete shallow slab.
The above mentioned technology has been designed to deliver greater rigidity and strength to the foundation slabs of
buildings constructed on soils where moderate to significant land damage from liquefaction is possible in future large
earthquakes (e.g. TC3 soils).
The added strength of the ARMADILLO™ Foundation System is created by a unique and patent protected interweaving
waffle design utilising high strength pulp moulded cardboard for the internal formwork. This unique design makes the
foundation strong enough to withstand re-levelling at specifically formed jacking cavities created around the perimeter of the
foundation.
Each cavity is equipped with a UHMWPE jacking pad – capable of a 250 kN bearing capacity.
The ARMADILLO™ Foundation System ensures that in the event of settlements due to liquefaction of the soil, the entire
structure can be lifted and re-levelled without constraint of weight or depth of settlement, therefore, this technology is not
only compliant, but exceeds the requirements documented in Chapter 15.4.8 relevellable concrete surface structures Part C.
TC3 Technical Guidance Build it Right Canterbury – The groundwork for good decision December 2012 Version C
document (in particular regarding the limit of weight of the cladding and of the roof and the limit of 100 mm of SLS vertical
settlement).
Currently the ARMADILLO™ Foundation System is an alternative to the conventional solutions.
Cresco Engineers New Zealand Ltd confirms that, prior to the preparation of the design detailed in this calculation note and
annexed drawings, review was made of the geotechnical report. The Ultimate Bearing Capacity used in the foundation
design is that which is provided in this report.
REFERENCES:
Yours faithfully
on behalf of CRESCO ENGINEERS NEW ZEALAND LTD
Fabio Parodi
SENIOR STRUCTURAL ENGINEER
Dott. Ing. (IT.GE 7776)
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ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 1 / 26
SUMMARY
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
This report contains the following chapters:
1. Executive summary
2. List of checks
3. Methodology and construction sequence
4.Methodology and re-leveling sequence
5. Structural Calculations
6. Notation
7.Annexes
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 2 / 26
EXECUTIVE SUMMARY
Christchurch
RIBS
2) ΦM,rg- = 54.6 kNm > Mmin,rg = 23.53 kNm
3) ΦM,rg+ = 70.77 kNm > Mmax,rg = 11.74 kNm
4) 0,5×ΦVc,rg = 27.49 kN > Vmax,rg = 17.63 kN
5) dmax,rg = 0.41 mm < dall,rg = 5 mm
6) ΦM,lr = 70.77 kNm > Mmax,l = 44.47 kNm
7) 0,5×ΦVc,lr = 27.49 kN > Vmax,l = 24.25 kNSLAB 8) flr = 11.52 mm < dall,lr = 25 mm
1) ΦM,sg = 6.93 kNm/m > Mmax,sg = 2.47 kNm/m
EXTERNAL FOOTINGS
9) ΦM,f1 = 88.32 kNm > M*,1 = 33.34 kNm
10) 0,5×ΦVc,f1 < V*,1 - shear reinforcement required
11) ΦM,f2+ = 88.32 kNm > M*,2 = 33.34 kNm
12) 0,5×ΦVc,f2 < V*,f2 - shear reinforcement required
13) ff1 = 0.09 mm < 5 mm
14) ff2 = 0.07 mm < 5 mm
15) ΦM,lf = 88.32 kNm > Mmax,lf = 51.93 kNm
16) 0,75×(Vc,lf+Vs,lf) = 93.615 kN > Vmax,lf = 86.56 kN
SOIL
17) pult,rg = 36.89 kPa < Dbc = 100 kPa JACKING PAD
18) pset,rl = 23.71 kPa < Abc = 66.67 kPa 20) Npad,lf = 173.11 kN < 250 kN
19) Pult,f = 41.37 kPa < Dbc = 100 kPa 21) pspad = 297.53 kPa - Plate test required near Pad
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 3 / 26
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
LIST OF CHECKS
Flexural strength check of living slab in standard load case
Flexural strength check (top reinforcement) of living ribs in standard load case
Flexural strength check (bottom reinforcement) of living ribs in standard load case
Shear strength check of living ribs in standard load case
Deflection check of living ribs in standard load case
Flexural strength check of ribs in lifting conditions
Shear strength check of ribs in lifting conditions
Deflection check of ribs in lifting condititons
Flexural strength check (beneath section) of external footings in standard load case
Shear strength check (beneath section) of external footings in standard load case
Flexural strength check (extreme section) of external footings in standard load case
Shear strength check (extreme section) of external footings in standard load case
Deflection check (beneath section) of external footings in standard load case
Deflection check (extreme section) of external footings in standard load case
Flexural strength check of external footings in lifting conditions
Shear strength check of external footings in lifting conditions
Soil dependable bearing capacity check under living ribs in standard load case
Soil allowable bearing capacity check under living ribs in standard load case
Soil allowable bearing capacity check under external footings in standard load case
Maximum load on jacking pad check in lifting condition
Maximum pressure on soild under jacking pad check in lifting condition
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 4 / 26
CONSTRUCTION METHODOLOGY AND SEQUENCE
Dbc = 100 kPa
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
ARMADILLO™ JACKING
PADS
Place the ARMADILLO™ Jacking Pads 250 according to the engineering drawings
layout and details.
EARTHWORKS Clear topsoil and form a level building platform (levels according to drawings,
hardfill according to geotechnical engineer). Ensure or confirm the dependable
bearing capacity Dbc required on all foundation surface oversized of 200 mm (or
the depth of the hardfill whichever is greater). Alternatively ensure the required
dependable bearing capacity DBci for a footprint fw,si width under the external
footings. Cover building platform with 20 mm sand blinding. Council might need
to inspect site before slab construction commences.
INSPECTION Engineer inspection
REINFORCING MESH Place reinforcing mesh to mesh chairs on top of the ARMADILLO™ 500 pods. Ensure
50mm cover to edge of formwork. Lap and tie mesh. Tie reinforcing bar to perimeter
mesh. Re-entrant corners and foundation slab edge need additional steel, refer to the
engineering drawings layout and details.
ARMADILLO™ THERMAL
DPM
Cover blinding with a DPM or with the ARMADILLO™ Thermal DPM. Cut around and
tape securely all the laps. The DPM does not have to cover the ARMADILLO™ Jacking
pads.
FORMWORKS Mount the lateral formworks (and rebate if needed) taking care to predispose the
cavities for the jacking points according to the engineering drawings layout and details.
ARMADILLO™ PODS Place ARMADILLO™ 500 pods by starting with four from a corner of the foundation
layout. Lock these first formworks with the ARMADILLO™ keystone. Proceed with two
adjacent formworks, locking them with the keystone as well. Repeat the process for the
rest of the foundation.
PLUMBING Install the plumbing and any other utility, in accordance with the drawings and the local
codes. In order to accommodate the design settlements special precautions have to be
taken at the interface between the urban sewerage infrastructure and the foundation
embedded pipes.
REINFORCING BARS Place reinforcing bars in edge beams and ribs according to the engineering drawings
details being careful to ensure the steel is positioned in the lugs provided in the
ARMADILLO™ keystones for the rebar of the ribs. The ARMADILLO™ keystone is
provided with a bar retainer that prevents any undesirable movement of the rebar,
therefore all the steel bars joined with the keystone don't need to be tied. All XD12
Grade 500 laps shall be 600 mm minimum and all XD20 Grade 500 laps shall be 1000
mm minimum.
INSPECTION Engineer inspection.
POURING Pour topping slab, internal and lateral ribs in one operation taking care to ensure that
the ARMADILLO™ 500 pods remain in place. For convenience it is easiest to use a
concrete pump. It is desirable to pour some concrete over the ARMADILLO™ 500 pods
before placing in the ribs. Pour the concrete starting from the center of the slab and
proceed with the filling of the ribs in a spiral so that layers 100 mm thick of the concrete
are placed at every step. Therefore about five steps of casting are expected to
completely fill the ribs. A wrong pouring procedure can cause damage to the formworks.
FINISHING Vibrate concrete, finish surface and ensure adequate curing takes place n accordance
with the good building practices. Preferably a DPM has to be placed on top of the slab
immediately after pouring. Saw cut the slab surface for shrinkage control.
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 5 / 26
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
RELEVELLING METHODOLOGY AND SEQUENCE
INSPECTION Engineer inspection
PLUMBING Locally disconnect the plumbing and the utilities of the house from the urban
infrastructure.
FORMWORKS Fit formwork inside the cavities down to the top surface of the ARMADILLO™ Jacking
Pads (to prevent grout entering the cavity).
LIFTING Proceed with the lifting. During this phase the operators have to constantly check the
levels of the foundation and the pressure of the circuit. By acting on the valves, the
operators must ensure that on every lifting point the jacks are adequately working. This
phase might require a pack and jack iterative work.
LOCKING Once the dwelling is re-levelled and it has been raised at the desired height fit wedges
on either side of each jack cavity in the space between the bottom of the external
footing and the ARMADILLO™ Jacking Pads. Make sure the wedges sit on the pads
(both sides of the jacking cavities), not the ground surface.
INSPECTION Engineer inspection
LEVELS ASSESSMENT Measure the floor levels over the jacking pad positions (lifting points). Locally excavate
in correspondence of the lifting points.
SOIL ASSESSMENT Carry out plate tests near the jacking pads in order to check the expected maximum
ultimate soil pressure. If the check is negative then locally improve the soil (please note:
after a liquefaction event the soil undergoes an alteration, generally favorable, of its
bearing capacity, therefore assumptions and tests before made before an event can be
unreliable at the time of re-levelling).
GROUTING Grout under the foundation in order to create a new planar surface at the right level. The
ARMADILLO™ Thermal DPM is designed to remain attached to the foundation,
nonetheless, if it did not, replace it on top of the new grout taking care to double the
overlapping (instead of taping). In case of conventional DPM or in case the thermal
insulation does not have to be restored the grout can be poured on top of the DPM.
PREPARATION Carefully clean the surface of the jacking pads and place the jacks in the cavities.
Remove all possible loads inside the house and secure unstable objects (please note:
NO elements of the superstucture need to be removed, including heavy weight
claddings and heavy roof tiles).
FINISHING Once the grout has cured remove the formworks. All ARMADILLO™ foundation
performances (re-levelability included) have been fully restored.
LOWERING Once the grout has cured the dwelling can be lowered on top of it. All the precautions
described for the lifting phase have to be take into account. This phase might require a
pack and jack iterative work.
PLUMBING Locally connect the plumbing and the utilities of the house with the urban infrastructure.
The ARMADILLO™ 500 has been expressly designed to be re-levelleable, nonetheless an
incorrect lifting procedure can cause severe damage to the foundation structure.
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 6 / 26
STRUCTURAL CALCULATIONS GENERAL DATA
CLIENT
CLIENT CHRISTCHURCH BUILDERS LTD
ADDRESS Christchurch
STRUCTURE FEATURES
Roof type Light, corrugated iron roof Gr = 0.45 kN/m²
Max roof span Rs = 9 m
1st floor exterior walls Heavy, brick cladding Gew = 2.2 kN/m²
Max wall height Hew = 2.5 m
2nd floor exterior walls Heavy, brick cladding Gew2 = 0 kN/m²
Max wall height Hew2 = 0 m
2nd floor selfweight G2nd = 0 kN/m²
Ground floor permanent load Ggf = 0 kN/m²
Max dimension of buildings Dbuild = 10 m
max dimension of 2nd floor D2nd = 0 m
MATERIALS
Reinforcing steel
Strength Fv = 500 MPa
Strength of steel mesh Fv,m = 500 MPa
Concrete
Strength fc = 25 MPa
Elastic modulus Ec = 23500 MPa
Selfweight γc = 24 kN/m³
Soil
Ultimate Bearing Capacity Ubc = 200 kPa
Dependable Bearing Capacity Dbc = 100 kPa
Allowable Bearing Capacity Abc = 66.7 kPa
LOADS
Dead load Dead load Uniform Gsup = 0.5 kN/m² NZS 1170.1 cl. 2.3
Live load Garage Uniform Qg = 2.5 kN/m² NZS 1170.1 tab. 3.1
Garage Point load Pg = 13 kN NZS 1170.1 tab. 3.1
Domestic Uniform Qd = 1.5 kN/m² NZS 1170.1 tab. 3.1
Roof Uniform Qr = 0.25 kN/m² NZS 1170.1 tab. 3.2
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 7 / 26
STRUCTURE: LIVING PART: SLAB CASE: STANDARD LOAD CASE
GEOMETRY
Slab span Ls = 0.500 m
Slab thickness ts = 0.085 m
Ribs width br = 0.170 m
Total height of ribs (rib+slab) hr = 0.585 m
Distance between ribs ir = 0.750 m
LOADS
Dead loads
Slab self weight Gslab = 2.04 kN/m²
Sdl Gsup = 0.50 kN/m²
Ground floor permanent load Ggf = 0 kN/m²
Live loads Domestic QD = 1.50 kN/m²
Total load on slab qsl = 5.30 kN/m² NZS 1170.0 cl. 4.2.2
RESISTANCE CHECK
Hp: Two way square slab supported on each side
Maximum bending moment Mmax,sl = 0.06 kNm/m
Strength of steel mesh Fv,m = 500 MPa
Provisioned reinforcement (mesh) As,sl = 318.00 mm²/m
Minimal shrinkage reinforcement Asmin,sl = 119.00 mm²/m NZS 3101 cl. 8.8.1
Concrete cover (to center) csl = 30 mm
Effective depth of reinforcement dsl = 55.00 mm
Neutral axis asl = 7.48 mm
Flexural strength ΦM,sl = 6.93 kNm/m
>
Mmax,sl = 0.06 kNm/m
OK
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
According to simply supported plates, the maximum bending moment is evaluated here after, Reference is made to
"TIMOSHENKO, Theory of plates and shells, Table 5"
= + γc x ts
= + qsl · Ls2 / 20.9
= 0.7 / Fv,m · ts · 1 · 1000000
= + (As,sl · Fv) / (0.85 · 1000 · fc)
= 0.85 · As,sl · Fv · (dsl - asl / 2) / 1000000
= 1.2 · (Gslab + Gsup + Ggf) + 1.5 · QD
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 8 / 26
STRUCTURE: LIVING PART: RIBS CASE: STANDARD LOAD CASE
GEOMETRY
Slab span Ls = 0.500 m
Slab thickness ts = 0.085 m
Ribs width br = 0.170 m
Total height of ribs (rib+slab) hr = 0.585 m
Distance between ribs ir = 0.750 m
Inertia modulus of ribs Ir = 2836189688 mm4
LOADS
Dead loads
Slab self weight Gs,r = 1.53 kN/m
Sdl Gsup,r = 0.38 kN/m
Ground floor permanent load Ggf = 0.00 kN/m²
Ribs self weight Rsw = 2.04 kN/m
Cross ribs selfweight CR,sw = 1.36 kN/m
Live Loads Domestic Qd,rl = 1.13 kN/m
Seismic combinations
Uniform load on rib wrl = 5.64 kN/m Canterbury guide cl.15.4.8
Point load on rib
prl = 5.90 kN Canterbury guide cl.15.4.8
ACTIONS
2m Cantilever edge Rib
Length of rib LR1= 2.00 m
Minimum bending moment Mmin1,rl = 23.08 kNm
Maximum shear Vmax1,rl = 17.18 kN
4m Span
Length of rib LR2 = 4.00 m
Maximum bending moment Mmax2,rl = 11.29 kNm
Minimum bending moment Mmin2,rl= 9.03 kNm NZS 3101 cl. 6.7.2
Maximum shear Vmax2,rl = 11.29 kN
Maximum bending moment for ribs Mmax,rl = 11.29 kNm
Minimum bending moment for ribs Mmin,rl = 23.08 kNm
Maximum shear Vmax,rl = 17.18 kN
RESISTANCE CHECK
Flexural strength and shear strength check
Top reinforcement
Provisioned reinforcement As,sl = 238.50 mm²
Additional reinforcement 0 Φ As'prov,rl = 0.00 mm²
Total top reinforcement As',rl = 238.50 mm²
Minimal reinforcement Reo provided > 1.33×Reo required Asmin,rl = - mm² NZS 3101 cl. 9.3.8.2.3
Concrete cover (to center) cr = 30 mm
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
According to document "Repairing and rebuilding houses affected by the Canterbury earthquakes", clause 15.4.8 for relevellable concrete surface
structures (key performances expectations, point 2) , foundations shall withstand a maximum unsupported length of 4 m beneath sections or 2 m at
the extremes of the floor. Deflection shall be limited to 5 mm at sls.
= Ggf · ir
= γc · br · (hr - ts)
= γc · br · (hr - ts) · Ls / ir
= Qd · ir
= 1 · (Gs,r + Gsup,r + Ggf + Rsw + CR,sw) + 0.3 · Qd,rl
= wrl · LR12 / 2 + prl · LR1
= wrl · LR1 + prl
= wrl · LR22 / 8
= wrl · LR22 / 10
= wrl · LR2 / 2
= Gsup · ir
= γc · ts · ir
= ir · (1 · [Gew · Hew + Gew2 · Hew2 + Gr · Rs / 2 + G2nd · D2nd / 2] + 0.3 · [Qr · Rs / 2 + Qd · D2nd / 2])
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 9 / 26
STRUCTURE: LIVING PART: RIBS CASE: STANDARD LOAD CASE
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
Effective depth dr = 555.00 mm
Neutral axis arl1 = 33.01 mm
Flexural strength ΦM,rl- = 54.58 kNm
ΦM,rl- >Mmin,rl OK
Bottom reinforcement
Provisioned reinforcement 1 Φ 20 Asprov,rl = 314.16 mm²
Total bottom reinforcement As,rl = 314.16 mm²
Minimal reinforcement Reo provided > 1.33×Reo required Asmin,rl = - mm² NZS 3101 cl. 9.3.8.2.3
Concrete cover (to center) cr = 50 mm
Effective depth dr = 535.00 mm
Neutral axis arl2 = 9.86 mm
Flexural strength ΦM,rl+ = 70.77 kNm
ΦM,rl+ >Mmax,rl OK
Shear capacity
Effective shear area of ribs Acv,rl = 140250 mm²
Ratio of tension reinforcement ρrl = 0.0035
Shear resisted by concrete vc,rl = 0.52 MPa NZS 3101 cl. C.9.3.9.3.4
Nominal shear strength resisted by concrete ΦVc,rl = 54.98 kN
0.5 ΦVc,rl > Vmax,rl OK NZS 3101 cl. C.9.3.9.4.13
DEFLECTION CHECK
Seismic combination
Total load on rib ws,rl = 5.64 kN/m Canterbury guide cl.15.4.8
1) 2m Cantilever edge Rib
Length of rib LR1= 2.00 m
Maximum deflection dmax1,rl = 0.41 mm
2) 4m Span
Length of Rib LR2 = 4.00 m
Maximum deflection dmax2,rl = 0.28 mm
Maximum deflection dmax,rl = 0.41 mm
Maximum allowable deflection dall,rl = 5.00 mm
dmax,rl<dall,rl OK
= (As',rl · Fv) / (0.85 · br · 1000 · fc)
= 0.85 · As',rl · Fv · (dr - arl1 / 2) / 1000000
= (As,rl · Fv) / (0.85 · ir · 1000 · fc)
= 0.85 · Asprov,rl · Fv · (dr - arl2 / 2) / 1000000
= (br · dr / 1000 + [ir - br] · ts) · 1000000
= As,rl / (br · dr · 1000)
= max(min[{0.07 + 10 · ρrl} · √{fc},0.2 · √{fc}],0.08 · √[fc])
= 0.75 · vc,rl · Acv,rl / 1000
= ws,rl · [LR1 · 1000]4
[8 · Ec · Ir]
+ 1000 · prl · [LR1 · 1000]3
[3 · Ec · Ir]
= 5 · ws,rl · [LR2 · 1000]4
384 · Ec · Ir
= (Gs,r + Gsup,r + Ggf + Rsw + CR,sw) + 0.3 · Qd,rl
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 10 / 26
STRUCTURE: LIVING PART: RIBS CASE: SOIL BEARING CAPACITY
GEOMETRY
Slab span Ls = 0.500 m
Slab thickness ts = 0.085 m
Ribs width br = 0.170 m
Height of ribs hr = 0.585 m
Distance between ribs ir = 0.750 m
LOADS
Dead loads
Slab self weight Spsw = 1.15 kN
Sdl Gpsdl,r = 0.28 kN
Ground floor permanent load Ggf = 0.00 kN/m²
Ribs self weight Rp,rs = 2.04 kN
Live Loads Domestic Qpd = 0.84 kN
Total load on ribs for ultimate bearing pressure
wult,rl = 5.43 kN NZS 1170.0 cl. 4.2.2
Total load on ribs for settlement bearing pressure (long term combination)
wset,rl = 3.81 kN NZS 1170.0 cl. 4.3
BEARING CHECK
Maximum ultimate soil pressure pult,rl = 31.9 kPa
Dependable Bearing Capacity Dbc = 100 kPa
pult,rl<Dbc OK
Maximum ultimate soil pressure pset,rl = 22.39 kPa
Allowable bearing Capacity Abc = 66.7 kPa
pset,rl<Abc OK
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
= Qd · ir · ir
= 1.2 · (Spsw + Gpsdl,r + Ggf + Rp,rs) + 1.5 · Qpd
= (Spsw + Gpsdl,r + Ggf + Rp,rs) + 0.4 · Qpd
= wult,rl / (4 · Ls · br / 2)
= wset,rl / (4 · Ls · br / 2)
= 4 · (γc · br · [hr - ts] · Ls) / 2
= Ggf · ir · ir
= γc · ts · ir · ir
= Gsup · ir · ir
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 11 / 26
STRUCTURE: LIVING PART: EXTERNAL FOOTINGS CASE: STANDARD LOAD CASE
MINIMUM BEAM WIDTH SOIL BEARING CAPACITY
GEOMETRY
Beam height hf = 0.585 m
Beam min width bf,min = 0.3 m
Beam average width bf = 0.26 m
Pe pad dimension Pd = 0.8 m
Pe pad surface Ap = 0.64 m²
Pad span Sp = 3 m
Loading surface Aload = 1.3 m²
Beam inertia If = 0.00434 m4
LOADS
Dead (kN/m) Live (kN/m)
Roof(*)
2.03 Dr,f = 1.13 qr
Wall 1st floor(*)
5.50 Dw1,f
Wall 2nd floor(*)
0.00 Dw2,f
2nd floor(*)
0.00 D2f = . q2f
Footing 3.12 Df
Ground floor selfweight 1.30 Dgf = 1.28 q1f
Total Gf = 11.94 Qf = 2.40
Soil pressure(*)
Used for point load
Equivalent beam width bload,f = 0.4 m
The ultimate bearing load under external footing is:
Pult,f = 41.4 kPa
that is less than the Dependable Bearing Capacity Dbc = 100 kPa
CONCRETE DESIGN
The design line load is then wf = 12.66 kN/m
The point load is then pf = 4.01 kN
CASE A: UNSUPPORTED LENGHT BENEATH SECTION (SIMPLY SUPPPORTED BEAM)
Moment capacity
Design bending moment M*,1 = 33.3 kNm
Steel section provided 2 Φ 16 Asprov,f1 = 402.1 mm²
Total bottom reinforcement As,f1 = 402.12 mm²
Minimal reinforcement Reo provided > 1.33×Reo required Asmin,f1 = - mm² NZS 3101 cl. 9.3.8.2.3
Concrete cover (to center) cf = 50 mm
Effective height df = 535 mm
The stress block height is:
af1 = = 36.39 mm
Then the ultimate moment is ΦM,f1 = 88.3 kNm
That is more than the design bending moment M*,1 33.3 kNm
OK
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
According to document "Repairing and rebuilding houses affected by the Canterbury earthquakes", clause 15.4.8 for relevellable concrete surface
structures (key performances expectations, point 2) , foundations shall withstand a maximum unsupported length of 4 m beneath sections or 2 m at
the extremes of the floor. Deflection shall be limited to 5 mm at sls.
= Gr · Rs / 2
= Gew · Hew
= Gew2 · Hew2
= G2nd · D2nd / 2
= bf · (hf - ts) · γc
= Qr · Rs / 2
= Qd · D2nd / 2
= Aload / Sp
= (1.2 · Gf + 1.5 · Qf) / bload,f
=(bf+Ls/2)*[(Dr,f+Dw1,f+Dw2,f)+0.3*(qr+q2f)]
= (ts · γc + Gsup + Ggf) · (Ls / 2 + bf) = max([Qg],[Qd]) · (Ls / 2 + bf)
= Gf + 0.3 · Qf
= wf · 42 / 8 + pf · 4 / 2
= + hf · 1000 - cf
= Asprov,f1 · Fv
0.85 · 1000 · bf · fc= 0.85 · Asprov,f1 · Fv · ( - af1 / 2 + df) / 1000000
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 12 / 26
STRUCTURE: LIVING PART: EXTERNAL FOOTINGS CASE: STANDARD LOAD CASE
MINIMUM BEAM WIDTH SOIL BEARING CAPACITY
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
Shear capacity
Design shear V*,f1 = 27 kN
Ratio of tension reinforcement ρ,f1 = 0.0029
Shear stress section Av,f1 = 139100 mm²
Design shear stress
vc,f1 = 0.49 MPa NZS 3101 cl. C.9.3.9.3.4
Nominal shear strenght ΦVc,f1 = 51.6 kN
Design shear force V*,1 27 kN
0.5 ΦVc,f1 < V*,1 See lifting condition NZS 3101 cl. C.9.3.9.4.13
Deflection
The deflection is ff1 = 0.47 mm
That is less than 5 mm OK
CASE B: UNSUPPORTED LENGHT AT EXTREME (CANTILEVER BEAM)
Moment capacity
Design bending moment M*,2 = 33.3 kN
Design shear V*,2 = 29 kN
Steel section provided 2 Φ 16 As'prov = 402.1 mm²
Provisioned reinforcement (mesh) As'prov = 95.4 mm²
Total top reinforcement As' = 497.52 mm²
Minimal reinforcement Reo provided > 1.33×Reo required Asmin = - mm² NZS 3101 cl. 9.3.8.2.3
Concrete cover (to center) cf= 50 mm
Effective height df = 535 mm
The stress block height is: af2 = = 36.39 mm
Tthe ultimate moment is ΦM = 88.3 kNm
That is more than the design bending moment M*,2 33.3 kNm
OK
Shear capacity
The ratio of tension reinforcement is ρf2 = 0.0029
The shear stress section is Acv,f2 = 139100 mm²
The design shear stress is vc,f2 = 0.49 MPa NZS 3101 cl. C.9.3.9.3.4
The nominal shear strenght is ΦVc,f2 = 51.6 kN
Design shear force V*,2 29 kN
0.5 ΦVc,f2 < V*,2 See lifting condition NZS 3101 cl. C.9.3.9.4.13
Deflection
The deflection is ff2 = 0.35 mm
That is less than 5 mm OK
= (wf · 4) / 2 + pf / 2
= Asprov,f1 / (df · bf · 1000)
= bf · df · 1000
= max(min[{0.07 + 10 · ρ,f1} · √{fc},0.2 · √{fc}],0.08 · √[fc])
= 0.75 · Av,f1 · vc,f1 / 1000
= 5 · wf · 44
384 · Ec · If
+ pf · 43
48 · Ec · If
= wf · 22 / 2 + pf · 2
= (wf · 2) + pf
= As'prov · Fv
0.85 · 1000 · bf · fc
= As'prov / (df · bf · 1000)
= + bf · df · 1000
= max(min[{0.07 + 10 · ρf2} · √{fc},0.2 · √{fc}],0.08 · √[fc])
= 0.75 · Acv,f2 · vc,f2 / 1000
= wf · 24
8 · Ec · If
+ pf · 23
3 · Ec · If
= 0.85 · As'prov · Fv · ( - af2 / 2 + df) / 1000000
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 13 / 26
STRUCTURE: LIVING PART: EXTERNAL FOOTINGS CASE: STANDARD LOAD CASE
MAXIMUM BEAM WIDTH SOIL BEARING CAPACITY
GEOMETRY
Beam height hf = 0.585 m
Beam max width bf,max = 0.6 m
Beam average width bf = 0.6 m
Pe pad dimension Pd = 0.8 m
Pe pad surface Ap = 0.64 m²
Pad span Sp = 3 m
Loading surface Aload = 1.96 m²
Beam inertia If = 0.01001 m4
LOADS
Dead (kN/m) Live (kN/m)
Roof(*)
2.03 Dr,f = 1.13 qr
Wall 1st floor(*)
5.50 Dw1,f
Wall 2nd floor(*)
0.00 Dw2,f
2nd floor(*)
0.00 D2f = . q2f
Footing 7.20 Df
Ground floor selfweight 2.16 Dgf = 2.13 q1f
Total Gf = 16.88 Qf = 3.25
Soil pressure(*)
Used for point load
Equivalent beam width bload,f = 0.7 m
The ultimate bearing load under external footing is:
Pult,f = 38.5 kPa
that is less than the Dependable Bearing Capacity Dbc = 100 kPa
CONCRETE DESIGN
The design line load is then wf = 17.86 kN/m
The point load is then pf = 6.68 kN
CASE A: UNSUPPORTED LENGHT BENEATH SECTION (SIMPLY SUPPPORTED BEAM)
Moment capacity
Design bending moment M*,1 = 49.1 kNm
Steel section provided 3 Φ 16 Asprov,f1 = 603.2 mm²
Total bottom reinforcement As,f1 = 603.19 mm²
Minimal reinforcement Reo provided > 1.33×Reo required Asmin,f1 = - mm² NZS 3101 cl. 9.3.8.2.3
Concrete cover (to center) cf = 50 mm
Effective height df = 535 mm
The stress block height is:
af1 = = 23.65 mm
Then the ultimate moment is ΦM,f1 = 134.1 kNm
That is more than the design bending moment M*,1 49.1 kNm
OK
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
According to document "Repairing and rebuilding houses affected by the Canterbury earthquakes", clause 15.4.8 for relevellable concrete surface
structures (key performances expectations, point 2) , foundations shall withstand a maximum unsupported length of 4 m beneath sections or 2 m at
the extremes of the floor. Deflection shall be limited to 5 mm at sls.
= Gr · Rs / 2
= Gew · Hew
= Gew2 · Hew2
= G2nd · D2nd / 2
= bf · (hf - ts) · γc
= Qr · Rs / 2
= Qd · D2nd / 2
= Aload / Sp
= (1.2 · Gf + 1.5 · Qf) / bload,f
=(bf+Ls/2)*[(Dr,f+Dw1,f+Dw2,f)+0.3*(qr+q2f)]
= wf · 42 / 8 + pf · 4 / 2
= + hf · 1000 - cf
= 0.85 · Asprov,f1 · Fv · ( - af1 / 2 + df) / 1000000
= (ts · γc + Gsup + Ggf) · (Ls / 2 + bf) = max([Qg],[Qd]) · (Ls / 2 + bf)
= Gf + 0.3 · Qf
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 14 / 26
STRUCTURE: LIVING PART: EXTERNAL FOOTINGS CASE: STANDARD LOAD CASE
MAXIMUM BEAM WIDTH SOIL BEARING CAPACITY
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
Shear capacity
Design shear V*,f1 = 39 kN
Ratio of tension reinforcement ρ,f1 = 0.0019
Shear stress section Av,f1 = 321000 mm²
Design shear stress
vc,f1 = 0.44 MPa NZS 3101 cl. C.9.3.9.3.4
Nominal shear strenght ΦVc,f1 = 106.9 kN
Design shear force V*,1 39 kN
0.5 ΦVc,f1 > V*,1 OK NZS 3101 cl. C.9.3.9.4.13
Deflection
The deflection is ff1 = 0.29 mm
That is less than 5 mm OK
CASE B: UNSUPPORTED LENGHT AT EXTREME (CANTILEVER BEAM)
Moment capacity
Design bending moment M*,2 = 49.1 kN
Design shear V*,2 = 42 kN
Steel section provided 3 Φ 16 As'prov = 603.2 mm²
Provisioned reinforcement (mesh) As'prov = 190.8 mm²
Total top reinforcement As' = 793.99 mm²
Minimal reinforcement Reo provided > 1.33×Reo required Asmin = - mm² NZS 3101 cl. 9.3.8.2.3
Concrete cover (to center) cf= 50 mm
Effective height df = 535 mm
The stress block height is: af2 = = 23.65 mm
Tthe ultimate moment is ΦM = 176.5 kNm
That is more than the design bending moment M*,2 49.1 kNm
OK
Shear capacity
The ratio of tension reinforcement is ρf2 = 0.0019
The shear stress section is Acv,f2 = 321000 mm²
The design shear stress is vc,f2 = 0.44 MPa NZS 3101 cl. C.9.3.9.3.4
The nominal shear strenght is ΦVc,f2 = 106.9 kN
Design shear force V*,2 42 kN
0.5 ΦVc,f2 > V*,2 OK NZS 3101 cl. C.9.3.9.4.13
Deflection
The deflection is ff2 = 0.23 mm
That is less than 5 mm OK
= (wf · 4) / 2 + pf / 2
= Asprov,f1 / (df · bf · 1000)
= bf · df · 1000
= max(min[{0.07 + 10 · ρ,f1} · √{fc},0.2 · √{fc}],0.08 · √[fc])
= 0.75 · Av,f1 · vc,f1 / 1000
= 5 · wf · 44
384 · Ec · If
+ pf · 43
48 · Ec · If
= wf · 22 / 2 + pf · 2
= (wf · 2) + pf
= As'prov · Fv
0.85 · 1000 · bf · fc
= 0.85 · As'prov · Fv · ( - af2 / 2 + df) / 1000000
= As'prov / (df · bf · 1000)
= + bf · df · 1000
= max(min[{0.07 + 10 · ρf2} · √{fc},0.2 · √{fc}],0.08 · √[fc])
= 0.75 · Acv,f2 · vc,f2 / 1000
= wf · 24
8 · Ec · If
+ pf · 23
3 · Ec · If
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 15 / 26
STRUCTURE: LIVING PART: RIBS CASE: LIFTING
EXTERNAL FOOTINGS
GEOMETRY
During lifting, we will consider the bottom slab as a two-way slab simply supported on perimeter
beams. The irregular shape of the slab will be simplified in a rectangular shape covering the
Surface
Dimension Lx (min) Lx = 10 m
Dimension Ly (max) Ly = 14.2 m
Length of internal wall Lp = 0 m
ratio Ly/Lx 1.42
Slab span Ls = 0.500 m
Slab thickness ts = 0.085 m
Base of ribs br = 0.170 m
Total height of ribs (rib+slab) hr = 0.585 m
Distance between ribs ir = 0.750 m
Inertia modulus of ribs Ir = 2836189688 mm4
Total Surface Atot = 141.00 m2
Number of Armadillo pieces narm = 196
Volume of Armadillo piece varm = 0.15 m3
LOADS
Surface loads
Slab self weight Gslab = 2.04 kN/m²
Internal surface. load Gis = 1.00 kN/m²
Ground floor permanent load Ggf = 0 kN/m²
Ribs self weight Rswd = 2.72 kN/m²
Cross rib weight CR,swd = 2.10 kN/m²
Total ws,l = 7.86 kN/m²
Uniform load on rib wr,l = 5.90 kN/m
Line load
Point load (per meter) ps,l = 0 kN/m
Point load on rib pr,l = 0.00 kN
ACTIONS ON RIBS
According to simply supported plates tables, the maximum bending moment is evaluated here after
Maximum Bending moment = ir x ws x Lx^2/13.26 Msurf,l = 44.47 kNm
where: a = L x , a 1 =0.2, b = L y , b 1 = L p
The total load is Pp,l = 0.00 kN
a1/a 0.01
b1/a 0.00
Coefficient from Timoshenko Tables β1 = 0.156
Coefficient from Timoshenko Tables β2 = 0.072
Moment on short direction is Mx,l = 0.0 kNm/m
Moment on long direction is My,l = 0.0 kNm/m
Then the maximum load is the maximum between Mx and My multiplied by the distance between
the ribs Mline,l = 0.0 kN
The total design moment is then on each rib Mmax,l = 44.5 kNm
Shear forces are evaluated according to simply supported tables (TIMOSHENKO, Table 5)
Shear force, for each rib is then = ir x ws x Lx/2.24 Vsurf,l = 24.25 kN
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
We can take into account also the concentrated load from walls, that is distributed along a length parallel to long side Ly, that is named Lp. The load is
considered distributed on a surface of Lpx0.2 m . Reference is made to "TIMOSHENKO, Theory of plates and shells, Table 17-18-19"
= γc · ts
= ws,l · ir
= Gslab + Gis + Ggf + Rswd + CR,swd
= 1 / ir · (1 - br / ir) · (br · [hr - ts] · γc)
= γc · br · (hr - ts) / ir
= + ps,l · ir
= Msurf,l + Mline,l
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 16 / 26
STRUCTURE: LIVING PART: RIBS CASE: LIFTING
EXTERNAL FOOTINGS
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
For concentrated load, shear forces are evaluated according to simply supported beam formula
Shear force, for each rib is then Vline,l = 0.00 kN
The total design shear is then on each rib Vmax,l = 24.25 kN
RESISTANCE AND DEFLECTION RIBS CHECK
Moment capacity
Bottom reinforcement
Provisioned reinforcement 1 Φ 20 Asprov,lr = 314.16 mm²
Total bottom reinforcement As,lr = 314.16 mm²
Minimal reinforcement Reo provided > 1.33×Reo required Asmin,lr = - mm² NZS 3101 cl. 9.3.8.2.3
Effective depth dr = 535.00 mm
Neutral axis ar = 9.86 mm
Flexural strength ΦM,lr = 70.77 kNm
That is more than the design moment Mmax,l 44.47 kNm
OK
Shear Capacity
Effective shear area of ribs Acv,lr = 140250 mm²
Tension reinforcement ratio ρlr = 0.0035
Shear resisted by concrete vc,lr = 0.52 MPa
Total nominal shear strenght, only resisted by concrete ΦVc,lr = 54.98 kN
Vmax 24.25 kN
Then no shear reinforcement is required 0.5 ΦVc,lr > Vmax,l OK
Deflection check
(simply supported beam)
Lenght of rib LR,l = 10.00 m
Maximum deflection flr = 11.52 mm
Maximum allowable deflection (1/400) dall,lr = 25.00 mm
OK
ACTION ON EXTERNAL FOOTINGS
Beam height (total) hf = 0.585 m
Beam width bf = 0.26 m
Average Load from concrete foundation is: ws,lf = 45.2 kN/m
We have to add:
- Weigth of 1st floor wall Dw1,f = 5.5 kN/m
- Weigth of 2nd floor wall Dw2,f = 0 kN/m
- Tributary area of roof Dr,f = 2.025 kN/m
- Tributary area of second floor D2f = 0 kN/m
- Ground floor permanent load ggf = 0 kN/m
- Internal surface load gis = 5 kN/m
Total load wlf = 57.7 kN/m
To evaluate forces on members, we will consider a continuous beam.
Span Lf,l = 3.0 m
Design moment is then Mmax,lf = 51.9 kNm
Design shear is then Vmax,lf = 86.6 kN
= Vsurf,l + Vline,l
= (Asprov,lr · Fv) / (0.85 · ir · 1000 · fc)
= 0.85 · Asprov,lr · Fv · (dr - ar / 2) / 1000000
= (br · dr / 1000 + [ir - br] · ts) · 1000000
= max(min[{0.07 + 10 · ρlr} · √{fc},0.2 · √{fc}],0.08 · √[fc])
= Asprov,lr / (br · dr · 1000)
= 0.75 · vc,lr · Acv,lr / 1000
= 5wr,l[LR,l · 1000]4
384EcIr= + LR,l / 400 · 1000
= ([{Atot · hr} - {narm · varm}] · γc · Lx / 2) / Atot
= Gew · Hew
= Gew2 · Hew2
= Gr · Rs / 2
= G2nd · D2nd / 2
= Ggf · Lx / 2
= Gis · Lx / 2
= ws,lf + Dw1,f + Dw2,f + Dr,f + D2f + ggf + gis
= 1 / 10 · wlf · Lf,l2
= 0.5 · wlf · Lf,l
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 17 / 26
STRUCTURE: LIVING PART: RIBS CASE: LIFTING
EXTERNAL FOOTINGS
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
RESISTANCE AND DEFLECTION EXTERNAL FOOTINGS CHECK
Moment capacity
Reinforcement
Provisioned reinforcement 2 Φ 16 Asprov,lf = 402.12 mm²
Total bottom reinforcement As,lf = 402.12 mm²
Minimal reinforcement Reo provided > 1.33×Reo required Asmin,lf = 347.75 mm² NZS 3101 cl. 9.3.8.2.1
Concrete cover cf = 50.00 mm
Effective depth df = 535.00 mm
Neutral axis alf = 36.39 mm
Flexural strength ΦM,lf = 88.32 kNm
That is more than the design moment mmax,lf 51.93 kNm
OK
Shear capacity
Stirrups 1 Φ 10 Av,fl = 78.54 mm²
Stirrup spacing s,lf = 375.00 mm
Tension reinforcement ratio ρlf = 0.0029
Effective shear area of external footings Acv,lf = 139100 mm²
Shear resisted by concrete vc,lf = 0.49 MPa NZS 3101 cl. C.9.3.9.3.4
Nominal shear strength resisted by concrete Vc,lf = 68.79 kN
Nominal shear strength from reinforcement Vs,lf = 56.0 kN
That is be more than Vmax,lf 46.6 kN
OK
Shear capacity
Nominal shear strenght resisted by concrete ΦVc,lf = 51.59 kN
distance from support where 0.5 ΦVc,rg > Vmax,rg (no stirrups necessary) dVc,lf = 1.05 m
PADS AND SOIL BEARING CAPACITY CHECK
Maximum shear acting on a single beam Vc,lf = 86.6 kPa
Maximum force acting on a single jacking pad Npad,lf = 173.11 kN
OK
Pad dimension Lpad = 0.80 m
Pad area Apad = 0.64 m²
Maximum ultimate soil pressure pspan = 297.53 kPa
The external footings are considered as countinuous supported beam. The span represents the distance between pads
Npad<250 kN
Which is acceptable considering the temporary and rare condition of load and the safety factors assumed to calculate the allowable bearing capacity (generally
the allowable bearing capacity includes a factor of safety of 3).
= 2 · Vc,lf
= 1.1(Npad,lf / Apad)
= (Asprov,lf · Fv) / (0.85 · bf · 1000 · fc)
= 0.85 · Asprov,lf · Fv · (df - alf / 2) / 1000000
= Asprov,lf / (df · bf · 1000)
= bf · df · 1000
= max(min[{0.07 + 10 · ρlf} · √{fc},0.2 · √{fc}],0.08 · √[fc])
= vc,lf · Acv,lf / 1000
= Av,fl · Fv · df / s,lf / 1000
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 18 / 26
NOTATION
Hereby listed, by alphabetical order, all symbols that appear in the Calculation notes:
a1 Width of wall load on the equivalent plate m
Abc Allowable bearing capacity kPa
Acv,f1 Effective shear area of external footings in central section mm²
Acv,f2 Effective shear area of external footings in extreme section mm²
Acv,lf Effective shear area of external footings - lifting condition mm²
Acv,lr Effective shear area of ribs - lifting condition mm²
Acv,rg Effective shear area of garage ribs mm²
Acv,rl Effective shear area of living ribs mm²
Acv,sir Effective shear area of ribs - soil improvement under external footings mm²
af1 Neutral axis position on external footings in central section mm
af2 Neutral axis position on external footings in extreme section mm
ag Neutral axis position on garage slab mm
alf Neutral axis position on external footings - lifting condition mm
Aload Loading surface m²
Aload,si External footings loading surface - soil improvement under external footings mm²
alr Neutral axis position on ribs - lifting condition mm
Ap Pad surface m
Apad Jacking pad area m²
arg1 Neutral axis position on garage ribs in extreme section mm
arg2 Neutral axis position on garage ribs in central section mm
arl1 Neutral axis position on living ribs in extreme section mm
arl2 Neutral axis position on living ribs in central section mm
As,f1 Total top reinforcement on external footings in central section mm²
As',f2 Total top reinforcement on external footings in extreme section mm²
As,g Cross sectional area of reinforcement in garage slab mm²
As,lf Total reinforcement on external footings - lifting condition mm²
As,lr Total top reinforcement on ribs - lifting condition mm²
As',rg Total top reinforcement on garage ribs mm²
As',rl Total top reinforcement on living ribs mm²
As,sir Total top reinforcement on ribs - soil improvement under external footings mm²
As,sl Cross sectional area of reinforcement in living slab mm²
asir Neutral axis position on ribs - soil improvement under external footings mm
asl Neutral axis position on living slab mm
Asmin,f1 Minimal reinforcement on external footings in central section mm²
As'min,f2 Minimal reinforcement on external footings in extreme section mm²
Asmin,g Minimum cross sectional area of reinforcement in garage slab mm²
Asmin,lf Minimal reinforcement on external footings - lifting condition mm²
Asmin,lr Minimal reinforcement on ribs - lifting condition mm²
Asmin,rg Minimal reinforcement on garage ribs mm²
Asmin,rl Minimal reinforcement on living ribs mm²
Asmin,sir Minimal reinforcement on ribs - soil improvement under external footings mm²
Asmin,sl Minimum cross sectional area of reinforcement in living slab mm²
Asprov,f1 Provisioned bottom reinforcement on external footings in central section mm²
As'prov,f2 Provisioned bottom reinforcement on external footings in extreme section mm²
Asprov,lf Provisioned reinforcement on external footings - lifting condition mm²
Asprov,lr Provisioned reinforcement on ribs - lifting condition mm²
As'prov,rg Provisioned top reinforcement on garage ribs mm²
As'prov,rl Provisioned top reinforcement on living ribs mm²
Asprov,sir Provisioned reinforcement on ribs - soil improvement under external footings mm²
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 19 / 26
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
Atot Total living suface m2
Av,rl Stirrups area on ribs - lifting condition mm²
Av,rsi Stirrups area on ribs - soil improvement under external condition mm²
b1 Length of wall load on the equivalent plate m
Bci Necessary soil bearing capacity improvement kPa
bf External footings avarage width m
bf,min External footings minimum width m
bfload,si Equivalent external footings width - soil improvement under external footings m
bload,f Equivalent external footings width - standard load condition m
br Ribs width m
c Concrete cover mm
cf Concrete cover in external footings mm
clr Concrete cover in on ribs - lifting condition mm
cr Concrete cover in ribs mm
CR,sw Cross ribs selfweight kN/m
CR,swd Crossribs selfweight distributed - lifting condition kN/m²
cs Concrete cover in slab mm
D2f 2nd floor selfweight on external footings kN/m
dall,lr Maximum allowable deflection - lifting condition mm
dall,rg Maximum allowable deflection on garage ribs mm
dall,rl Maximum allowable deflection on living ribs mm
dall,sir Maximum allowable deflection - soil improvement under external footings mm
DBci Required dependable bearing capacity - soil improvement under external footings kPa
Dbc Dependable bearing capacity kPa
Df External footings selfweight kN/m
df Effective depth of reinforcement on external footings mm
Dgf Slab load on external footings kN/m
dlr Effective depth of reinforcement on ribs - lifting condition mm
dmax,rg Maximum deflection on garage ribs mm
dmax,rl Maximum deflection on living ribs mm
dmax1,rg Maximum deflection on external garage ribs mm
dmax1,rl Maximum deflection on external living ribs mm
dmax2,rg Maximum deflection on central garage ribs mm
dmax2,rl Maximum deflection on central living ribs mm
dr Effective depth of reinforcement in ribs mm
Dr,f Roof dead load on external footings kN/m
ds Effective depth of reinforcement in slab mm
dVc,lf Distance from support where stirrups are not necessary - lifting condition m
Dw1,f 1st floor wall dead load on external footings kN/m
Dw2,f 2nd floor wall dead load on external footings kN/m
Ec Modulus of elasticity of concrete MPa
fc Compressive strength of concrete MPa
ff1 Maximum deflection on external footings in extreme section mm
ff2 Maximum deflection on external footings in extreme section mm
flr Maximum deflection on ribs - lifting condition mm
fsir Maximum deflection on ribs - soil improvement under external footings mm
Fv Lower characteristic yield strength of non-prestressed reinforcement MPa
Fv,m Lower characteristic yield strength of non-prestressed reinforcement of wired mesh MPa
fw,si Perimetral soil improvement footprint width m
G2nd 2nd floor selfweight kN/m²
gc Concrete density kN/m³
Gew 1st floor external walls weight kN/m²
Gew2 2nd floor external wall weight kN/m²
Gf Total dead load on external footings kN/m
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 20 / 26
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
Ggf Ground floor permanent load kN/m²
Gis Internal surface load - lifting condition kN/m²
Gpsdl,r Point superimposed deadload acting onribs kN
Gr Roof selfweight kN/m²
Grg Superimposed dead load acting on garage ribs kN/m
Gs,rg Slab garage selfweight acting on garage ribs kN/m
Gs,rl Slab living selfweight acting on ribs kN/m
Gslab Slab selfweight kN/m²
Gsup Superimposed dead load kN/m²
Gsup.rl Superimposed dead load acting on living ribs kN/m
Hew 1st floor external walls selfweight m
Hew2 2nd floor external walls selfweight m
hf Height of external footings m
hr Total height of ribs m
If Inertia modulus of external footings m
ir Distance between ribs m
Ir Inertia modulus of ribs mm4
Lf,l Span of external footings - lifting condition m
Lp Length of internal wall m
LR,l Length of ribs in lifting condition m
LR,si Length of ribs - soil improvement m
LR1,rg Lenght of extreme ribs in garage zone m
LR1,rl Length of extreme ribs in living zone m
LR2,rg Length of central section of ribs in garage zone m
LR2,rl Length of central section of ribs in living zone m
Ls Slab span m
Lx Equivalent minimum dimension of building m
Lx,si Equivalent minimum dimension of building - soil improvement under external footings m
Ly Equivalent maximum dimension of building m
Ly,si Equivalent maximum dimension of building - soil improvement under external footings m
M*,1 Maximum bending moment acting on external footings kNm
M*,2 Minimum bending moment acting on external footings kNm
Mline,l Moment due to wall acting on each rib in lifting condition kNm
Mline,si Moment due to wall acting on each rib- soil improvement under external footings kNm
Mmax,g Maximum bending moment acting on garage slab kNm/m
Mmax,l Maximum moment acting on each rib in lifting condition kNm
Mmax,lf Maximum moment acting on external footings - lifting condition kNm
Mmax,rg Minimum bending moment acting on ribs in garage zone kNm
Mmax,rl Minimum bending moment acting on ribs in living zone kNm
Mmax,si Maximum moment acting on each rib - soil improvement under external footings kNm
Mmax,sl Maximum bending moment acting on living slab kNm/m
Mmax2,rg Minimum bending moment acting on central ribs in garage zone kNm
Mmax2,rl Minimum bending moment acting on central section of ribs in living zone kNm
Mmaxdead,sg Maximum bending moment due to dead loads acting on garage slab kNm/m
Mmaxlive,sg Maximum bending moment due to live load acting on garage slab kNm/m
Mmaxpoint,sg Maximum bending moment due to point load acting on garage slab kNm/m
Mmin,rg Minimum bending moment acting on ribs in garage zone kNm
Mmin,rl Minimum bending moment acting on ribs in living zone kNm
Mmin1,rg Minimum bending moment acting on extreme section of ribs in garage zone kNm
Mmin1,rl Minimum bending moment acting on extreme section of ribs in living zone kNm
Mmin2,rg Minimum bending moment acting on central section of ribs in garage zone kNm
Mmin2,rl Minimum bending moment acting on central sectiion of ribs in living zone kNm
Msurf,l Maximum bending moment for equivalent plate, - lifting condition kNm
Msurf,si Maximum bending moment for equivalent plate - soil improvement under external footings kNm
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 21 / 26
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
Mx,l Moment in short direction due to distributed load - lifting condition kNm/m
Mx,si Moment in short direction due to distributed load - soil improvement under external footings kNm/m
My,l Moment in long direction due to distributed load - lifting condition kNm/m
My,si Moment in long direction due to distributed load - soil improvement under external footings kNm/m
Npad,lf Maximum vertical load on jacking pad in lifting condition kN
narm Number of Armadillo pieces
Pd Jacking pad dimension m
pf Ultimate limit states point load on external footings kN/m
Pg Garage point live load kN
Pp,l Total load on equivalent plate - lifting condition kN
Pp,si Total load on equivalent plate - soil improvement under external footings kN
pr,l Point load on ribs - lifting condition kN
pr,si Point load on ribs - soil improvement kN
prg Ultimate limit state point load acting on garage ribs kN/m
prl Ultimate limit state point load acting on living ribs kN/m
ps,l Point load (per meter) - lifting condition kN/m
ps,pad Maximum soil pressure under jacking pad in lifting condition kPa
ps,si Point load (per meter) - soil improvement kN/m
pset,rg Maximum ultimate soil pressure for settlement in living ribs kPa
pset,rl Maximum ultimate soil pressure for settlement in living ribs kPa
Pult,f Ultimate bearing load under external footings kPa
pult,rg Maximum ultimate soil pressure in garage ribs kPa
pult,rl Maximum ultimate soil pressure in living ribs kPa
q1f 1st floor live load on external footings kN/m
q2f 2nd floor live load on external footings kN/m
Qd Domestic live load kN/m²
Qd,rg Live domestic load acting on garage ribs kN/m
Qd,rl Live domestic load acting on living ribs kN/m
Qf Total live load on external footings kN/m
Qg Garage distributed live load kN/m²
Qgf Maximum live load on ground floor kN/m²
Qpd Point domestic live load kN
Qpg Point garage live load kN
Qr Roof live load kN/m²
qrf Roof live load on external footings kN/m
qsg Ultimate limit states combined distributed load on garage slab kN/m²
qsl Ultimate limit states combined distributed load on living slab kN/m²
Rp,rs Point ribs selfweight kN
Rs Max roof span m
Rsw Ribs selfweight kN/m
Rswd Ribs selfweight distributed - lifting condition kN/m²
Dbuild Building max dimension m
Sp Pad span m
Spsw Point slab selfweight acting on ribs kN
sv,lf Stirrups surface in external footings mm
ts Slab thickness m
Ubc Ultimate bearing capacity kPa
V*,1 Maximum shear acting on external footings kN
V*,2 Maximum shear acting on external footings kN
varm Volume of Armadillo piece m3
vc,f2 Shear resisted by concrete in external footings in extreme section Mpa
vc,lf Shear resisted by concrete in ribs - lifting condition Mpa
Vc,lf Nominal shear strength resisted by concrete of foundation beam - lifting condition kN
vc,lr Shear resisted by concrete in ribs - lifting condition Mpa
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 22 / 26
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
Vc,lr Nominal shear strength resisted by concrete of ribs - lifting condition kN
vc,rg Shear resisted by concrete in garage ribs Mpa
vc,rl Shear resisted by concrete in living ribs Mpa
Vc,sir Nominal shear strength resisted by concrete of ribs - soil improvement under external footings kN
Vline,l Shear force due to wall load acting on each rib in lifting condition kN
Vline,si Shear force due to wall load acting on each rib - soil improvement under external footings kN
Vmax,l Shear force acting on each rib in lifting condition kN
Vmax,lf Maximum shear acting on external footings - lifting condition kN
Vmax,rg Maximum shear acting on ribs in garage zone kN
Vmax,rl Maximum shear acting on ribs in living zone kN
Vmax,si Shear force acting on each rib - soil improvement under external footings kN
Vmax1,rg Maximum shear acting on extreme section of ribs in garage zone kN
Vmax1,rl Maximum shear acting on extreme section of ribs in living zone kN
Vmax2,rg Maximum shear acting on central ribs in garage zone kN
Vmax2,rl Maximum shear acting on central section of ribs in living zone kN
Vs,lf Nominal shear strength resisted by concrete of external footings - lifting condition kN
Vsurf,l Shear force due to ditributed load acting on each rib - lifting condition kN
Vsurf,si Shear force due to ditributed load acting on each rib - soil improvement under external footings kN
wf Ultimate limit states distributed load on external footings kN/m
wfb,si Total load on external footings - soil improvement under external footings kN/m
wfbL,si Total load on external footings (long term combination) - soil improvement under external footings kN/m
wfs,si Total load for unit length on external footings - soil improvement under external footings kN/m
wlf Total load on external footings - lifting condition kN/m
wr,l Total distributed load on ribs - lifting condition kN/m²
wr,si Total distributed load on ribs - soil improvement kN/m
wr,sis Total distributed load on ribs in seismic condition - soil improvement kN/m
wrg Ultimate limit states uniform load acting on garage ribs kN/m
wrl Ultimate limit states uniform load acting on living ribs kN/m
ws,l Total uniform load - lifting condition kN/m²
ws,rg Seismic combined uniform load on garage ribs kN/m
ws,rl Seismic combined uniform load on living ribs kN/m
ws,si Total uniform load - soil improvement kN/m²
wset,rg Total load on living slab for settlement bearing pressure in living ribs kN
wset,rl Total load on living slab for settlement bearing pressure in living ribs kN
wult,rg Total load on living slab for dependable bearing pressure in garage ribs kN
wult,rl Total load on living slab for dependable bearing pressure in living ribs kN
αrl Inclination of bent bars in ribs - lifting condition °
αsir Inclination of bent bars in ribs - soil improvement under external footings °
β1 Coefficient from "timoshenko theory of plates and shells" tables 17-18-19
β2 Coefficient from "timoshenko theory of plates and shells" tables 17-18-19
ρf1 Ratio of tension reinforcement in external footings in central section
ρf2 Ratio of tension reinforcement in external footings in extreme section
ρlf Ratio of tension reinforcement in external footings - lifting condition
ρlr Ratio of tension reinforcement in ribs - lifting condition
ρrg Ratio of tension reinforcement in garage ribs
ρrl Ratio of tension reinforcement in living ribs
ρsir Ratio of tension reinforcement in ribs - soil improvement under external footings
ΦM,f1 Nominal flexural strength of the garage external footings in central section kNm
ΦM,f2 Nominal flexural strength of the garage external footings in extreme section kNm
ΦM,lf Nominal flexural strength of external footings - lifting condition kNm
ΦM,lr Nominal flexural strength of ribs - lifting condition kNm
ΦM,rg- Nominal flexural strength of the garage ribs section due to top reinforcement kNm
ΦM,rg+ Nominal flexural strength of the garage ribs section due to bottom reinforcement kNm
ΦM,rl- Nominal flexural strength of the living ribs section due to top reinforcement kNm
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 23 / 26
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
ΦM,rl+ Nominal flexural strength of the living ribs section due to bottom reinforcement kNm
ΦM,sg Nominal flexural strength of the garage slab section kNm/m
ΦM,sir Nominal flexural strength of ribs - soil improvement under external footings kNm
ΦM,sl Nominal flexural strength of the living slab section kNm/m
ΦVc,f1 Nominal shear strength resisted by concrete in external footings in central section kN
ΦVc,f2 Nominal shear strength resisted by concrete in external footings in extreme section kN
ΦVc,lr Nominal shear strength resisted by concrete in ribs - lifting condition kN
ΦVc,rg Nominal shear strength resisted by concrete in garage ribs kN
ΦVc,rl Nominal shear strength resisted by concrete in living ribs kN
ΦVc,sir Nominal shear strength resisted by concrete in ribs - soil improvement under external footings kN
Φvc,sir Shear resisted by concrete in ribs - soil improvement under external footings Mpa
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 24 / 26
ANNEXES
TIMOSHENKO, Theory of plates and shells, Table 5
TIMOSHENKO, Theory of plates and shells, Table 17
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 25 / 26
CALCULATION REPORT NO. 1326_A
ARMADILLO™ Foundation System Design
TIMOSHENKO, Theory of plates and shells, Table 18
TIMOSHENKO, Theory of plates and shells, Table 19
ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 26 / 26
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