ARMADILLO-500R Calculation Note

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)

Cre

sco’

s lo

go is

a r

egis

tere

d tr

adem

ark

– C

resc

o is

UN

I EN

ISO

900

1:20

08 q

ualit

y ce

rtifi

ed b

y S

INC

ER

T –

Thi

s do

cum

ent m

ay n

ot b

e re

ad o

r re

prod

uced

oth

er th

an in

its

entir

ety.

ANNEX 2 rev 01.xls CRESCO ENGINEERS NEW ZELAND LTD. 1 / 26

SUMMARY


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


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






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)


CONSTRUCTION METHODOLOGY AND SEQUENCE

Dbc = 100 kPa



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.




RELEVELLING METHODOLOGY AND SEQUENCE


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.


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.


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




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


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



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


STRUCTURE: LIVING PART: RIBS CASE: STANDARD LOAD CASE

GEOMETRY






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



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])


STRUCTURE: LIVING PART: RIBS CASE: STANDARD LOAD CASE



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


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


STRUCTURE: LIVING PART: RIBS CASE: SOIL BEARING CAPACITY

GEOMETRY




Height of ribs hr = 0.585 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



= 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


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






= 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



MINIMUM BEAM WIDTH SOIL BEARING CAPACITY



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


The stress block height is: af2 = = 36.39 mm

Tthe ultimate moment is ΦM = 88.3 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


0.5 ΦVc,f2 < V*,2 See lifting condition NZS 3101 cl. C.9.3.9.4.13

Deflection



= (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



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


The stress block height is:

af1 = = 23.65 mm

Then the ultimate moment is ΦM,f1 = 134.1 kNm


OK






= 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



MAXIMUM BEAM WIDTH SOIL BEARING CAPACITY



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


0.5 ΦVc,f1 > V*,1 OK NZS 3101 cl. C.9.3.9.4.13

Deflection



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


The stress block height is: af2 = = 23.65 mm

Tthe ultimate moment is ΦM = 176.5 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


0.5 ΦVc,f2 > V*,2 OK NZS 3101 cl. C.9.3.9.4.13

Deflection



= (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


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



Base of ribs br = 0.170 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


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



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



EXTERNAL FOOTINGS



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


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



EXTERNAL FOOTINGS



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


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






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




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




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




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




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


ANNEXES

TIMOSHENKO, Theory of plates and shells, Table 5










Documents

ARMADILLO-500R Calculation Note