<content> utilities </content>

393abb15-576f-431e-8951-0cac52a6c3e1 378 1 5 true false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Community Centre in Gopalnagar

Structural Design by algebraic calculations & graphic statics verifications

Laurent Fournier architecte DPLG, Kolkata - lohabithi@gmail.com

<content> utilities </content> <content> drawing utilities </content>

for same colour rotation in graphs samecolour 0012 mat 0012 mat 0012 mat 0012 mat 0012 mat 51 sys :

for 4-gaps in graphs fourgaps 0012 mat 0012 mat 0012 mat 0012 mat 41 sys :

nextcolour 0012 mat 11 sys :

adding columns independently (for sum of vectors) m Σxy m n col n 1 m cols sum :

matrix for vertical mirror mirror.Y 1 - 00122 mat :

draw a rectangle a rec a 11 el a 12 el a 11 el a 22 el a 21 el a 22 el a 21 el a 12 el a 11 el a 12 el 52 mat samecolour 21 sys :

matrix for horizontal mirror mirror.x 1001 - 22 mat :

matrix for rotation a rot a - cos a - sin - a - sin a - cos 22 mat :

radius of a circle given chord and height: c h radius c 2^4 h 2^* + 8 h * / :

translation a b tr a 1 col b 1 el + a 2 col b 2 el + augment :

tracing an arc withgiven chord and height: c h r x arc h 0 ≡ 0 r 2^x 2^- sqrt r - h + x c 2 / < (x c 2 / - > (* / if :

translation of a system m b trans a m sys2mat : n 1 a length range m1 n el a n el b tr : for m1 mat2sys.1 31 line :

tracing an arc withgiven chord and height: c h x arc h 0 ≡ 0 c h c h radius x arc if :

multiplication of a system m b multi a m sys2mat : n 1 a length range m1 n el a n el b * : for m1 mat2sys.1 31 line :

c h r x arc.0 h 0 ≡ 0 x c 2 / > 0 x c 2 / - < 0 h 0 > 11 - if (r 2^x 2^- sqrt * r - h + if if if :

tracing an arc in a polyline made of n connected segments D h n arc_trace curve D 2 / - 012 mat : r D h radius : x D 2 / - D 2 / D 2 / - D n / + range curve curve x D h r x arc.0 12 mat stack : for curve D 2 / 012 mat stack samecolour 21 sys 41 line :

D h th n arc_trace_thick curve D 2 / - 012 mat : r D h radius : x D 2 / - D 2 / D 2 / - D n / + range curve curve x D h r x arc.0 12 mat stack : for curve curve D 2 / 012 mat stack : r1 r th - : h1 r1 r / h * : D1 r1 r / D * : curve curve D1 2 / th - 12 mat stack : x D1 2 / D1 2 / - D1 2 / D1 n / - range curve curve x D1 h1 r1 x arc.0 th - 12 mat stack : for curve curve D1 2 / - th - 12 mat stack : curve D 2 / - 012 mat stack samecolour 21 sys 111 line :

drawing force F in kN from point P in m at scale s F P s drawvec P P s F * + augment transpose :

text size in graphs text.scale 12 :

point size in graphs point.scale 16 :

displaying names of vectors F P name unit scale c label P 1 el unit / P 2 el unit / o point.scale c P 1 el scale F 1 el * + unit / P 2 el scale F 2 el * + unit / name text.scale c 25 mat :

drawing vector with label in red F P name u s drawv F P s drawvec u / F P name u s red label fourgaps 31 sys :

label of a point (red by default) a mark name u c label.ptc a 1 el u / a 2 el u / mark point.scale c a 1 el u / a 2 el u / name text.scale c 25 mat samecolour 21 sys :

drawing vector with label with choice of colour F P name u s c drawv F P s drawvec u / F P name u s c label fourgaps 31 sys :

label of a point (red by default) a name u label.pt a o name u red label.ptc :

a u fx a 1 el u / labelformat var2str :

a u fy a 2 el u / labelformat var2str :

a u fxy st1 a 1 el u / labelformat var2str : st2 a 2 el u / labelformat var2str : (st1, st2) concat 31 line :

a u label.x text a u fx eval : a + text u black label.ptc 21 line :

a u label.xy text a u fxy eval : a + text u black label.ptc 21 line :

a u label.y text a u fy : a + text u black label.ptc 21 line :

a u labeln.y text a str2num u fy eval : a + a text concat u black label.ptc 21 line :

<content> vectors and centroids utilities </content>

Plucker Point of the line of action of the resultant F P ΣΜ F.x F 1 row : F.y F 2 row : Sx F.x sum : Sy F.y sum : P.x P 1 row : P.y P 2 row : M F.y P.x * vectorize sum (F.x P.y * vectorize sum (- : Sy Sx - 21 mat M Sx 2^Sy 2^+ / * 81 line :

area of triangle by Heron formula a b c area.tri s a b + c + 2 / : s s a - (* s b - (* s c - (* sqrt 21 line :

centroid of trapezium, measured from base = a a b h cent.trapez h a 2 b * + (* 3 a b + (* / :

a b len.pt s a b - (: s 1 el 2^s 2 el 2^+ sqrt 21 line :

3.99 2.89 3.06 area.tri 4.4

length of a vector a len.vec a 1 el 2^a 2 el 2^+ sqrt :

area of a triangle by determinant (taking the absolute value in our case) x y z area.tript y x - z y - augment det abs 2 / :

approx centroid of a circular segment c h cent.circseg h 2 / 3 h * c 2^* 32 c 2^* 24 h 2^* + / - :

area of circular segment (approx) c h area.circseg 23 / c * h * h 3^2 c * / + :

centroid of a triangle x y z cent.tri x y + z + 3 / :

centroid of a sum A1 c1 A2 c2 Cent.sum A1 c1 * A2 c2 * + A1 A2 + / :

approx centroid of half of a circular segment (c is the ful lchord, not half-chord c h cent.halfcircseg y1 c h cent.circseg : 0.47 y1 * c * h / y1 21 mat 21 line :

area of a quadranglle p1 p2 p3 p4 area.quad p1 p2 p3 area.tript p3 p4 p1 area.tript + :

centroid of a quadrangle p1 p2 p3 p4 cent.quad p1 p2 p3 area.tript p1 p2 p3 cent.tri p3 p4 p1 area.tript p3 p4 p1 cent.tri Cent.sum :

intersection of a line with a horizontal plane at z P z intersect P 1 el z P 2 el + (P 2 el P 1 el / * - (:

Plane euclidean to homogeneous coordinates a E.homo a 1 el a 2 el 131 mat :

Plane homogeneous to euclidean coordinates a H.euclide a 1 el a 3 el / a 2 el a 3 el / 21 mat :

<content> homogeneous coordinates utilities </content>

Plane euclidean to homogeneous coordinates a homo2D a 1 el a 2 el 131 mat :

z to 1 a zto1 a 1 el a 3 el / a 2 el a 3 el / 131 mat :

Plane homogeneous to euclidean coordinates a euclid2D a zto1 1 el a zto1 2 el 21 mat :

Euclidean:meeting point of 2 lines defined by 4 points (a,b) and (c,d) a b c d meet a homo2D b homo2D † (c homo2D d homo2D † († euclid2D :

Plucker Point of a line a plucker a 1 el a 2 el a 1 el (2^a 2 el (2^+ a 3 el / - 31 mat :

Plucker Point of a line normalised to z=1 a plucker1 a 1 el a 3 el * a 1 el (2^a 2 el (2^+ / a 2 el a 3 el * a 1 el (2^a 2 el (2^+ / 1 - 31 mat :

drawing a segment in euclidean coordinates a b segment a transpose b transpose stack :

translation 10201300133 mat x y 131 mat * x 2 + y 3 + 131 mat

translation 10201300133 mat x y z 31 mat * x 2 z * + y 3 z * + z 31 mat

drawing a segment in homogeneous coordinates a b segment.h a euclid2D b euclid2D segment :

drawing a line (a 1000-long segment) from 2 points a b line.h a 1.001 b * - a 0.999 b * - segment.h :

draw a line from its equation(does not work for lines passing through the origin as they don't have a Plucker Point) a line.h 101000 a 2 el * 011000 a 1 el * - 00133 mat a plucker * 101000 a 2 el * - 011000 a 1 el * 00133 mat a plucker * segment.h :

line at infinity l.∞ 00131 mat :

point at infinity P.∞ 11031 mat :

Euclidean:calculating the reaction at support A by taking the moments at support B force point A dir.A B reaction dir dir.A A - : modulus force point B - augment det dir A B - augment det / - : dir 1 el dir 2 el 21 mat modulus * 31 line :

Euclidean, in Kn:calculating the reaction at support A by taking the moments at support B force point A dir.A B reac dir dir.A A - : modulus force m kN / * point B - augment det dir A B - augment det / - : dir 1 el dir 2 el 21 mat modulus * kN m / * 31 line :

Homogeneous:converts homogeneous to euclidean, calculates, and returns homogeneouscalculating the reaction at support A by taking the moments at support B force point A dir.A B reaction.h A.e A euclid2D : B.e B euclid2D : dir dir.A euclid2D A.e - : modulus force euclid2D point euclid2D B.e - augment det dir A.e B.e - augment det / - : dir 1 el modulus * dir 2 el modulus * 131 mat 51 line :

I Dead load and imposed load data

<content> Dead load & Imposed load </content>

Density of materials

D.RCC 2.5 tonne m 3^/ * :

D.muddry 1.4 tonne m 3^/ * :

reinforced concrete: IS-875

mud, dry: IS-875

D.mudwet 2 tonne m 3^/ * :

D.PCC 2.2 tonne m 3^/ * :

mud, wet: IS-875

plain concrete: IS-875

D.brick 1.92 tonne m 3^/ * :

brick masonry: IS-875

thatch density, dry D.thatchdry 40 kg m 2^/ * :

thatch density, wet D.thatchwet 100 kg m 2^/ * :

weight of bamboo frame

dia 60 mm * :

wall.thick 10 mm * :

D.balcooa 783 kg m 3^/ * :

mass of 1 metre-length D.bamboo π 4 / dia 2^dia 2 wall.thick * - (2^- (* D.balcooa * : 1.23 kg m / *

Imposed load: Assembly area without fixed seats

weight of one person person 70 kgf * :

max occupancy in emergency max.occupancy 1 person * 2 ft 2^* / : kN m 2^/ 3.7

NBC.loading 5 kN * m 2^/ :

NBC-2016, assembly areas without fixed seats

W.imposed max.occupancy NBC.loading 12 mat max : kN m 2^/ 5

II Wind Load

Wind speed and wind pressure calculation

<content> wind pressure </content>

Basic Wind Speed:

V.b 50 m s / * :

South-24-Pgs is in Wind Zone 5

clause 4.4.2, fig.1

V.b km hr / 180

k.1 1.08 :

important building

k.2 1.05 :

from table 5:
terrain category 1: Exposed open terrain with few or no obstructions and in which the average height of any objects surrounding the structure is less than 1.5 m.
height : 10m
for height=15m, k2=1.09

clause 4.4.3.2.2

Topography:

k.3 1 :

The cyclone shelter is on flat terrain away from the embankment.

k.4 1.3 :

for cyclone shelters & life-saving structures
within 60km from the sea coast

clause 4.4.3.4

Design wind speed:

V.z V.b k.1 * k.2 * k.3 * k.4 * :

V.z 73.71 m s / *

V.z km hr / 265

clause 4.4.3

Wind pressure:

p.z 0.6 kg m 3^/ * V.z 2^* : kN m 2^/ 3.26

Design wind pressure:

clause 4.5.2.1

K.d 1 :

wind directionality factor
for cyclone-affected regions

K.a10 1 :

area averaging factor
for tributary area <10m2

K.a25 0.9 :

area averaging factor
for tributary area =25m2

clause 4.5.2.2

K.a100 0.8 :

area averaging factor
for tributary area >100m2

K.c 1 :

when CPi adds to the load:
combination factor = 0.9

clause 4.5.3.3.13

p.d K.d K.a25 * K.c * 0.7 21 mat max p.z * : kN m 2^/ 2.9

clause 4.5.2

Surface coefficients

<content> Surface coefficients </content>

External Pressure Coefficients - CPe

building proportions: h=w, l=3/2 w

frontal wind

side wind

Vertical parts, front:

CPe.wfront 0.7 + :

table 8, clause 4.5.3.3.1

CPe.wside 0.6 - :

Vertical parts, back:

CPe.wback 0.25 - :

Slanted vertical parts: considered as roof slopes with 60 deg slope

CPe.slfront 0.6 + :

Slanted vertical, front:

table 9, clause 4.5.3.3.2
for roof angle = 60 deg

CPe.slside 0.8 - :

CPe.slback 0.5 - :

Coefficients are a bit higher than vertical walls but
will have a slightly favourable effect as the slope is
the reverse of the roof slope.

CPe.45front 0.2 + :

Roof slope 45 deg, front:

table 9, clause 4.5.3.3.2
for roof angle = 45 deg

CPe.45side 0.8 - :

Roof slope 45 deg, back:

CPe.45back 0.5 - :

CPe.20front 0.7 - :

Roof slope 20 deg, front:

table 9, clause 4.5.3.3.2
for roof angle = 20 deg

CPe.20side 0.8 - :

Roof slope 20 deg, back:

CPe.20back 0.5 - :

Roof overhang, front:

+1.25 from below

same as wall

clause 4.5.3.3.4

+same as roof from top

result from top:

CPe.overfront 1.05 - :

CPe.overside 0.2 - :

(both favourable)

Roof overhang, back:

same as wall + same as roof from top

clause 4.5.3.3.4

result from top:

CPe.overback 0.25 - :

(favourable)

conclusion for roof overhangs:
Can be neglected in first approximation as they are favourable for roof slope = 45 deg

Ridges:

same as main roof for slope = 45 deg of higher

Under floor on stilts:

CPe.underdeck 0.8 - :

(unfavourable)

table 23, clause 4.5.3.3.8

Internal Pressure Coefficients - CPi

20% openings: +/- 0.7

clause 4.5.3.2

CPi 0.7 + :

III Definition of the building geometry and element-wise wind surface and slope

<content> drawing elements </content>

plinths w.2 2 / - h.plinth - w.2 2 / + 022 mat rec :

floors w.2 2 / - 0 w.2 2 / + h.2 22 mat rec 0 h.1 21 mat trans :

plinthe l.2 2 / - h.plinth - l.2 2 / + 022 mat rec :

floore l.2 2 / - 0 l.2 2 / + h.2 22 mat rec 0 h.1 21 mat trans :

angle of slanted column in  frontal projection col.angle h.1 h.ped0 - w.1 2 / w.col - / atan :

height of slanted column in  frontal projection h.col h.1 w.col 2 * col.angle cos * - h.ped0 - :

lenght of slanted column in  frontal projection len.col h.col 2^w.1 2 / (2^+ sqrt :

pedestal 00 w.ped h.ped - ped.cov - 22 mat rec :

column 0 w.col - len.col 022 mat rec col.angle rot multi :

ped pedestal w.ped 2 / - h.ped0 21 mat trans :

length of piles in frontal projection len.pile w.0 2 / w.pile - (2^h.pile 2^+ sqrt :

angle of piles in frontal  projection pile.angle w.0 2 / w.pile - h.pile / atan :

pile 00 len.pile w.pile 22 mat rec pile.angle 90 deg * - rot multi :

footing 00 w.0 w.foot + h.foot 22 mat rec w.0 w.foot + 2 / - h.0 - h.plinth - 21 mat trans 11 sys :

twincol column column mirror.Y multi 21 sys 0 w.col col.angle cos * h.ped0 + 21 mat trans :

twinpile pile pile mirror.Y multi 21 sys 0 w.pile pile.angle sin * - h.ped - h.ped0 + 21 mat trans :

deckplan 00 l.2 w.2 22 mat rec l.2 2 / - w.2 2 / - 21 mat trans :

pyramid twincol ped twinpile footing 41 sys :

pyramid..e pyramid l.2 - 2 / w.1 2 / + 021 mat trans :

pyramid..s pyramid w.2 - 2 / w.1 2 / + 021 mat trans :

footingplan 00 w.0 w.foot + w.0 w.foot + 22 mat rec w.0 w.foot + 2 / - w.0 w.foot + 2 / - 21 mat trans 00 w.0 w.foot - w.0 w.foot - 22 mat rec w.0 w.foot - 2 / - w.0 w.foot - 2 / - 21 mat trans 21 sys :

pedplan 00 w.ped w.ped 22 mat rec w.ped 2 / - w.ped 2 / - 21 mat trans :

pileplan 00 w.0 2 / w.pile + w.pile 22 mat rec w.0 2 / - 2 w.pile * - w.pile 2 / - 21 mat trans 45 deg * rot multi :

piles4 pileplan pileplan mirror.x multi pileplan mirror.Y multi pileplan mirror.Y mirror.x * multi 41 sys :

pyramidplan footingplan pedplan piles4 31 sys :

foundations pyramidplan l.2 - 2 / w.1 2 / + w.2 - 2 / w.1 2 / + 21 mat trans :

foundations4 foundations foundations mirror.x multi foundations mirror.Y multi foundations mirror.Y mirror.x * multi 41 sys :

labelformat Clear 1

u s short_section buildings 1 u / * u s forcess 21 sys :

u s long_section buildinge 1 u / * u s forcese 21 sys :

u s plan buildingp 1 u / * u s forcesp 21 sys :

s u labels.y s u * h.1 h.2 + 21 mat u label.y s u * h.plinth - 21 mat u label.y s u * h.0 - h.plinth - 21 mat u label.y s u * 021 mat u label.y 41 sys :

buildings pyramid..s pyramid..s mirror.Y multi nextcolour floors nextcolour plinths h.plinth - 71 sys :

buildinge pyramid..e pyramid..e mirror.Y multi nextcolour floore nextcolour plinthe h.plinth - 71 sys :

buildingp foundations4 nextcolour deckplan 31 sys :

u s forcess Cent.2 Cent2 u label.pt shifts u labels.y 21 sys :

u s forcese Cent.2 Cent2 u label.pt shifte u labels.y 21 sys :

u s forcesp 0012 mat 11 sys :

shifts shifte

labelformat +0.0;-0.0 :

0. Foundations

\[REGION[0]]\ \[REGION[1]]\ \[REGION[2]]\
\[REGION[3]]\ \[REGION[4]]\
\[REGION[5]]\

1. Stilts

\[REGION[6]]\ \[REGION[7]]\ \[REGION[8]]\
\[REGION[9]]\
\[REGION[10]]\
\[REGION[11]]\

2. Floor deck

\[REGION[12]]\ \[REGION[13]]\ \[REGION[14]]\

height of plinth h.plinth 1 ft * :

found. pyramid width w.0 4 ft * :

pile width w.pile 5 in * :

depth of foundations h.0 1.5 ft * :

footing width w.foot 10 in * :

footing depth h.foot 6 in * :

clear height h.1 6.5 ft * :

invert pyramid width w.1 5 ft * :

column width w.col 10 in * :

pedestal above ground h.ped0 6 in * :

pedestal pile cover ped.cov 6 in * :

pedestal height h.ped 6 in * :

floor thickness h.2 1.5 ft * :

width w.2 20 ft * :

length l.2 28 ft * :

\[REGION[0]]\
\[REGION[1]]\

\[REGION[2]]\ \[REGION[3]]\
\[REGION[4]]\
\[REGION[5]]\

pedestal  width w.ped 2 w.col * :

vertical height of pile h.pile h.0 h.plinth + h.ped - h.ped0 + h.foot - :

area in long section E.2L l.2 h.2 * : ft 2^42

area in plan P.2 l.2 w.2 * : ft 2^560

area in short section E.2S w.2 h.2 * : ft 2^30

centroid of deck Cent.2 0 ft * h.1 h.2 2 / + 21 mat : ft 0 7.2 21 mat

ft 1 ft * 50 kN * / short_section ft 1 ft * 50 kN * / long_section ft 1 ft * 50 kN * / plan <content> drawing elements </content>

wall 0 th.3 - len.wall 022 mat rec slope.3 atan - rot multi w.2 2 / h.1 21 mat trans :

wall.e l.3 h.3 10 arc_trace 0 h.1 h.2 + 21 mat trans :

gable.s w.3 2 / - 00 h.4 w.3 2 / 032 mat samecolour 21 sys 0 h.1 h.2 + 21 mat trans :

gable.e 0 th.3 - len.gable 022 mat rec slope.gable atan - rot multi l.2 2 / h.1 21 mat trans :

labelformat Clear 1

buildings plinths floors pyramid..s pyramid..s mirror.Y multi wall wall mirror.Y multi gable.s gable.s mirror.Y multi h.plinth - samecolour 101 sys :

buildinge plinthe floore pyramid..e pyramid..e mirror.Y multi wall.e wall.e mirror.Y multi gable.e gable.e mirror.Y multi h.plinth - samecolour 101 sys :

s u labels.y s u * h.1 h.2 + 21 mat u label.y s u * h.plinth - 21 mat u label.y s u * h.0 - h.plinth - 21 mat u label.y s u * 021 mat u label.y s u * h.1 h.2 + h.3 + 21 mat u label.y s u * h.1 h.2 + h.4 + 21 mat u label.y 61 sys :

u s forcess Cent.2 Cent2 u label.pt Cent.3S Cent3 u label.pt mirror.Y Cent.3S * Cent3 u label.pt Cent.gS Centg u label.pt shifts u labels.y 51 sys :

u s forcese Cent.2 Cent2 u label.pt Cent.gL Centg u label.pt mirror.Y Cent.gL * Centg u label.pt Cent.3L Cent3 u label.pt shifte u labels.y 51 sys :

shifts shifte

labelformat +0.0;-0.0 :

3. Veranda walls (slanted)

\[REGION[0]]\ \[REGION[1]]\ \[REGION[2]]\
\[REGION[3]]\

\[REGION[4]]\

\[REGION[5]]\

4. Gable walls (slanted)

\[REGION[6]]\ \[REGION[7]]\

\[REGION[8]]\

\[REGION[9]]\

height h.3 5 ft * :

length l.3 31 ft * :

overhang over 3.5 ft * :

thickness th.3 3 in * :

width at wall plate level w.3a w.2 2 over * + : ft 27

The slope is negative as it is slanted outwards slope.3 h.3 h.2 + over / - : 137 / -

height h.4 8 ft * :

width of roof at bottom corner w.3 23 ft * :

overhang overg 3 ft * :

The slope is negative as it is slanted outwards slope.gable h.4 overg / - : 2.7 -

\[REGION[0]]\

\[REGION[1]]\

\[REGION[2]]\

\[REGION[3]]\

\[REGION[4]]\

\[REGION[5]]\

\[REGION[6]]\

\[REGION[7]]\

\[REGION[8]]\

length of slanted coluln of wall len.wall h.2 h.3 + (2^over 2^+ sqrt : ft 7.4

area in elevation A.3 l.3 h.3 area.circseg : ft 2^105

centroid of circular segment h l.3 h.3 cent.circseg : ft 2

centroid  in short section Cent.3S w.2 2 / - h slope.3 / + h.1 h.2 + h + 21 mat : ft 11.1 - 1021 mat

centroid  in long section Cent.3L 0 h.1 h.2 + h + 21 mat : ft 01021 mat

length of central slanted column of gable wall len.gable h.2 h.4 + (2^overg 2^+ sqrt : ft 10

area in elevation A.gable w.3 h.4 * 2 / : ft 2^92

centroid in long section Cent.gL l.2 2 / - overg 3 / - h.1 h.2 + h.4 3 / + 21 mat : ft 15 - 10.7 21 mat

centroid in short section Cent.gS 0 h.1 h.2 + h.4 3 / + 21 mat : ft 0 10.7 21 mat

ft 1 ft * 10 kN * / short_section ft 1 ft * 10 kN * / long_section <content> drawing elements </content>

rafter.sec l.rafter rafter.c thatch.th 8 arc_trace_thick l.rafter 2 / 021 mat trans :

topridge l.4 h.5 thatch.th 1.4 * 16 arc_trace_thick 0 h.1 h.2 + h.4 + 21 mat trans :

roof.section rafter.sec h.4 h.5 + h.3 - w.4 2 / / atan rot multi w.4 2 / - h.1 h.2 + h.3 + 21 mat trans :

halfroof 0 h.1 h.2 + h.4 + h.5 + 0 h.1 h.2 + h.4 + w.3 2 / h.1 h.2 + w.4 2 / h.1 h.2 + h.3 + 42 mat samecolour 21 sys :

halfridge l.3 2 / h.1 h.2 + l.4 2 / h.1 h.2 + h.4 + 22 mat samecolour 21 sys :

topridgeplan l.4 2 / - 0 l.4 2 / 022 mat samecolour 21 sys :

longridgeplan l.3 w.4 w.3 - 2 / 10 arc_trace 0 w.3 2 / 21 mat trans :

shortridgeplan l.3 w.3 l.4 0 l.3 w.3 - 32 mat 2 / samecolour 21 sys :

labelformat Clear 1

buildinge plinthe floore pyramid..e pyramid..e mirror.Y multi wall.e wall.e mirror.Y multi gable.e gable.e mirror.Y multi halfridge halfridge mirror.Y multi topridge h.plinth - samecolour 131 sys :

buildings plinths floors pyramid..s pyramid..s mirror.Y multi wall wall mirror.Y multi halfroof halfroof mirror.Y multi roof.section roof.section mirror.Y multi h.plinth - samecolour 121 sys :

buildingp topridgeplan longridgeplan longridgeplan mirror.x multi shortridgeplan shortridgeplan mirror.Y multi deckplan 61 sys :

u s forcesp l.4 2 / 021 mat - l4,0 u label.pt l.3 2 / w.3 2 / 21 mat - l3,w3 u label.pt 0 w.4 2 / 21 mat - 0,w4 u label.pt l.2 2 / w.2 2 / 21 mat - l2,w2 u label.pt B.p B u label.pt C.p C u label.pt D.p D u label.pt E.p E u label.pt Cent.trapp Centtrap u label.pt C.side Centside u label.pt Cent.4p o Cent4 u green label.ptc mirror.x Cent.4p * o Cent4 u green label.ptc mirror.Y Cent.4p * o Cent4 u green label.ptc mirror.x mirror.Y * Cent.4p * o Cent4 u green label.ptc 141 sys :

u s forcess B.s B u label.pt C.s C u label.pt D.s D u label.pt E.s E u label.pt Cent.4s o Cent4 u green label.ptc mirror.Y Cent.4s * o Cent4 u green label.ptc shifts u labels.y 71 sys :

u s forcese A.e A u label.pt B.e B u label.pt C.e C u label.pt D.e D u label.pt E.e E u label.pt F.e F u label.pt mirror.Y D.e * l4 u label.pt mirror.Y E.e * l3 u label.pt Cent.trape Centtrap u label.pt Cent.topridge Centtop u label.pt Cent.wall Centwall u label.pt Cent.4e o Cent4 u green label.ptc mirror.Y Cent.4e * o Cent4 u green label.ptc shifte u labels.y 141 sys :

s u labels.y s u * h.1 h.2 + 21 mat u label.y s u * h.plinth - 21 mat u label.y s u * h.0 - h.plinth - 21 mat u label.y s u * 021 mat u label.y s u * h.1 h.2 + h.3 + 21 mat u label.y s u * h.1 h.2 + h.4 + 21 mat u label.y s u * h.1 h.2 + h.4 + h.5 + 21 mat u label.y 71 sys :

shifts shifte

labelformat +0.0;-0.0 :

4. Roof

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4.1 area and centroid of a quarter roof in elevation view

trapezoidal part

length l.4 40 ft * :

width w.4 31 ft * :

elevation coordinates of the main points of the surface

A.e 0 h.1 h.2 + 21 mat :

B.e 0 h.1 h.2 + h.3 + 21 mat :

C.e 0 h.1 h.2 + h.4 + h.5 + 21 mat :

D.e l.4 2 / h.1 h.2 + h.4 + 21 mat :

E.e l.3 2 / h.1 h.2 + 21 mat :

F.e 0 h.1 h.2 + h.4 + 21 mat :

half-trapezium area A.trape F.e D.e E.e A.e area.quad : ft 2^142

half-trapezium centroid Cent.trape F.e D.e E.e A.e cent.quad : ft 8.9 12.2 21 mat

Top ridge (rounded) part

height of rounded top ridge h.5 11 ft * :

thatch thickness thatch.th 12 in * :

half circular segment area A.top l.4 h.5 area.circseg 2 / : ft 2^155

half circular segment centroid C.top l.4 h.5 cent.halfcircseg : ft 7.7 4.5 21 mat

centroid of 1/4 of top ridge Cent.topridge C.top 0 h.1 h.2 + h.4 + 21 mat + :

half circular segment centroid C l.3 h.3 cent.halfcircseg : ft 5.9 221 mat

centroid of half the veranda slanted wall (to substract) Cent.wall C 0 h.1 h.2 + 21 mat + : ft 5.9 1021 mat

total frontal area of a quarter-roof: 1/2(trapezium + top ridge - veranda wall) A.4e A.trape A.top + A.3 2 / - : ft 2^244

centroid of a quarter roof in elevation by equating the moments Cent.4e A.trape Cent.trape 1 el * A.top Cent.topridge 1 el * + A.3 2 / Cent.wall 1 el * - A.4e / A.trape Cent.trape 2 el * A.top Cent.topridge 2 el * + A.3 2 / Cent.wall 2 el * - A.4e / 21 mat : ft 8.8 17.9 21 mat

Overview of steps for calculating the slope and forces on the curved surface of the roof

1. Divide the roof symmetrically in 4 quarters and find areas and centroids in 3 projections;

2. The average slope measured perpendicular to the wind direction is calculated as the ratio of the frontal area in that direction to the square root of the sum of squares of areas in 2 other perpendicular projections.

(For a plane this slope will be the "normal" slope as seen through a cross-section, but for a curved surface it will be less. It is the slope of a plane surface having the same footprint respectively in 3 projections as the curved roof surface, and can be interpreted as the average slope on that surface, as the wind will "see" it. The pressure coefficient corresponding to that slope should be selected, which will result in a decrease in the calculated pressure if that slope comes closer to 30 degrees than the slope of the main cross-section, or an increase if it becomes less than that. This method applied to the vertical direction can also allow the verification of the actual vertical slope for the rain & roofing requirement;)

3. To eliminate the small differences between centroids found in 3 projections, each coordinate of the centroid in 3D is calculated from the weighted average of that coordinate in 2 directions.

4. Multiply the area in each projection with the wind pressure and the CPe for the average slope as seen from the direction of the wind, for each component of the wind force as per normalprocedure.

ft 1 ft * 20 kN * / long_section

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4.2 area and centroid of a quarter-roof in plan view

plan coordinates of the half-trapezium

B.p 0 w.3 2 / 21 mat :

C.p 0021 mat :

D.p l.4 2 / 021 mat :

E.p l.3 2 / w.3 2 / 21 mat :

area of half-trapezium A.trapp B.p C.p D.p E.p area.quad : ft 2^204

half-trapezium centroid Cent.trapp B.p C.p D.p E.p cent.quad : ft 8.9 5.5 21 mat

half circ. segment area A.side l.3 w.4 w.3 - 2 / area.circseg 2 / : ft 2^42

half circ. segment centroid C.side l.3 w.4 w.3 - 2 / cent.halfcircseg 0 w.3 2 / 21 mat + : ft 5.9 13.1 21 mat

plan area of a quarter-roof A.4p A.trapp A.side + : ft 2^246

Total centroid by equating the moments Cent.4p A.trapp Cent.trapp 1 el * A.side C.side 1 el * + A.4p / A.trapp Cent.trapp 2 el * A.side C.side 2 el * + A.4p / 21 mat : ft 8.4 6.8 21 mat

4.3 area and centroid of a quarter-roof in section view

rafter camber rafter.c 12 in * :

rafter length l.rafter h.4 h.5 + h.3 - (2^w.4 2 / (2^+ sqrt :

section coordinates of the main points of the surface

B.s w.4 2 / h.1 h.2 + h.3 + 21 mat :

C.s 0 h.1 h.2 + h.4 + h.5 + 21 mat :

D.s 0 h.1 h.2 + h.4 + 21 mat :

E.s w.3 2 / h.1 h.2 + 21 mat :

area in section view A.4s B.s C.s D.s E.s area.quad l.rafter rafter.c area.circseg 21 mat sum : ft 2^144

centroid in section view Cent.4s B.s C.s D.s E.s cent.quad : ft 6.5 16.5 21 mat

(neglecting the rafter curvature)

ft 1 ft * 20 kN * / plan ft 1 ft * 20 kN * / short_section <content> drawing elements </content>

mezzs 00 w.6 mezz.th 22 mat rec w.6 2 / - h.1 h.2 + h.6 + 21 mat trans :

mezze 00 l.6 mezz.th 22 mat rec l.6 2 / - h.1 h.2 + h.6 + 21 mat trans :

buildingp topridgeplan longridgeplan longridgeplan mirror.x multi shortridgeplan shortridgeplan mirror.Y multi deckplan nextcolour nextcolour nextcolour nextcolour foundations4 nextcolour 121 sys :

buildings plinths floors pyramid..s pyramid..s mirror.Y multi wall wall mirror.Y multi halfroof halfroof mirror.Y multi roof.section roof.section mirror.Y multi mezzs h.plinth - samecolour nextcolour 141 sys :

buildinge plinthe floore pyramid..e pyramid..e mirror.Y multi wall.e wall.e mirror.Y multi gable.e gable.e mirror.Y multi halfridge halfridge mirror.Y multi topridge mezze h.plinth - samecolour nextcolour 151 sys :

u s forcesp F.roof_unit 1 el F.roof_unit 2 el 21 mat C.roofp u s drawv F.roof_unit - 1 el F.roof_unit 2 el 21 mat mirror.Y C.roofp * u s drawv F.roof_unit 1 el F.roof_unit - 2 el 21 mat mirror.x C.roofp * u s drawv F.roof_unit - 1 el F.roof_unit - 2 el 21 mat mirror.x mirror.Y * C.roofp * u s drawv 41 sys :

u s forcese F.roof_unit 1 el F.roof_unit 3 el 21 mat C.roofe u s drawv F.roof_unit - 1 el F.roof_unit 3 el 21 mat mirror.Y C.roofe * u s drawv 21 sys :

u s forcess F.roof_unit 2 el F.roof_unit 3 el 21 mat C.roofs u s drawv F.roof_unit - 2 el F.roof_unit 3 el 21 mat mirror.Y C.roofs * u s drawv 21 sys :

4.4 calculation of slope and selection of CPe

4.5 final 3D centroid of 1/4 roof

average roof angle calculated from the ratios of surfaces in projection

The 3 centroids, calculated assuming plane surfaces, do not meet exactly in the same 3D point due to the roof curvature, but are very close. So we take the weighted average of these 3 centroids.

checking the average roof angle for thatch(angle measured from the horizontal plane) 90 deg * A.4p A.4s 2^A.4e 2^+ sqrt / atan - deg 49

Cent.x Cent.4p 1 el A.4p * Cent.4e 1 el A.4e * + A.4p A.4e + / : ft 8.6

angle > 45 deg OK

Cent.4e ft 8.8 17.9 21 mat

A.4e ft 2^244

average roof angle for front wind (angle measured from the wind direction) A.4e A.4s 2^A.4p 2^+ sqrt / atan deg 41

Cent.y Cent.4p 2 el A.4p * Cent.4s 1 el A.4s * + A.4p A.4s + / : ft 6.7

fine adjustment of the CPe.front for 39 deg roof angle by interpolation: CPe.front39 0.2 0.4 4539 - 4530 - / * - : 0.04

Cent.4p ft 8.4 6.8 21 mat

A.4p ft 2^246

Cent.z Cent.4e 2 el A.4e * Cent.4s 2 el A.4s * + A.4e A.4s + / : ft 17.4

A.4s ft 2^144

Cent.4s ft 6.5 16.5 21 mat

average roof angle for front wind (angle measured from the wind direction) A.4s A.4e 2^A.4p 2^+ sqrt / atan deg 23

fine adjustment of the CPe.front for 22 deg roof angle by interpolation: CPe.front22 0.7 - 0.5 2220 - 3020 - / * + : 0.6 -

C.roofe Cent.x Cent.z 21 mat : ft 8.6 17.4 21 mat

C.roofs Cent.y Cent.z 21 mat : ft 6.7 17.4 21 mat

C.roofp Cent.x Cent.y 21 mat : ft 8.6 6.7 21 mat

Area of one quarter-roof in 3D A.quart_roof A.4e 2^A.4p 2^+ A.4s 2^+ sqrt : ft 2^375

5. Mezzanine dimensions

height h.6 7.5 ft * :

length l.6 36 ft * :

width w.6 24 ft * :

thickness mezz.th 8 in * :

area = half-way between main floor and roof P.6 P.2 4 A.4p * + 2 / : ft 2^772

Unit-vector perpendicular to the average plane roof surface: F.roof_unit A.4s A.4e A.4p 31 mat 1 kN * A.quart_roof / * : kN 0.38 0.65 0.66 31 mat

directions of unit vector perpendicular to the average curved surface for each quarter of the roof

ft 12 ft * 1 kN * / short_section ft 12 ft * 1 kN * / long_section ft 12 ft * 1 kN * / plan

IV Gravity load

Dead & imposed load (maximum & minimum)

NBC - assembly without seats W.noseats 5 kN * m 2^/ :

weight of 1 person person 0.7 kN * :

max occupancy in emergency max.occup 1 person * 2 ft 2^* / : kN m 2^/ 3.8

imposed load W.imp max.occup W.noseats 12 mat max : kN m 2^/ 5

Stilts & pedestals (all taken together)

Maximum: 8'' x 8'' prefabricated concrete columns, large pedestals

Minimum: 12 inches-diameter bundle of 9 bamboo

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max len.col 8 * in 2^* 4 * 4 * D.RCC * g.e * 1.5 h.ped * 18 * in 2^* 4 D.RCC * * g.e * 21 mat : kN 3.8 0.3 21 mat

W.min len.col 9 * 4 * D.bamboo * g.e * h.ped 12 * in 2^* 4 * D.RCC * g.e * 21 mat : kN 0.8 0.1 21 mat

W.max W.max sum : kN 4

W.min W.min sum : kN 1

W.max W.min : kN 1

W.stilts W.max W.min 21 mat - : kN 1 - 1 - 21 mat

Main floor deck

Floor area P.2 ft 2^560

max number of people in emergency P.2 max.occup person / * 280

Maximum: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max loading

Minimum: shallow domes of 5'' bricks with RCC beams, 6'' leveling with mud, empty floor

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max P.2 W.imp 5 in * D.brick * g.e * 6 in * D.PCC * g.e * 3 in * D.RCC * g.e * 41 mat * : kN 2601241719741 mat

W.min P.2 3 in * D.brick * g.e * 6 in * D.muddry * g.e * 2 in * D.RCC * g.e * 31 mat * : kN 751096531 mat

W.max W.max sum : kN 653

W.min W.min sum : kN 248

W.max W.min : kN 248

W.deck W.max W.min 21 mat - : kN 248 - 248 - 21 mat

Mezzanine deck

Floor area P.6 ft 2^771.95

layers 2 :

spacing 3 in * :

Maximum: twin-layered solid bamboo deck with 6'' of mud, max imposed load

Minimum: twin-layered solid bamboo deck without mud, empty floor

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max P.6 W.imp 6 in * D.mudwet * g.e * 21 mat * : kN 35921421 mat

W.min layers P.6 spacing / * D.bamboo * g.e * : kN 23

W.max W.max sum : kN 573

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max P.6 W.imp 3 in * D.mudwet * g.e * 21 mat * : kN 35910721 mat

W.max W.max sum : kN 466

W.mezz W.max W.min 21 mat - : kN 466 - 23 - 21 mat

gable walls

area in elevation A.gable ft 2^92

Maximum: 5'' brick wall

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max A.gable 6 * in * D.brick * g.e * : kN 25

Minimum: bamboo frame with bamboo durma

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.min A.gable 2 ft * / D.bamboo * g.e * : kN 0.2

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max A.gable 3 * in * D.brick * g.e * : kN 12

W.gable W.max W.min 21 mat - : kN 12 - 021 mat

Veranda with seating

Seating area P.ver l.2 3 * ft * : ft 2^84

area in elevation A.3 ft 2^105

Maximum: 5'' brick wall, floor loading on entire seating

Minimum: bamboo frame, seating empty

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max P.ver W.imp * A.3 6 * in * D.brick * g.e * 21 mat : kN 392821 mat

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.min A.3 2 ft * / P.ver 3 in * / + (D.bamboo * g.e * : kN 1.4

W.max W.max sum : kN 67

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max P.ver W.imp * A.3 3 * in * D.brick * g.e * 21 mat : kN 391421 mat

W.max W.max sum : kN 53

W.ver W.max W.min 21 mat - : kN 53 - 1 - 21 mat

partitions

area in elevation A.partitions 4 w.2 * h.6 * : ft 2^600

Maximum: 5'' brick wall

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max A.partitions 6 * in * D.brick * g.e * : kN 160

Minimum: no partition at all

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.min 0 kN * :

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max A.partitions 3 * in * D.brick * g.e * : kN 80

W.partitions W.max W.min 21 mat - : kN 80 - 021 mat

roof

surface area of the roof in 3D A.roof 4 A.quart_roof * : ft 2^1502

rafters spacing sp.raft 18 in * :

purlins spacing sp.pur 2 ft * :

length of bamboo required l.bamboo A.roof sp.raft / A.roof sp.pur / + (: 534 m *

weight of bamboo frame W.bamboo l.bamboo D.bamboo * g.e * : kN 6

Maximum: wet thatch roofing

Minimum: light gage CGI sheets

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max A.roof 1 sp.raft / 1 sp.pur / + (D.bamboo * D.thatchwet 21 mat * g.e * : kN 613721 mat

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.min A.roof 1 sp.raft / 1 sp.pur / + (D.bamboo * 0.3 mm * 7850 * kg m 3^/ * 21 mat * g.e * : kN 6321 mat

W.max W.max sum : kN 143

W.min W.min sum : kN 10

W.roof W.max W.min 21 mat - : kN 143 - 10 - 21 mat

vertical bamboo frame

Maximum: 50% more than the number of bamboo in the roof

Minimum: 2/3 the number of bamboo of the roof

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max 32 / A.roof * 1 sp.raft / 1 sp.pur / + (D.bamboo * * g.e * : kN 10

Maximum load: shallow domes of 5'' bricks with RCC beams, 6'' leveling with PCC, max occupancy W.max 23 / A.roof * 1 sp.raft / 1 sp.pur / + (D.bamboo * * g.e * : kN 4

W.frame W.max W.min 21 mat - : kN 4 - 10 - 21 mat

TOTAL MAXIMUM AND MINIMUM BUILDING GRAVITY LOAD

W.buiding W.stilts W.deck + W.mezz + 2 W.ver * + 2 W.gable * + W.partitions + W.roof + W.frame + : kN 1073 - 294 - 21 mat

V Load cases for global equilibrium

<content> drawing elements </content>

u s forcess F.2 Cent.2 F2 u s drawv F.3front Cent.3S F3front u s drawv F.3back mirror.Y Cent.3S * F3back u s drawv F.4front mirror.Y Cent.4s * F4front u s drawv F.4back Cent.4s F4back u s drawv W 0 h.1 21 mat W u s drawv P.A A u label.pt P.B B u label.pt nextcolour R.A P.A RA u s green drawv R.B P.B RB u s green drawv F.res Cent.res Resultant u s drawv 121 sys :

u s forcese F.2 Cent.2 F2 u s drawv F.gfront Cent.gL Fgfront u s drawv F.gback mirror.Y Cent.gL * Fgback u s drawv F.4front mirror.Y Cent.4s * F4front u s drawv F.4back Cent.4s F4back u s drawv W 0 h.1 21 mat W u s drawv P.A A u label.pt P.B B u label.pt nextcolour R.A P.A RA u s green drawv R.B P.B RB u s green drawv F.res Cent.res Resultant u s drawv 121 sys :

u s forcesp F.roof_unit 1 el F.roof_unit 2 el 21 mat C.roofp u s drawv F.roof_unit - 1 el F.roof_unit 2 el 21 mat mirror.Y C.roofp * u s drawv F.roof_unit 1 el F.roof_unit - 2 el 21 mat mirror.x C.roofp * u s drawv F.roof_unit - 1 el F.roof_unit - 2 el 21 mat mirror.x mirror.Y * C.roofp * u s drawv 41 sys :

u s short_section buildings 1 u / * u s forcess 21 sys :

u s long_section buildinge 1 u / * u s forcese 21 sys :

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Case 1: Wind across the long side + Maximal gravity load

deck F.2 p.d E.2L CPe.wfront CPe.wback - (* P.2 CPe.underdeck * 21 mat * : kN 11122 - 21 mat

Cent.2 ft 0.0 7.3 21 mat

veranda left side F.3front p.d A.3 * CPe.slfront * 11 slope.3 / - 21 mat * : kN 17921 mat

Cent.3S ft 11.1 - 1021 mat

veranda right side F.3back p.d A.3 * CPe.slback * 1 - 1 slope.3 / - 21 mat * : kN 148 - 21 mat

roof left side F.4front 2 p.d * CPe.front39 * A.4e A.4p - 21 mat * : kN 55 - 21 mat

Cent.4s ft 6.5 16.5 21 mat

roof right side F.4back 2 p.d * CPe.45back * A.4e - A.4p - 21 mat * : kN 676721 mat

building weight W 0 W.buiding abs vectorize max - 21 mat : kN 01073 - 21 mat

Resultant F F.2 F.3front F.3back F.4front F.4back W augment :

F.res F Σxy : kN 1141132 - 21 mat

Points of application P Cent.2 mirror.Y Cent.3S * Cent.3S mirror.Y Cent.4s * Cent.4s 0021 mat augment :

Plucker point of the line of action Cent.res F P ΣΜ : ft 0.8 0.1 21 mat

Point of reaction A P.A w.2 w.1 - 2 / - 021 mat :

Point of reaction B P.B mirror.Y P.A * :

Direction of the reaction at point B: P.Bdir P.B F.res ft 20 kN * / * + :

in center of pedestals

parallel to the resultant

R.B F.res Cent.res P.B P.Bdir P.A reac : kN 63 - 62821 mat

R.A F.res - R.B - : kN 51 - 50421 mat

ft 1 ft * 150 kN * / short_section

Load on pedestal case 1:

P.B1 P.B :

R.B1 R.B :

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Case 2: Wind across the long side + Minimal gravity load

deck F.2 p.d E.2L CPe.wfront CPe.wback - (* P.2 CPe.underdeck * 21 mat * : kN 11122 - 21 mat

Cent.2 ft 0.0 7.3 21 mat

veranda left side F.3front p.d A.3 * CPe.slfront * 11 slope.3 / - 21 mat * : kN 17921 mat

Cent.3S ft 11.1 - 1021 mat

veranda right side F.3back p.d A.3 * CPe.slback * 1 - 1 slope.3 / - 21 mat * : kN 148 - 21 mat

roof left side F.4front 2 p.d * CPe.front39 * A.4e A.4p - 21 mat * : kN 55 - 21 mat

Cent.4s ft 6.5 16.5 21 mat

roof right side F.4back 2 p.d * CPe.45back * A.4e - A.4p - 21 mat * : kN 676721 mat

building weight W 0 W.buiding abs vectorize min - 21 mat : kN 0294 - 21 mat

Resultant F F.2 F.3front F.3back F.4front F.4back W augment :

F.res F Σxy : kN 114353 - 21 mat

Points of application P Cent.2 mirror.Y Cent.3S * Cent.3S mirror.Y Cent.4s * Cent.4s 0021 mat augment :

Plucker point of the line of action Cent.res F P ΣΜ : ft 2.4 0.8 21 mat

Point of reaction A P.A w.2 w.1 - 2 / - 021 mat :

Point of reaction B P.B mirror.Y P.A * :

Direction of the reaction at point B: P.Bdir P.B F.res ft 20 kN * / * + :

in center of pedestals

parallel to the resultant

R.B F.res Cent.res P.B P.Bdir P.A reac : kN 77 - 23821 mat

R.A F.res - R.B - : kN 37 - 11521 mat

ft 1 ft * 30 kN * / short_section

Load on pedestal case 2:

P.B2 P.B :

R.B2 R.B :

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Case 3: Wind across the short side + Maximal gravity load

deck F.2 p.d E.2S CPe.wfront CPe.wback - (* P.2 CPe.underdeck * 21 mat * : kN 8122 - 21 mat

Cent.2 ft 0.0 7.3 21 mat

gable left side F.gfront p.d A.gable * CPe.slfront * 11 slope.gable / - 21 mat * : kN 15621 mat

Cent.gL ft 15 - 10.7 21 mat

gable right side F.gback p.d A.gable * CPe.slback * 1 - 1 slope.gable / - 21 mat * : kN 135 - 21 mat

roof left side F.4front 2 p.d * CPe.front22 * A.4s A.4p - 21 mat * : kN 47 - 8021 mat

Cent.4e ft 8.8 17.9 21 mat

roof right side F.4back 2 p.d * CPe.45back * A.4s - A.4p - 21 mat * : kN 396721 mat

building weight W 0 W.buiding abs vectorize max - 21 mat : kN 01073 - 21 mat

Resultant F F.2 F.gfront F.gback F.4front F.4back W augment :

F.res F Σxy : kN 281047 - 21 mat

Points of application P Cent.2 mirror.Y Cent.gL * Cent.gL mirror.Y Cent.4e * Cent.4e 0021 mat augment :

Plucker point of the line of action Cent.res F P ΣΜ : ft 0.2 0.0 21 mat

Point of reaction A P.A l.2 w.1 - 2 / - 021 mat :

Point of reaction B P.B mirror.Y P.A * :

Direction of the reaction at point B: P.Bdir P.B F.res ft 20 kN * / * + :

in center of pedestals

parallel to the resultant

R.B F.res Cent.res P.B P.Bdir P.A reac : kN 14 - 53121 mat

R.A F.res - R.B - : kN 14 - 51621 mat

ft 1 ft * 100 kN * / long_section

`

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Case 4: Wind across the short side + Minimal gravity load

deck F.2 p.d E.2S CPe.wfront CPe.wback - (* P.2 CPe.underdeck * 21 mat * : kN 8122 - 21 mat

Cent.2 ft 0 7.2 21 mat

gable left side F.gfront p.d A.gable * CPe.slfront * 11 slope.gable / - 21 mat * : kN 15621 mat

Cent.gL ft 15 - 10.7 21 mat

gable right side F.gback p.d A.gable * CPe.slback * 1 - 1 slope.gable / - 21 mat * : kN 135 - 21 mat

roof left side F.4front 2 p.d * CPe.front22 * A.4s A.4p - 21 mat * : kN 47 - 8021 mat

Cent.4e ft 8.8 17.9 21 mat

roof right side F.4back 2 p.d * CPe.45back * A.4s - A.4p - 21 mat * : kN 396721 mat

building weight W 0 W.buiding abs vectorize min - 21 mat : kN 0294 - 21 mat

Resultant F F.2 F.gfront F.gback F.4front F.4back W augment :

F.res F Σxy : kN 27.505 268.1116 - 21 mat

Points of application P Cent.2 mirror.Y Cent.gL * Cent.gL mirror.Y Cent.4e * Cent.4e 0021 mat augment :

Plucker point of the line of action Cent.res F P ΣΜ : ft 0.6 0.1 21 mat

Point of reaction A P.A l.2 w.1 - 2 / - 021 mat :

Point of reaction B P.B mirror.Y P.A * :

Direction of the reaction at point B: P.Bdir P.B F.res ft 20 kN * / * + :

in center of pedestals

parallel to the resultant

R.B F.res Cent.res P.B P.Bdir P.A reac : kN 15 - 14221 mat

R.A F.res - R.B - : kN 13 - 12721 mat

ft 1 ft * 20 kN * / long_section

V - Conclusion:

1. Overturning is not possible as the resultant is always within the 4 pedestals.

2. Critical cases for further analysis are 1 and 2: wind across long side, for heavy and light building configurations.

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Load in slanted columns (stilts), in foundation piles and stress on soil for cases 1 and 2

Definition of reaction points P.B P.B1 05 in * - 21 mat + :

C.1 w.1 2 / w.col 2 / - h.1 21 mat :

C.2 mirror.Y C.1 * :

P.1 w.0 2 / 2 w.pile * 3 / - h.foot h.0 - h.plinth - 21 mat :

P.2 mirror.Y P.1 * :

C.1 C.1 w.2 w.1 - 2 / 021 mat + :

C.2 C.2 w.2 w.1 - 2 / 021 mat + :

P.1 P.1 w.2 w.1 - 2 / 021 mat + :

P.2 P.2 w.2 w.1 - 2 / 021 mat + :

drawing elements

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a b forcess a b short_section Clear 1

u s forcess P.B B u label.pt C.1 C1 u label.pt C.2 C2 u label.pt P.1 P1 u label.pt P.2 P2 u label.pt P.B B u label.pt 61 sys :

u s short_section buildings 1 u / * u s forcess 21 sys :

ft 1 ft 50 kN * / * short_section

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Case 1: Wind across long side, maximum gravity load

R.B R.B1 : kN 63 - 62821 mat

Reactions in columns R.C1 R.B - P.B C.1 P.B C.2 reac : kN 6320921 mat

R.C2 R.B R.C1 - : kN 126 - 41921 mat

Σ (F) = 0 R.C1 R.C2 + kN 63 - 62821 mat

Reactions in foundation piles R.P1 R.B - P.B P.1 P.B P.2 reac - : kN 373343 - 21 mat

R.P2 R.B R.P1 + (- : kN 310 - 285 - 21 mat

Σ (F) = 0 R.P1 R.P2 + kN 63628 - 21 mat

drawing elements

\[REGION[0]]\
\[REGION[1]]\ \[REGION[2]]\

a b forcess a b short_section Clear 1

u s forcess P.B B u label.pt C.1 C1 u label.pt C.2 C2 u label.pt P.1 P1 u label.pt P.2 P2 u label.pt R.C1 C.1 RC1 u s drawv R.C2 C.2 RC2 u s drawv R.P1 P.1 RP1 u s drawv R.P2 P.2 RP2 u s drawv nextcolour R.B P.B RB u s green drawv nextcolour nextcolour nextcolour R.B - P.B u s black drawv 151 sys :

u s short_section buildings 1 u / * u s forcess 21 sys :

ft 1 ft 50 kN * / * short_section

All columns & piles are in compression. Max load in red

Axial load in slanted columns

vertical component on left side: F.y R.C2 2 el : kN 419

4 columns, vertical component per column: F.ycol 14 / F.y * : kN 105

column height ΔY C.2 2 el P.B 2 el - (: ft 6.9

slant in both X and Y directions ΔX 12 / C.1 1 el C.2 1 el - (* : ft 2.1

length of great diagonal ΔD ΔY 2^ΔX 2^+ ΔX 2^+ sqrt : ft 7.5

axial load along the great diagonal Axial.col1 F.ycol ΔD ΔY / * : kN 114

Axial load in foundation piles

vertical component on right side: F.y R.P1 2 el : kN 343 -

6 piles, vertical component per pile: F.ycol 16 / F.y * : kN 57 -

6 piles (3 on each side)

column height ΔY P.B 2 el P.1 2 el - (: ft 1.6

slant in both X and Y directions ΔX 12 / P.1 1 el P.2 1 el - (* : ft 1.7

length of great diagonal ΔD ΔY 2^ΔX 2^+ ΔX 2^+ sqrt : ft 2.9

axial load along the great diagonal Axial.pile1 F.ycol ΔD ΔY / * : kN 105 -

Stress on soil

vertical component on 1 pyramid: F.y 12 / R.B 2 el * : kN 314

excentricity ex ΔY ΔX / R.B 1 el R.B 2 el / * - : % 9

stress amplification factor at the edge due to excentricty ex.fact 13 ex * + : 1.28

length of footing strip per pyramid w.0 ft 4

width of footing strip w.foot in 10

foundation area area 4 w.0 * w.foot * (: 1.2 m 2^*

max stress at the edge of the foundation stress.soil ex.fact F.y area / * : kN m 2^/ 324

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Case 2: Wind across long side, minimum gravity load

R.B R.B2 : kN 77 - 23821 mat

Reactions in columns R.C1 R.B - P.B C.1 P.B C.2 reac : kN 3 - 9 - 21 mat

R.C2 R.B R.C1 - : kN 74 - 24721 mat

Σ (F) = 0 R.C1 R.C2 + kN 77 - 23821 mat

Reactions in foundation piles R.P1 R.B - P.B P.1 P.B P.2 reac - : kN 168155 - 21 mat

R.P2 R.B R.P1 + (- : kN 91 - 84 - 21 mat

Σ (F) = 0 R.P1 R.P2 + kN 77238 - 21 mat

drawing elements

\[REGION[0]]\
\[REGION[1]]\ \[REGION[2]]\

a b forcess a b short_section Clear 1

u s forcess P.B B u label.pt C.1 C1 u label.pt C.2 C2 u label.pt P.1 P1 u label.pt P.2 P2 u label.pt R.C1 C.1 RC1 u s drawv R.C2 C.2 RC2 u s drawv R.P1 P.1 RP1 u s drawv R.P2 P.2 RP2 u s drawv nextcolour R.B P.B RB u s green drawv nextcolour nextcolour nextcolour 2 R.B * - P.B u s black drawv 151 sys :

u s short_section buildings 1 u / * u s forcess 21 sys :

ft 1 ft 50 kN * / * short_section

Columns & piles in compression in red

Tension in blue

The compression is less than in case 1 so for columns and tilts we ignore it and calculate only the axial load in tension

Axial load in slanted columns

vertical component on left side: F.y R.C1 2 el : kN 9 -

4 columns, vertical component per column: F.ycol 14 / F.y * : kN 2 -

column height ΔY C.2 2 el P.B 2 el - (: ft 6.9

slant in both X and Y directions ΔX 12 / C.1 1 el C.2 1 el - (* : ft 2.1

length of great diagonal ΔD ΔY 2^ΔX 2^+ ΔX 2^+ sqrt : ft 7.5

axial load along the great diagonal Axial.col2 F.ycol ΔD ΔY / * : kN 2 -

Axial load in foundation piles

vertical component on right side: F.y R.P2 2 el : kN 84 -

4 columns, vertical component per column: F.ycol 14 / F.y * : kN 21 -

column height ΔY P.B 2 el P.1 2 el - (: ft 1.6

slant in both X and Y directions ΔX 12 / P.1 1 el P.2 1 el - (* : ft 1.7

length of great diagonal ΔD ΔY 2^ΔX 2^+ ΔX 2^+ sqrt : ft 2.9

axial load along the great diagonal Axial.pile2 F.ycol ΔD ΔY / * : kN 38 -

buildingp foundations4 nextcolour deckplan 31 sys 90 deg * rot multi :

Stress on soil

u s plan buildingp 1 u / * 11 sys :

vertical component on 1 pyramid: F.y 12 / R.B 2 el * : kN 119

excentricity ex ΔY ΔX / R.B 1 el R.B 2 el / * - : % 30

stress amplification factor at the edge due to excentricty ex.fact 13 ex * + : 1.89

ft 1 ft 50 kN * / * plan

length of footing strip per pyramid w.0 ft 4

width of footing strip w.foot in 10

foundation area area 4 w.0 * w.foot * (: 1.2 m 2^*

max stress at the edge of the foundation stress.soil ex.fact F.y area / * : kN m 2^/ 182

VI Design of Foundations piles and Stilt Columns

Design of Slanted Columns

Material: Bamboo (Bambusa Balcooa)

Material data on Bambusa Balcooa in green condition (dry is generally 10-20% better, so green data is on the safe side)

Mode of calculation: As per NBC 2005-2016.
Working stress method,
Round bamboo calculated as a hollow section,
Columns calculated as per Euler buckling load = π2 E I/L2

Bending strength f.r 65.4 MPa * :

safety coefficient in bending γ.r 4 :

working stress in bending σ.r 1 γ.r / f.r * : MPa 16.4

Compressive strength f.c 65.4 MPa * :

safety coefficient in compression γ.c 4.5 :

working stress in compression σ.c 1 γ.c / f.c * : MPa 14.5

Modulus of elasticity E.b 7310 MPa * :

safety coefficient for E (column buckling) γ.e 3.5 :

E for column buckling E.bc 1 γ.e / E.b * : MPa 2089

Minimum dimensions at mid-height for the bamboo to be selected for the columns supporting the platform, and section properties

external diameter ϕ.e 75 mm * :

wall thickness th.w 12 mm * :

internal diameter ϕ.i ϕ.e 2 th.w * - (: mm 51

Section area A.s π 4 / ϕ.e 2^ϕ.i 2^- (* : mm 2^2375

Moment of Inertia I π 64 / ϕ.e 4^ϕ.i 4^- (* : mm 4^1221070

Section modulus Z 2 I * ϕ.e / : mm 3^32562

square of radius of gyration r2 I A.s / : mm 2^514

square of radius of gyration r2 ϕ.e 2 / (2^ϕ.e 2 / th.w - (2^+ 4 / : mm 2^541

Verifying the buckling load by Euler-Rankine method

length of slanted column:

clear column height ΔY h.1 h.ped0 - : ft 6

slant in both directions ΔX w.1 w.col - 2 / : ft 2.1

length of great diagonal L ΔY 2^ΔX 2^+ ΔX 2^+ sqrt : ft 6.7

radius of gyration r ϕ.e (2^ϕ.e 2 th.w * - (2^+ sqrt 4 / : mm 23

end conditions:

pinned pinned -

K 1 :

L K L * : 2.0 m *

Nb of bamboo in the column section:

Nb.bamboo 6 :

excentricity 1 ΔD1 ϕ.e : mm 75

excentricity 2 ΔD2 ϕ.e 2 / : mm 38

(measured from the CAD drawing)

total moment of inertia, bundle of 6 bamboo I.total I 2 I A.s ΔD1 2^* + (* + 4 I A.s ΔD2 2^* + (* + : cm 4^4860

Euler critical load, 1 bamboo

N.CE π 2^E.bc * I * L 2^/ : kN 5

30 deg * cos 0.866

Note: Only the bottom part of the best bamboos will be selected for making these 16 composite columns.

It is actually easy to find bamboos that are straight over 7 feet and between 75 to 90mm-thick at mid-length.

Euler critical load, composite bamboo column N.CE π 2^E.bc * I.total * L 2^/ : kN 241

column axial load in compression: N Axial.col1 : kN 114

3 sqrt 2 / 0.866

OK no buckling risk

excentricity 3 ΔD3 ϕ.e 3 sqrt 3 / * : mm 43

Euler critical load, 3 bamboos

N.CE π 2^E.bc * 3 I A.s ΔD3 2^* + (* * L 2^/ : kN 75

Max compressive load, 6 bamboo 6 A.s * σ.c * kN 207

OK comfortable

Design of Foundation Piles

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Material: Pre-cast Reinforced Concrete
Mode of calculation: As per IS:456 and BS:8110

length of slanted pile:

clear  pile depth ΔY h.0 h.plinth + h.foot - h.ped - h.ped0 + : ft 2

slant in both directions ΔX w.0 2 / : ft 2.0

length of great diagonal L ΔY 2^ΔX 2^+ ΔX 2^+ sqrt : ft 3.5

weight of 1 pile:  W < 100 kg   OK W.pile L w.pile 2^* D.RCC * : kg 43

L 1.1 m *

end conditions:

fixed - pinned, braced

K 0.7 :

L.E K L * : 0.7 m *

width of pile w.pile in 5

slenderness K L.E * w.pile / 4.1

slenderness <12, column is short

factored axial load:

column axial load in compression: Axial.pile1 kN 105 -

factored load N.u 1.5 Axial.pile1 * : kN 157 -

minimum eccentricity e.min L 500 / w.pile 30 / + 2 cm * 21 mat min : mm 6.3

minimum moment N.u e.min * kN m * 1.0 -

longitudinal reinforcement : A.sc 4 π * 16 mm * 2 / (2^* : mm 2^804

f.y 415 MPa * :

area of concrete: A.c w.pile 2^A.sc - : mm 2^15325

f.ck 20 MPa * :

We will use 1:1:2 concrete with 1/4'' stone chips to facilitate concreting and prevent long-term corrosion.

Galvanised 12mm-dia rebards and 4mm-dia GI wire for links would triple the lifespan of the structure in the Sundarbans. 4mm GI links can be at 3 inches interval.

The prefabricated piles are less than 100kg to facilitate the manipulation and ensure a safe and accurate work process.

VII Design of Roof Rafters and Vertical Bamboo Structure

Geometry of the vertical bamboo frame

C.1 w.1 2 / - w.col 2 / + h.1 21 mat :

B.s w.4 2 / h.1 h.2 + h.3 + 21 mat :

C.s 0 h.1 h.2 + h.4 + h.5 + 21 mat :

C.2 mirror.Y C.1 * :

C.1 C.1 w.2 w.1 - 2 / 021 mat + :

C.2 C.2 w.2 w.1 - 2 / 021 mat + :

D.s 0 h.1 h.2 + h.4 + 21 mat :

E.s w.3 2 / h.1 h.2 + 21 mat :

C.3 mirror.Y C.1 * :

C.4 mirror.Y C.2 * :

A.s C.1 0 h.2 21 mat + :

B.s A.s 1 el 21 ft * 21 mat :

A.e l.2 2 / w.1 - h.1 h.2 + 21 mat :

B.e A.e 1 el 21 ft * 21 mat :

C.s mirror.Y A.s * :

D.s mirror.Y B.s * :

E.e mirror.Y A.e * :

F.e mirror.Y B.e * :

A.1s A.s 0 h.6 21 mat + :

C.1s C.s 0 h.6 21 mat + :

A.1e A.e 0 h.6 21 mat + :

E.1e E.e 0 h.6 21 mat + :

\[REGION[0]]\
\[REGION[1]]\

u s forcess C.1 C1 u label.pt C.2 C2 u label.pt C.3 C3 u label.pt C.4 C4 u label.pt A.s A u label.pt B.s B u label.pt C.s C u label.pt D.s D u label.pt A.1s A1 u label.pt C.1s C1 u label.pt B.s transpose A.s transpose D.s transpose C.s transpose B.s transpose stack 1 u / * 111 sys :

u s short_section buildings 1 u / * u s forcess 21 sys :

\[REGION[0]]\
\[REGION[1]]\

u s forcese A.e A u label.pt B.e B u label.pt E.e E u label.pt F.e F u label.pt A.1e A1 u label.pt E.1e E1 u label.pt 61 sys :

u s long_section buildinge 1 u / * u s forcese 21 sys :

ft 1 ft * 50 kN * / short_section ft 1 ft * 50 kN * / long_section

Design of Roof Rafters

Material: Bamboo (Bambusa Balcooa)

Material data on Bambusa Balcooa in green condition (dry is generally 10-20% better, so green data is on the safe side)

Mode of calculation: As per NBC 2005-2016.
Working stress method,
Round bamboo calculated as a hollow section,
Columns calculated as per Euler buckling load = π2 E I/L2

Bending strength f.r 65.4 MPa * :

safety coefficient in bending γ.r 4 :

working stress in bending σ.r 1 γ.r / f.r * : MPa 16.4

Compressive strength f.c 65.4 MPa * :

safety coefficient in compression γ.c 4.5 :

working stress in compression σ.c 1 γ.c / f.c * : MPa 14.5

Modulus of elasticity E.b 7310 MPa * :

safety coefficient for E (column buckling) γ.e 3.5 :

E for column buckling E.bc 1 γ.e / E.b * : MPa 2088.5714

Minimum dimensions at mid-height for the bamboo to be selected for the columns supporting the platform, and section properties

external diameter ϕ.e 80 mm * :

wall thickness th.w 12 mm * :

internal diameter ϕ.i ϕ.e 2 th.w * - (: mm 56

Section area A.s π 4 / ϕ.e 2^ϕ.i 2^- (* : mm 2^2563.5396

Moment of Inertia I π 64 / ϕ.e 4^ϕ.i 4^- (* : mm 4^1527869.6048

Section modulus Z 2 I * ϕ.e / : mm 3^38196.7401

square of radius of gyration r2 I A.s / : mm 2^596