An example problem problem on wind load load calculation according to NSCP NSCP 2010 ;) A 20-meter-high square-plan five-storey five-storey building with flat roof roof and 4m-high floors, floors, located in Makati !", has sides of #0 meters length each, and a large open front door on the first floor floor that is 2m $ 2m in dimension% Assuming that & ' 0%() and that torsion is negligible, 1. Show how this this mabe mabe is an open! open! partiall partiall enclose enclosed! d! or enclosed enclosed buildi building. ng. 2. "ete "etermin rminee the interna internall pressure pressure coe##ici coe##icients ents.. $. "etermine the external pressure coe##icients coe##icients #or the design o# main girders girders and shear walls. %. "etermine the base reactions reactions due to to along&wind loads acting on the #ront wall o# the building. 1. 'he building satis#ies all de#initions o# a partiall enclosed building (NSCP 2010 Section 20.2). 2. 'he internal pressure coe##icients #or a partiall enclosed building (*Cpi) (*Cpi) are +,& 0.-- (NSCP igure 20&-). $. 'he external pressure coe##icients on /S (#rom NSCP 2010 igure 20&) are as #ollows3 & windward wall! Cp 4 0.5 & leeward wall! Cp 4 &0.- since 6 4 10m! 7 4 10m! and 6,7 4 1 & side walls! Cp 4 &0. & whole roo#! Cp 4 &1.0% or &0.15 since h 4 20m! h,6 4 2! 6 84 h,2 4 10m! and oo# Area 4 100 s9.m : $ s9.m %. 'he base reactions can be calculated a#ter we calculate the design wind #orce at each le
ing x 4 along&wind direction! 4 across& wind direction! ? 4 es it much easier3
Assume3 Bxposure 'errain Categor 7 Case 2! w 4 1.0! 1.0! Dd 4 0.5-! D?t D?t 4 1.0! @ 4 200 >ph indward wall p? (>Pa) 6eeward wall p? (>Pa) ? (m) D? 9? (>Pa) with +*cpi with &*cpi with +*cpi with &*cpi 20 0.55 1.%2 0.15 1.&1.$5 0.15
1 12 5 % 0
0.52 0. 0. 0.- 0.-
1.$2 1.22 1.05 0.2 0.2
0.12 0.0&0.0&0.1 &0.1
1.5 1.1 1.-2 1.%1 1.%1
&1.$5 &1.$5 &1.$5 &1.$5 &1.$5
0.15 0.15 0.15 0.15 0.15
Net along wind pressures Net along wind loads ? 7ase bending moment p? (>Pa) (>N) contribution /!? (>Nm) A#? (s9m) with +*cpi with &*cpi with +*cpi with &*cpi with +*cpi with &*cpi 1.- 1.- 20 $1 $1 20 20 1.1.%0 0 0 0 0 1.%$ 1.%$ %0 - - 5% 5% 1.$$ 1.$% %0 -$ -% %2% %$2 1.22 1.2$ %0 % % 1 1 1.22 1.2$ 20 2% 20 0 Vx (kN) = 274 27 6 2884 2892 My (kNm) =
A#!roo# (s9m) 100
oo# loads 1! p oo# loads 2! p @? 4 oo# @? 4 oo# (>Pa) (>Pa) loads 1 (>N) loads 2 (>N) with with with with with with with with +*cpi &*cpi +*cpi &*cpi +*cpi &*cpi +*cpi &*cpi &2.0% &0.% &1 0.- &20% &% &100 - *+ k. ' -204 )/
Thefi r s tt hi ngy ouneedt ok no wi nc al c ul at i ngt hewi ndl oadi st hel oc at i onoft hes t r uc t ur eorbui l di ng.I twi l l t el l y out hebas i cwi nds peed ( V)t haty ou’ l l c ons i deri ny ourc omput at i on.
Basi cWi Wi ndSpeed I nt ab l e2 07 1 ,t h ep r o v i n ce so rl o ca t i on si nt hePh i l i p pi n eswi t hi t sco r r e sp on di ngb as i cwi n ds pe edar es ho wn .
Test / Exam Ti p! Th ep r o f e ss orma yon l ygi v ey out h el o ca t i onoft hest r u ct u r e .Fo re x amp l e ,t hebu i l d i n gi spr o po se da tBo r a c ay .I fy o ud on ’ tk no w wh at pr o vi n ceBo r a c ayi sl o cat e da t ,t h eni twi l l b eabi gp r o bl e mf o ry o ua sad es i g ne r .Bemi n df u lo fc e r t a i np op ul a rs po t si nt h ec ou nt r yand t hei rc o r r es pondi ngl oc at i ons( p r o v i nc e) .
Exposur eCat egor y Thene xts t epi st ot ak ei t sexposur ecat egory .I td epe nd sma i n l yont h es t r u ct u r e ’ ss ur r ou nd i n ge nv i r o nmen t . Exposur eB Ur b anands ubu r b anar e a,wo od enar ea ,o ro t h ert e r r a i nwi t hnu me me r o usc l o se l ys pa ce do bs t r u ct i onha vi n gt h es i z eofs i n gl e f ami l y dwel l i ngsorl ar ger . Exposur eC Op ent e r r a i nwi t hs c at t e r e do bs t r u ct i onh av i n gh ei g ht sge ne r a l l yl e sst h an9me t e r s .Th i sca t e gor yi n cl u de sfl ato pe nc ou nt r y ,g r a s sl an ds , an da l l wat e rs u r f a ce si nr e gi o nswi t hr e c or d so fe xt r emet y pho on s. Exposur eD Fl a t ,u no bs t r u c t e da r e asan dwa t e rs u r f a c es .Th i sc at e go r yi n c l u de ss mo mo ot hmu dfl a t san ds a l tfl at s .
I mpor t anceFact or
Ev er ys t r uc t ur ehasi t si mpor t anc ef ac t or( I d ep en di n go ni t soc c up an cyc at e gor y .Re f e rt ot a bl e s2 07 3( I a n d1 0 31( Oc c u p a nc y w) w) Ca t e go r y ) .
Wi ndDi r ect i onal i t yFa ct or ,K
d
Th i si sso l e l yba se do nwh ats t r u ct ur al t y pe / p ar ty oua r ede si g ni ng .
Test / Exam Ti p! Mo r eof t e nt h atn ot ,t h e“ Ma i nWi Wi n dFo r c eRe s i s t i n gSy s t e m( MWFRS) ”a nd“ Co mp mp on en t sa n dCl a dd i n gs ”a r eb ei n gc on s i d er e ds i n c ewe a r ed ea l i n gmo s t l ywi t hb ui l d i n gsan dwa r e ho us e s. Mai nWi Wi ndFor ceResi st i ngSyst ems ms a r es t r u ct u r a le l e me me nt st h ats up po r tl a r g ear eaex po se dt ot h ewi n d.Me an wh i l e ,Comp mponent sand Cl a dd i n g a r et hest r u ct u r a le l e me me nt st h ats upp or ts ma ma l la r e ase xp os edt ot h ewi n d.
Exposur eCoeffic ffici ent , / KK z
h
Th ev e l o c i t ypr e s su r ee x po s ur ec o effic i e nt s( KzorKh )g oe sl a r g e ra st h eh ei g hta bo v et h eg r o u ndi n c r e a s es .Al l p os s i b l eo r ap pl i c ab l eva l ue so f“ h ei g hta bo v eg r o un dl e v el ”s ho ul dbet a ke ni n t oco ns i de r a t i on .Wh eny ou rs t r u ct ur el a nd si nex po sur eB,c on si d ert wo cases( Case1andCase2) .
Test / Exam Ti p!
I n t e r p ol a t et hede si r e dv al u ei ft h eh ei g htf a l l sb et we ent wok no wnv a l u es .Cl i c kher ei fy oudon ’ tk no w ho wt oi nt er pol at e.
T opogr a phi cF ac t or ,K
z t
Fors i mpl i c i t ypur pos es ,Kz ti sus ual l yequal st o1. NOTE:Fo rmo r ede t a i l e dc o mp mp ut a t i o no fKzt,r ead2 0 7 . 5 . 7 . 2 and d2 2 0 7 . 5 . 7 . 1.
Gus tFa ct or ,G u se dmo s to ft h et i me ) Fo rs t i ffb ui l d i n gsan ds t r u ct u r e s ,u seG =0 . 8 5 .( Forr i gi dbui l di ngs ,r ead 207. 5. 8. 1. Pr e s s u r eCo e ffic ffic i e n t
Th ep r e s s ur ec oe ffic ffic i e nt( Cp)a r eba sedo nt h een cl o su r ec at e go r yoft h es t r u ct u r ean dl o ca t i ono nas t r u ct u r ef o rwh i c hap r e s s ur ei st o becomp mput ed.
L =Ho r i z on t a ld i me ns i o no fb ui l d i n gmea su r e dn or ma l / p er p en di c ul a rt owi n dd i r e ct i o n B =Ho r i z on t a l d i me ns i o no fb ui l d i n gmea su r e dp ar a l l e lt owi n dd i r e ct i o n H =Me anRo ofHe i g ht( He i g htf r o mt h eg r o u ndt ot h emi d dl epa r t o ft h er o of )
* I f a ngl ei sl es st h anore qua l st o10de gr e e s,u seeavehei ght ( h ei ghtoft hes t r uc t ur ee xc l udi ngt her oof )
Fo rr o ofs l o pe sgr e at e rt h an80de gr e es ,u s eCp =0 . 8 * I nt e r p ol a t et h ed es i r e dc oe ffic ffic i e nti fang l ei sbe t wee nt wokn ownv al ue s.
Wi n dwa r d ,L e ewa r d ,Si d eWa Wa l l
Si g nCo nv e nt i o ns Pos i t i v e –Th ep r e s su r ei st o war d st h es t r u ct u r e . Ne ga t i v e –Th ep r e s s ur ei spo i n t i n ga wa yf r o mt h es t r u ct u r e( s u c t i o n) .
GCpi
* Va l u eso fGCpi s hal l beus edw wi i t hei t herqz orqh ( You’ l ll ear nt heus eoft hi si nt hen ex tp ar toft hi st ut or i al ) . * T wov al u esmu mu s ta l wa y sbec on s i d er e d:p os i t i v ean dn eg at i v e .
Pos i t i v eandNegat i v eI nt er nal Pr es s ur es
I nco mp mp ut i n gt h ewi n dl o adofas t r u c t u r e ,y o umu s tc o ns i d ert h es et woca s es :
Le t ’ sno wg os t r ai g htt ot heco mp mp ut a t i onpr o ce ss .We ’ l l b et a l k i n ga bo utt h ewo r k i n gf o r mu l a sa ndho wt oa ppl yi t . T ak eno t et h aty o uMUST uM r e adpar t 1 andp dpar t2oft hi st u t o r i al i nor d ert of ul l yunder s t andt hi st o pi c . P=Wi n dp r e s su r e( t h i si swh atwewa ntt oge ta tt h ee nd ) P =qGCp–q( GCpi )–––f o r mu l a1 q=4 7. 3x10-6KzKztKdV2I –f o r mu l a2 w –– Eavehei ght= hei ghtofwal l ( e x cl udi ngt her oof ) Meanr oofhei ght( h )= hei ghtofwal l +( hei ghtofr oof / 2)
Cons i de rt hef ol l owi ngwi wi nddi r e ct i ons : 1. Wi n dNo r ma l / Pe r p en di c u l a rt oRi d ge 2. Wi n dPa r a l l el t oRi d ge
Wi ndNor mal / Per pendi cul arToRi Ri dge
Wi ndwa war dWa Wal l P=qzGCp–q GCpi ) h( P=qzGCp–q GCpi ) h( 1.Comp mput eq f o re v er yapp l i c ab l eh ei g ht( s t at edi nt a bl e2 07 4 )i n cl u di n gt heme anr o ofh ei g ht( h ) .Fore x amp l e ,t h ee av eh ei g hto fa war e hou sei s6. 5me t e r sa ndi t sme me anr o ofh ei g hti s13 . 5.I nt hi sc as e,y ou ’ l l n ee dc omp ut ef o rf o urv a l u esofq :q0-4.5, q6,q6.5 andq13.5.
2 .Th ev a l u eo fCp f orwi ndwar dwal l i s0. 8. 3.G i sus ual l yequal st o0 . 8 5 u nl e ssot h er wi s es t a t e d. 4 .Co mp mp ut et wov a l u esofPc o ns i d er i n gt h ep eposi t i v ea eand ne ga t i v e v al u esofGCpi( i . e.+0. 18and0. 18) . •
Posi t i veGCpi –Pos i t i v eI nt er nal Pr es sur e
•
Negat i veGCpi –Ne ga t i v eI n t e r n al Pr e ss ur e
Leewar dWal l P=qhGCp–q GCpi ) h( P=qhGCp–q GCpi ) h( 1 .Co mp mp ut eon l y1v a l u eo fqc o ns i d er i n gt h eme anr o o fh ei g ht ,qh. 2 .Th ev a l u eo fCp f o rl ee wa r dwa l l wi l l de pen do nt h ev al u eo fy ou rL/ B.
3.G i sus ual l yequal st o0 . 8 5 u nl e ssot h er wi s es t a t e d. 4 .Co mp mp ut et wov a l u esofPc o ns i d er i n gt h ep eposi t i v ea eand ne ga t i v e v al u esofGCpi( i . e.+0. 18and0. 18) . •
Posi t i veGCpi –Pos i t i v eI nt er nal Pr es sur e
•
Negat i veGCpi –Ne ga t i v eI n t e r n al Pr e ss ur e
Si deWal l Sa me mepr o c ed ur ewi t ht h ec omp ut a t i o nf o rl e ewa r dwa l l b ute qu at eCpt o0 . 7.
Roof Us et h et a bl eab ov ef ort h ev al u esofCpf orbot hwi n d wa r da ndl e e wa r d . F ore nc l o se dbu i l di ngs P=qhGCp–q GCpi ) h( P=qhGCp–q GCpi ) h( Forpa r t i a l l yenc l os edbui l di ngs Pos i t i v eI nt e r na lPr e ss ur e : P=qhGCp–q ( GCpi ) z
qz=l e vel oft hehi ghes topeni ngi nt hebui l di ngt hatc oul daff ec tt hepos i t i v ei nt er nalpr es sur e. Ne ga t i v eI nt e r n alPr e ss ur e : P=qhGCp–q GCpi ) h(
Wi ndPar al l elToRi dge
P=qhGCp–q GCpi ) h( P=qhGCp–q GCpi ) h( 1 .Co mp mp ut ef o rqh. 2 .Ca l c ul a t ef o rt hewi n dp r e s su r e sata l l a ppl i c abl eh or i z on t a ld i s t an ce sf r o mt h ewi n dwa r ded ge .
3.Asy ouha veno t i c ed,al l t heval uesar enegat i v e.I tmeansal l t hef or c eswi l l besuc t i onorpoi nt i ngawa yf r om t hest r uc t ur e. 4 .Wi n dp r e s s ur e satt h ewi n dwa r dan dl e ewa r dwa l l swi l lb ed ea l tt h es a mewa me yasa bo v e .
Given: The enclosed ofce building building shown in Figure Figure 7.4.1.1. The building is located in a region with a wind speed (3-sec gust) o o 12 !ph. The e"posure e"posure is #"posure #"posure $. $. The building is on %at terrain. Figure 7.4.1.1 Building Defnition
Wanted: The wind pressures pressures applied to the suraces and the net orces orces applied to the building. Solution: To sol&e this proble!' we need to independentl independe ntl loo at two di*erent wind directions' but +rst we will de+ne a ew para!eters. ,eter!ine critical ele&ations •
ean /oo /oo 0eight h 211 (3512)2652 (3512)2652 26.1 t t
•
ean 2nd Floor 0eight 0eight h 11 1152 1.6 t
•
ean 1st Floor 0eight h 1152 6.6 t t
2 $o!pute the 8elocit 9ressures' : ; .26 < ; < ;t 7-6 #:uation -16) ;t < d 8 = (>?$# 7-6
•
< ;t ;t 1 (Flat Terrain)
•
< d .@6 (>?$# 7-6 Table -4' Auildings)
•
= 1. (>?$# 7-6 Table -1' $ategor == building)
•
< ; &aries with ele&ation 2.1(!a"(h'16)5B)(25B.6)' (>?$# 7-6 Tables -2 and -3)
Roof 2nd flr 1st flr
h (ft) 25.125 16.5 5.5
$o!pute the =nternal 9ressures' : hC$pi •
C$pi .1@ (>?$# 7-6 Figure Figure -6)
•
:h 2B.7 ps
•
qhGCpi = + .!4 p"#
,eter!ine the Cust Factor' C
Kz 0.946 0.866 0.849
qz (psf) 29.7 27.1 26.6
•
C .@6 (>?$# 7-6' [email protected])
Dind in the E5? ,irection For this part o the t he proble! we need to deter!ine pressure coefcients or the locations shown in Figure Figure 7.4.1.2 as well as or the side walls. These coefcients are are then co!bined with the gust actor and &elocit pressures pressures to obtain the e"ternal pressures pressures in each region. Figure 7.4.1.$ %&S Building Se'tion
The pressure pressure coefcients or the walls are ound ound in >?$# 7-6 Figure Figure - (pg 4B) For the Dindward wall (91 92)' $ p is .@ or all ele&ations. For the Geeward wall (96 9)' $ p is dependent on the ration o G5A. =n this case G5A 65B .66' so $ p -.6 or all ele&ations. For the sidewalls (not shown in Figure Figure 7.4.1.2)' the &alue o $p is -.7 in all cases.
For the roo' roo' the slope angle is 14. degrees. degrees. This is close to 16 degrees and probabl probabl not worth interpolating between the &alues gi&en gi&en in >?$# 7-6 Figure Figure -. De also need to now that h5G 26.156 .6. Fro! the Figure Figure we get that the &alues &alues o $ p or the Dindward side o the roo roo is -.7 and -.1@. These &alues represent represent two di*erent di*erent load cases. cases. For the the Geeward side' $ p is -.6. De can now co!pute the e"ternal pressures' :C$ p' or each surace. surace. The ollowing table shows the co!putation results
!"nd#$rd !$ll !"nd#$rd Roof 'ee#$rd Roof 'ee#$rd !$ll "de !$lls
Pressure
Cp
P1 P2 P% P% P4 P5 P6 P7
0.8 0.8 &0.7 &0.18 &0.5 &0.5 &0.5 &0.7
q (psf) 26.6 27.1 29.7 29.7 29.7 29.7 29.7 29.7
qCp (psf) 18.1 18.5 &17.6 &4.5 &12.6 &12.6 &12.6 &17.6
$o!bining with the internal pressures pressures ou get the ollowing our load cases where •
•
•
$ase = includes the !a"i!u! windward pressure (-17. ps) and positi&e internal pressure $ase == includes the !ini!u! !i ni!u! windward pressure (-4.6 ps) and positi&e internal pressure $ase === includes the !a"i!u! windward pressure pressure (-17. ps) and negati&e internal pressure
•
$ase =8 includes the !ini!u! windward pressure (-4.6 ps) and negati&e internal pressure
The net orces orces are ound b !ultipling the appropriate appropriate pressures pressures b the areas areas o&er which the act. =n this building all but the gable ends are rectangles' rectangles' !aing the area calculation calculation easier. easier. Eote that we are co!puting actual surace areas (as opposed to proHected areas) in each o the cases below. below. >lso' the sign is i!portant. Eegati&e signs indicate a orce orce that is outward ro! ro! the surace and a positi&e sign is inward. >ll orces are nor!al nor!al to their respecti&e respecti&e suraces. Pre Pressur ssure e !"nd#$rd !$ll !"nd#$rd Roof 'ee#$rd Roof 'ee#$rd !$ll "de !$lls
P1 P2 P% P4 P5 P6 P7
et et Pres Pressu sure res* s* C$se $se C$se -(psf) (psf) 12.8 12.8 1%.1 1%.1 &2%.0 &9.9 &17.9 &17.9 &17.9 &17.9 &17.9 &17.9 &2%.0 &2%.0
C$se $se ----(psf) 2%.4 2%.8 &12.% &7.% &7.% &7.% &12.%
C$se $se - (psf) 2%.4 2%.8 0.8 &7.% &7.% &7.% &12.%
/re /re$s (ft2) 990 990 2%19 2%19 990 990 141%
et et +or, +or,e e C$se () 12.62 12.99 &5%.29 &41.60 &17.76 &17.76 &%2.46
C$se $se -() 12.62 12.99 &22.90 &41.60 &17.76 &17.76 &%2.46
C$se $se --() 2%.19 2%.55 &28.54 &16.85 &7.19 &7.19 &17.%8
C$se $se - () 2%.19 2%.55 1.86 &16.85 &7.19 &7.19 &17.%8
=t is oten useul to resol&e each orce into its global co!ponents so that the can be easil added &ectoriall. &ectoriall. Figure 7.4.1.3 shows the location o each o the resulting orces. Figure 7.4.1.! Building For'e" #or %&S Wind
+or,e !"nd#$rd !$ll !"nd#$rd Roof 'ee#$rd Roof 'ee#$rd !$ll "de !$lls
+1 +2 +% +4 +5 +6 +7$ +7
C$se C$se ! () 0.00 0.00 0.00 0.00 0.00 0.00 &%2.46 %2.46
() 12.62 12.99 &12.9% 10.09 17.76 17.76 0.00 0.00
3ert. () 0.00 0.00 51.70 40.%6 0.00 0.00 0.00 0.00
C$se C$se -! () 0.00 0.00 0.00 0.00 0.00 0.00 &%2.46 %2.46
() 12.62 12.99 &5.55 10.09 17.76 17.76 0.00 0.00
3ert. () 0.00 0.00 22.22 40.%6 0.00 0.00 0.00 0.00
C$se C$se --! () 0.00 0.00 0.00 0.00 0.00 0.00 &17.%8 17.%8
() 2%.19 2%.55 &6.92 4.09 7.19 7.19 0.00 0.00
3ert. () 0.00 0.00 27.69 16.%4 0.00 0.00 0.00 0.00
C$se C$se - ! () 0.00 0.00 0.00 0.00 0.00 0.00 &17.%8 17.%8
() 2%.19 2%.55 0.45 4.09 7.19 7.19 0.00 0.00
3ert. () 0.00 0.00 &1.80 16.%4 0.00 0.00 0.00 0.00
u
0.00
58.29
92.06
0.00
65.66
62.58
0.00
58.29
44.03
0.00
65.66
14.54
Eote that the !a"i!u! uplit and !a"i!u! hori;ontal orce do not occur in the sa!e load casesI ,o not co!bined the two cases' design or each each indi&iduall. indi&iduall. Jou Jou will also notice that the internal internal pressure pressure has no e*ect e*ect on the net hori;ontal hori;ontal orce. The net orce orce in the lateral direction direction is ;ero ;ero since the orces orces on the side walls will cancel each other. Dind in the #5D ,irection Figure 7.4.1.4 de+nes the pressures (with the t he e"ception o the lateral5side wall pressures) pressures) that need to be co!puted or wind loading ro! ro! the #5D direction. =n this case we co!bined all the leeward wall seg!ents into one because the all ha&e the sa!e pressures. Figure 7.4.1.4 (&W Building Se'tion
The pressure pressure coefcients are are taen taen ro! >?$# 7-6 7-6 Figure Figure -. Eote that the coefcient coefcient or the leeward wall is obtained b interpolation with an G5A ratio o 1.@.
!"nd#$rd !$ll
Roof
'ee#$rd !$ll "de !$lls
Pressure
Cp
P8 P9 P10 P11 P11 P12 P12 P1% P1% P14 P15
0.8 0.8 0.8 &0 &0.9 &0.18 &0.5 &0.18 &0.% &0.18 &0.%4 &0.7
q (psf) 26.6 27.1 29.7 29 29.7 29.7 29.7 29.7 29.7 29.7 29.7 29.7
qCp (psf) 18.1 18.5 20.2 &22.7 &4.5 &12.6 &4.5 &7.6 &4.5 &8.6 &17.6
Eote that so!e o the pressures pressures are applied to di*erentl di*erentl oriented suraces. Dhen the sa!e pressure is applied to a di*erent surace' we ha&e chosen to label on as KaK and the other as KbK. ?ee Figure Figure 7.4.1.6 or orce applications. Four Four cases are co!puted' based on co!binations o !a"i!u!5!ini!u! roo pressures and internal pressures. Figure 7.4.1. Building For'e" #or (&W Wind
The net orces orces on each surace' surace' in ter!s o direction relati&e relati&e the surace' are as ollows
Pre Pressur ssure e !"nd#$rd !$ll
Roof
'ee#$rd !$ll "de !$lls
C$se $se -
C$se $se --
(psf) 12.8 1%.1 14.8 &28.0 &28.0 &17.9 &17.9 &12.9 &12.9 &1%.9 &2%.0 &2%.0
P8 P9 P10 P11$ P11 P12$ P12 P1%$ P1% P14 P15$ P15
C$se $se -----
(psf) 12.8 1%.1 14.8 &9.9 &9.9 &9.9 &9.9 &9.9 &9.9 &1%.9 &2%.0 &2%.0
C$s C$se -
(psf) 2%.4 2%.8 25.5 &17.% &17.% &7.% &7.% &2.2 &2.2 &%.2 &12.% &12.%
/re$ /re$ 2
(psf) 2%.4 2%.8 25.5 0.8 0.8 0.8 0.8 0.8 0.8 &%.2 &12.% &12.%
(ft ) 550 550 156 647 647 647 647 1026 1026 1256 1980 1980
C$se -
C$se $se --
C$se $se ---
C$s C$se e -
() 7.01 7.21 2.%2 &18.12 &18.12 &11.60 &11.60 &1%.2% &1 &1%.2% &17.47 &45.50 &45.50
() 7.01 7.21 2.%2 &6 & 6.%9 &6.%9 &6.%9 &6.%9 &10.1% &10.1% &17.47 &45.50 &45.50
() 12.88 1%.09 %.98 &11.22 &11.22 &4.70 &4.70 &2.28 &2.28 &4.06 &24.%6 &24.%6
() 12.88 1%.09 %.98 0.52 0.52 0.52 0.52 0.82 0.82 &4.06 &24.%6 &24.%6
/estating the orces in ter!s o the global coordinate sste! we get Pressure !"nd#$rd !$ll
Roof
'ee#$rd !$ll "de !$lls u
+8 +9 +10 +11$ +11 +12$ +12 +1%$ +1% +14 +15$ +15
C$se C$se ! () 7.01 7.21 2.%2 0.00 0.00 0.00 0.00 0.00 0.00 17.47 0.00 0.00
() 0.00 0.00 0.00 4.40 &4.40 2.81 &2.81 %.21 &%.21 0.00 45.50 &45.50
3ert. () 0.00 0.00 0.00 17.58 17.58 11.26 11.26 12.8% 12.8% 0.00 0.00 0.00
C$se C$se -! () 7.01 7.21 2.%2 0.00 0.00 0.00 0.00 0.00 0.00 17.47 0.00 0.00
() 0.00 0.00 0.00 1.55 &1.55 1.55 &1.55 2.46 &2.46 0.00 45.50 &45.50
3ert. () 0.00 0.00 0.00 6.20 6.20 6.20 6.20 9.82 9.82 0.00 0.00 0.00
C$se C$se --! () 12.88 1%.09 %.98 0.00 0.00 0.00 0.00 0.00 0.00 4.06 0.00 0.00
() 0.00 0.00 0.00 2.72 &2.72 1.14 &1.14 0.55 &0.55 0.00 24.%6 &24.%6
3ert. () 0.00 0.00 0.00 10.88 10.88 4.56 4.56 2.21 2.21 0.00 0.00 0.00
C$se C$se - ! () 12.88 1%.09 %.98 0.00 0.00 0.00 0.00 0.00 0.00 4.06 0.00 0.00
() 0.00 0.00 0.00 &0.1% 0.1% &0.1% 0.1% &0.20 0.20 0.00 24.%6 &24.%6
3ert. () 0.00 0.00 0.00 &0.50 &0.50 &0.50 &0.50 &0.80 &0.80 0.00 0.00 0.00
34.01
0.00
83.34
34.01
0.00
44.43
34.01
0.00
35.31
34.01
0.00
-3.60 
