HomeMy WebLinkAboutSTRUCTURAL CALCS - 07-00357 - 304 Jill Dr - New SFRFor&
Structural
0
-Calculations
Kartchner Homes
Pian #: Winchester C W/ Bonus Room
Location: Lot 47 Block 7 H
From -
William York G
2329 W. Spri
Morgan, Uta
Design Criteria IRC 200'-):
Roof Load,
Live Load (PSP)
Dead Load (PSN
Floor Load.,
Live Load (PSP)
Dead Load (PSF)
Seismic Zone: D I
40
10
Sub.
L. C.
Road
(sol) 876-3501
30 July 2007
0 7 0 0357
304 .Till Drm,-Ka chner
Wind Speed: 90 mph X1 10 mph 3 second gust}
Exposure: C
Material Pro ertzes & Assum tions
Concrete PSI (ff): 25Q0 (found.), 3000 (slabs), 4000 (cusp. slab
Concrete Reinforcement: ASTM A615 grade 60 �
Z1ONACOx
�H
4 � �
�I f
J
Site Conditions: Dry & Stable granular based, 1500 PSF Searing Capacity, Granular Based
Backfill (KH -35 pcf, KP= -225),., Slope not to exceed 20%, Minimum setback from slopes of 25'
Dimensional Lumber. Hem or Doug Fir #2 & BTR p
Steel.- ASTM A-36
Use Simpson straps and tie downs., and meed nailing, reinforcement and other structural
requirements as noted on the drawing and within the pages of this document, These structural
calculations are based on conditions and assumptions listed above. If the conditions listed herein
are not met or are different. if shall be brought to the attention of the engineer. Roof Truss and
beam sYstem to be engineered by the supplier. Th
is engineering assumes that the drybuildingand stable, a high water table oar adverse soils such as plastic claysdlls eic. could cae��e is
future flooding, settIement,site xnstabiIity, or gather adverse conditions. Verification of and
liab r '14y for the soli bearing pressure, site stability, and all other site conditions, including'te
englneerlttg as required, i.s the responsibility of others. These cal[;ulationS a1�l.d are for
the new building structure only and do not provide any engineeringanalysis 'engineering
liability/warranty for the non- structural portions of tI�e bu��dzn or �� y of or
the structural engineer oz11�r and c�oe� not assume the role of "Re isle e site itself. W1111am York 1s
this project. The purpose of these calculations and engineering � � Design Professional" an
� g to help reduce structural
damage and lass of life due to seismic activity d
/or high wind condition' . � o a � r = ��-
verify all conditions, dimensions and structural details of tie d1-aw'ITlM� � �� � °�
calculations is not permitted.AUG 6 2007
g �e�- ��� i f
CITY 6*41116
U r
X11 exterior wars shad be sheathed with 7116" APA rated structural woad pane. Block all
1"1 111'7nvti fr,� .,. .-1 .._.. 1 1 /11 • ,
1%J1 UUgcs i -r2 nominal or wYder. Sheathing shah extend continuous from floor to top
plate and be named at least 4'' O.C. along sill plate. Extend sheathing overable end to wTalljolnts
& over rim joist between floors and nail to rim and walk pIaice 611 O.C.
Shear Wail Schedule
ly-p—P SheathimzN ail Edge Field Anchor Bolts
Typical 7/16 one SldF'.�' Sd 6 C).C.loft O.C. V211 32" O.C.
SW -1 7/1611 one side gd 411 O.C. loft O.C. %" 32" O.C.
Staples. may be used in place of Sd nails at %2 the .spacing
The following general requirements shah be followed during construction;
7 . Contractor to verify all dimensions, spars, & conditions and notify engineer of any e7-rQrs,
omissions, or discrepancies prior to construction.
2. Use Simpson A35 ties each cantilevered joist to sill or tap plate.
3. Use simpson,Hl -or equiv. ties each end of each truss.
D_ Foundation reinforcement as per Utah State Amendment
6. Use 2: #4 bars continuous for'all footings
Z: # 4 bars each side of openings & 2 # 4 bars top & bottom extend 36" beyond openina
8. Use �/�" x 10" J bolts 32" Q.C. all foundation wars
9. If discrepancies are found,. the more stringent specification shah be followed.
10. All multiple beams and headers to be nailed using 16d two rows 12" 0. C.
1 1 . Contractor shall assure that all materials are used per manufactures recommendations.
1Z. Geotech engineer shall verify overall global stability of the building site.
13. Connect beams & headers over 6.ft.." fo trimmers with appropriate connectors/hangers.
14. Contractor shall assure that footings are properly drained and that soil is dry and that footings
rest on undisturbed native soil 30" below finished grads and that building horizontal clearazice
from footings to adjacent slopes be a minimum of 2.5 feet and that the intent of IRC section
R403.1.7.2 is net. If set back requirements of 8403.1.7.2 can not be met then contact en ineer
dor Further design requirements.
g
15. The contractor shad conform with all building codes and practices asper the 2003 IR16. Use baliQon framing method when connecting floors �n split leuel designs. C.
17. Nail all shear walls io floor j�aist usilxg 2: 16d 1 O.C. Add additional floorjoist as reI $. Provide joist and rafter hangers as per manufacturersspeczficatians. �d
19. Foundation steps shall not exceed 4 feed or V2the horizontal distance b tu, S eps. Horz.
rebar shall be 12." Q.C. through step downs and extend 4g" either side of step
20H garage return walls are fess than 3Z" wide then extend headers across return malls with 2
king Muds on ether end extending from the top of the header to the bollitom plate or instar(2)MST 36 straps each end of header extend across ming wars.
2 1. Use a minimum of 2-9 %2" LVLs for aIl headers. carrying girder Toads.
22. Allow foundation 14 days to cure prior to backfill
23, Use 1 1 lS" wide timberstrand or equiv. for all rim joist
24. Provide solid blocki*ng through structure dowen to footing far a1� load paths.
25. Builder shall Fallow a�I reconlmendatians found in all applicable Geotechnical areports.
26. Stacking a�two sill pates is permitted with 51g" J -bolts through bath plates. Stackin more
than two plates is not permitted without special engineering
�
a
Date r
Location
Micro -Lam Bear
Uniform Loads
Uniform Floor span {ft}
Total Uniform Floor Load (pif)
Wail Height (ft)
Wal! Weight (pso
Wal! load (pl�
Uniform Roof Span [ff)
Total Uniform Roof Load (plf}
Paint Lads
1 Distance from Left (ft)
1 Paan# dive Lead (!b)
1 Point Dead Load (fb}
2 Distance from Left {ft}
2 Paint Lige Load {Ib}
2 Point Dead Load (Ib)
PartiaEy Uniform Loads
fi Uniform Span {ft}
1 Live Lead (ptf)
1 Dead Load (plfj
1 Distance of left side (fit)
I Distance of right side (ft)
2 Uniform Span (ft)
2 Live Load (plfj
2 Dead Load (pl�
2 Distance of left side (ft)
2 Distance of right side (ft)
Tapered Load
Tapered toad left (pJfj
Tapered load right (plf}
Left Distance (ftp
Right Distance (ft)
Beam Weight (plf)
Reactions &Moment
Duration increase
Seam Span(ft)
Left Reaction (ib)
Right Reaction (Ib)
Max Moment FtLb
Max Mom dist from Leis
Max Sear Lb
Max Shear Stress (psi)
Determine Size
Depth Estimate (in)
VVidth Estimate (in)
Cross area in'1
Max Moment 100%
MOMemt of Iner-tia I
Factor Of Safety=
Max Shear 100%
Factor Of Safety
Bearing Required
Load
Beam
Factor of Safety
E (psi)
D f ectio n LL (in)
LJ360
LL Deflection F of
Deflection TL (in)
L/40
TL Deflection F of
Selection
7/30/2007
Lot #7 Block 7, H r derSon sub.
0
0
10
275
0
0
300
112.5
.
0
0
6
8
9.64
4
2750.0
4686.4
.
2750.0
82.7
9.50
15
33.25
11406.60
0.0
.x.43
124,06
2.30
1.4
21-63
52,65
2,43
1900000
0.03
0.1
5.82
0.04
0.25
6.31
1/"
LVL
Plan: Winchester
Dat 0 July 2007
Location, Lot #7 Block 7, HendersonSub.
Wind Loading Calculations using Main lndforce-F esi tin
Longitudinal Direction
tem �i� �i �
Win De ign Coefficjents
P=Wind iead*exp c eff*dw
P"Desi n Pressure
Horiz nt21l Find Load (frorn table 1609.6-2. 1 1
`all Load (sf)
end zo-)e (A) 16.1
interior zone (C) 11.7
Roof Load (pf)=
end zone B) 2.6
interior zone �D) _7
Vertical Wind Load (from table 1609.6.2,1(1
Roof Load pf )=
end zorle windward (E) -7.
end zone leeward (F) -9.8
interior zone windward ( -5.2
interior zone leeward (H)
Epo ire Coefficient (from table 1609,6,2.1(4)
lw=I nportanCe Factor (from table 1,604.5)
Ind Speed
Exposure
Roof Slope;--
Roof
lope=Roof Angle (de:g)= 26,56
P --,:wind Ieadke p oeff*iw
Height
horizontal wall interior
14,1
rh orF .onta l wall' end zone
19.48
horizontal roof interior
3.27
horizontal roof end zone
3.1
vertical end zone indrard
-3.1
vertical er°d zone leeward
-11.86
vertical interior zone windward
-6.29
Verlreal interior zone leeward
-6.29
End Zone Width (ft)
Interior one "width (ft)
Gable Roof Loan!
End
Inte.rlor
Hip R<>of Load End
Interior
Wall Load
End
Interior
Vertical Force
end zone wi-ndward
leeward
interior zone windward
and
leeward
Floor Diaphragm Shear
Total Shear albs)
Left Wall Length
Right 'Fall Length
Floor 1 Diaphragm Shear
Total Shear Ob)
Left Wall Length
[ ht Wall l Length
basement Diaphragm Shear
Total Shear albs)
Left Wall Length
Right Wall Length
Critical Wall Length ()=
Left 'Fall Deal Lead (plf)=
LeffWall Critical Length (ft)=
Right all Dead Load (plf)
Right la Wall Critical Length (ft)=
34e3
10
10
10211
3
31
11007
10
10
Roof Height 7.25
afl Height
Truss Span 29
112
Sine= 0.4472
Minimum Pressure
Adjusted
14.16
19,43
10.00
10.00
0.00
0.00
0.00
0.00
4,3 2nd stvr End Zone "width (ft)
44 4 2nd Storyinterior Zone Width ft
fid-th
Height
Wind Load
Force (lbs)
.3
_1
19.48
173
44.4
2.5914.16
185
2927
Surma _
3099.5068
Area
3,84.25
10.00
3843
0
10.00
0
Taal
3843
Width
Height
Wind Load
Force (Itis)
4,3
1.0
19.48
168
44.4
1.00
14,16
629
Suri =
796,1 074
Width
length
Wird Load
Force Obs)
4
42,85
0.00
0
4
42.8.E
0.00
44
42,85
0.00
0
44
42.85
0.00
Shear Wall Loads (plf)
of App I i a ble
Not ppli re
Shear Wa l I Loads (plf)
160
Shear Wall Loads (plf)
Not Applicable
Not ApplIcable
583 Taal 9008
3 Total (plf) 4
313
6
Calculate Upl ft , Force eq'd to Prevent OT (lbs)
panel Length (ft)
Front 41
al 721
3
4
153
-11
-652
-1188
588
45,5
185
-79
10
-1725
-345
4.3
44.4
2nd Story
Eln
Fila m Winchester
Date. 30 July 2007
Location: Lot #7 Block 7, Henderson Sub.
Wind Loading g alculations Laing Mala indf rc Longitudinal Direction
i ndOesign Coefficients
P� ind load*exp o *l
P=Dein Pressure
Horizontal VVind toad (from table 1609-6.2.1 (1)
Wall Load (f)
end zoo (A) 16.1
interior zone 11.7
Fol Load (Pf)=
end zone 8) 2.6
interior zone (D) 2.7
e rtj a I Win d Load (from table 1609- 6.2. 1 (1)
Roof Load (psf)=
end zone windward (E) -72
end zone ie and (F) -9-8
int
-
int rior zona windward ) -5.2
interior zone leeward (H) --
Exposure Coefficient from table 1609.0,2.1(4) 1,21
1 =importance Factor (from table 1004-) 1 -
Wind Speed
Exposure
Roof Slope
Roof Anglo (deg)=
P:; --wind 102d" -exp ooeWlw
horizontal wall interior
h o rrzonta f wall end zone
horizontal roof arterior
horizontal roof end zoo,
vertical end zone windward
vertical end zona leeward
vertical interior zone indwar
vortical lnterior zone leeward
-4'-Hcan
-`t'*base
End Zone Width (ft)
J nferior Zone Width (fit)
Gable Roof load
Hip Roof Load
Wall Load
Vertical Force
Floor 2 Diaphragm Shear
Total Shear Ob)
Front Weal Length
Back I f Length
door 1 Maphragm Shear
Total Shear (lbs)
Front Wall Length
Back Wall Length
basement Diaphragm Shear
Total Shear Obs)
Front Wall Length
Back Wall Length
0 Roof Height 7-
Valla Height
Truss Span 29
End
lnt riD.
End
Interior
End
Interior
and zone windward
leeward
interior zone windward
leeward
Critical Wall Length (f` )=
Front VVaj[ Dead Load (pif)=
Front' afi Critical Length (ft)=
Back WaN [Dead Load (pff)=
Back all Critical Length (ft) -
-
3118
10
10
8354
ll
7
708
3
600
3
5.05
4.
4.0 2nd stor End Zone Width (ft)
34.4 2nd StoryInterior Zone Width eft)
Calculate Uplift , Force Regld to Prevent OT Obs)
Panel Length (ft)
FrontBack 4
385
Width Freight
4.3 2.1
34.4 2,50
Area
011.75
0
'mind Load
10.8
14,10
Sum
Wird Load
10.00
10,00
`J-ota i
Farce Obs)
173
2208
2440.,33
Force Obs)
3118
0
3118
Width
112
26.00
Sire = 0,4472
4.3
J lirlimam Pressure
19-48
Adjusted
14,16
14.16
10-4
19-48
-
3,27
.7
10.00
.1
10-0
--71
000
-11.86
0,00
-0.20
0.00
-6,29
0.00
End
lnt riD.
End
Interior
End
Interior
and zone windward
leeward
interior zone windward
leeward
Critical Wall Length (f` )=
Front VVaj[ Dead Load (pif)=
Front' afi Critical Length (ft)=
Back WaN [Dead Load (pff)=
Back all Critical Length (ft) -
-
3118
10
10
8354
ll
7
708
3
600
3
5.05
4.
4.0 2nd stor End Zone Width (ft)
34.4 2nd StoryInterior Zone Width eft)
Calculate Uplift , Force Regld to Prevent OT Obs)
Panel Length (ft)
FrontBack 4
385
Width Freight
4.3 2.1
34.4 2,50
Area
011.75
0
'mind Load
10.8
14,10
Sum
Wird Load
10.00
10,00
`J-ota i
Farce Obs)
173
2208
2440.,33
Force Obs)
3118
0
3118
Width
Weight
Wind Loyd
Force ObIft)
4.3
1,0
19-48
108
34.4
1.00
14.10
487
Sum v
054,5374
Width
length
Wind Load
Force Obs)
4
24.35
0-00
0
4
4-00
0.00
0
4
24.35
&00
0
4
24.35
0,0
0
Shear lull Loads (plf)
Not p,plicabf E?
Not applicable
Shear Wali Lords (plf)
199
155
Shear Wall Loads (plf)
Not ,applicable
Not ApplicaNe
Total
Total (pff
11007
7
4.
34.4
2nd Story
Force t I bift)
1
-2710
-2328
4
0
8 10
217
-100
-758
-1409 -2000
114
-107
700
-1243 -1785
4.
34.4
2nd Story
Force t I bift)
1
-2710
-2328
Plan:
Winchester
53 25 1325
Cate-,
30 July
200'7
Total Mass Tributary to Roof Levels =
Seismic Cal(; Location:
Lot #7 Bloch 7. Henderson
Loading Summary
' idth
53 10 580
43
Floor Card Lead (pf)
10
Seismic Zone
E
Floor Live Load( f)
40
Floor 1Length '(pf) left
Ii
idth
WallEt)(f)
20
Iocif L L sf
o
'all (Int fF
Shear ( )(fb Floor L ve[
Roof Dead Load(psf
1
Roof Slope
/1
Exterior
combination
Snow Load Reduction
Seismic Parar titers
Slope
26",56
*W/1,4
Snow
50.00
Fa=
1
Pitch over 20
j=
Rs
Reduction
Sms=
L.L.- Reduction
80.00
Sds=
Teel Load 65,00
Cs=
0.236
Adj. Factor
1.4
Cs=
0.1686
table 1617.6
1.772
1..7 e. 16-16
1. 18eg16-1 a
Per eq. 16-49
Roof Len th PSO Lb/ft
Width
53 25 1325
43
roof wall
Total Mass Tributary to Roof Levels =
Shear ( )(Ib ) Roof Levels -,
Floor Length ' "(p f) Ib/ft
' idth
53 10 580
43
wall height 0
Total Mass Tributary to Floor
he2r ( )(1b ) Floor Levels =
Floor 1Length '(pf) left
Ii
idth
8 10 530
4
ill height
Total M a ss Tri butar to f=lour 1 _
Shear ( )(fb Floor L ve[
Floor 1 Lateral Force
Ffoor 2 Lateral Force 0
Roof Lateral Force 10900
Total Seismic Mass ' 88498
Total Lateral Force = 10900
(Ib)
58975
7680
64855
10900
VV
0
7680
0
0
`' (J b)
14240
9000
23840
401
Seismic Force Distribution
Roof Sections H') VV'p kip VV () H () % Force Total Sheet Force (K -1p)
Floor 1 100-00% �l 0,00887
1.0 0 0 0.00% 10-9003897
Floor 2 O'D 0 0 0:00
% 10.9003897
V/sTotals � �
urr-� v' 1 'f�-Mid = 0.01335 Total Shear (Ibs) _ 10900
Basement Sheer Wall .F(total') Length
Total Lead (kips) 10.9 Shear ti ,CJI Load (If)
right side -5 10
10 fF
left id it Applicable
cable
front 5,5 10 Not Applicable
Not bac Applicable
Not Applicable
Floor 1 Sheer Wall F(tatal) Lengllh
Total Laid (kips) 10,9 Shear Wall
ri.ht Ido ,� �oad (plf)
176
left side 5-5 32 170
front 5.5 1 260
back 5.5 27 202
Floor 2 Sheer Wall F(totail) Length
Total Load (kips) 10.9 Shear VVall Loadif
right side 5., 1��'
left id,8t Applicable
0 ofApplicable
front . 10 of
back Applicable
. 10 Not Applicabie
Shear Wall Critical Length, "Fall DL Floor .CSL Roof D,L CSLIf
Fant � 0 �p critical i �)
� 708
Bach 280 0 621
600 6
Right 00 0 270 313 10
Left 200 0 675 583
Calculate Uplift Force q'd to Prevent OT (lbs)
Panel Length () 2 3 4
Freie 3256 2548 8 10 1
Back 2433 1833 1233 -
-2408 -3824
i ht 2 539 2226 1913 � �
Right -2367 -3567
Left °0 4 -592
1900 1317 735 481 -1596 -2762 -3927
LVL Beam
Load Parameters
Floor LL (psf)
Total Floor Load(psf)
Floor Span (ft)
Total Floor Load (plf)
Wall Height,(ft)
Wall Weight (psf)
Wall Load (plf)
Roof LL (psf)
Total Roof Load (psf)
Roof Span (ft)
Roof Load (plf)
Beam Weight (plf)
Live Load (plf)
Total Load (plf)
Plan: V Chester C
Date: 30 July 2007
Location: Lot #7 Block 7, Henderson Sub.
IN
50
6
35
210
50
65
r:
65
12.1
90
337
Reactions & Moment
Duration Increase 1
Beam Span(ft) 16
Reaction 1 (Ib) 2696
Reaction 2 (Ib) 2696
Max Moment FtLb 10786
Max Shear Lb 2696
Max Shear Stress (psi) 65
Determine Size
Depth Estimate (in) 11088
Width Estimate (in) 1$
Cross Area (in A 2) 42
Allowable Bending Stress = 26,04
Allowable Moment = 17862
Mornemt of Inertia I = 489
Factor Of Safety = 1.66
Allowable Sheer Stress (psi)= 2g5
Allowable Sheer Force (lb) 7900
Factor Of Safety = 2m93
Bearing Required = 1.03
E (psi) 1900000
Deflection LL (in) 0.14
LLoad Def. Limit L/ 360
Allowable Deflection (in) 0.53
LL Deflection F/S 3.73
Deflection TL (in) 0.53
TLoad Def. Limit U 240
Allowable Deflection (in) 0.80
TL Deflection FIS 1.50
Selection,2
11 7/8
.. ..
Plan: V11,� hester C
w
Date.- 30 July 2007
Location: Lot #7 Block 7, Henderson Sub.
Exterior Footing Calculations
back
Concrete Specs
Density (pcf)
Strength (psi)
Clear Cover Thickness (in)
Foundation
Overall Height (ft)
Height (in)
Wall Thickness (ft)
Thickness (in)
Weight (kips/Ift)
Footing Specs
Width (ft)
Width (in)
Height (ft)
Height (in)
Weight (klips/ift)
Area per Ift
Soil Specs
Density (Pcf)
Soil Pressure (psf)
Weight (kips/lft)
Building Loads
Roof span
Roof (ki'ps/lft)
Wall Height (ft)
Wall Load (kips/Ift)
Floor span
Floor Loads (kips/Ift)
Total (kipsAft),
Calculations
Total Weight on Soil (kips)
Soil Load (ksf)
Required Footing Width (*In)
Required Footing Depth (in)
brant
150
3000
3
J
left
150
3 00 0
'93
right
15 0
3000
3
3.00
3.00
3.00
3.00
36
36
36
36
0.67
0.67
0.67
0.67
8
8
8
8
0.30
0.30
6.30
0.30
1.67
20
0.83
1.67
20
0.83
1.67
20
0.83
1.67
20
0.83
10 10 10 10
0.21 0.21 0.21 0.21
1.67 1.67 1.67 1.67
125
125
125
125
1500
1500
1500
1500
0.19
0.19
0.19
0.19
23 29 25 10
0.62 0.78 0.68 0.27
14 14 10 10
0.28 0.28 0.20 0.20
0 0 p p
0.00 0.00 0.00 0.00
0.90 1.06 0.88 0.47
1.41
0.85
1.57
0.94
1.38
0.83
6
20 20 20 20
10 10 10 10
Plans Winch .'er C
Date.- 30 July 2007
Location: Lot #7 Block 7, Henderson Sub.
Sawn Lumber RB -2 RB -4 R13-5
Load Parameters
Floor Live Load(psf)
Floor Total Load(psf)
Floor 1 Span(ft)
Total Floor Load(plf)
Wall Height (ft)
Wall Weight (psf)
Wal! Load(plf)
Roof ILL (psf)
Total Roof Load(psf)
Roof Span(ft)
Total Roof Load(plf)
Beam Weight (plf)
Live Load (plf)
Total Load (plf)
Reactions & Moment
Duration Increase
Beam Span(ft)
Reaction 1 (Ib)
Reaction 2 (Ib)
Max Moment FtLb
Max Shear Lb
Determine Beam Size
Depth Estimate (in)
Width Estimate (in)
CF
Area -
IVlomemt of Inertia P
Maximum Bend Stress =
Allowable bead Stress
Factor Of Safety =
Allowable Sheer Stress
Max Shear Cap (Ibs) =
Factor Of Safety
Bearing Required =
E (psi)
Deflection ILL (ln)
LLoad [def. Limit L/
Allowable Deflection (in)
LL Deflection FIS
Deflection TL (in)
TLoad Def. Limit LI
Allowable Deflection (in)
TL Deflection FIS
40 40 40
50 50 50
10 0 0
250 0 0
0 0 0
20 20 20
0 0 0
50 50 50
65 65 65
22 29 10
715 943 325
6.5 6.5 5.1
750 725 250
971 949 330
T 1 1
4 3 5
1943
1943
1943
1943
9.25
3.5
1.20
32.38
231
467
1020
2.18
180
3885
2.00
1.37
1300000
0.01
360
0.13
9.26
0.02
240
0.2
10.73
1423
1423
3068
1423
9.25
3.5
1.20
32.38
231
257
1020
3.97
2.73
1.00
1300000
o.00
360
0.10
22.71
0.01
240
0.15
26.03
Selection 2: 2 x 10 2: 2 x 10
825
825
1031
825
7.25
3.5
1.30
25.38
111
404
11 05
2.74
195
3299
4.00
0.58
1300000
2:2 x 8
0.02
360
0.17
6.85
0.03
240
0.25
7.78