Patio Canopy Design

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BY

Gugi

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Table of Contents

Building Background …………………………………………………………………. 2

Patio Slab ……………………………………………………………………………………2

Timber Structural Calculations……………………………………………………….2

Column Stability ………………………………………………………………………….. 7

Wind Loading Calculations ……………………………………………………………10

Frame anchoring Calculations from Wind Load Tension and Lateral

Loading………………………………………………………………………………………..10

APPENDIX A Design Drawings………………………………………………………16

APPENDIX B Materials…………………………………………………………………21

BUILDING BACKGROUND

The structure was established in 1978. The building is about 40 years old and is a single stoiry wood

frame structure with an external veneer made of rock. The foundation of the building rests on limestone

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and free from expansive soils. No structural deficiencies appear to exist in the superstructure and the

foundation.

PATIO SLAB

An attaché slab exists on the north side of the structure that extends 12 feet further on the longer axis

of the building and has a length of 40 feet. It is not known about the presence, extent or absence of

reinforcement of the slab.

The slab is currently without an canopy and surrounded on the eastern position with trees. The slab

appears I a reasonable condition except for contraction/tension cracks running at 45 degree angle

across the slab where a stair pedestrian comes in contact with the slab. There was no control joints

placed during the pour of the slab.

Proir to this design, a CMU wall about 4 feet in height has been placed that extended alng bthe

perimeter of the slanb to about 10 feet of the northern perimeter. The CMU wall is not reinforced

The objective of the design is to extend a partially open roof over 75% of the slab, that rxpends from the

eastern corner to about four feet from the entrance door. The canopy shall be of NO: 2 grdae structural

timber. Roof loading is expected to be minimal as it is not going to be subject to loading from

equipment or personnel. A load of 10 PSF is expected to be sufficient to effectively bear trhe load of

four persons for repair.

WOOD FRAME STRUCTURAL CALCULATIONS

Readily available timber species is the southern pine or yellow pine in Southern Texas. This woood is

generally used for residential framing. The engineering characteristics of this type of wood are:

Modulus of Elasticity (E): 1100000 psi

Bending Strength (Fb: ) 1336.87 psi

Bearing Strength (Fcp): 335 psi

Shear Strength (Fv): 135 psi

The following plan has been drafted as dimensions of the canopy. The post locations are shown. The

wood rafter and joist are be placed within the dimensions of the posts. Post A and past Be are about 8

inches away from the CMU wall

Long length = 24 feet

Width between post center to center c-c = 9 feet

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The American Wood Council has extensive engineering information. The engineering calvulations for

deflection, shear, torsion, can be done manually, however a very good AWC furnished calculator is

available that can be used to calculate joist span and spacing calculations based on wood type used.

Lumber design values used to calculate maximum horizontal spans include modulus of elasticity (E),

bending strength (Fb), and shear strength (Fv). Bearing strength in compression perpendicular to grain

(Fcp) is used to determine the minimum required bearing length at each end of joists and rafters.

Calculated spans incorporate design value adjustments appropriate for repetitive-member use (Cr =

1.15), duration of load (CD), lumber size (CF), wet service conditions (CM), and incised lumber (Ci). The

2005 National Design Specification® for Wood Construction (NDS®) specifies appropriate magnitudes for

lumber design values and adjustment factors.

Maximum horizontal joist and rafter spans are taken as the smallest span (L) calculated from the

following three formulas:

(A)

16

12 8.5

28

25 till past door

11.5 12

9 9

Figure 1

A

B

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based on bending strength (Fb)

where s = spacing between joists or rafters

Sx = section modulus for strong-axis bending of joist or rafter

wT = total distributed load (D + L, or D + Lr, or D + S)

supported by joist or rafter, in terms of load per unit area

(B)

Based on deflection limit and modulus of elasticity (E)

where Ix = strong axis moment of inertia for joist or rafter

wL = distributed live load (L or Lr) or distributed snow load (S) supported by joist or rafter, in terms of

load per unit area

deflection constant = constant term in denominator of

deflection limit (e.g., L/360). Here L/240 shall be used as ot much loading is anticipated

(C)

based on shear strength (Fv)

where A = cross-sectional area of joist or rafter

BEARING LENGTH

The minimum required bearing length (lb) at each end of a joist or rafter is determined from the

following formula:

Where t=thickness of joist or rafter

Using the equation, as the designer, joist and rafter sizes chosen aree 9 feet center to center of the 4 by

4 treated wood columns (posts). The calculator input is as shown in table 2

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The calculator gives an allowable span is 9’-11” which is OK for this span design for joists

For the rafter, with about 12 iches center to center on which the joists will be attached in perpendicular.

Calculations show that a single 4 by 10 (No: 2 structural wood lumber of southern pine) is minimally

sufficient.

Figure 2: Calculator input

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These are conservative values. In my professional opinion two 2*6 lumber rafter can be used to support

the joists on either end.

COLUMN STABILITY)

The slenderness ratio Le/d for solid column shall not exceed 50 for service load and shall not exceed 75

for construction. Le=KeL is effective length of column, Ke is slenderness ratio, L is unsupported length of column. For rectangular section, Le/d shall be evaluated in both directions. Maximum compressive stress, fc must not exceed allowable stress parallel to grain, F’c = Fc*CD*CM*Ct*CF*Cp Where Fc is allowable bending stress in NDS supplement. CD is load duration factor, (see beam design) CM is wet service factor, (use when moisture of timber is higher than 19%)

Ct is temperature factor, (when timber is used in temperature higher than 150F) CF is size factor, (apply only to visually graded sawn lumber members, and to round timber bending members, not apply simultaneously with Cv for glued laminated timber) Cp is column stability factor (see below)

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According to NDS 3.7.1, column stability factor shall be determined as Fully supported laterally throughout its length, Cp=1. Otherwise, Cp shall be calculated as

Fc*=Compressive design value in NDS tables multiplied by all other adjustment factor except Cp,

FcE= KcEE’/(Le/d)2, KcE=0.3 for visually graded lumber and machine evaluated lumber, (note: KcE=0.418 for machine stress rated lumber and glued laminated timber), C=0.8 for sawn lumber, (note: c = 0.85 for round timber piles and 0.9 for glued laminated timber). Calculation:

Attempt 4 by 4, 10 foot column Southern pine, moisture less than 19%, used in normal room

temperature.

Floor area supported by column: A = 30 ft2

Unsupported length of column, L = 10 ft

Floor live load: WL = 10 psf

Floor dead load: WD = 5 psf

Superimposed dead load: WSD = 5 psf

Calculation step 1. Select southern pine, 4"x4" stud grade, d = 3.5 in

Actual cross section: Ac = 12.25 in2.

Allowable compressive stress parallel to grain: Fc = 975 psi

Calculation step 2. Calculate slenderness ratio: Ke = 1, Le =KeL = 10 ft, Le/d = 34 < 50 OK

Calculation step 3. Calculate compressive stress with load duration factor

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Load duration factor for dead load: CD = 0.9

Load duration factors for live load: CD = 1.0 (Use 1 per NDS)

Calculate Design load: P = [WD + WSD+ WL]A =[5 + 5+ 10]30= 600 lb

Column compressive stress, fc=P/Ac = 600/12.25= 50 psi

Calculation step 4. Calculate allowable stress without Cp.

CM=1, Ct=1, Cf=1

Fc* = FcCMCtCF = 975 psi

Calculation step 5. Calculate elasticity modulus for this wood species

E’=ECMCt = 1.4106 psi

Calculation step 6. Calculate FcE

KcE=0.3

FcE= KcE*E’/(Le/d)2= 1*1.4106 /(34)2 = 1211 psi

Calculation step 7. Calculate Cp

c = 0.8

Cp=

Cp = 0.76

Calculation step 8. Calculate allowable compressive stress

F”c = Fc*Cp = 9750.76= 741 psi > fc= 293.8 psi (in NDS tables)

The whole column can support 3.5*741 psi = 2,593 lbs. The patio roof is not expected to be

subject to live load except occasion a few persons for repair, which will be far less the column

compressive ability.

Column O.K.

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WIND LOADING CALCULATIONS

The manual calculations are extensive and tedious. Therefore a calculator input has been used o

generate the negative and positive pressures on the open roof. The posive wind loading from 80 mile

per hour winds is used (although 90mph is the code) as the roof shall be surrounded by trees. Dead load

and occasion temporary live loads from individual stepping on the roof for repair is minimal.

A higher negative wind loading is used as an conservative measure with a safety factor of 23/18 =1.27.

The structure is a monoslope with partial enclosure of CMY walls about 4.5 foot in heights. Column base

plate/ anchoring stability calculations are developed further based on tension loading based on wind

loading calculations. The area is going to be used for external to building gas based cooking.

FRAME ANCHORING CALCULATIONS FROM WIND LOAD TENSION AND LATERAL LOADINGS (ASCE- 05,

Appendix D Building Code)

The support columns are to be placed at 12 feet separation along the slab facing the structure and at 9

feet CC towards opposite of boiling superstructure. As each column supports a portion of the loads per

tributary area for aech column. An approximate tributary for each columns is 6*5 for central columns.

The tension wind, conservative to actual wind loads is approximated as 23 psf (pounds per square foot).

That gives a tensile wind loading of per column

Therefore: 5ft*6ft*23 = 690 psf vertical tensile uplift pressure on column per tributary area for columns

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Although the tributary area of columns “A: abd “B” are less, the approximation will still hold for the

larger tributary areas.

\

Bolts: ¾” headed hex bold

Futa: = 70,000

Embedment in grout pads: = 6 “

Concrete F’c := 4000 psi

Slab thickness := 18 inches

Loads in vertical tension: = 700 lbs on column

Load in shear in x-direction: = 1000 lbs

Load in shear in y-direction: = 1000 lbs

Bolts at x-y distance = 4”

Top Edge:= 15”

Bottom Edge:= 15”

Left Edge:= 15”

Right Edge:= 15”

6”

700

18”

1000 lbs

1000 lbs

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Bolt Tension (D.5.1 ASCE 315)

ϕ Nsa = ϕn Ase.futa ……………………………………………..(a)

where bolt area and f is and ϕ is the strength reduction factor, Nsa is strength of group of anchors, n is

the number of anchors, futa specified tensile strength of single anchor from manufacturers catalogue

ϕ= 0.7 , n = 4 , Ase = 0.334 in2, futa = 70 ksi

ϕ Nsa = ϕn Ase.futa =47.5 kips

Concrete Breakout (D.5.2, ASCE 318)

ϕ Ncb = ϕ (Anc/Anco) ΨecΨedΨcΨcpNb ………………………………………………………(b)

ϕ= Modification factor for concrete breakout strength = 0.7

Anc = Projected concrete breakout area = 484 in2

Anco = Total projected shear failure area = 324 in2

Ψec= Modification factor for an anchor group loaded eccentrically = 1.0

Tributary Area D

Tributary Area A

Tributary Area B

Tributary Area C Tributary Area E

Tributary Area F

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Ψed= Modification factor for edge effect in shear = 1.0

Ψc= Modification factor based on presence or absence of cracks in concrete = 1.0

Ψcp= Modification factor for post weld type of anchor = 1.0

Nb= Modification factor for breakout strength of single anchor in shear = 22,3 kips

Hef = Embedment depth = 6”

Kc = 24

ϕ Ncb = 23.3 kips

Pullout (D.5.3, ASCE 318)

ϕNpn = ϕ ΨcNp …………………………………………………………..(c)

ϕ= strength reduction factor in pull out strength = 0.7

Ψc= Modification factor for breakout strength in presence of concrete cracks = 1.0

Np= 22.2 kips

ϕNpn = 62.1 kips

Side Face Blowout (D.5.4, ASCE 318)

ϕNsb=ϕ(1+s/(6Ca1(Argf’c)^0.5……………………………………………….(d)

ϕ= 0.7

Ca1= 15

ϕNsb= Not Applicable

Shear Calculation X-Direction Bolt Shear (D.6.1, ASCE 318)

ϕ Vsa = ϕn Asefuta ……………………………………………..(e)

ϕ = 0.65

n= 4

Ase=0.334 in2

futa= 70 ksi

ϕ Vsa = 24.7

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Shear Calculation X-Direction Concrete Breakout (D.6.2, ASCE 318)

ϕ Vcb = ϕ (AVc/AVco) ΨecΨedΨcΨcpVb ………………………………………………………(f)

ϕ = 0.7

AVc = Projected concrete breakout area = 612 in2

AVco = Total projected shear failure area = 648 in2





Vb= Modification factor for breakout strength of single anchor in shear = 24.2 kips


Ca1= 12 “

ϕ Vcb =27.7 kips

Shear Calculation X-Direction Concrete pry out (D.6.3, ASCE 318)

ϕ Vcp = ϕn KcpNcb ……………………………………………..(g)

ϕ = 0.7

Kcp= 2

ϕ Vcp = 46.7 kips

Shear Calculation y-Direction Bolt Shear (D.6.1, ASCE 318)

ϕ Vsa = ϕn Asefuta ……………………………………………..(h)

ϕ = 0.65

n= 4

Ase=0.334 in2

futa= 75 ksi

ϕ Vsa = 24.7

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Shear Calculation X-Direction Concrete Breakout (D.6.2, ASCE 318)

ϕ Vcb = ϕ (AVc/AVco) ΨecΨedΨcΨcpVb ………………………………………………………(f)

ϕ = 0.7

AVc = Projected concrete breakout area = 612 in2

AVco = Total projected shear failure area = 648 in2





Vb= Modification factor for breakout strength of single anchor in shear = 24.2 kips


Ca1= 12 “

(&Psih = 1.0)

ϕ Vcb = 27.7 kips

Shear Calculation Y-Direction Concrete pry out (D.6.3, ASCE 318)

ϕ Vcp = ϕn KcpNcb ……………………………………………..(g)

ϕ = 0.7

Kcp= 2

ϕ Vcp = 46.7 kips

Results Summery

X and Y interaction = 0.0086

Tensile Capacity ϕNn= 23.3 kips Breakout controls

Shear X Capacity ϕVnx = 24.7 Kips Breakout controls

Shear Y Capacity ϕVny = 24.7 Kips Breakout controls

Design OK

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APPENDIX A

Design Drawings

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APPENDIX B Materials

(Partial List)

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1. Rafters 2 by 4 Structural wood #2 2. Psts (3) 4 by 4, 10 feet high and (3) 10.5 ft high, treated lumber 3. Post holders = 6 4. Hex bolts = 24 5. Beams = four 2 by 10 , each side 2 by 10 coupled or one 4 by 10 each side 6. Apoxy 7. Hammer drill 8. Blower 9. Self drilling nails 10. Connectors 11. Drill

4 by 6 by 12 Beam

4 by 4 4 by 4

4 by 4

11.5 10

4 by 6 by 12 Beam

12’

1’-5”

12’-6”

T-Connection

bracket-Connection

2 by 6 by 12 Beam

Non Load Bearing Connection

Build

ing

4 by

6

4 by

6

Flashing

Corrugated roof

Eave= 1’-5 “

Setback

1’-0”

9’

2 by 4 Joist, 16” spacing

1’-4”

Eave= 1’-9 “ 12-6

12

16” c-c

12

10’ span between columns

11’-5” span between columns

4 by 4 Column

2 by 4 by 12 Joist

4 by 46by 12 Beam

4 by 46by 12 Beam