steel roof load calculation for custom home

1. STEEL ROOF JOIST LOAD
CALCULATION
FOR
CUSTOM HOME -AREA 1
FINAL DESIGN REPORT AREA. 01
PUTIKA ASHFAR KHOIRI

2. Reference Output
Steel Roof Joist Load Calculation Custom Home
Joist sizes used
Area 1 joist spacing is 24'' OC
1a 1000S 200-54
1b span 1 1000S 250-97
1b span 2 1000S 200-54
1c span 1 1000S 200-97
1c span 2 1000S 200-97
1c span 3 1000S 200-54
1d span 1 1000S 250-97
1d span 2 1000S 200-54
1d span 3 1000 S 200-97
Loading on Roof
Deck weight = 2.3 psf
= 0.110124 kNm^2
Ceiling Dead Load = 0.3 kNm^2
Total Dead load on roof = 0.41 kNm^2 8.6psf
Roof & ceiling live load = 0.75 kNm^2
=
Total live load on roof = 0.75 kNm^2 15.7 psf
Net wind load calculated = 1 kNm^2
20.1 psf(acting
upward)
Spacing of joists and studs = 0.6 m 24 inches
= 0.41x0.6
= 0.246 kNm
= 0.75x0.6
= 0.45 kNm
= 1x0.6
= 0.6 kNm
These load applied on joists in the prepared model
Calculation
Roof live load acting on unit length of one roof
joist
Roof dead load acting on unit length of
one roof joist
Roof wind load acting on unit length of
one roof joist

3. Reference Output
Calculation
Analysis Modal prepared using SAP 2000

4. Reference Output
Calculation
Load combinations used
Load combination 2
Section properties of 1000S 200-54 joist section
Total height h = 254 mm
Total width of flange b = 50.8 mm
Lip depth c = 15.9 mm
Nominal thickness t = 1.44 mm
Steel grade G16 (50ksi)
Basic yield strength fyb = 344 N/mm^2
Second moment of area z-z Iz-z = 1.57x10^5 mm^4
Warping constant = 2.06x10^9 mm^6
Torsional constant = 372.9 mm^4
Effective section modulus Weff,y = 2.8x10^4 mm^3

5. Reference Output
Calculation
Section properties of 1000S 200-97 joist section
Total height h = 254 mm
Total width of flange b = 50.8 mm
Lip depth c = 15.9 mm
Nominal thickness t = 2.55 mm
Steel grade G12 (50ksi)
Basic yield strength fyb = 344 N/mm^2
Second moment of area z-z Iz-z = 2.53x10^5 mm^4
Warping constant = 3.41x10^9 mm^6
Torsional constant = 2114 mm^4
Effective section modulus Weff,y = 6.12x10^4 mm^3
Section properties of 1000S 250-97 joist section
Total height h = 254 mm
Total width of flange b = 63.5 mm
Lip depth c = 15.9 mm
Nominal thickness t = 2.55 mm
Steel grade G12 (50ksi)
Basic yield strength fyb = 344 N/mm^2
Second moment of area z-z Iz-z = 4.45x10^5 mm^4
Warping constant = 5.8x10^9 mm^6
Torsional constant = 2260 mm^4
Effective section modulus Weff,y = 6.85x10^4 mm^3

6. Reference Output
Calculation
Section 1a Floor joist check
Joist section used is 1000S-200-54
Span = 4.06 m (13'4'')
Design Bending moment MEd = 2.28 kNm SAP Modal result
Check of bending resistance Mc,Rd = Weff,y * fyb/ƳM0
ƳM0=1.0 (partial
safety factor)
= 9.63 kNm
MEd = 0.237 <1
Mc,Rd
Hence OK for Bending

7. Reference Output
Calculation
Buckling strength of member = Mb,Rd
χ LT = 1/(φLT+√Φ^2LT-λ^2LT)
ΦLT = 0.5*(1+αLT(λlt-0.2)+λ^2LT
buckling curve b αLT = 0.34
λLT = (Weff,y*fyb/Mcr)^0.5
Mcr = C1*(Π2
EIz/L2
)*(Iw/Iz+L2
GIt/Π2
EIz)
= 2.689 kNm
λLT = 1.893
ΦLT = 2.58
χ LT = 0.231
Mb,Rd = χLT*Weff,y*fyb/ƳM1
= 2.30
MEd/Mb,Rd = 0.99 <1
Hence Ok for buckling.
Design deflection for section 1a joist = 0.0032 m
= 0.126 inches
Length of joist = 165.4 inches
Deflection limit of joist = L/240 for total load
= 0.689 inches
Hence actual deflection < Deflection limit
Hence OK for Deflection

8. Reference Output
Calculation
Section 1b Span 1, Design Check
Section 1b span1, Floor joist check
Span = 6.2 m (20'5'')
Design Bending moment MEd = 3.58 kNm SAP Modal result
ƳM0=1.0
Check of bending resistance Mc,Rd = Weff,y * fyb/ƳM0
= 23.56 kNm
MEd = 0.152 <1
Mc,Rd
Selected member is ok for bending
Joist section used in section 1b Span1 is 1000S 250-97 and intermediate
web stiffners used

9. Reference Output
Calculation
Buckling strength of member = Mb,Rd
χ LT = 1/(φLT+√Φ^2LT-λ^2LT)
ΦLT = 0.5*(1+αLT(λlt-0.2)+λ^2LT
αLT = 0.34
λLT = (Weff,y*fyb/Mcr)^0.5
Mcr = C1*(Π2
EIz/L2
)*(Iw/Iz+L2
GIt/Π2
EIz)
= 3.867 kNm
λLT = 2.469
ΦLT = 3.93
χ LT = 0.143
Mb,Rd = χLT*Weff,y*fyb/ƳM1
= 3.59
MEd/Mb,Rd = 1.00 <1
Hence Ok for buckling.
Design deflection for section 1b span 1 joist
= 0.0062 m
= 0.244 inches
Length of joist = 244 inches
Deflection limit of joist = L/240 for total load
= 1.02 inches
Hence actual deflection < Deflection limit
Deflection check is ok

10. Reference Output
Calculation
Section 1b, Span 2, Design Check
Section 1b span2, Floor joist check
Span = 4.06 m (13'4'')
Design Bending moment MEd = 2.07 kNm SAP Modal result
Check of bending resistance Mc,Rd = Weff,y * fyb/ƳM0
ƳM0=1.0 (partial
safety factor)
= 9.63 kNm
MEd = 0.21 <1
Mc,Rd
Hence Ok for bending
Joist section used in section 1b span 2 is 1000S200-54 joist section

11. Reference Output
Calculation
Buckling strength of member = Mb,Rd
χ LT = 1/(φLT+√Φ^2LT-λ^2LT)
ΦLT = 0.5*(1+αLT(λlt-0.2)+λ^2LT
αLT = 0.34
λLT = (Weff,y*fyb/Mcr)^0.5
Mcr = C1*(Π2
EIz/L2
)*(Iw/Iz+L2
GIt/Π2
EIz)
= 2.643 kNm
λLT = 1.909
ΦLT = 2.61
χ LT = 0.227
Mb,Rd = χLT*Weff,y*fyb/ƳM1
= 2.191
MEd/Mb,Rd = 0.94 <1
Hence Ok for buckling.
Design deflection for section 2-2, span 2 joist
= 0.0014 m
= 0.055 inches
Length of joist = 161.4 inches
Deflection limit of joist = L/240 for total load
= 0.6725 inches
Hence actual deflection <Deflection limit
Deflection check is Ok

12. Reference Output
Calculation
Section 1c, / design check of 3 spans
Section 1c ,Span 1, design check
Section 1c span1, Floor joist check
Span = 5.58 m (18'4'')
Design Bending moment MEd = 2.28 kNm SAP Modal result
Check of bending resistance Mc,Rd = Weff,y * fyb/ƳM0
ƳM0=1.0 (partial
safety factor)
= 21.05 kNm
MEd = 0.11 <1
Mc,Rd
Hence Ok for bending
Joist section used in section 1c is 1000 S200-97 joist section and with 0.45m
intermediate web stifners at support

13. Reference Output
Calculation
Buckling strength of member = Mb,Rd
χ LT = 1/(φLT+√Φ^2LT-λ^2LT)
ΦLT = 0.5*(1+αLT(λlt-0.2)+λ^2LT
αLT = 0.34
λLT = (Weff,y*fyb/Mcr)^0.5
Mcr = C1*(Π2
EIz/L2
)*(Iw/Iz+L2
GIt/Π2
EIz)
= 2.919 kNm
λLT = 2.686
ΦLT = 4.53
χ LT = 0.122
Mb,Rd = χLT*Weff,y*fyb/ƳM1
= 2.57
MEd/Mb,Rd = 0.89 <1
Hence Ok for buckling.
Design deflection for section 1c, span 1 joist
= 0.0025 m
= 0.11 inches
Length of joist = 212.5 inches
Deflection limit of joist = L/240 for total load
= 0.885 inches
Hence actual deflection <Deflection limit
Deflection check is Ok

14. Reference Output
Calculation
Section 1c ,Span 2 design check
Section 1c span2, Floor joist check
Span = 6.22 m (20'5'')
Design Bending moment MEd = 1.99 kNm SAP Modal result
Check of bending resistance Mc,Rd = Weff,y * fyb/ƳM0
ƳM0=1.0 (partial
safety factor)
= 21.05 kNm
MEd = 0.09 <1
Mc,Rd
Hence Ok for bending
Joist section used in section 1c span 2 is 1000 S200-97 and intermediate
web stiffners 0.5m length from either side at center of support

15. Reference Output
Calculation
Buckling strength of member = Mb,Rd
χ LT = 1/(φLT+√Φ^2LT-λ^2LT)
ΦLT = 0.5*(1+αLT(λlt-0.2)+λ^2LT
αLT = 0.34
λLT = (Weff,y*fyb/Mcr)^0.5
Mcr = C1*(Π2
EIz/L2
)*(Iw/Iz+L2
GIt/Π2
EIz)
= 2.468 kNm
λLT = 2.920
ΦLT = 5.23
χ LT = 0.105
Mb,Rd = χLT*Weff,y*fyb/ƳM1
= 2.20
MEd/Mb,Rd = 0.90 <1
Hence Ok for buckling.
Design deflection for section 1c, span 2 joist
= 0.0026 m
= 0.1 inches
Length of joist = 240 inches
Deflection limit of joist = L/240 for total load
= 1.0 inches
Hence actual deflection <Deflection limit
Deflection check is Ok

16. Reference Output
Calculation
Section 1c ,Span 3 design check
Section 1C span3, Floor joist check
Span = 4.37 m (14'4'')
Design Bending moment MEd = 1.06 kNm SAP Modal result
Check of bending resistance Mc,Rd = Weff,y * fyb/ƳM0
ƳM0=1.0 (partial
safety factor)
= 9.63 kNm
MEd = 0.11 <1
Mc,Rd
Hence Ok for bending
Joist section used in section 1c span 3 is 1000S200-54 joist section and web
stiffner of 0.3m length is used at intermediate support

17. Reference Output
Calculation
Buckling strength of member = Mb,Rd
χ LT = 1/(φLT+√Φ^2LT-λ^2LT)
ΦLT = 0.5*(1+αLT(λlt-0.2)+λ^2LT
αLT = 0.34
λLT = (Weff,y*fyb/Mcr)^0.5
Mcr = C1*(Π2
EIz/L2
)*(Iw/Iz+L2
GIt/Π2
EIz)
= 2.344 kNm
λLT = 2.027
ΦLT = 2.87
χ LT = 0.204
Mb,Rd = χLT*Weff,y*fyb/ƳM1
= 1.97
MEd/Mb,Rd = 0.54 <1
Hence Ok for buckling.
Design deflection for section 1c, span 3 joist
= 0.0006 m
= 0.023 inches
Length of joist = 161 inches
Deflection limit of joist = L/240 for total load
= 0.671 inches
Hence actual deflection <Deflection limit
Deflection check is Ok

18. Reference Output
Calculation
Section 1d, 3 Span design check
Section 1d ,Span 1 design check
Section 1d span1, Floor joist check
Span = 5.58 m (18'4'')
Design Bending moment MEd = 2.97 kNm SAP Modal result
Check of bending resistance Mc,Rd = Weff,y * fyb/ƳM0
ƳM0=1.0 (partial
safety factor)
= 23.56 kNm
MEd = 0.126 <1
Mc,Rd
Hence Ok for bending
Joist section used in section 1d span 1 is 1000 S250-97 joist section

19. Reference Output
Calculation
Buckling strength of member = Mb,Rd
χ LT = 1/(φLT+√Φ^2LT-λ^2LT)
ΦLT = 0.5*(1+αLT(λlt-0.2)+λ^2LT
αLT = 0.34
λLT = (Weff,y*fyb/Mcr)^0.5
Mcr = C1*(Π2
EIz/L2
)*(Iw/Iz+L2
GIt/Π2
EIz)
= 4.627 kNm
λLT = 2.257
ΦLT = 3.40
χ LT = 0.169
Mb,Rd = χLT*Weff,y*fyb/ƳM1
= 3.97
MEd/Mb,Rd = 0.748 <1
Hence Ok for buckling.
Design deflection for section 1d, span 1 joist
= 0.004 m
= 0.157 inches
Length of joist = 212.6 inches
Deflection limit of joist = L/240 for total load
= 0.886 inches
Hence actual deflection <Deflection limit
Deflection check is Ok

20. Reference Output
Calculation
Section 1d ,Span 2 design check
Section 1d span2, Floor joist check
Span = 3.94 m (12'11'')
Design Bending moment MEd = 2.2 kNm SAP Modal result
Check of bending resistance Mc,Rd = Weff,y * fyb/ƳM0
ƳM0=1.0 (partial
safety factor)
= 9.63 kNm
MEd = 0.23 <1
Mc,Rd
Hence Ok for bending
Joist section used in section 1d span 2 is 1000S200-54 joist section and

21. Reference Output
Calculation
Buckling strength of member = Mb,Rd
χ LT = 1/(φLT+√Φ^2LT-λ^2LT)
ΦLT = 0.5*(1+αLT(λlt-0.2)+λ^2LT
αLT = 0.34
λLT = (Weff,y*fyb/Mcr)^0.5
Mcr = C1*(Π2
EIz/L2
)*(Iw/Iz+L2
GIt/Π2
EIz)
= 2.907 kNm
λLT = 1.820
ΦLT = 2.43
χ LT = 0.247
Mb,Rd = χLT*Weff,y*fyb/ƳM1
= 2.38
MEd/Mb,Rd = 0.92 <1
Hence Ok for buckling.
Design deflection for section 1d, span 2 joist
= 0.0009 m
= 0.035 inches
Length of joist = 153.5 inches
Deflection limit of joist = L/240 for total load
= 0.64 inches
Hence actual deflection <Deflection limit
Deflection check is Ok

22. Reference Output
Calculation
Section 1d ,Span 3 design check
Section 1d span3, Floor joist check
Span = 4.95 m (16'3'')
Design Bending moment MEd = 2.88 kNm SAP Modal result
Check of bending resistance Mc,Rd = Weff,y * fyb/ƳM0
ƳM0=1.0 (partial
safety factor)
= 21.05 kNm
MEd = 0.14 <1
Mc,Rd
Hence Ok for bending
Joist section used in section 1d span 3 is 1000S200-97joist section

23. Reference Output
Calculation
Buckling strength of member = Mb,Rd
χ LT = 1/(φLT+√Φ^2LT-λ^2LT)
ΦLT = 0.5*(1+αLT(λlt-0.2)+λ^2LT
αLT = 0.34
λLT = (Weff,y*fyb/Mcr)^0.5
Mcr = C1*(Π2
EIz/L2
)*(Iw/Iz+L2
GIt/Π2
EIz)
= 3.535 kNm
λLT = 2.440
ΦLT = 3.86
χ LT = 0.146
Mb,Rd = χLT*Weff,y*fyb/ƳM1
= 3.08
MEd/Mb,Rd = 0.94 <1
Hence Ok for buckling.
Design deflection for section 1d, span 3 joist
= 0.0039 m
= 0.153 inches
Length of joist = 181.1 inches
Deflection limit of joist = L/240 for total load
= 0.75 inches
Hence actual deflection <Deflection limit
Deflection check is Ok

24. Reference Output
Calculation
Roof floor joists
Section 1a
No of spans = 1
Floor joist type used = 1000 S 200-54
Spacing = 0.6 m
24'' OC Joist
spacing
Span = 13'4'' ft
Deflection check = OK
Bending resistance = OK
Buckling resistance = OK
Section 1b
No of spans = 2
Span 1 = 20'5'' ft
Floor joist type used = 1000S 250-97
Spacing = 0.6 m 24'' OC
Deflection check = OK
Bending resistance = OK
Buckling resistance = OK
Span 2 = 13'4'' ft
Floor joist type used = 1000S 200-54
Spacing = 0.6 m 24'' OC
Deflection check = OK
Bending resistance = OK
Buckling resistance = OK
Section 1C
No of spans = 3
Span 1 = 18'4'' ft
Floor joist type used = 1000 S200-97
Spacing = 0.6 m 24'' OC
Deflection check = OK
Bending resistance = OK
Buckling resistance = OK
Span 2 = 20'5'' ft
Floor joist type used = 1000 S200-97
Spacing = 0.6 m 24'' OC
Deflection check = OK
Bending resistance = OK
Buckling resistance = OK

25. Reference Output
Calculation
Span 3 = 14'4'' ft
Floor joist type used = 1000 S200-54
Spacing = 0.6 m 24'' OC
Deflection check = OK
Bending resistance = OK
Buckling resistance = OK
Section 1D
No of spans = 3
Span 1 = 18'4'' ft
Floor joist type used = 1000 S250-97
Spacing = 0.6 m 24'' OC
Deflection check = OK
Bending resistance = OK
Buckling resistance = OK
Span 2 = 12'11'' ft
Floor joist type used = 1000S200-54
Spacing = 0.6 m 24'' OC
Deflection check = OK
Bending resistance = OK
Buckling resistance = OK
Span 3 = 16'3'' ft
Floor joist type used = 1000S200-97
Spacinf = 0.6 m 24''
Deflection check = OK
Bending resistance = OK
Buckling resistance = OK

26. Reference Output
Calculation
Design Summary of AREA 1
Area 1 joist spacing is 24'' OC
1a 1000S 200-54
1b span 1 1000S 250-97
1b span 2 1000S 200-54
1c span 1 1000S 200-97 + Web stifner (0.5m)
web stifner at
support
1c span 2 1000S 200-97 + Web stifner (0.5m)
web stifner at
support
1c span 3 1000S 200-54 + web stifner (0.3m)
web stifner at
support
1d span 1 1000S 250-97
1d span 2 1000S 200-54
1d span 3 1000 S 200-97
Web stiffner at intermediate support
Notes
Design Carried out using Eurocode guidelines
Design code = EN 1993-1-3: 2006