3. Key Facts
• Used UPVC roof sheet
• Designed for Sylhet
• Used BNBC code 2006
• Computer Analysis of truss (Using GRASP)
4. Design Data:
Span = 40’
Rise = 10’
Span to rise ratio = 4:1
Slope = tan-1(6/20) = 26.5651 ⁰ (Degree)
Location: Sylhe, Basic Wind Speed 56.7 m/s = 204.12 km/hr
Exposure Category: A
Truss is supported on brick wall of height = 12 feet
5. Design Loads:
Dead load:
Self-weight of truss = 60 lb per ft. horizontal span of truss.
Sag rod + bracing = 1 psf. (approximately known)
UPVC sheet roofing = 340kg per 100 square meter = 1psf
Purlin (self-weight) = 1.5 psf. (assumed)
Wind load = according to BNBC 2014 (Bangladesh National Building Code 2014).
Snow load = not applicable for our country.
Design Method:
Design method followed here is AISC/ASD
Steel to be used: A36 (Yield stress (Fy = 36 ksi))
Electrode to be used: E60XX (electrode material tensile strength (FEXX) = 60 ksi)
6. Analysis and Design of Purlin for Dead Load:
Calculation of total dead load on purlin:
UPVC sheet roofing = 1 psf (known)
Self-weight of purlins = 1.5 psf (assumed but will be checked later)
Sagrod weight = negligible
Total dead load = 2.50 psf
Uniformly distributed load (UDL) on purlin, WDL = 2.50 psf × purlin spacing
= 2.50 psf × 7.453 ft. = 18.6325
Component of WDL in X direction, WDLx = WDL ×sinθ = 18.6325× sin(26.565) = 8.33 lb/ft
Component of WDL in Y direction, WDLy = WDL ×cosθ = 18.6325× cos(26.565) = 16.66 lb/ft
Purlin span = 25 feet for loading in Y direction (loading perpendicular to the plane of roof surface)
Purlin span = 12.5 feet + 12.5 feet for loading X direction (loading in the plane of roof surface)
7. Analysis and Design of Purlin for Dead Load:
Mxx = 1.3 Kip-ft, Myy = 0.163 Kip-ft
Allowable bending stress, Fb= 0.66Fy = 0.66 X 36 = 23.76 ksi
Section Sxx (inch3) Syy (inch3) Actual bending
stress (f) in ksi
Allowable
bending stress
(Fb) in ksi
Comments
C 3×4.1 1.10 0.202 23.86 23.76 Not OK
C 3×5 1.24 0.233 20.97 23.76 OK
Check self-weight of purlin:
For C 3×5 channel, self-weight is 5 lb/ft which is
equivalent to = 0.6708 psf
8. Wind Load Calculation (according to BNBC 2014)
Truss location: Sylhet
Vb= Basic wind speed in km/h = 204.12 km/h
B = Horizontal dimension of the building,
in meters measured normal to wind direction = 25 feet = 7.6219 meter.
L = Horizontal dimension of the building, in meters measured parallel to wind
direction = span of truss = 40 feet = 12.1951 meter.
H = average/mean height of the roof in meters = 17 feet = 5.1829 meter.
z = Height above the ground in meters
θ = Angle of the plane of roof from horizontal, degrees = 26.56510 (degree)
Cc= Velocity-to-pressure conversion co-efficient = 47.21 x 10-6
CI = Structure importance co-efficient = 1.00 for standard occupancy structures
CZ = Combined height and exposure co-efficient = 0.3897 for exposure A
Cz = 0.1879(z)0.4435 = 0.1879(5.1829)0.4435 =0.3897(>0.368)
CG = = Gust response co-efficient = 1.6257 exposure A
Cpe = External pressure co-efficient = -0.14345 for windward side
Cpe = External pressure co-efficient = -0.70 for leeward side
qz = Sustained wind pressure in kN/m2
Pz = Design wind pressure in kN/m2
qz = Cc CI CZ Vb
2 = (47.2x10-6 ) × (1) × (0.3897) × (204.12)2 = 0.766
kN/m2
Pz = CG Cpe qz
Design wind pressure for windward side:
Pz = -0.1786 kN/m2 = -3.72 psf
Design wind pressure for leeward side:
Pz = -0.872 kN/m2 = -18.20 psf
10. Calculation of UDL on purlin:
UDL on purlin on windward side = (design wind pressure on the windward side × purlin spacing)
= -3.72 psf × 7.4535 feet = - 27.73 lb/ft
UDL on purlin on leeward side = (design wind pressure on the leeward side × purlin spacing)
= -18.20 psf × 7.4535 feet = - 135.654 lb/ft
Since wind load acts perpendicular to the roof surface, these loads will be combined with the Y
component of the dead load (WDLy) to get the resultant load
Resultant load in Y direction Wy = WDLy + Pz = 16.66 lb/ft - 135.654 lb/ft = -118.994 lb/ft
Again Checking Purlin:
Mxx = -9.296 Kip-ft,
Myy = 0.163 Kip-ft (moment about Y axis remains the same)
Section Sxx (inch3) Syy (inch3)
Actual
bending
stress (f) in ksi
Allowable
bending
stress
(Fb) in ksi
Comments
C 3×5 1.24 0.233 81.566 23.76 Not OK
C6x8.2 4.38 0.492 21.49 23.76 OK
Finally selected channel for
purlins: C6x8.2; self weight
= 8.2 lb/ft = 1.100154 psf.
11. Analysis of the Truss: (Dead load calculation &
wind load calculation)
Dead load calculation
UPVC sheet roofing = 1 psf (known)
Self-weight of purlins = 1.5 psf (assumed value is greater than the purlin)
Sagrod + bracing = 1psf
Total dead load = 3.50 psf
Total 4.50 psf dead load = (3.50 psf) × (purlin spacing) × (bay)
= 3.50 psf × 7.4535 feet × 25 feet = 652.18 lb
Self-weight of the truss (assumed) = 60 lb/ft horizontal span of truss
The self-weight of the truss will be equally divided among the top chord and bottom chord.
Total 60 lb/ft = 30 lb/ft in top chord & 30 lb/ft in bottom chord