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CE 133 TIMBER DESIGN
Design of Purlins and Rafters
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INTRODUCTION
Purlins
A horizontal structural element (beam) found in a
roof whose purpose is to resist wind loads and
weight of the roof.
Can be made of timber or steel (C shapes)
Rafters
A sloped beam that supports the entire roof abuilding. It also
carries roof live loads and wind
loads.
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INTRODUCTION
Geometry of purlins and rafters
Pitch is the ratio of the height of the truss to the
length of the bottom chord
Roof Pitch angle
angle made by the rafter with
respect to horizontal
Spacing of purlins, s
Bay Spacing of truss
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INTRODUCTION
Loads resisted by purlins and rafters
Wind Load,
Roof Live Load,
Roof Dead Load,
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INTRODUCTION
Loads resisted by purlins
Roof Dead Load,
= ()
Where is the roof dead load in pressure
is the spacing of purlins on center
is the normal component of dead load
is the tangential component of dead load
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INTRODUCTION
Loads resisted by purlins
Roof Live Load,
= ( cos )
Where is the roof live load in pressure
is the spacing of purlins on center
is the normal component of dead load
is the tangential component of dead load
is the angle of the rafter or roof pitch angle
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INTRODUCTION
Loads resisted by purlins
Wind Load,
Normal Wind Load,
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INTRODUCTION
Loads resisted by purlins
Normal Wind Load,
= ()= 0
Where is the spacing of purlins on center
is the normal component of wind load
is the normal component of wind in psf
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INTRODUCTION
Total distributed load in the normal direction
Total distributed load in the tangential direction
WnRLnDntotaln
wwww
RLnDntotalt
www
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INTRODUCTION
Maximum shear and bending moment
Total shear stress and bending stress in thepurlin
2
max
LwV tt
2
max
LwV nn
8
2
max
LwM tt
8
2
max
LwM nn
22
nvtvv fff
nbtbb fff
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INTRODUCTION
Total deflection in beam
22 nttotal
y
tt
IE
Lw
'384
5 4
x
nn
IE
Lw
'384
5 4
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INTRODUCTION
Loads resisted by rafters
Roof Dead Load,
= ()
= cos= sin
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INTRODUCTION
Loads resisted by rafters
Roof Live Load,
Lh
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INTRODUCTION
Loads resisted by rafters
Normal Wind Load,
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INTRODUCTION
Total distributed load carried by the rafter
Maximum shear and bending moment in the
rafter
WnRLnDntotaln
wwww
AVfv 5.1 2
6bdMfv
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INTRODUCTION
Load Duration Factor,
Consider nomalized loads
Check for each directions (for purlins)
Higher normalized load will govern in the design
Load Combination Normalized Load
D+Lr 1.25 +
D+W 1.60 +
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INTRODUCTION
Check for bearing stress
If length of bearing is given, then check for
adequacy
If length of bearing is not given, determine the
required length of bearing
c
n
dreqb bF
R
l '',
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SAMPLE PROBLEM
Determine the adequacy of 2x4 purlins in thestructure below.
Also, design for the rafter.
Neglect the effect of overhang and the notches
at the support. Neglect deflections in the
design and analysis.
16 in
16 ft
4 ftBay Spacing = 8 ft
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SAMPLE PROBLEM
LO DS
D = 10 psf including weight of purlins
purlin: Lr = 21 psf; W = 23 psf (normal to roof)
rafter: Lr = 16 psf; W = 18 psf (normal to roof)
16 in
16 ft
4 ftBay Spacing = 8 ft
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SAMPLE PROBLEM
Conditions
Moist service condition
Normal temperature
Roof sheathing provided as lateral support to thepurlins and
blocking is provided for the rafter
Materials:
Species: Hem-Fir
Stress Grade: No. 1
Weight = 35 lb/ft^3
Property
= 1100
= 150
= 405
= 1,500,000
