DESIGN OF PRATT TRUSS
CALCULATION
OF LOADS
Span of truss = 10m
Slope of the sheeting = 30⁰
Number of panels = 3
(on both sides)
Spacing of truss = 1/3rd
– 1/5th of span
≈ 4m
3.1 LIVE LOAD
Imposed
load,
= 0.75 – (0.02 x 20)
= 0.35 KN/m2.
As per the IS code imposed load should
not be less than 0.4 KN/m .
≈ 0.4 KN/m2.
Imposed load in horizontal for trusses,
= 2/3rd of imposed load
= 2/3 x 0.4
= 0.267 KN/m2.
3.2 WIND LOAD
Basic wind speed at10m height for the
region “Coimbatore”,
Vb = 9m/sec
The design wind speed,
Vz = Vb
x k1 x k2 x k3
Where,
K1 =
1.0
K2 = 0.91
K3 =
1
Vz =
39
x 1 x 0.91 x 1
= 35.49 m/sec
Design wind pressure,
Pz = 0.6 x Vz2
=
0.6
x ( 35.49)2
=
755.72 N/m2.
Wind pressure on roof ,
F = (
Cpe - Cpi )Pz
|
WIND NORMAL TO THE RIDGE
|
TOTAL PRESSURE,
F = ( Cpe - Cpi )Pz
|
|
|
Windward
cpe = -0.2
|
Cpi= + 0.5
|
Cpe = - 0.5
|
|
-
529.025
|
-
226.716
|
|
|
Leeward = -0.5
|
-
755.72
|
0
|
|
WIND PARALLEL TO RIDGE
|
|
|
|
Windward
cpe = -0.8
|
-
982.436
|
-227.716
|
|
Leeward = -0.8
|
-
982.436
|
-227.716
|
Maximum wind load
= -
982.436 N/m2 uplift on both
slopes.
3.3 DEAD LOAD
Dead
load of sheeting = 112.7 N/m.
DESIGN OF PURLIN
Spacing of Purlin = 1.92m
Weight of 20 gauge (GI
sheets) = 112.7 N/m2
Load on purlin per meter
length
1.
Weight on sheeting = 112.7 x 1.9
= 216.38 N/m
2.
Weighting on purlin (assume) = 100
N/m
Total dead load = 316.38N/m
Imposed load = 400
x 1.92 Cos 30 ̊
= 665.11
N/m
Wind load = -
982.436 x 1.92
= 1886.27
N/m
Dead load + Imposed load = 316.38 + 665.11
= 981.48N/m
Dead load + wind load = 316.38 – 1886.27
= 1569.89
N/m
Since increase in permissible stress is 33.33%,
when wind load is considered, D.L + W.L may consider 33.33% less effective.
1886.27/1.33 = 1418.25 N/m
> 981.48
N/m
Maximum bending moment = w l 2 /10
= (141.25
x 4
2 )/10
= 2269.2Nm
= 2269.2KNmm
For angle
purlin Zx required = (2269.2 x 103)/1.65
= 13752.72mm3
= 13.752
x 103 mm3
Trial section;
Minimum
depth = L/45
=
4000/45
=
88.89
mm
Minimum
width = L/60
=
4000/60
=
66.67
mm
Providing
the section ISA 90 x 90 x 8 mm @ 108 N
Zx provided = Zx required
16.0 x 103 mm3 = 13.752 x 103
mm3
Hence it is safe
LOADS ON TRUSSES
1. Dead load (assumed to be acting on top
panel)
GI sheets = 112,7 x 4 x (10/cos30 ̊)
= 5205.4N
Purlin
= 108
x 4 x 8
= 3456N
Truss (assume 100 N/m2 )
= 100 x 4 x 10
= 4000N
Total dead load = 12661.4N
Dead load on end panel points.
= 2110.23/2
= 1055.11N
2.
Imposed
load:
For
truss on top panel point
= 267 x 4 x 10
= 10680N
Imposed
load per panel = 10680/6
= 1780N
Imposed
load at two ends = 890N
3.Wind
load on each of the top panel
Uplift
force:
= - 982.436 x 1.92 x 4
= -
7545.11N
Download
force = o
The
force due to imposed load are calculating by force due imposed load by dead
load .
= imposed load / dead load
= 1780 / 2110.23
Effective
length of Prismatic compression member
Column pin-ended
at Both Ends le
= 1.0l
Column
pin-ended at One End and fixed at the other le = 0.8l
Column
Fixed at Both Ends le = 0.65l
Column
Fixed at One End and on roller support at the other,le = 1.2l
Column
Fixed at One End and Free at the other le = 2l
Using limit state
method the design force are calculated as follows are
Principle rafter:
1.5
x – 19.44 = - 29.16KN (compression)
1.5x
– 32.74 = + 49.11KN (tension)
Main
tie:
1.5x
– 11.281 = - 16.92 (compression)
1.5x
– 16.829 = +25.24 (tension)
Main
sling:
1.5x
– 11.281 = -16.92KN (compression)
1.5
x +6.806 = +10.209KN (tension)
Main strut:
1.5
x -5.894 = - 8.841KN (compression)
1.5
x +10.066 = +15.099 (tension)
Minor
sling:
1.5
x – 8.671 = - 13KN (compression)
1.5
x +5.075 = + 7.612KN (tension)
Minor strut:
1.5
x – 3.888 = - 5.832KN (compression)
1.5
x + 6.643 = + 7.612KN (tension)
1.Principle
rafter:
Cross
area of angles, Ag = 2 x 568
= 1136mm2
Strength
governed by yielding:
(Ag.fy)/Ï’mo = (1136 x 250)/1.1
= 258.18KN
Compression
strength:
Effective
length(KL) = 0.7 x L
= 0.7
x 5.8
= 4060mm
Iy = 2[12.9 x 104 + 568(14.5 +
4)2
= 646796mm4
ry = √(646796/1136)
= 23.8mm
KL/r = 4060/23.8
= 170.58
For
KL/r = 170
; fcd = 48.1
N/mm2
For
KL/r = 180 ; fcd = 43.9
N/mm2
For
KL/r = 170.58
Fcd = 48.1 –[ ((170.58 – 170)/10)(48.1 – 43.9)]
= 47.85 N/mm2
Pd = 2 x 568 x 47.85
= 54.35 KN
2.
Main tie :
Design
load = - 16.92KN(compression)
= + 25.24KN(tension)
Tension
strength:
(Ag.fy)/Ï’mo = (1136 x 250)/1.1
= 258.18KN
Compression
strength:
Effective
length = 0.7
x 5000
KL = 3500mm
Iy = 2[12.9
x 104 + 568(14.5 + 4)2
= 646796mm4
ry = √(646796/1136)
= 23.8mm
KL/r = 3500/23.8
= 147.05
KL/r = 140 ; fcd = 66.2
KL/r = 150 ; fcd = 59.2
For
KL/r = 147.05
Fcd = 66.2
– [((147.05-140)/10) x (66.2 – 59.2)]
= 61.26 N/mm2
Pd = 2 x 568 x 61.26
= 60.59KN.
3.
Main sling:
Design load = -
16.92KN(compression)
= +10.209KN(tension)
Try
the section ISA 50 x 50 x 6mm
Tension strength = 258.18KN
Compression
strength:
Effective
length = 0.7
x 3330
KL = 2310mm
ry = √I/A
= 23.8mm
KL/r = 2310/23.8
= 97.05
N/mm2
KL/r = 90 ; fcd = 121 N/mm2
KL/r = 100 ; fcd = 107 N/mm2
For
KL/r = 97.05
Fcd = 121
– [((97.05 – 90)/10) x (121 – 107)
= 111.13 N/mm2
Pd = 2
x 568 x 111.13
= 126.24KN
4.Main
strut:
Design
loads = - 8.84KN
= + 15.099KN
Try
the section ISA 40 x 40 x 6mm
Tension strength:
(Ag.fy)/Ï’mo
Ag = 2
x 447
= 894mm2
= (894 x 250)/1.1
= 203.18KN
Tension
strength = 203.18KN
Compression
strength:
ffective
length KL = 0.7 x 1920
= 1344mm
From
steel table ry = 11.9mm
KL/r = 1344/11.9
= 112.94
KL/r = 110 ; fcd = 94.6 N/mm2
KL/r = 120 ; fcd = 83.7 N/mm2
For KL/r = 112.94
Fcd = 94.6 – [((112.94 – 110)/10) x (94.6 –
83.7)]
= 91.39 N/mm2
Pd = 894 x 91.39
= 81.70KN
5.
Minor sling:
Design loads = - 8,671KN
= +
5.075KN
Tension
strength = 203.18KN
Compressive strength:
Effective
length KL = 0.7
x 2560
= 1792mm
From
steel table ry = 11.9mm
KL/r = 1792/11.9
= 150.58
KL/r = 150 ; fcd = 59.3 N/mm2
KL/r = 160 ; fcd = 53.3 N/mm2
For KL/r = 150.58
Fcd = 59.2 – [((150.88 – 150)/10) x (59.2 –
53.3)]
= 58.68 N/mm2
Pd = 58.68
x 894
= 52.46KN
Since
the other members are not severely loaded, a single ISA 40 x 40 x 6mm will be
sufficient for minor sling and minor strut.
DESIGN OF JOINTS
Design
loads = 32.74KN
Factored
load = 1.5 x 32.74
= 49.11KN
Thickness
of weld:
1. Size
of the weld = ¾ x 8
= 6mm
2. At
top thickness should not exceed
S = t
– 1.5
= 8 – 1.5
= 6.5mm
Size
of weld = 6mm
Each
load carry a factored pull of
= 49.11/2
= 24.55KN
Let
lw be the total length of the weld required assuming normal weld
t = 0.7
x 6
design
strength of weld = Lw x t x (fu/√3) x (1/1.25)
= Lw
x 0.7 x 6 x (410/√3) x (1/1.25)
Equating it to the
factored load. We get,
24.55 x 103 = Lw x 0.7 x 6 x (410/√3) x
(1/1.25)
Lw = 30.86mm
Centre of gravity of
the section is at a distance 15mm from top
L1 x
1.5 = L2 x (50 – 15)
L1 = 35/15 x L2
L1 +
L2 = 30.86mm
L2 + (35/15) x L2 = 30.86
L2 = 9.26mm
≈ 10mm
L1 = 21.6mm
≈ 25mm
REFERENCE
1. S.S.
BHAVIKATTI ‘Design Of Steel Structures’2nd Edition, I.K.
International Publishing House Pvt.Ltd.
2. L.S.NEGI
‘Design Of Steel Structures’2nd Edition, Tata McGraw-Hill Publishing
Company Limited, New Delhi.
3. Dr.B.C.PUNMIA,
Ashok Kumar Jain, Arun Kumar Jain ‘Design
Of Steel Structures’2nd Edition, Lakshmi publications (P) Ltd, New
Delhi.
4. IS
800-2007, Indian Standard General Construction In Steel(Code Of Practice)Third
Revision, Bureau Indian Standards, New Delhi .
5. IS
875-1987 PART – I, Dead Load ( Code of
practice for design loads (other than earthquake) for buildings and structures,
Second Revision, Bureau Indian Standards, New Delhi.
6. IS
875-1987 PART – II Live Load (Code of
practice for design loads (other than earthquake) for buildings and
structures), Second Revision, Bureau
Indian Standards, New Delhi.
7.
IS 875-1987 PART - III Wind Load
(Code of practice for design loads (other than earthquake) for buildings
and structures), Second Revision, Bureau
Indian Standards, New Delhi.
