This presentation defines, describes and presents the most effective and easy way to design a roof truss with all the necessary steps and calculations based on Allowable Stress Design. Soft-wares like MD Solids, Truss Analysis have been used. It is most convenient way to design a roof truss which is being the most important structural components of All types of steel bridges.

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UNIVERSITY OF ENGINEERING AND
TECHNOLOGY LAHORE
Steel structures lab
Design ASSIGNMENT
Submitted By:
HAMZA WAHEED
2015-CIV-111
Section C
Submitted To:
Dr. Qasim Shaukat Khan
DEPARTMENT OF CIVIL ENGINEERING
UET LAHORE

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Assignment#01: Design of Truss Roof
Givendata:
Galvanized Iron corrugated sheet as a roofing material
N0 = -750
R = N - N0 = 56 – (-750) (where N is the registration number)
Truss spacing = s = 2.5 + (R-700) / 50 (m)
Span of truss = L = 10 + (R-700) / 5 (m)
Solution:
R = N - N0 = 56 – (-750) = 806
Truss spacing = s = 2.5 + (R-700) / 50 (m) = 2.5 + (806-700) / 50 = 4.62 m
Span of truss = L = 10 + (R-700) / 5 (m) = 10 + (806-700) / 5 = 31.2 m
Panel Length = p = L / 8 = 31.2 / 8 = 3.9 m
Angle of top chord = Ө = tan-1 (1.3 / 15.6) = 4.764○
Dead load of roofing (GI corrugated sheet) = 15 kg / m2
Dead load of insulation boards = 5 kg / m2
Self-weight of purlins = 10 kg / m2
Self-weight of bracing elements = 5 kg / m2
Miscellaneous = 5 kg / m2
Total dead load excluding truss self-weight = 15 + 5 + 10 + 5 + 5 = 40 kg / m2

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Live load from design aids (for Ө = 4.764○) = 100 kg / m2
Total gravity load = w = 40 + 100 = 140 kg / m2
Now, using Thayer’s Formula:
Self-weight of truss = √
𝑤
𝑠
(
𝐿
8.5
+ 0.5) = √
140
4.62
(
31.2
8.5
+ 0.5) = 22.96kg / m2
Total dead load = 40 + 22.96 = 62.96 kg / m2
Leeward wind pressure = Pl = 1250 Cq = 1250 (-0.7) = -875 N / m2
Windward wind pressure = Pw = 1250 Cq = 1250 (-0.7) = -875 N / m2
(for Ө = 0○ to 9.5○, Cq =-0.7)
Panel dead load = PD = w * p * s = 62.96 * 3.9 * 4.62 * 9.81 / 1000 = 11.13 KN
Panel live load = PL = w * p * s = 100 * 3.9 * 4.62 * 9.81 / 1000 = 17.68 KN
Panel wind load on Leeward side = Plw = Pl * (p / cosӨ) * (s / 1000)
= (-875) * (3.9 / cos 4.764○) * (4.62 / 1000)
Plw = -15.82 KN
Panel wind load on Leeward side = Pww = Pw * (p / cos Ө) * (s / 1000)

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= (-875) * (3.9 / cos 4.764○) * (4.62 / 1000)
Pww = -15.82 KN
Unitgravityload analysis of truss roof:
Unitwindload analysisonhinge side oftruss roof:

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Unitwindload analysisonroller side oftrussroof:

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So, the values required for the table of forces are as follows:
Panel dead load = PD = 11.13 KN
Panel live load = PL = 17.68 KN
Panel wind load on Leeward side = Plw = -15.82 KN
Panel wind load on Leeward side = Pww = -15.82 KN
Table of forces
Member
Name
Member
Force
Under
Unit
Gravity
Load
Member
Force
Under
Unit Wind
Load On
Hinge
Side
Member
Force
Under
Unit
Wind
Load On
Roller
Side
(1.2Pd+1.6
Pl)*Col2
(1.2Pd+
0.5Pl)*
Col2+
(1.3Pww*
Col3)+
(1.3Plw)*
Col4
(1.2Pd+
0.5Pl)*
Col2+
(1.3Pww*
Col4)+
(1.3Plw)*
Col3
(0.9Pd)*
Col2+
(1.3Pww)
*Col3+
(1.3Plw)*
Col4
(0.9Pd)*Col2
+ (1.3Pww)*
Col4+
(1.3Plw)*
Col3
Max
Factored
Tension
Max
Factored
Compression
Remarks
AB 0 0.32 -0.32 0 0 0 0 0 0.000 0.000
BC 4.67 3.59 1.05 194.47748 8.22908 8.22908 -48.64685 -48.64685 194.477 48.647 Tension
L89X76X
7.9
CD 7.2 5 2.15 299.8368 12.7643 12.7643 -74.9245 -74.9245 299.837 74.925 Tension
L89X76X
7.9
DE 8.18 5.07 3.05 340.64792 14.56736 14.56736 -85.05686 -85.05686 340.648 85.057 Tension
L89X76X
7.9
EF 8.18 3.37 4.75 340.64792 14.56736 14.56736 -85.05686 -85.05686 340.648 85.057 Tension
L89X76X
7.9

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FG 7.2 2.47 4.68 299.8368 12.7643 12.7643 -74.9245 -74.9245 299.837 74.925 Tension
L89X76X
7.9
GH 4.67 1.37 3.27 194.47748 8.22908 8.22908 -48.64685 -48.64685 194.477 48.647 Tension
L89X76X
7.9
HI 0 0 0 0 0 0 0 0 0.000 0.000
IK -4 -1.03 -2.95 -166.576 -6.93132 -6.93132 41.78468 41.78468 41.785 166.576 Compr…
L89X76X
7.9
KM -4.68 -1.38 -3.32 -194.89392 -7.21708 -7.21708 49.78064 49.78064 49.781 194.894 Compr…
L89X76X
7.9
MO -7.22 -2.48 -4.82 -300.66968 -10.12332 -10.12332 77.80906 77.80906 77.809 300.670 Compr…
L102X89
X9.5
OQ -8.21 -3.38 -4.96 -341.89724 -10.70872 -10.70872 89.28087 89.28087 89.281 341.897 Compr…
L102X89
X9.5
QR -8.03 -4.13 -4.09 -334.40132 -9.18136 -9.18136 88.61601 88.61601 88.616 334.401 Compr…
L102X89
X9.5
RP -8.03 -4.09 -4.13 -334.40132 -9.18136 -9.18136 88.61601 88.61601 88.616 334.401 Compr…
L102X89
X9.5
PN -8.21 -4.96 -3.38 -341.89724 -10.70872 -10.70872 89.28087 89.28087 89.281 341.897 Compr…
L102X89
X9.5
NL -7.22 -4.82 -2.48 -300.66968 -10.12332 -10.12332 77.80906 77.80906 77.809 300.670 Compr…
L102X89
X9.5
LJ -4.68 -3.32 -1.38 -194.89392 -7.21708 -7.21708 49.78064 49.78064 49.781 194.894 Compr…
L89X76X
7.9
JA -4 -2.95 -1.03 -166.576 -6.93132 -6.93132 41.78468 41.78468 41.785 166.576 Compr…
L89X76X
7.9
JB 5.61 3.93 1.65 233.62284 9.76128 9.76128 -58.56291 -58.56291 233.623 58.563 Tension
L89X76X
7.9
LB -3.11 -2.18 -0.91 -129.51284 -5.48062 -5.48062 32.39607 32.39607 32.396 129.513 Compr…
L89X76X
7.9
LC 3.17 1.77 1.37 132.01148 5.78408 5.78408 -32.82335 -32.82335 132.011 32.823 Tension
L89X76X
7.9
NC -1.9 -1.06 -0.82 -79.1236 -3.50832 -3.50832 19.63178 19.63178 19.632 79.124 Compr…
L89X76X
7.9
ND 1.28 0.08 1.17 53.30432 2.70338 2.70338 -12.88574 -12.88574 53.304 12.886 Tension
L89X76X
7.9
PD -0.82 -0.05 -0.75 -34.14808 -1.74792 -1.74792 8.23886 8.23886 8.239 34.148 Compr…
L89X76X
7.9
PE -0.25 -1.29 1.02 -10.411 0.00382 0.00382 3.04857 3.04857 3.049 10.411 Compr…
L89X76X
7.9
RE 0.33 0.18 0.18 13.74252 -0.07908 -0.07908 -4.09815 -4.09815 13.743 4.098 Tension
L89X76X
7.9
QE -0.25 1.02 -1.29 -10.411 0.00382 0.00382 3.04857 3.04857 3.049 10.411 Tension
L89X76X

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7.9
QF -0.82 -0.75 -0.05 -34.14808 -1.74792 -1.74792 8.23886 8.23886 8.239 34.148 Compr…
L89X76X
7.9
OF 1.28 1.17 0.08 53.30432 2.70338 2.70338 -12.88574 -12.88574 53.304 12.886 Tension
L89X76X
7.9
OG -1.9 -0.82 -1.06 -79.1236 -3.50832 -3.50832 19.63178 19.63178 19.632 79.124 Compr…
L89X76X
7.9
MG 3.17 1.37 1.77 132.01148 5.78408 5.78408 -32.82335 -32.82335 132.011 32.823 Tension
L89X76X
7.9
MH -3.11 -0.91 -2.18 -129.51284 -5.48062 -5.48062 32.39607 32.39607 32.396 129.513 Compr…
L89X76X
7.9
KH 5.61 1.65 3.93 233.62284 9.76128 9.76128 -58.56291 -58.56291 233.623 58.563 Tension
L89X76X
7.9
Assignment#02: Design of purlin
Givendata:
Galvanized Iron corrugated sheet as a roofing material
N0 = -750
R = N - N0 = 56 – (-750) (where N is the registration number)
Truss spacing = s = 2.5 + (R-700) / 50 (m)
Span of truss = L = 10 + (R-700) / 5 (m)

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Solution:
R = N - N0 = 56 – (-750) = 806
Truss spacing = s = 2.5 + (R-700) / 50 (m) = 2.5 + (806-700) / 50 = 4.62 m
Span of truss = L = 10 + (R-700) / 5 (m) = 10 + (806-700) / 5 = 31.2 m
Panel Length = p = L / 8 = 31.2 / 8 = 3.9 m
Angle of top chord = Ө = tan-1 (1.3 / 15.6) = 4.764○
Dead load of roofing (GI corrugated sheet) = 25 kg / m2
Dead load of insulation boards = 6 kg / m2
Miscellaneous = 9 kg / m2
Live load from design aids (for Ө = 4.764○) = 100 kg / m2
Total Gravity Load = 25 + 6 + 9 + 100 = 140 kg / m2
Assumed self-weight of purlin = 0.15 * Total Gravity Load = 0.15 * 140 = 21 kg / m2
No. of truss panels = 8

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Dead Load = (25 * 6 * 9) * 3.9 * 9.81 + (21 * 3.9 * 9.81) = (1530.36 + 803.44) N/m
Live Load = (100 * 3.9 * 9.81) = 3825.9 N/m
Total Gravity Load = ((1530.36 + 3825.9) + 803.44)= (5356.26 + 803.44)N/m
Now
Mx = wcosӨ (S2/8)
= 6159.7cos4.764 (4.622/8)
Mx = 16377.61 N/m
My = wsinӨ (S2/8) + wsinӨ (S2/8)
= 5356.26sin4.764 (4.622/8) + 803.44sin4.764 (4.622/8)
My = (1186.87+ 178.03) N/m
Now For Channel Section:
Mx (assumed)= Mx + 15My
= 16377.61 + 15(1186.87 + 178.03)

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= 36851.11 Nm
Sx (Required) = Mx (assumed) / 0.66 Fy
= (36851.11 * 1000) / (0.66 * 250) = 223340 mm3 = 223.3 * 103 mm3
dmin. = S / 27.5 = 4.62 / 27.5 = 0.168 m = 168 mm
Trial Section No. 1:
C250 * 30
dmin. Check:
d = 254 mm >dmin. OK.
Applied Stress Check:
Sx = 259 * 103mm3
Sy = 21.6 * 103mm3
fb = Mx / Sx + My / (Sy/2) + My / Sy
= (16377.61 * 1000) / (259 * 103) + (1186.87 * 1000) / ((21.6/2) * 103) +
(178.03 * 1000) / (21.6 * 103)
fb = 181.37MPa>Fb NOT OK.
Trial Section No. 2:
C250 * 37
dmin. Check:
d = 254 mm >dmin. OK.
Applied Stress Check:
Sx = 298 * 103mm3
Sy = 24.3 * 103mm3
fb = Mx / Sx + My / (Sy/2) + My / Sy
= (16377.61 * 1000) / (298 * 103) + (1186.87 * 1000) / ((24.3/2) * 103) +
(178.03 * 1000) / (24.3 * 103)
fb = 159.97 MPa<Fb OK.

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Compactness Check:
bf / tf = 73 / 11.1 = 6.6 < 10.7 OK.
Check for self-weight of purlin:
Actual Self-Weight of purlin = 37 * 10 / 31.2 = 11.86 Kg / m2< 1.2 * 21 OK.
So the final section is
Now For W Section:
Mx (assumed)= Mx + 15My
= 16377.61 + 15(1186.87 + 178.03)
= 36851.11 Nm
Sx (Required) = Mx (assumed) / 0.66 Fy
= (36851.11 * 1000) / (0.66 * 250) = 223340 mm3 = 223.3 * 103 mm3
dmin. = S / 27.5 = 4.62 / 27.5 = 0.168 m = 168 mm
Trial Section No. 1:
W310 * 21
dmin. Check:
d = 302 mm >dmin. OK.
Applied Stress Check:
Sx = 244 * 103mm3
Sy = 19.5 * 103mm3
fb = Mx / Sx + My / (Sy/2) + My / Sy
= (16377.61 * 1000) / (244 * 103) + (1186.87 * 1000) / ((19.5/2) * 103) +
(178.03 * 1000) / (19.5 * 103)
fb = 197.98 MPa>Fb NOT OK.
C250 * 37

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Trial Section No. 2:
W250 * 28.4
dmin. Check:
d = 259 mm >dmin. OK.
Applied Stress Check:
Sx = 308 * 103mm3
Sy = 35.1 * 103mm3
fb = Mx / Sx + My / (Sy/2) + My / Sy
= (16377.61 * 1000) / (308 * 103) + (1186.87 * 1000) / ((35.1/2) * 103) +
(178.03 * 1000) / (35.1 * 103)
fb = 125.87MPa<Fb OK.
Compactness Check:
bf / tf = 102 / 10 = 10.2< 10.7 OK.
Check for self-weight of purlin:
Actual Self-Weight of purlin = 28.4 * 10 / 31.2 = 9.10 Kg / m2< 1.2 * 21 OK.
So the final section is
As angle Ө = 4.764○
; so there is no need to design the “sag rod”.
W250 * 28.4

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Assignment # 03: Design of corrugated sheet
Givendata:
Design of 75 * 20 Galvanized Iron corrugated sheet
Number of sheets required = ?
N0 = -750
R = N - N0 = 56 – (-750) (where N is the registration number)
Truss spacing = s = 2.5 + (R-700) / 50 (m)
Span of truss = L = 10 + (R-700) / 5 (m)
Solution:
R = N - N0 = 56 – (-750) = 806
Truss spacing = s = 2.5 + (R-700) / 50 (m) = 2.5 + (806-700) / 50 = 4.62 m
Span of truss = L = 10 + (R-700) / 5 (m) = 10 + (806-700) / 5 = 31.2 m
Panel Length = p = L / 8 = 31.2 / 8 = 3.9 m
Angle of top chord = Ө = tan-1 (1.3 / 15.6) = 4.764○
Assumed dead load of roofing = 20 kg / m2
Insulation not attached to the sheet
Miscellaneous load = 6 kg / m2
Live load from design aids (for Ө = 4.764○) = 100 kg / m2

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Live load from design aids (for Ө = 4.764○) = 100 kg / m (For 1 m wide strip)
Total Gravity Load w = 25 + (1/3)6 + 100 + 100 = 127 kg / m2
No. of truss panels = 8
Number of trusses = 9
Sheet projection beyond center of truss support = 300 mm
Total gravity load = w = 127 * 9.81 = 124 6 N/m2
w = 1246 N/m for 1 meter wide strip
Length of one sheet = L = (np / cos Ө ) + E
L1 = (1* 3.9 / cos 4.7640 ) + 0.2 = 4.11 m (Not possible because 1.5 m < L < 4 m)
L2 = (2 * 3.9 / cos 4.7640 ) + 0.2 = 8.03 m (Not possible because 1.5 m < L < 4 m)
L3 = (3 * 3.9 / cos 4.7640 ) + 0.2 = 11.94 m (Not possible because 1.5 m < L < 4 m)
As no length is satisfying so we increase the number of purlins. We introduce another purlim in
between the two purlins.

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Now;
Panel length = p = 3.9 / 2 = 1.95 m
So
L1 = (1* 1.95 / cos 4.7640 ) + 0.2 = 2.16 m
L2 = (2 * 1.95 / cos 4.7640 ) + 0.2 = 4.11 m (Not possible because 1.5 m < L < 4 m)
L3 = (3 * 1.95 / cos 4.7640 ) + 0.2 = 6.07 m (Not possible because 1.5 m < L < 4 m)
So length of one sheet = L = 2.25 m
Mmax = w * p2 / 8 = 1246 * 1.952 / 8 = 592.24 Nm
(Sx)Required = Mmax * 1000 / 0.6 Fy = 592.24 * 1000 / 0.6 * 250 = 3.95 * 103 mm3
Trial sheet gage 1 = 22; I = 4.23 * 104 mm4
Self weight of roofing check:
Actual self weight of roofing = 77.6 N/m2
Assumed self weight of roofing = 20 * 9.81 = 196.2 N/m2
Now
(1.35 * 77.6 = 104.76) < (1.2 * 196.2 = 235.44) OK.
Maximum deflection check:
Live load = wL = 100 Kg / m = 100 * 9.81 = 981 N/m = 0.981 N / mm
For simply supported sheet:
∆max = 0.013 wL * p4 / EI
∆max = 0.013 * 0.981 * 19504 / 200000 * 4.23 * 104 = 21.8 mm
For S.S Sheet with partial fixity at one end
∆max = 0.01 wL * p4 / EI
∆max = 0.01 * 0.981 * 19504 / 200000 * 4.23 * 104 = 16.8 mm
So
∆max = 21.8 mm
Now

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∆allowed= span / 90 = 1950 / 90 = 21.7 mm
So
∆max = 21.8 mm > ∆allowed= 21.7 mm NOT OK.
Trial sheet gage 2 = 20; I = 5.04 * 104 mm4
Self weight of roofing check:
Actual self weight of roofing = 91.5 N/m2
Assumed self weight of roofing = 20 * 9.81 = 196.2 N/m2
Now
(1.35 * 91.5 = 123.5) < (1.2 * 196.2 = 235.44) OK.
Maximum deflection check:
Live load = wL = 100 Kg / m = 100 * 9.81 = 981 N/m = 0.981 N / mm
For simply supported sheet:
∆max = 0.013 wL * p4 / EI
∆max = 0.013 * 0.981 * 19504 / 200000 * 5.04 * 104 = 18.3 mm
For S.S Sheet with partial fixity at one end
∆max = 0.01 wL * p4 / EI
∆max = 0.01 * 0.981 * 19504 / 200000 * 5.04 * 104 = 14.1 mm
So
∆max = 18.3 mm
Now
∆allowed= span / 90 = 1950 / 90 = 21.7 mm
So
∆max = 18.3 mm < ∆allowed= 21.7 mm OK.
Now
Number of sheet panels required for 100 m2 of roof area = N100 = 108 / C (L-E)
N100 = 108 / 585 (2160 – 200) = 87.21 = 88
Now
The inclined roof area on one side = A = ((L / 2 + Sheet projection) * (Nt – 1) * S) / cos Ө

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A = (31.2 / 2 + 0.3) * (9 – 1) * 4.62 / cos 4.7640
A = 589.7 m2
Number of sheets on one side = N1 = (A * N100) / 100
= 589.7 * 88 / 100
= 519
Total number of sheets = 2 * N1 = 2 * 519 = 1038
Final Results:
Gage of G.I Corrugated sheet = 20 gage
Standard Designation = 75 * 20
Sheet panel size = 0.7 * 2.25 m
Total number of sheets = 1038