This document presents the design of a roof with a total length of 36 meters. It is divided into three equal spans of 12 meters each. The document provides details on the dimensions, materials, loads, and results of a structural analysis using stiffness matrix methods. The analysis calculated stresses on various parts of the structure, as well as deflections. All calculated stresses were found to be below allowable limits and all deflections were within allowable tolerances of 80 mm. A purlin design of cross-section Z300*72*78*20*3.0 was selected to be used in all three spans.

1. 1. Design data Code : 2
L=12m L=12m L=12m
L = 600 ( mm )
B = 1.159 ( m )
ROD : 1 (cm) No= 2 const
i = 50 ( % ) 58.86 q
tt
x = 58.86 q
tt
x = 58.86
anpha = 0.46 rad 117.71 qtt
y = 117.71 qtt
y = 117.71
2. Load
47 n1 = 1
57 n2 = 1
51.37 n3 = 1
Total roof load = 104
Total purlin load= 120.54
3. Material
Modulus of elasticity: 2,100,000 ( kG/cm2
)
Strength calculation: 2 ( kG/cm2)
4. Stress
- By structural analysis using Stiffness Matrix analysis are obtained
X axis
1 2 3 5 6 8 9
2354.24 -7180.43 -9416.96 2354.24 -7180.43 -7180.43 2354.24
Y axis
1 2 3 5 6 8 9
122502.28 -129563.16 -178758.58 77994.65 -138501.09 -129563.16 122502.28
Stress
1 2 3 5 6 8 9
1192.27 1555.16 1352.76 812.74 1631.38 1555.16 1192.27
s = kG/cm2
< [s] = ( kG/cm2
) OK
s = kG/cm
2
< [s] = ( kG/cm
2
) OK
s = kG/cm2
< [s] = ( kG/cm2
) OK
5. Deflection:
- By structural analysis using Stiffness Matrix analysis are obtained
X axis
Y axis
Total deflection
ResultPosition mid-first span mid-second span mid-final span
STRESS PASS & DEFLECTION PASS
[f] (mm) 80 80 80
Checking OK OK OK
Position mid-first span mid-second span mid-final span Final-span
value(mm) 43.056 22.611 43.056 Z300*72*78*20*3.0
Position mid-first span mid-second span mid-final span Mid-span
value(mm) -42.130 -20.795 -42.130 Z300*72*78*20*3.0
Select Purlin
Position mid-first span mid-second span mid-final span First-span
value(mm) -8.880 -8.880 -8.880 Z300*72*78*20*3.0
(kG/m
2
)
(kG/m )
Position 4
Value(kG/cm2) 1631.38 1352.76
Checking
- 1St Pulin 1555.16 2156.25
- Mid Pulin 1631.38 2156.25
- Final Pulin 1555.16 2156.25
Value(kg.cm) -138501.09 -178758.58
Position 4 7
7
Value(kg.cm) -7180.43 -9416.96
Position 4 7
Z PURLIN CALCULATION
L= 36 m
SPAN (m) FIRST MID FINAL
LAP(each side) Divide in to 2 parts:
DISTANCE (m) first-span Mid-span final-span
LENGHT(m) 12.00 12.00 12.00
PURLIN Z300*72*78*20*3.0 Z300*72*78*20*3.0 Z300*72*78*20*3.0
Wind load (kG/m2
)
( kG/m ) ( kG/m ) ( kG/m )
SLOPE: qtt
x =
ANGLE: q
tt
y =
Dead load (kG/m
2
)
Live load (kG/m2
)