Appendix C-Roof structure Design Calculations.pdf
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- Procure services to refurbish LGF Bathroom building works within the U. S. Embassy Juba, South Sudan
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About this file
This file is a detailed structural engineering calculation document for a roof structure design, including analysis of dead loads, live loads, and wind loads according to ASCE 7-16 standards. The calculations detail a monoslope roof structure measuring 9230mm x 6460mm with a 14-degree pitch and height to eaves of 4216mm, utilizing HSS (Hollow Structural Section) steel members. The document includes comprehensive load calculations with dead load derived from frame self-weight, live load of 0.96 KN/m2 for maintenance purposes, and wind load calculations using a basic wind speed of 62 m/s.
The analysis examines multiple load combinations and provides detailed member deflection calculations, axial forces, and stress analyses using AISC 360 15th Edition ASD method. The structure consists of top and bottom chords made of HSS 63.5x38.1x3.2 sections and internal members of HSS 88.9x38.1x3.2 sections, all using A501 steel with yield stress of 248 N/mm2. The calculations demonstrate that the design meets all required strength and deflection criteria, with the most critical compression member utilizing only 3.7% of its allowable capacity.
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1.0 DESIGN LOADING.
1.1 DEAD LOAD (𝑫)
The characteristic dead load was determined as the combined weight of the supporting frame, with the unit weights of the materials derived from ASCE 7-16 Table C3.1-2.
In this design, the dead loads due to the frame members self-weight were calculated automatically by modelling software.
1.2 LIVE LOAD (𝑳)
The characteristic live load for maintenance purposes was derived from ASCE 7-16 Table C4.3-1.
In this design, live loads was adopted as 0.96 KN/m2.
1.3 WIND LOAD (𝑾).
The characteristic wind load exerted on the roof structure was calculated in accordance with ASCE 7-16, Minimum Design Loads for Buildings and Other Structures.
This load was determined using the directional procedure outlined in ASCE 7-16, Clause 2.1.
The basic wind speed for the site was sourced from the OBO Building Code and Other Structures 2021, Table 1609, with value of 62 m/s.
Building data
Type of roof; Monoslope
Length of building; b = 9230 mm
Width of building; d = 6460 mm
Height to eaves; H = 4216 mm
Pitch of roof; 0 = 14.0 deg
Mean height; h = 5021 mm
General wind load requirements
Basic wind speed; V = 62.0 m/s
Risk category; II
Velocity pressure exponent coef (Table 26.6-1); Kd = 0.85
Ground elevation above sea level; zgl = 0 m
Ground elevation factor; Ke = exp(-0.000119 zgl/1m)= 1.00
Exposure category (cl 26.7.3); B
Enclosure classification (cl.26.12); Enclosed buildings
Internal pressure coef +ve (Table 26.13-1); GCpi_p = 0.18
Internal pressure coef –ve (Table 26.13-1); GCpi_n = -0.18
Gust effect factor; Gf = 0.85
Minimum design wind loading (cl.27.1.5); pmin_r = 0.38 kN/m2
Topography
Topography factor not significant; Kzt = 1.0
Velocity pressure equation; q = 0.6131N/m2 Kz Kzt Kd V2 / (1m/s)2;
Velocity pressures table z (mm) Kz (Table 26.10-1) qz (kN/m2)
4215 0.57 1.14
4572 0.57 1.14
5021 0.58 1.17
5828 0.61 1.22
Peak velocity pressure for internal pressure
Peak velocity pressure – internal (as roof press.); qi = 1.171 kN/m2
Pressures and forces
Net pressure; p = q Gf Cpe - qi GCpi;
Net force; Fw = p Aref;
Roof load case 1 - Wind 0, GCpi 0.18, -cpe
Zone Ref.
height (m)
Ext pressure coefficient cpe
Peak velocity pressure qp
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A (-ve) 5.02 -0.92 1.17 -1.12 61.45 -69.08
Total vertical net force; Fw,v = -67.03 kN
Total horizontal net force; Fw,h = -16.71 kN
Walls load case 1 - Wind 0, GCpi 0.18, -cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A 4.22 0.80 1.14 0.57 38.91 22.00
B 5.02 -0.50 1.17 -0.71 53.78 -38.11
C 5.02 -0.70 1.17 -0.91 32.44 -29.44
D 5.02 -0.70 1.17 -0.91 32.44 -29.44
Overall loading
Projected vertical plan area of wall; Avert_w_0 = b H = 38.91 m2
Projected vertical area of roof; Avert_r_0 = b d tan(0) = 14.87 m2
Minimum overall horizontal loading; Fw,total_min = pmin_w Avert_w_0 + pmin_r Avert_r_0 = 35.6 kN
Leeward net force; Fl = Fw,wB = -38.1 kN
Windward net force; Fw = Fw,wA = 22.0 kN
Overall horizontal loading; Fw,total = max(Fw - Fl + Fw,h, Fw,total_min) = 43.4 kN
Roof load case 2 - Wind 0, GCpi -0.18, -0cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A (+ve) 5.02 -0.18 1.17 0.03 61.45 1.94
Total vertical net force; Fw,v = 1.89 kN
Total horizontal net force; Fw,h = 0.47 kN
Walls load case 2 - Wind 0, GCpi -0.18, -0cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A 4.22 0.80 1.14 0.99 38.91 38.41
B 5.02 -0.50 1.17 -0.29 53.78 -15.43
C 5.02 -0.70 1.17 -0.49 32.44 -15.77
D 5.02 -0.70 1.17 -0.49 32.44 -15.77
Overall loading
Projected vertical plan area of wall; Avert_w_0 = b H = 38.91 m2
Projected vertical area of roof; Avert_r_0 = b d tan(0) = 14.87 m2
Minimum overall horizontal loading; Fw,total_min = pmin_w Avert_w_0 + pmin_r Avert_r_0 = 35.6 kN
Leeward net force; Fl = Fw,wB = -15.4 kN
Windward net force; Fw = Fw,wA = 38.4 kN
Overall horizontal loading; Fw,total = max(Fw - Fl + Fw,h, Fw,total_min) = 54.3 kN
Roof load case 3 - Wind 90, GCpi 0.18, -cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A (-ve) 5.02 -0.93 1.17 -1.14 16.72 -18.99
B (-ve) 5.02 -0.88 1.17 -1.09 16.72 -18.21
C (-ve) 5.02 -0.52 1.17 -0.73 28.02 -20.35
Total vertical net force; Fw,v = -55.83 kN
Total horizontal net force; Fw,h = 0.00 kN
Walls load case 3 - Wind 90, GCpi 0.18, -cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A1 4.57 0.80 1.14 0.57 29.28 16.56
A2 5.83 0.80 1.22 0.62 3.16 1.96
B 5.02 -0.41 1.17 -0.62 32.44 -20.22
C 5.02 -0.70 1.17 -0.91 38.91 -35.32
D 5.02 -0.70 1.17 -0.91 53.78 -48.81
Overall loading
Projected vertical plan area of wall; Avert_w_90 = d (H + d tan(0) / 2) = 32.44 m2
Projected vertical area of roof; Avert_r_90 = 0.00 m2
Minimum overall horizontal loading; Fw,total_min = pmin_w Avert_w_90 + pmin_r Avert_r_90 = 25.0 kN
Leeward net force; Fl = Fw,wB = -20.2 kN
Windward net force; Fw = Fw,wA_1 + Fw,wA_2 = 18.5 kN
Overall horizontal loading; Fw,total = max(Fw - Fl + Fw,h, Fw,total_min) = 38.7 kN
Roof load case 4 - Wind 90, GCpi -0.18, +cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A (+ve) 5.02 -0.18 1.17 0.03 16.72 0.53
B (+ve) 5.02 -0.18 1.17 0.03 16.72 0.53
C (+ve) 5.02 -0.18 1.17 0.03 28.02 0.89
Total vertical net force; Fw,v = 1.89 kN
Total horizontal net force; Fw,h = 0.00 kN
Walls load case 4 - Wind 90, GCpi -0.18, +cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A1 4.57 0.80 1.14 0.99 29.28 28.90
A2 5.83 0.80 1.22 1.04 3.16 3.30
B 5.02 -0.41 1.17 -0.20 32.44 -6.54
C 5.02 -0.70 1.17 -0.49 38.91 -18.91
D 5.02 -0.70 1.17 -0.49 53.78 -26.14
Overall loading
Projected vertical plan area of wall; Avert_w_90 = d (H + d tan(0) / 2) = 32.44 m2
Projected vertical area of roof; Avert_r_90 = 0.00 m2
Minimum overall horizontal loading; Fw,total_min = pmin_w Avert_w_90 + pmin_r Avert_r_90 = 25.0 kN
Leeward net force; Fl = Fw,wB = -6.5 kN
Windward net force; Fw = Fw,wA_1 + Fw,wA_2 = 32.2 kN
Overall horizontal loading; Fw,total = max(Fw - Fl + Fw,h, Fw,total_min) = 38.7 kN
Roof load case 5 - Wind 180, GCpi 0.18, -cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A (-ve) 5.02 -0.57 1.17 -0.77 61.45 -47.61
Total vertical net force; Fw,v = -46.20 kN
Total horizontal net force; Fw,h = -11.51 kN
Walls load case 5 - Wind 180, GCpi 0.18, -cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A1 4.57 0.80 1.14 0.57 42.20 23.86
A2 5.83 0.80 1.22 0.62 11.59 7.20
B 5.02 -0.50 1.17 -0.71 38.91 -27.57
C 5.02 -0.70 1.17 -0.91 32.44 -29.44
D 5.02 -0.70 1.17 -0.91 32.44 -29.44
Overall loading
Projected vertical plan area of wall; Avert_w_180 = b (H + d tan(0)) = 53.78 m2
Projected vertical area of roof; Avert_r_180 = b d tan(0) = 14.87 m2
Minimum overall horizontal loading; Fw,total_min = pmin_w Avert_w_180 + pmin_r Avert_r_180 = 47.1 kN
Leeward net force; Fl = Fw,wB = -27.6 kN
Windward net force; Fw = Fw,wA_1 + Fw,wA_2 = 31.1 kN
Overall horizontal loading; Fw,total = max(Fw - Fl - Fw,h, Fw,total_min) = 70.2 kN
Roof load case 6 - Wind 180, GCpi -0.18, -cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A (+ve) 5.02 -0.57 1.17 -0.35 61.45 -21.70
Total vertical net force; Fw,v = -21.06 kN
Total horizontal net force; Fw,h = -5.25 kN
Walls load case 6 - Wind 180, GCpi -0.18, -cpe
Zone Ref.
height (m)
(kN/m2)
Net pressure p
(kN/m2)
Area Aref (m2)
Net force Fw
(kN)
A1 4.57 0.80 1.14 0.99 42.20 41.66
A2 5.83 0.80 1.22 1.04 11.59 12.09
B 5.02 -0.50 1.17 -0.29 38.91 -11.17
C 5.02 -0.70 1.17 -0.49 32.44 -15.77
D 5.02 -0.70 1.17 -0.49 32.44 -15.77
Overall loading
Projected vertical plan area of wall; Avert_w_180 = b (H + d tan(0)) = 53.78 m2
Projected vertical area of roof; Avert_r_180 = b d tan(0) = 14.87 m2
Minimum overall horizontal loading; Fw,total_min = pmin_w Avert_w_180 + pmin_r Avert_r_180 = 47.1 kN
Leeward net force; Fl = Fw,wB = -11.2 kN
Windward net force; Fw = Fw,wA_1 + Fw,wA_2 = 53.7 kN
Overall horizontal loading; Fw,total = max(Fw - Fl - Fw,h, Fw,total_min) = 70.2 kN
1.4 DESIGN LOAD COMBINATIONS
The various load combinations outlined in ASCE 7-16, which encompass dead, wind, and earthquake loads, were utilized to ensure that the structures are robustly designed to endure a range of potential loading scenarios. Here are the basic load combinations involving dead (D), wind (W), and earthquake (E) loads, and other load cases not considered.
Load Cases and load combinations are listed below:
Load Cases Dead load Imposed load Wind load
Load Combinations
1.4D
𝐷 𝐿 𝑊
1.2D + 1.6L + 0.5Lr
1.2D + 1.6L + 0.5S
1.2D + 1.6L + 0.5R
1.2D + 1.0L + 1.6Lr
1.2D + 1.0L + 1.6S
1.2D + 1.0L + 1.6R
1.2D + 1.6Lr + 0.5W
1.2D + 1.6S + 0.5W
1.2D + 1.6R + 0.5W
1.2D + 1.0L + 0.5Lr + 1.0W
1.2D + 1.0L + 0.5S + 1.0W
1.2D + 1.0L + 0.5R + 1.0W
(1.2 + 0.2 x SDS)D + 1.0L + 0.2S + 1.0E
0.9D + 1.0W
(0.9 - 0.2 x SDS)D + 1.0E
2. DESIGN CALCULATIONS
2.1 ANALYSIS & DESIGN OF MEMBERS
Geometry
Geometry (m) - Steel (AISC)
Materials
Name Density Youngs Modulus Shear Modulus Thermal Coefficient
(kg/m3) kN/mm2 kN/mm2 C-1
Steel (AISC) 7849.0369382 199.9477038 77.2211822 0.000012
Sections
Name Area Moment of inertia Shear area parallel to
Major Minor Minor Major
(cm2) (cm4) (cm4) (cm2) (cm2)
Top - HSS 63.5x38.1x3.2
5.4 27.8 12.5 3.4 2
Bottom - HSS 63.5x38.1x3.2
5.4 27.8 12.5 3.4 2
Internal - HSS 88.9x38.1x3.2
6.9 65.3 17.1 4.8 2.1
Nodes
Node Co-ordinates Freedom Coordinate system
Spring
X Z X Z Rot. Name Angle X Z Rot.
(m) (m) () (kN/m) (kN/m) kNm/ 1 0 0 Fixed Fixed Free 0 0 0 0
2 1.615 0 Free Free Free 0 0 0 0
Node Co-ordinates Freedom Coordinate system
Spring
X Z X Z Rot. Name Angle X Z Rot.
(m) (m) () (kN/m) (kN/m) kNm/ 3 3.23 0 Free Free Free 0 0 0 0
4 4.845 0 Free Free Free 0 0 0 0
5 6.46 0 Free Fixed Free 0 0 0 0
6 0 0.01 Free Free Free 0 0 0 0
7 1.615 1.073 Free Free Free 0 0 0 0
8 3.23 2.135 Free Free Free 0 0 0 0
9 4.845 3.198 Free Free Free 0 0 0 0
10 6.46 4.26 Free Free Free 0 0 0 0
Elements
Element Length Nodes Section Material Releases Rotated
(m) Start End Start moment
End moment
Axial
1 1.615 1 2 Bottom - HSS 63.5x38.1x3.2
Steel (AISC) Fixed Fixed Fixed
2 1.615 2 3 Bottom - HSS 63.5x38.1x3.2
Steel (AISC) Fixed Fixed Fixed
3 1.615 3 4 Bottom - HSS 63.5x38.1x3.2
Steel (AISC) Fixed Fixed Fixed
4 1.615 4 5 Bottom - HSS 63.5x38.1x3.2
Steel (AISC) Fixed Fixed Fixed
5 1.933 6 7 Top - HSS 63.5x38.1x3.2
Steel (AISC) Fixed Fixed Fixed
6 1.933 7 8 Top - HSS 63.5x38.1x3.2
Steel (AISC) Fixed Fixed Fixed
7 1.933 8 9 Top - HSS 63.5x38.1x3.2
Steel (AISC) Fixed Fixed Fixed
8 1.933 9 10 Top - HSS 63.5x38.1x3.2
Steel (AISC) Fixed Fixed Fixed
9 0.01 1 6 Internal - HSS 88.9x38.1x3.2
Steel (AISC) Free Free Fixed
10 1.615 6 2 Internal - HSS 88.9x38.1x3.2
Steel (AISC) Free Free Fixed
11 1.073 2 7 Internal - HSS 88.9x38.1x3.2
Steel (AISC) Free Free Fixed
12 2.677 8 2 Internal - HSS 88.9x38.1x3.2
Steel (AISC) Free Free Fixed
13 2.135 3 8 Internal - HSS 88.9x38.1x3.2
Steel (AISC) Free Free Fixed
14 2.677 8 4 Internal - HSS 88.9x38.1x3.2
Steel (AISC) Free Free Fixed
15 3.198 4 9 Internal - HSS 88.9x38.1x3.2
Steel (AISC) Free Free Fixed
16 4.556 10 4 Internal - HSS 88.9x38.1x3.2
Steel (AISC) Free Free Fixed
Element Length Nodes Section Material Releases Rotated
(m) Start End Start moment
End moment
Axial
17 4.26 5 10 Internal - HSS 88.9x38.1x3.2
Steel (AISC) Fixed Fixed Fixed
Members
Name Elements
Start End
Bottom Chord 1 4
Top Chord 5 8
Internal Member-
11 11
Internal Member-
12 12
Internal Member-
13 13
Internal Member-
14 14
Internal Member-
15 15
Internal Member-
16 16
Internal Member-
17 17
Loading
Self weight included (Self weight x 1)
Self weight - Loading (kN/m)
Dead - Loading (kN)
Wind - Loading (kN)
Live - Loading (kN)
Load combination factors
Load combination
S el f w ei gh t
D ea d
W in d
L iv e
LC1 (Strength) 1.40 1.40
LC2 (Strength) 0.90 0.90 1.00
LC3 (Strength) 1.20 1.00 1.00
Node loads
Node Load case Force Moment
X Z
(kN) (kN) (kNm)
8 Dead 0.1 0.3 0
8 Wind 0.5 1.9 0
8 Live 2.2 8.8 0
Results
Total deflection
LC1 (Strength) - Total deflection
Member results
Load combination: LC1 (Strength)
Member Deflection Axial deflection
Pos Max Pos Min Pos Max Pos Min
(m) (mm) (m) (mm) (m) (mm) (m) (mm)
Bottom Chord 2.457 0.2 6.46 0 6.46 0 0 0
Top Chord 2.851 0.2 7.733 0 0 0 7.733 -0.1
Internal Member-
1.073 0.1 0 0 0 -0.2 1.073 -0.2
Internal Member-
1.303 0.4 2.677 0.1 2.677 0.1 0 0.1
Internal Member-
2.135 0 0 0 2.135 -0.2 0 -0.2
Internal Member-
1.311 0.3 2.677 0.1 0 0.2 2.677 0.1
Internal Member-
0 0 3.198 0 0 -0.2 3.198 -0.2
Internal Member-
2.343 1.1 0 -0.1 4.556 0.1 0 0.1
Internal Member-
0 0 4.26 -0.1 0 0 4.26 0
LC2 (Strength) - Total deflection
Load combination: LC2 (Strength)
Member Deflection Axial deflection
Pos Max Pos Min Pos Max Pos Min
(m) (mm) (m) (mm) (m) (mm) (m) (mm)
Bottom Chord 2.618 0.3 6.46 0 6.46 0.1 0 0
Top Chord 2.953 0.3 7.733 0 0 0 7.733 -0.1
Internal Member-
1.073 0.1 0 0 0 -0.3 1.073 -0.3
Internal Member-
1.19 0.4 2.677 0.2 2.677 0.2 0 0.2
Internal Member-
2.135 0.1 0 0 2.135 -0.3 0 -0.3
Internal Member-
1.255 0.2 2.677 0.1 0 0.3 2.677 0.2
Internal Member-
0 0.1 3.198 0 0 -0.2 3.198 -0.2
Internal Member-
2.446 0.8 0 -0.1 4.556 0.2 0 0.1
Internal Member-
0 0.1 4.26 -0.1 0 0 4.26 -0.1
LC3 (Strength) - Total deflection
Load combination: LC3 (Strength)
Member Deflection Axial deflection
Pos Max Pos Min Pos Max Pos Min
(m) (mm) (m) (mm) (m) (mm) (m) (mm)
Bottom Chord 2.582 0.4 6.46 0 6.46 0.1 0 0
Top Chord 2.931 0.4 7.733 0 0 0 7.733 -0.2
Internal Member-
1.073 0.1 0 0 0 -0.3 1.073 -0.3
Internal Member-
1.221 0.4 2.677 0.2 2.677 0.2 0 0.2
Internal Member-
2.135 0.1 0 0 2.135 -0.3 0 -0.3
Internal Member-
1.27 0.3 2.677 0.1 0 0.3 2.677 0.3
Internal Member-
0 0.1 3.198 0 0 -0.3 3.198 -0.3
Internal Member-
2.418 1 0 -0.1 4.556 0.2 0 0.1
Internal Member-
0 0.1 4.26 -0.1 0 0 4.26 -0.1
Node deflections
Node Deflection Rotation Co-ordinate system
X Z
(mm) (mm) ()
1 0 0 0.01381
2 0 0.2 0.00152
3 0 0.2 -0.00009
4 0 0.2 -0.00341
5 0 0 -0.006
6 0 0 0.01596
7 0.1 0.2 0.00011
8 0 0.2 -0.00053
9 0 0.2 -0.00237
10 -0.1 0 -0.00589
Load combination: LC2 (Strength)
Node Deflection Rotation Co-ordinate system
X Z
(mm) (mm) ()
1 0 0 0.01503
2 0 0.3 0.00437
3 0 0.3 -0.00017
4 0.1 0.2 -0.00619
5 0.1 0 -0.00733
6 0 0 0.01591
7 0.1 0.3 0.00297
8 0.1 0.3 -0.00098
9 0 0.2 -0.0051
10 -0.1 0.1 -0.00621
Load combination: LC3 (Strength)
Node Deflection Rotation Co-ordinate system
X Z
(mm) (mm) ()
1 0 0 0.01781
2 0 0.3 0.0046
3 0 0.3 -0.00019
4 0.1 0.3 -0.00681
5 0.1 0 -0.00852
6 0 0 0.01917
Node Deflection Rotation Co-ordinate system
X Z
(mm) (mm) ()
7 0.1 0.3 0.00291
8 0.1 0.3 -0.00107
9 0 0.3 -0.0055
10 -0.1 0.1 -0.0074
Total base reactions
Load case/combination Force
FX FZ
(kN) (kN)
LC1 (Strength) -0.1 2.9
LC2 (Strength) -0.5 3.7
LC3 (Strength) -0.5 4.3
Reactions
LC1 (Strength) - Local node reactions - Node: (Horiz (kN), Vert (kN), Mom (kNm))
Node Force Moment
Fx Fz My
(kN) (kN) (kNm)
1 -0.1 1.1 0
5 0 1.7 0
LC2 (Strength) - Local node reactions - Node: (Horiz (kN), Vert (kN), Mom (kNm))
Fx Fz My
(kN) (kN) (kNm)
1 -0.5 1.5 0
5 0 2.2 0
LC3 (Strength) - Local node reactions - Node: (Horiz (kN), Vert (kN), Mom (kNm))
Fx Fz My
(kN) (kN) (kNm)
1 -0.5 1.7 0
Fx Fz My
(kN) (kN) (kNm)
5 0 2.6 0
Element end forces
Load combination: LC1 (Strength)
Element Length Nodes Axial force Shear force Moment
(m) Start/End (kN) (kN) (kNm)
1 1.615 1 0.1 0 0
2 -0.1 -0.1 0
2 1.615 2 1.2 0 0
3 -1.2 0 0
3 1.615 3 1.2 0 0
4 -1.2 0 0
4 1.615 4 0 0 0
5 0 -0.1 0
5 1.933 6 -1.8 0 0
7 1.7 -0.1 0
6 1.933 7 -1.8 0 0
8 1.7 0 0
7 1.933 8 -0.7 0 0
9 0.7 0 0
8 1.933 9 -0.7 0 0
10 0.7 0 0
9 0.01 1 -1.1 0 0
6 1.1 0 0
10 1.615 6 1.5 -0.1 0
2 -1.5 -0.1 0
11 1.073 2 -0.2 0 0
7 0.1 0 0
12 2.677 8 0.6 -0.1 0
2 -0.5 -0.1 0
13 2.135 3 0.1 0 0
8 -0.3 0 0
14 2.677 8 -1 -0.1 0
4 1.1 -0.1 0
15 3.198 4 -0.3 0 0
9 0.1 0 0
16 4.556 10 1.8 -0.1 0
4 -1.5 -0.1 0
17 4.26 5 -1.7 0 0
10 1.4 0 0
Element Length Nodes Axial force Shear force Moment
(m) Start/End (kN) (kN) (kNm)
1 1.615 1 0.5 0 0
2 -0.5 0 0
2 1.615 2 2.4 0 0
3 -2.4 0 0
3 1.615 3 2.4 0 0
4 -2.4 0 0
4 1.615 4 0 0 0
5 0 0 0
5 1.933 6 -2.6 0 0
7 2.5 0 0
6 1.933 7 -2.6 0 0
8 2.5 0 0
7 1.933 8 -1.1 0 0
9 1.1 0 0
8 1.933 9 -1.1 0 0
10 1.1 0 0
9 0.01 1 -1.5 0 0
6 1.5 0 0
10 1.615 6 2.1 0 0
2 -2.1 0 0
11 1.073 2 -0.1 0 0
7 0.1 0 0
12 2.677 8 0.4 0 0
2 -0.3 0 0
13 2.135 3 0.1 0 0
8 -0.2 0 0
14 2.677 8 -2.5 0 0
4 2.6 0 0
15 3.198 4 -0.2 0 0
9 0.1 0 0
16 4.556 10 2.7 0 0
4 -2.5 0 0
17 4.26 5 -2.2 0 0
10 2 0 0
Load combination: LC3 (Strength)
Element Length Nodes Axial force Shear force Moment
(m) Start/End (kN) (kN) (kNm)
1 1.615 1 0.5 0 0
2 -0.5 0 0
2 1.615 2 2.7 0 0
3 -2.7 0 0
Element Length Nodes Axial force Shear force Moment
(m) Start/End (kN) (kN) (kNm)
3 1.615 3 2.7 0 0
4 -2.7 0 0
4 1.615 4 0 0 0
5 0 0 0
5 1.933 6 -2.9 0 0
7 2.8 0 0
6 1.933 7 -2.9 0 0
8 2.8 0 0
7 1.933 8 -1.3 0 0
9 1.2 0 0
8 1.933 9 -1.3 0 0
10 1.2 0 0
9 0.01 1 -1.7 0 0
6 1.7 0 0
10 1.615 6 2.4 -0.1 0
2 -2.4 -0.1 0
11 1.073 2 -0.2 0 0
7 0.1 0 0
12 2.677 8 0.5 -0.1 0
2 -0.4 -0.1 0
13 2.135 3 0.1 0 0
8 -0.2 0 0
14 2.677 8 -2.6 -0.1 0
4 2.7 -0.1 0
15 3.198 4 -0.3 0 0
9 0.1 0 0
16 4.556 10 3.1 -0.1 0
4 -2.8 -0.1 0
17 4.26 5 -2.5 0 0
10 2.2 0 0
Forces
Strength combinations - Moment envelope (kNm)
Strength combinations - Shear envelope (kN)
All combinations - Axial force envelope (kN)
Service combinations - Axial deflection envelope (mm)
Envelope - Strength combinations
Member Shear force Moment
Pos Max abs Pos Max Pos Min
(m) (kN) (m) (kNm) (m) (kNm)
Bottom Chord 1.615 -0.1 0.695 0 6.46 0 (min)
Top Chord 1.933 -0.1 0.813 0 3.866 0 (min)
Internal Member-
0 0 0 0 0 0
Member Shear force Moment
Pos Max abs Pos Max Pos Min
(m) (kN) (m) (kNm) (m) (kNm)
Internal Member-
0 0.1 (max abs) 1.339 0 0 0
Internal Member-
0 0 0 0 0 0
Internal Member-
0 0.1 (max abs) 1.339 0 0 0
Internal Member-
0 0 0 0 0 0
Internal Member-
0 0.1 (max abs) 2.278 0.1 (max) 0 0
Internal Member-
0 0 4.26 0 0 0 (min)
Envelope - All combinations
Member Axial force
Pos Max Pos Min
(m) (kN) (m) (kN)
Bottom Chord 4.845 0 1.615 -2.7
Top Chord 1.933 2.9 (max) 7.733 0.7
Internal Member-
0 0.2 1.073 0.1
Internal Member-
2.677 -0.3 0 -0.6
Internal Member-
0 -0.1 2.135 -0.3
Internal Member-
2.677 2.7 0 1
Internal Member-
0 0.3 3.198 0.1
Internal Member-
4.556 -1.5 0 -3.1 (min)
Internal Member-
0 2.5 4.26 1.4
Envelope - All combinations
Member Axial deflection
Pos Max Pos Min
(m) (mm) (m) (mm)
Bottom Chord 6.46 0.1 0 0
Top Chord 0 0 7.733 -0.2
Internal Member-
0 -0.2 1.073 -0.3
Internal Member-
2.677 0.2 0 0.1
Internal Member-
2.135 -0.2 0 -0.3 (min)
Member Axial deflection
Pos Max Pos Min
(m) (mm) (m) (mm)
Internal Member-
0 0.3 (max) 2.677 0.1
Internal Member-
0 -0.2 3.198 -0.3
Internal Member-
4.556 0.2 0 0.1
Internal Member-
0 0 4.26 -0.1
LC1 (Strength) - Moment (kNm)
LC1 (Strength) - Shear (kN)
LC1 (Strength) - Axial force (kN)
LC1 (Strength) - Axial deflection
Member Shear force Moment
Pos Max abs Pos Max Pos Min
(m) (kN) (m) (kNm) (m) (kNm)
Bottom Chord 1.615 -0.1 0.695 0 6.46 0
Top Chord 1.933 -0.1 0.813 0 3.866 0 (min)
Internal Member-
0 0 0 0 0 0
Internal Member-
0 0.1 (max abs) 1.339 0 0 0
Internal Member-
0 0 0 0 0 0
Internal Member-
0 0.1 (max abs) 1.339 0 0 0
Internal Member-
0 0 0 0 0 0
Internal Member-
0 0.1 (max abs) 2.278 0.1 (max) 0 0
Internal Member-
0 0 4.26 0 0 0
Load combination: LC1 (Strength)
Member Axial force
Pos Max Pos Min
(m) (kN) (m) (kN)
Bottom Chord 4.845 0 3.23 -1.2
Top Chord 1.933 1.8 (max) 7.733 0.7
Internal Member-
0 0.2 1.073 0.1
Member Axial force
(m) (kN) (m) (kN)
Internal Member-
2.677 -0.5 0 -0.6
Internal Member-
0 -0.1 2.135 -0.3
Internal Member-
2.677 1.1 0 1
Internal Member-
0 0.3 3.198 0.1
Internal Member-
4.556 -1.5 0 -1.8 (min)
Internal Member-
0 1.7 4.26 1.4
Load combination: LC1 (Strength)
Member Axial deflection
Pos Max Pos Min
(m) (mm) (m) (mm)
Bottom Chord 6.46 0 0 0
Top Chord 0 0 7.733 -0.1
Internal Member-
0 -0.2 1.073 -0.2
Internal Member-
2.677 0.1 0 0.1
Internal Member-
2.135 -0.2 0 -0.2 (min)
Internal Member-
0 0.2 (max) 2.677 0.1
Internal Member-
0 -0.2 3.198 -0.2
Internal Member-
4.556 0.1 0 0.1
Internal Member-
0 0 4.26 0
LC2 (Strength) - Moment (kNm)
LC2 (Strength) - Shear (kN)
LC2 (Strength) - Axial force (kN)
LC2 (Strength) - Axial deflection
Member Shear force Moment
Pos Max abs Pos Max Pos Min
(m) (kN) (m) (kNm) (m) (kNm)
Bottom Chord 6.46 0 0.75 0 6.46 0 (min)
Top Chord 1.933 0 0.859 0 7.733 0
Internal Member-
0 0 0 0 0 0
Member Shear force Moment
Pos Max abs Pos Max Pos Min
(m) (kN) (m) (kNm) (m) (kNm)
Internal Member-
2.677 0 (max abs) 1.339 0 0 0
Internal Member-
0 0 0 0 0 0
Internal Member-
2.677 0 (max abs) 1.339 0 0 0
Internal Member-
0 0 0 0 0 0
Internal Member-
0 0 (max abs) 2.278 0 (max) 0 0
Internal Member-
0 0 4.26 0 0 0 (min)
Load combination: LC2 (Strength)
Member Axial force
Pos Max Pos Min
(m) (kN) (m) (kN)
Bottom Chord 4.845 0 1.615 -2.4
Top Chord 1.933 2.6 (max) 7.733 1.1
Internal Member-
0 0.1 1.073 0.1
Internal Member-
2.677 -0.3 0 -0.4
Internal Member-
0 -0.1 2.135 -0.2
Internal Member-
2.677 2.6 (max) 0 2.5
Internal Member-
0 0.2 3.198 0.1
Internal Member-
4.556 -2.5 0 -2.7 (min)
Internal Member-
0 2.2 4.26 2
Load combination: LC2 (Strength)
Member Axial deflection
Pos Max Pos Min
(m) (mm) (m) (mm)
Bottom Chord 6.46 0.1 0 0
Top Chord 0 0 7.733 -0.1
Internal Member-
0 -0.3 1.073 -0.3
Internal Member-
2.677 0.2 0 0.2
Internal Member-
2.135 -0.3 0 -0.3 (min)
Member Axial deflection
(m) (mm) (m) (mm)
Internal Member-
0 0.3 (max) 2.677 0.2
Internal Member-
0 -0.2 3.198 -0.2
Internal Member-
4.556 0.2 0 0.1
Internal Member-
LC3 (Strength) - Moment (kNm)
LC3 (Strength) - Shear (kN)
LC3 (Strength) - Axial force (kN)
LC3 (Strength) - Axial deflection
Member Shear force Moment
Pos Max abs Pos Max Pos Min
(m) (kN) (m) (kNm) (m) (kNm)
Bottom Chord 6.46 0 0.735 0 6.46 0 (min)
Top Chord 1.933 0 0.846 0 7.733 0
Internal Member-
0 0 0 0 0 0
Internal Member-
2.677 0.1 (max abs) 1.339 0 0 0
Internal Member-
0 0 0 0 0 0
Internal Member-
2.677 0.1 (max abs) 1.339 0 0 0
Internal Member-
0 0 0 0 0 0
Internal Member-
0 0.1 (max abs) 2.278 0.1 (max) 0 0
Internal Member-
0 0 4.26 0 0 0 (min)
Load combination: LC3 (Strength)
Member Axial force
Pos Max Pos Min
(m) (kN) (m) (kN)
Bottom Chord 4.845 0 1.615 -2.7
Top Chord 1.933 2.9 (max) 7.733 1.2
Internal Member-
0 0.2 1.073 0.1
Member Axial force
(m) (kN) (m) (kN)
Internal Member-
2.677 -0.4 0 -0.5
Internal Member-
0 -0.1 2.135 -0.2
Internal Member-
2.677 2.7 0 2.6
Internal Member-
0 0.3 3.198 0.1
Internal Member-
4.556 -2.8 0 -3.1 (min)
Internal Member-
0 2.5 4.26 2.2
Load combination: LC3 (Strength)
Member Axial deflection
Pos Max Pos Min
(m) (mm) (m) (mm)
Bottom Chord 6.46 0.1 0 0
Top Chord 0 0 7.733 -0.2
Internal Member-
0 -0.3 1.073 -0.3
Internal Member-
2.677 0.2 0 0.2
Internal Member-
2.135 -0.3 0 -0.3 (min)
Internal Member-
0 0.3 (max) 2.677 0.3
Internal Member-
0 -0.3 3.198 -0.3
Internal Member-
4.556 0.2 0 0.1
Internal Member-
STEEL MEMBER DESIGN (AISC 360)
In accordance with AISC360 15th Edition published 2016 using the ASD method
Safety factors Shear; v = 1.67
Flexure; b = 1.67
Tensile yielding; t,y = 1.67
Tensile rupture; t,r = 2.00
Compression; c = 1.67
Design section 1
Section details
Section type; HSS 88.9x38.1x3.2 (AISC 15th Edn (v15.0))
ASTM steel designation; A501
Steel yield stress; Fy = 248 N/mm2
Steel tensile stress; Fu = 400 N/mm2
Modulus of elasticity; E = 199948 N/mm2
Analysis results
Required compressive strength; Pr = 2.2 kN
Restraint spacing
Major axis lateral restraint; Lx = 1615 mm
Minor axis lateral restraint; Ly = 1615 mm
Torsional restraint; Lz = 1615 mm
Classification of sections for local buckling - Section B4
Classification of flanges in flexure - Table B4.1b (case 17)
Width to thickness ratio; (bf - 3 t) / t = 9.92
Limiting ratio for compact section; pff = 1.12 [E / Fy] = 31.79
Limiting ratio for non-compact section; rff = 1.40 [E / Fy] = 39.74; Compact
Classification of web in flexure - Table B4.1b (case 19)
Width to thickness ratio; (d - 3 t) / t = 27.14
Limiting ratio for compact section; pwf = 2.42 [E / Fy] = 68.69
Limiting ratio for non-compact section; rwf = 5.70 [E / Fy] = 161.78; Compact
Section is compact in flexure
Classification of flanges in uniform compression - Table B4.1a (case 6)
Width to thickness ratio; (bf - 3 t) / t = 9.92
Limiting ratio for non-compact section; rfc = 1.40 [E / Fy] = 39.74; Nonslender
Classification of web in uniform compression - Table B4.1a (case 6)
Width to thickness ratio; (d - 3 t) / t = 27.14
Limiting ratio for non-compact section; rwc = 1.40 [E / Fy] = 39.74; Nonslender
Section is nonslender in compression
Design of members for compression - Chapter E
Required compressive strength; Pr = 2.2 kN
Slenderness limitations and effective length - Section E2
Unbraced length; Lb,x = 1615 mm
Effective length factor; Kx = 1.00
Effective length; Lcb,x = Kx Lb,x = 1615 mm
Column slenderness; x = Lcb,x / rx = 52.606
Major axis column slenderness ratio does not exceed recommended limit of 200
Slenderness limitations and effective length - Section E2
Unbraced length; Lb,y = 1615 mm
Effective length factor; Ky = 1.00
Effective length; Lcb,y = Ky Lb,y = 1615 mm
Column slenderness; y = Lcb,y / ry = 102.866
Minor axis column slenderness ratio does not exceed recommended limit of 200
Flexural buckling of members without slender elements - Section E3
Elastic critical buckling stress - eq E3-4; Fe,x = 2 E / (Lcb,x / rx)2 = 713 N/mm2
Flexural buckling stress - eq E3-2; Fcr,x = [0.658F y / F e,x] Fy = 215 N/mm2
Nominal compressive strength for flexural buckling - eq E3-1;
Pn,fb,x = Fcr,x A = 148 kN
Elastic critical buckling stress - eq E3-4; Fe,y = 2 E / (Lcb,y / ry)2 = 186 N/mm2
Flexural buckling stress - eq E3-2; Fcr,y = [0.658F y / F e,y] Fy = 142 N/mm2
Nominal compressive strength for flexural buckling - eq E3-1;
Pn,fb,y = Fcr,y A = 98.1 kN
Allowable compressive strength - E1
Nominal compressive strength; Pn = min(Pn,fb,x, Pn,fb,y) = 98.1 kN
Allowable compressive strength; Pc = Pn / c = 58.8 kN
Pr / Pc = 0.037
PASS - Nominal compressive strength exceeds required compressive strength
File details come from the government source that posted it. Updated .