Steel Frame Design Manual

Norsok N-004 2013

 Norsok N-004 2013
Steel Frame Design Manual

for

Steel Frame Design Manual

ISO SAP112118M20 Rev. 0 November 2018

Proudly developed in the United States of America
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 Contents

1 Introduction 1

1.1 Units 1

1.2 Axes Notation 1

1.3 Symbols 1

2 Member Design 4

2.1 Tension Check 4

2.2 Compression Check 4

2.3 Flexure Check 5

2.4 Shear Check 6

2.5 Hoop Buckling Check 6

2.6 Axial Tension and Bending Check 7

2.6.1 Method A 7
2.6.2 Method B 8

2.7 Axial Compression and Bending Check 9

2.7.1 Method A 9
2.7.2 Method B 10

2.8 Interaction Shear and Bending Moment 11

2.9 Interaction Shear, Bending, and Torsional Moment 11

3 Joint Design 12

3.1 Joint Geometry 12

i
Steel Frame Design Norsok N-004 2013 Introduction

3.2 Characteristic Resistances 13

3.3 Axial and Bending Check 14

3.4 Overlapping Joints 14

4 References 15

ii
 1 Introduction

This manual describes the steel frame design algorithms in the software for the Norsok Standard
N-004 2013 (Standards Norway, 2013) design code. The design algorithms in the software for
Norsok N-004 cover ultimate limit state (ULS) checks for typical structural elements used in
offshore steel structures, as detailed in this manual. Such elements are tubular members and
tubular joints. For other types of structural elements, the software uses European Standard EN
1993-1-1 2005 (European Committee for Standardization, 2005). Requirements of the code not
documented in this manual should be considered using other methods.

This manual documents the design details for tubular sections having thickness t ≥ 6mm, D/t <
120.

It is important to read this entire manual before using the design algorithms to become familiar
with any limitations of the algorithms or assumptions that have been made.

1.1 Units
The Norsok N-004 design code is based on Newton, millimeter, and second units and so is this
manual, unless noted otherwise. Any units, imperial, metric, or MKS may be used in the
software in conjunction with Norsok N-004 design.

1.2 Axes Notation

The software analysis results refer to the member local axes system, which consists of the 2-2
axis and the 3-3 axis. The Norsok N-004 design code refers to y-y and z-z axes, which are
equivalent to the software 3-3 and 2-2 axes, respectively. These notations may be used
interchangeably in the design algorithms, although every effort has been made to use the design
code convention where possible.

1.3 Symbols
The following table provides a list of the symbols used in this manual, along with a short
description. Where possible, the same symbol from the design code is used in this manual.

Units 1
Steel Frame Design Norsok N-004 2013 Introduction

A Gross area of cross section, mm2

A Shear area, mm2
Ce Critical elastic buckling coefficient = 0.3
Cm Moment diagram factor
D Outside diameter, mm
E Modulus of elasticity, 2.1x105 N/mm2
fc Characteristic axial compressive strength, N/mm2
f ch,Rd Design axial compressive strength in the presence of external
hydrostatic pressure, N/mm2
f cl Characteristic local buckling strength, N/mm2
f cle Characteristic elastic local buckling strength, N/mm2
f cl,Rd Design local buckling strength, N/mm2
fE Smaller Euler buckling strength in y or z direction, N/mm2
fh Characteristic hoop buckling strength, N/mm2
f he Elastic hoop buckling strength, N/mm2
f h,Rd Design hoop buckling bending strength, N/mm2
fm Characteristic bending strength, N/mm2
f mh,Rd Design bending resistance in the presence of external hydrostatic
pressure, N/mm2
f th,Rd Design axial tensile resistance in the presence of external
hydrostatic pressure, N/mm2
fy Characteristic yield strength, N/mm2
f y,b Characteristic yield strength of brace, N/mm2
f y,c Characteristic yield strength of chord, N/mm2
i Radius of gyration
IP Polar moment of inertia, mm4
k Effective length factor
l Longer unbraced length in 2 or 3 direction, mm
L Length between stiffening rings, diaphragms, or end connections
M Rd Design bending resistance, N-mm
M Sd Design bending moment, N-mm
M T,Rd Design torsional resistance, N-mm
M T,Sd Design torsional moment, N-mm
M y,Rd Design in-plane bending resistance, N-mm
M y,Sd Design in-plane bending moment, N-mm

Symbols 2
Steel Frame Design Norsok N-004 2013 Introduction

M z,Rd Design out-of-plane bending resistance, N-mm

M z,Sd Design out-of-plane bending moment, N-mm
N c,Rd Design compression resistance, N
N cl,Rd Design axial local buckling resistance, N
N Ey Euler buckling strength about y-axis, N
N Ez Euler buckling strength about z-axis, N
N Rd Design axial resistance, N
N Sd Design axial force, N
N t,Rd Design tension resistance, N
p Sd Design hydrostatic pressure, N/mm2
Qf Chord action factor
Qg Gap factor
Qu Strength factor
Qβ Geometric factor
t Wall thickness, mm
V Rd Design shear resistance, N
V Sd Design shear force, N
W Elastic section modulus, mm3
Z Plastic section modulus, mm3
γΜ Partial factor for resistance of cross-sections
𝜆𝜆̅ Column slenderness parameter
µ Geometric parameter
σ a,Sd Design axial stress, N/mm2
σ ac,Sd Member axial stress, N/mm2
σ c,Sd Design axial compressive stress, N/mm2
σ my,Sd Design in-plane bending stress, N/mm2
σ mz,Sd Design out-of-plane bending stress, N/mm2
σ p,Sd Design hoop stress due to hydrostatic pressure, N/mm2
σ q,Sd Capped end design axial compressive stress due to external
hydrostatic pressure, N/mm2

Symbols 3
 2 Member Design

This chapter provides the details of the structural steel design and stress check algorithms that
are used for tubular member design and checking at each output station in accordance with
Norsok N-004.

Tubular members subjected solely to axial tension, axial compression, bending, shear, or
hydrostatic pressure are designed in accordance with Norsok N-004 Sections 6.3.2 to 6.3.6.
Tubular members subjected to combined loads without hydrostatic pressure are designed in
accordance with Norsok N-004 Section 6.3.8. Tubular members subjected to combined loads
with hydrostatic pressure are designed in accordance with Norsok N-004 Section 6.3.9.

2.1 Tension Check

Members subjected to axial tension are checked for the following condition:
𝑁𝑁𝑆𝑆𝑆𝑆
≤ 1.0 [Norsok 6.3.2]
𝑁𝑁𝑡𝑡,𝑅𝑅𝑅𝑅

The design tension resistance, N t,Rd , is defined as:

𝐴𝐴𝑓𝑓𝑦𝑦
𝑁𝑁𝑡𝑡,𝑅𝑅𝑅𝑅 = [Norsok 6.3.2]
𝛾𝛾𝑀𝑀

2.2 Compression Check

Members subjected to axial compression are checked for the following condition:
𝑁𝑁𝑆𝑆𝑆𝑆
≤ 1.0 [Norsok 6.3.3]
𝑁𝑁𝑐𝑐,𝑅𝑅𝑅𝑅

The design compression resistance, N c,Rd , is defined as:

𝐴𝐴𝑓𝑓𝑐𝑐
𝑁𝑁𝑐𝑐,𝑅𝑅𝑅𝑅 = [Norsok 6.3.3]
𝛾𝛾𝑀𝑀

Tension Check 4
Steel Frame Design Norsok N-004 2013 Member Design

In the absence of hydrostatic pressure, the characteristic axial compressive strength for
cylindrical members is the smaller of the in-plane or out-of-plane buckling strength computed
from the following equations.

The characteristic axial compressive strength, f c , is defined as:

�1.0 − 0.28𝜆𝜆2̅ �𝑓𝑓𝑐𝑐𝑐𝑐 for 𝜆𝜆̅ ≤ 1.34

𝑓𝑓𝑐𝑐 = �0.9 [Norsok Eq. 6.3 and 6.4]
𝑓𝑓𝑐𝑐𝑐𝑐 for 𝜆𝜆̅ > 1.34
𝜆𝜆2̅

𝑓𝑓𝑐𝑐𝑐𝑐 𝑘𝑘𝑘𝑘 𝑓𝑓𝑐𝑐𝑐𝑐

𝜆𝜆̅ = � = � [Norsok Eq. 6.5]
𝑓𝑓𝐸𝐸 𝜋𝜋𝜋𝜋 𝐸𝐸

The characteristic local buckling strength, f cl , is defined as:

𝑓𝑓𝑦𝑦
⎧𝑓𝑓𝑦𝑦 for ≤ 0.170
⎪ 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐
⎪
𝑓𝑓𝑦𝑦 𝑓𝑓𝑦𝑦 [Norsok Eq. 6.6,
𝑓𝑓𝑐𝑐𝑐𝑐 = �1.047 − 0.274 � 𝑓𝑓 for 0.170 < ≤ 1.911
⎨ 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 𝑦𝑦 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 6.7, and 6.8]
⎪
⎪𝑓𝑓 𝑓𝑓𝑦𝑦
for > 1.911
⎩ 𝑐𝑐𝑐𝑐𝑐𝑐 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐
𝑡𝑡
𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 = 2𝐶𝐶𝑒𝑒 E
𝐷𝐷
𝑓𝑓𝑦𝑦
For > 0.170 the cylindrical member is a class 4 cross-section and the γ M value is taken
𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐
from Norsok Section 6.3.7, equation 6.22.

2.3 Flexure Check

Members subjected to bending are checked for the following condition:
𝑀𝑀𝑆𝑆𝑆𝑆
≤ 1.0 [Norsok 6.3.4]
𝑀𝑀𝑅𝑅𝑅𝑅

The design moment resistance, M Rd , is defined as:

𝑓𝑓𝑚𝑚 𝑊𝑊
𝑀𝑀𝑅𝑅𝑅𝑅 = [Norsok 6.3.4]
𝛾𝛾𝑀𝑀

The characteristic bending strength, f m , is defined as:

Flexure Check 5
Steel Frame Design Norsok N-004 2013 Member Design

𝑍𝑍 𝑓𝑓𝑦𝑦 𝐷𝐷
⎧ 𝑓𝑓 for ≤ 0.0517
⎪ 𝑊𝑊 𝑦𝑦 𝐸𝐸𝐸𝐸
⎪ 𝑓𝑓𝑦𝑦 𝐷𝐷 𝑍𝑍 𝑓𝑓𝑦𝑦 𝐷𝐷
𝑓𝑓𝑚𝑚 = �1.13 − 2.58 � �� � � 𝑓𝑓 for 0.0517 < ≤ 0.1034
𝐸𝐸𝐸𝐸 𝑊𝑊 𝑦𝑦 𝐸𝐸𝐸𝐸
⎨
⎪ 𝑓𝑓 𝐷𝐷 𝑍𝑍 𝑓𝑓𝑦𝑦 𝐷𝐷 𝑓𝑓𝑦𝑦
⎪�0.94 − 0.76 � 𝑦𝑦 �� � � 𝑓𝑓𝑦𝑦 for 0.1034 < ≤ 120
⎩ 𝐸𝐸𝐸𝐸 𝑊𝑊 𝐸𝐸𝐸𝐸 𝐸𝐸

[Norsok Eq. 6.10, 6.11, and 6.12]

where, W and Z are taken from the frame section property, not the code.
𝑓𝑓𝑦𝑦
For > 0.170 the cylindrical member is a class 4 cross-section and the γ M value is used from
𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐
Norsok Section 6.3.7, equation 6.22.

2.4 Shear Check

Members subjected to shear are checked for the following condition:
𝑉𝑉𝑆𝑆𝑆𝑆
≤ 1.0 [Norsok 6.3.5]
𝑉𝑉𝑅𝑅𝑅𝑅

The design shear resistance, V Rd , is defined as:

𝐴𝐴𝑓𝑓𝑦𝑦
𝑉𝑉𝑅𝑅𝑅𝑅 = [Norsok 6.3.5]
2√3𝛾𝛾𝑀𝑀

Members subjected to shear from torsional moment are checked for the following condition:
𝑀𝑀𝑇𝑇,𝑆𝑆𝑆𝑆
≤ 1.0 [Norsok 6.3.5]
𝑀𝑀𝑇𝑇,𝑅𝑅𝑅𝑅

2𝐼𝐼𝑝𝑝 𝑓𝑓𝑦𝑦
𝑀𝑀𝑇𝑇,𝑅𝑅𝑅𝑅 = [Norsok Eq. 6.14]
𝐷𝐷√3𝛾𝛾𝑀𝑀

where,
𝜋𝜋
𝐼𝐼𝑝𝑝 = [𝐷𝐷 4 − (𝐷𝐷 − 2𝑡𝑡)4 ]
32

2.5 Hoop Buckling Check

Members subjected to external pressure are checked for the following condition:
𝑓𝑓ℎ
𝜎𝜎𝑝𝑝,𝑆𝑆𝑆𝑆 ≤ 𝑓𝑓ℎ,𝑅𝑅𝑅𝑅 = [Norsok Eq. 6.15]
𝛾𝛾𝑀𝑀

where,

Shear Check 6
Steel Frame Design Norsok N-004 2013 Member Design

𝑝𝑝𝑆𝑆𝑆𝑆 𝐷𝐷
𝜎𝜎𝑝𝑝,𝑆𝑆𝑆𝑆 = [Norsok Eq. 6.16]
2𝑡𝑡
𝑓𝑓𝑦𝑦 for 𝑓𝑓ℎ𝑒𝑒 > 2.44𝑓𝑓𝑦𝑦
⎧ 0.4
⎪ 𝑓𝑓 [Norsok Eq. 6.17,
𝑓𝑓ℎ = 0.7𝑓𝑓𝑦𝑦 � ℎ𝑒𝑒 � for 2.44𝑓𝑓𝑦𝑦 ≥ 𝑓𝑓ℎ𝑒𝑒 > 0.55𝑓𝑓𝑦𝑦
⎨ 𝑓𝑓𝑦𝑦 6.18, and 6.19]
⎪
⎩ 𝑓𝑓ℎ𝑒𝑒 for 𝑓𝑓ℎ𝑒𝑒 ≤ 0.55𝑓𝑓𝑦𝑦
𝑡𝑡
𝑓𝑓ℎ𝑒𝑒 = 2𝐶𝐶ℎ E [Norsok Eq. 6.20]
𝐷𝐷
𝑡𝑡 𝐷𝐷
⎧ 0.44 for 𝜇𝜇 ≥ 1.6
⎪ 𝐷𝐷 𝑡𝑡
⎪
⎪ 𝐷𝐷 3
𝑡𝑡 � � 𝐷𝐷 𝐷𝐷
𝑡𝑡
𝐶𝐶ℎ = 0.44 𝐷𝐷 + 0.21 𝜇𝜇4 for 0.825
𝑡𝑡
≤ 𝜇𝜇 < 1.6
𝑡𝑡
⎨
⎪ 0.737 𝐷𝐷
⎪ for 1.5 ≤ 𝜇𝜇 < 0.825
⎪ (𝜇𝜇 − 0.579) 𝑡𝑡
⎩ 0.80 for 𝜇𝜇 < 1.5

𝐿𝐿 2𝐷𝐷
𝜇𝜇 = �
𝐷𝐷 𝑡𝑡

2.6 Axial Tension and Bending Check

Members subjected to combined axial tension and bending loads, without hydrostatic pressure,
are checked for the following condition:

2 2
1.75 �𝑀𝑀𝑦𝑦,𝑆𝑆𝑆𝑆 + 𝑀𝑀𝑧𝑧,𝑆𝑆𝑆𝑆
𝑁𝑁𝑆𝑆𝑆𝑆 [Norsok Eq. 6.26]
� � + ≤ 1.0
𝑁𝑁𝑡𝑡,𝑅𝑅𝑅𝑅 𝑀𝑀𝑅𝑅𝑅𝑅

Members subjected to combined axial tension, bending, and hydrostatic pressure are checked
based on Method A or Method B, as specified in Norsok N-004 and selected in the design
preferences.

2.6.1 Method A
In Method A, the member axial stress, σ a,Sd , should not include the effect of the hydrostatic
capped-end axial stress.

For the net axial tension case, where 𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 ≥ 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 , the following condition is checked:

2 2
𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 �𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 + 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 [Norsok Eq. 6.34]
+ ≤ 1.0
𝑓𝑓𝑡𝑡ℎ,𝑅𝑅𝑅𝑅 𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑅𝑅

Axial Tension and Bending Check 7

Steel Frame Design Norsok N-004 2013 Member Design

where,

𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 = 0.5𝜎𝜎𝑝𝑝,𝑆𝑆𝑆𝑆

𝑓𝑓𝑦𝑦
𝑓𝑓𝑡𝑡ℎ,𝑅𝑅𝑅𝑅 = ��1 + 0.09𝐵𝐵2 − 𝐵𝐵2𝜂𝜂 − 0.3𝐵𝐵� [Norsok Eq. 6.35]
𝛾𝛾𝑀𝑀
𝑓𝑓𝑚𝑚
𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑅𝑅 = ��1 + 0.09𝐵𝐵2 − 𝐵𝐵2𝜂𝜂 − 0.3𝐵𝐵� [Norsok Eq. 6.36]
𝛾𝛾𝑀𝑀
𝜎𝜎𝑝𝑝,𝑆𝑆𝑆𝑆
𝐵𝐵 = ≤ 1.0 [Norsok Eq. 6.37]
𝑓𝑓ℎ,𝑅𝑅𝑅𝑅

𝑓𝑓ℎ
𝜂𝜂 = 5 − 4 [Norsok Eq. 6.38]
𝑓𝑓𝑦𝑦

For the net axial compression case, where 𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 < 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 , the following condition is checked:

2 2
�𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 � �𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 + 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 [Norsok Eq. 6.39]
+ ≤ 1.0
𝑓𝑓𝑐𝑐𝑐𝑐,𝑅𝑅𝑅𝑅 𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑅𝑅

where,
𝑓𝑓𝑐𝑐𝑐𝑐
𝑓𝑓𝑐𝑐𝑐𝑐,𝑅𝑅𝑅𝑅 = [Norsok Eq. 6.40]
𝛾𝛾𝑀𝑀
𝑓𝑓ℎ𝑒𝑒
If 𝜎𝜎𝑐𝑐,𝑆𝑆𝑆𝑆 > 0.5 and 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 > 0.5𝑓𝑓ℎ𝑒𝑒 , the following condition is also checked:
𝛾𝛾𝑀𝑀

2
𝑓𝑓ℎ𝑒𝑒
𝜎𝜎𝑐𝑐,𝑆𝑆𝑆𝑆 − 0.5 𝜎𝜎𝑝𝑝,𝑆𝑆𝑆𝑆
𝛾𝛾𝑀𝑀
+� � ≤ 1.0 [Norsok Eq. 6.41]
𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 𝑓𝑓ℎ𝑒𝑒 𝑓𝑓ℎ𝑒𝑒
− 0.5
𝛾𝛾𝑀𝑀 𝛾𝛾𝑀𝑀 𝛾𝛾𝑀𝑀

where,

𝜎𝜎𝑐𝑐,𝑆𝑆𝑆𝑆 = 𝜎𝜎𝑚𝑚,𝑆𝑆𝑆𝑆 + 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆

2 2
�𝑀𝑀𝑧𝑧,𝑆𝑆𝑆𝑆 + 𝑀𝑀𝑦𝑦,𝑆𝑆𝑆𝑆
𝜎𝜎𝑚𝑚,𝑆𝑆𝑆𝑆 =
𝑊𝑊

2.6.2 Method B
In Method B, the member axial stress, σ ac,Sd , should include the effect of the hydrostatic
capped-end axial stress. For this case, the following condition is checked:

2 2
+ 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆
𝜎𝜎𝑎𝑎𝑎𝑎,𝑆𝑆𝑆𝑆 �𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 [Norsok Eq. 6.42]
+ ≤ 1.0
𝑓𝑓𝑡𝑡ℎ,𝑅𝑅𝑅𝑅 𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑅𝑅

Axial Tension and Bending Check 8

Steel Frame Design Norsok N-004 2013 Member Design

2.7 Axial Compression and Bending Check

Members subjected to combined axial compression and bending loads, without hydrostatic
pressure, are checked for the following conditions:
2 2 0.5

𝑁𝑁𝑆𝑆𝑆𝑆 1 ⎧ 𝐶𝐶𝑚𝑚𝑚𝑚 𝑀𝑀𝑦𝑦,𝑆𝑆𝑆𝑆 𝐶𝐶𝑚𝑚𝑚𝑚 𝑀𝑀𝑧𝑧,𝑆𝑆𝑆𝑆 ⎫

+ � � +� � ≤ 1.0 [Norsok Eq. 6.27]
𝑁𝑁𝑐𝑐,𝑅𝑅𝑅𝑅 𝑀𝑀𝑅𝑅𝑅𝑅 ⎨ 1 − 𝑁𝑁𝑆𝑆𝑆𝑆 𝑁𝑁
1 − 𝑆𝑆𝑆𝑆 ⎬
⎩ 𝑁𝑁𝐸𝐸𝐸𝐸 𝑁𝑁𝐸𝐸𝐸𝐸 ⎭

2 2
�𝑀𝑀𝑦𝑦,𝑆𝑆𝑆𝑆 + 𝑀𝑀𝑧𝑧,𝑆𝑆𝑆𝑆
𝑁𝑁𝑆𝑆𝑆𝑆 [Norsok Eq. 6.28]
+ ≤ 1.0
𝑁𝑁𝑐𝑐𝑐𝑐,𝑅𝑅𝑅𝑅 𝑀𝑀𝑅𝑅𝑅𝑅

where,
𝑓𝑓𝑐𝑐𝑐𝑐 𝐴𝐴
𝑁𝑁𝑐𝑐𝑐𝑐,𝑅𝑅𝑅𝑅 =
𝛾𝛾𝑀𝑀

𝜋𝜋 2 𝐸𝐸𝐸𝐸
𝑁𝑁𝐸𝐸𝐸𝐸 =
𝑘𝑘𝑘𝑘 2 [Norsok Eq. 6.29]
� �
𝑖𝑖 𝑦𝑦

𝜋𝜋 2 𝐸𝐸𝐸𝐸
𝑁𝑁𝐸𝐸𝐸𝐸 =
𝑘𝑘𝑘𝑘 2 [Norsok Eq. 6.30]
� �
𝑖𝑖 𝑧𝑧

Members subjected to combined axial compression, bending, and hydrostatic pressure are
checked based on Method A or Method B, as specified in Norsok N-004 and selected in the
design preferences.

2.7.1 Method A
In Method A, the member axial stress, σ a,Sd , should not include the effect of the hydrostatic
capped-end axial stress. The following conditions are checked:
2 0.5
2
⎡ 𝐶𝐶 𝜎𝜎 ⎤
𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 1 𝐶𝐶 𝜎𝜎
+ ⎢� 𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 � + � 𝑚𝑚𝑚𝑚 𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 � ⎥ ≤ 1.0 [Norsok Eq. 6.43]
𝑓𝑓𝑐𝑐ℎ,𝑅𝑅𝑅𝑅 𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑅𝑅 ⎢ 1 − 𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 𝜎𝜎
1 − 𝑎𝑎,𝑆𝑆𝑆𝑆 ⎥
⎣ 𝑓𝑓𝐸𝐸𝐸𝐸 𝑓𝑓𝐸𝐸𝐸𝐸 ⎦

2 2
𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 + 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 �𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 + 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 [Norsok Eq. 6.44]
+ ≤ 1.0
𝑓𝑓𝑐𝑐𝑐𝑐,𝑅𝑅𝑅𝑅 𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑅𝑅

where,

Axial Compression and Bending Check 9

Steel Frame Design Norsok N-004 2013 Member Design

𝜋𝜋 2 𝐸𝐸
𝑓𝑓𝐸𝐸𝐸𝐸 =
𝑘𝑘𝑘𝑘 2 [Norsok Eq. 6.45]
� �
𝑖𝑖 𝑦𝑦

𝜋𝜋 2 𝐸𝐸
𝑓𝑓𝐸𝐸𝐸𝐸 =
𝑘𝑘𝑘𝑘 2 [Norsok Eq. 6.46]
� �
𝑖𝑖 𝑧𝑧

⎧1 𝑓𝑓𝑐𝑐𝑐𝑐 2𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 2𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 −1 ⎫

⎪ �𝜉𝜉 − + �𝜉𝜉 2 + 1.12𝜆𝜆2̅ � for 𝜆𝜆 < 1.34���1 − �� ⎪
⎪2 𝛾𝛾𝑀𝑀 𝑓𝑓𝑐𝑐𝑐𝑐 𝑓𝑓𝑐𝑐𝑐𝑐 𝑓𝑓𝑐𝑐𝑐𝑐 ⎪
𝑓𝑓𝑐𝑐ℎ,𝑅𝑅𝑅𝑅 =
⎨ ⎬
⎪𝑓𝑓 0.9 𝑓𝑓𝑐𝑐𝑐𝑐 2𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 −1 ⎪
⎪ 𝑐𝑐ℎ,𝑅𝑅𝑅𝑅 = 2 for 𝜆𝜆 ≥ 1.34���1 − �� ⎪
⎩ 𝜆𝜆̅ 𝛾𝛾𝑀𝑀 𝑓𝑓𝑐𝑐𝑐𝑐 ⎭

[Norsok Eq. 6.47 and 6.48]

𝜉𝜉 = 1 − 0.28𝜆𝜆2̅ [Norsok Eq. 6.49]

𝑓𝑓ℎ𝑒𝑒
If 𝜎𝜎𝑐𝑐,𝑆𝑆𝑆𝑆 > 0.5 and 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 > 0.5𝑓𝑓ℎ𝑒𝑒 , then Norsok equation 6.41 is also checked.
𝛾𝛾𝑀𝑀

2.7.2 Method B
In Method B, the member axial stress, σ ac,Sd , should include the effect of the hydrostatic
capped-end axial stress.

For the case where 𝜎𝜎𝑎𝑎𝑎𝑎,𝑆𝑆𝑆𝑆 > 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 , the following conditions are checked:

2 2 0.5
𝜎𝜎𝑎𝑎𝑎𝑎,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 ⎡ 𝐶𝐶𝑚𝑚𝑚𝑚 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 ⎤
1 𝐶𝐶𝑚𝑚𝑚𝑚 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆
+ ⎢� � +� ⎥
𝑓𝑓𝑐𝑐ℎ,𝑅𝑅𝑅𝑅 𝜎𝜎
𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑅𝑅 ⎢ 1 − 𝑎𝑎𝑎𝑎,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 𝜎𝜎𝑎𝑎𝑎𝑎,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 � ⎥
≤ 1.0
1−
⎣ 𝑓𝑓𝐸𝐸𝐸𝐸 𝑓𝑓𝐸𝐸𝐸𝐸 ⎦
[Norsok Eq. 6.50]

2 2
+ 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆
𝜎𝜎𝑎𝑎𝑎𝑎,𝑆𝑆𝑆𝑆 �𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 [Norsok Eq. 6.51]
+ ≤ 1.0
𝑓𝑓𝑐𝑐𝑐𝑐,𝑅𝑅𝑅𝑅 𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑅𝑅
𝑓𝑓ℎ𝑒𝑒 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 𝑓𝑓ℎ𝑒𝑒
If 𝜎𝜎𝑐𝑐,𝑆𝑆𝑆𝑆 > 0.5 and > 0.5 , then Norsok equation 6.41 is also checked.
𝛾𝛾𝑀𝑀 𝛾𝛾𝑀𝑀 𝛾𝛾𝑀𝑀

For the case where 𝜎𝜎𝑎𝑎𝑎𝑎,𝑆𝑆𝑆𝑆 ≤ 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 , the following condition is checked:

2 2
+ 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆
𝜎𝜎𝑎𝑎𝑎𝑎,𝑆𝑆𝑆𝑆 �𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 [Norsok Eq. 6.51]
+ ≤ 1.0
𝑓𝑓𝑐𝑐𝑐𝑐,𝑅𝑅𝑅𝑅 𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑅𝑅
𝑓𝑓ℎ𝑒𝑒 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 𝑓𝑓ℎ𝑒𝑒
If 𝜎𝜎𝑐𝑐,𝑆𝑆𝑆𝑆 > 0.5 and > 0.5 , then Norsok equation 6.41 is also checked.
𝛾𝛾𝑀𝑀 𝛾𝛾𝑀𝑀 𝛾𝛾𝑀𝑀

Axial Compression and Bending Check 10

Steel Frame Design Norsok N-004 2013 Member Design

2.8 Interaction Shear and Bending Moment

Members subjected to beam shear force and bending moment are checked for the following
conditions:

𝑀𝑀𝑆𝑆𝑆𝑆 𝑉𝑉𝑆𝑆𝑆𝑆 𝑉𝑉𝑆𝑆𝑆𝑆

≤ �1.4 − for ≥ 0.4 [Norsok Eq. 6.31]
𝑀𝑀𝑅𝑅𝑅𝑅 𝑉𝑉𝑅𝑅𝑅𝑅 𝑉𝑉𝑅𝑅𝑅𝑅

𝑀𝑀𝑆𝑆𝑆𝑆 𝑉𝑉𝑆𝑆𝑆𝑆
for < 0.4 [Norsok Eq. 6.32]
𝑀𝑀𝑅𝑅𝑅𝑅 𝑉𝑉𝑅𝑅𝑅𝑅

2.9 Interaction Shear, Bending, and Torsional Moment

Members subjected to beam shear force, bending moment, and torsional moment are checked
for the following conditions:

𝑀𝑀𝑆𝑆𝑆𝑆 𝑉𝑉𝑆𝑆𝑆𝑆 𝑉𝑉𝑆𝑆𝑆𝑆

≤ �1.4 − for ≥ 0.4 [Norsok Eq. 6.33]
𝑀𝑀𝑅𝑅𝑅𝑅𝑅𝑅,𝑅𝑅𝑅𝑅 𝑉𝑉𝑅𝑅𝑅𝑅 𝑉𝑉𝑅𝑅𝑅𝑅

𝑀𝑀𝑆𝑆𝑆𝑆 𝑉𝑉𝑆𝑆𝑆𝑆
≤ 1.0 for < 0.4
𝑀𝑀𝑅𝑅𝑅𝑅𝑅𝑅,𝑅𝑅𝑅𝑅 𝑉𝑉𝑅𝑅𝑅𝑅

where,
𝑊𝑊𝑓𝑓𝑚𝑚,𝑅𝑅𝑅𝑅𝑅𝑅
𝑀𝑀𝑅𝑅𝑅𝑅𝑅𝑅,𝑅𝑅𝑅𝑅 =
𝛾𝛾𝑀𝑀

𝜏𝜏 𝑇𝑇,𝑆𝑆𝑆𝑆 2
𝑓𝑓𝑚𝑚,𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑓𝑓𝑚𝑚 �1 − 3 � �
𝑓𝑓𝑑𝑑

𝑀𝑀𝑇𝑇,𝑆𝑆𝑆𝑆
𝜏𝜏 𝑇𝑇,𝑆𝑆𝑆𝑆 =
2𝜋𝜋𝑅𝑅 2 𝑡𝑡
𝑓𝑓𝑦𝑦
𝑓𝑓𝑑𝑑 =
𝛾𝛾𝑀𝑀

Interaction Shear and Bending Moment 11

 3 Joint Design

This chapter provides the details of the joint punching load check algorithms that are used for
tubular joints in accordance with Norsok N-004 Sections 6.4.3 and 6.4.4.

3.1 Joint Geometry

Figure 1 illustrates some of the geometric parameters used in the punching load check.

d Brace diameter, mm
D Chord diameter, mm
g Gap distance, mm
t Brace thickness, mm
T Chord thickness, mm
θ Angle measured from the chord to the brace

Brace
t

g Brace
T Chord

θ
D

Figure 1 - Joint geometry

Joint Geometry 12
Steel Frame Design Norsok N-004 2013 Joint Design

The following geometric parameters are derived from those in Figure 1.

𝑑𝑑 𝐷𝐷 𝑡𝑡
𝛽𝛽 = 𝛾𝛾 = 𝜏𝜏 =
𝐷𝐷 2𝑇𝑇 𝑇𝑇
The following limits on the geometric parameters are enforced:

0.2 ≤ 𝛽𝛽 ≤ 1.0 10 ≤ 𝛾𝛾 ≤ 50 30° ≤ 𝜃𝜃 ≤ 90°

3.2 Characteristic Resistances

The design axial resistance, N Rd , and design bending moment resistance, M Rd , are defined as:

𝑓𝑓𝑦𝑦 𝑇𝑇 2
𝑁𝑁𝑅𝑅𝑅𝑅 = 𝑄𝑄 𝑄𝑄 [Norsok Eq. 6.52]
𝛾𝛾𝑀𝑀 sin 𝜃𝜃 𝑢𝑢 𝑓𝑓

𝑓𝑓𝑦𝑦 𝑇𝑇 2 𝑑𝑑
𝑀𝑀𝑅𝑅𝑅𝑅 = 𝑄𝑄 𝑄𝑄 [Norsok Eq. 6.53]
𝛾𝛾𝑀𝑀 sin 𝜃𝜃 𝑢𝑢 𝑓𝑓

The strength factor, Q u , is determined based on Norsok Table 6-3. This value can also be
overwritten by the user.

Table 1 - Strength factor, Q u

Brace Action

Joint Axial Axial Compression In-plane Out-of-plane Bending

Class Tension Bending
K (16 + 1.2𝛾𝛾)𝛽𝛽1.2 𝑄𝑄𝑔𝑔
min �
40𝛽𝛽1.2 𝑄𝑄𝑔𝑔
Y 30𝛽𝛽 2.8 + (20 + 0.8𝛾𝛾)𝛽𝛽1.6 (5 + 0.7𝛾𝛾)𝛽𝛽1.2 2.5 + (4.5 + 0.2𝛾𝛾)𝛽𝛽2.6
min �
2.8 + 36𝛽𝛽1.6
2)
X 6.4𝛾𝛾 (0.6𝛽𝛽 (2.8 + (12 + 0.1𝛾𝛾)𝛽𝛽)𝑄𝑄𝛽𝛽

The geometric factor, Q β , is defined as:

0.3
for 𝛽𝛽 > 0.6
𝑄𝑄𝛽𝛽 = �𝛽𝛽(1 − 0.833𝛽𝛽)
1.0 for 𝛽𝛽 ≤ 0.6

The gap factor, Q g , is defined by the following and linearly interpolated between the limiting
values.

Characteristic Resistances 13
Steel Frame Design Norsok N-004 2013 Joint Design

2.8𝑔𝑔 3 𝑔𝑔
1 + 0.2 �1 − � ≥ 1.0 for ≥ 0.05
𝑄𝑄𝑔𝑔 = � 𝐷𝐷 𝐷𝐷
𝑔𝑔
0.13 + 0.65𝜙𝜙𝛾𝛾 0.5 for ≤ −0.05
𝐷𝐷
where,
𝑡𝑡𝑓𝑓𝑦𝑦,𝑏𝑏
ϕ=
𝑇𝑇𝑓𝑓𝑦𝑦,𝑐𝑐

The chord action factor, Q f , is defined as:

𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆
𝑄𝑄𝑓𝑓 = 1.0 + 𝐶𝐶1 − 𝐶𝐶2 − 𝐶𝐶3 𝐴𝐴2 [Norsok Eq. 6.54]
𝑓𝑓𝑦𝑦 1.62𝑓𝑓𝑦𝑦

The parameter A is defined as:

2 2 2
𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆 + 𝜎𝜎𝑚𝑚𝑚𝑚,𝑆𝑆𝑆𝑆
𝐴𝐴2 = � � +� � [Norsok Eq. 6.55]
𝑓𝑓𝑦𝑦 1.62𝑓𝑓𝑦𝑦2

The coefficients C 1 , C 2 , and C 3 are determined based on Norsok Table 6-4.

Table 2 - Coefficients C 1 , C 2 , and C 3

Joint Type C1 C2 C3
K joints under balanced axial loading 0.2 0.2 0.3
T/Y joints under brace axial loading 0.3 0 0.8
𝛽𝛽 ≤ 0.9 0 0 0.4
X joints under brace axial tension loading
𝛽𝛽 = 1.0 0.2 0 0.2
𝛽𝛽 ≤ 0.9 0.2 0 0.5
X joints under brace axial compression loading
𝛽𝛽 = 1.0 -0.2 0 0.2
All joints under brace moment loading 0.2 0 0.4

3.3 Axial and Bending Check

Joints with braces subjected to combined axial and/or bending loads are checked for the
following condition:
2
𝑁𝑁𝑆𝑆𝑆𝑆 𝑀𝑀𝑦𝑦,𝑆𝑆𝑆𝑆 𝑀𝑀𝑧𝑧,𝑆𝑆𝑆𝑆
+� � + ≤ 1.0 [Norsok Eq. 6.57]
𝑁𝑁𝑅𝑅𝑅𝑅 𝑀𝑀𝑦𝑦,𝑅𝑅𝑅𝑅 𝑀𝑀𝑧𝑧,𝑅𝑅𝑅𝑅

3.4 Overlapping Joints

Braces that overlap in-plane or out-of-plane at the chord member form overlap joints. The
overlap requirements of Norsok Section 6.4.4 are currently not checked by the software.

Axial and Bending Check 14

 4 References

European Committee for Standardization. (2005). Eurocode 3: Design of steel structures - Part 1-1:
General rules and rules for buildings. Brussels, Belgium: European Committee for
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