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Steel Frame Design Manual Norsok N-004 2013

Norsok N-004 2013 Steel Frame Design Manual

for

ISO SAP102816M17 Rev. 0 October 2016 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


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

fch,Rd Design axial compressive strength in the presence of external hydrostatic pressure, N/mm2

fcl Characteristic local buckling strength, N/mm2

fcle Characteristic elastic local buckling strength, N/mm2

fcl,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

fhe Elastic hoop buckling strength, N/mm2

fh,Rd Design hoop buckling bending strength, N/mm2

fm Characteristic bending strength, N/mm2

fmh,Rd Design bending resistance in the presence of external hydrostatic pressure, N/mm2

fth,Rd Design axial tensile resistance in the presence of external hydrostatic pressure, N/mm2

fy Characteristic yield strength, N/mm2

fy,b Characteristic yield strength of brace, N/mm2

fy,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

MRd Design bending resistance, N-mm

MSd Design bending moment, N-mm

MT,Rd Design torsional resistance, N-mm

MT,Sd Design torsional moment, N-mm

My,Rd Design in-plane bending resistance, N-mm

My,Sd Design in-plane bending moment, N-mm

Symbols 2


Mz,Rd Design out-of-plane bending resistance, N-mm

Mz,Sd Design out-of-plane bending moment, N-mm

Nc,Rd Design compression resistance, N

Ncl,Rd Design axial local buckling resistance, N

NEy Euler buckling strength about y-axis, N

NEz Euler buckling strength about z-axis, N

NRd Design axial resistance, N

NSd Design axial force, N

Nt,Rd Design tension resistance, N

pSd Design hydrostatic pressure, N/mm2

Qf Chord action factor

Qg Gap factor

Qu Strength factor

Qβ Geometric factor

t Wall thickness, mm

VRd Design shear resistance, N

VSd Design shear force, N

W Elastic section modulus, mm3

Z Plastic section modulus, mm3

γΜ Partial factor for resistance of cross-sections

�̅�𝜆 Column slenderness parameter

µ Geometric parameter

σa,Sd Design axial stress, N/mm2

σac,Sd Member axial stress, N/mm2

σc,Sd Design axial compressive stress, N/mm2

σmy,Sd Design in-plane bending stress, N/mm2

σmz,Sd Design out-of-plane bending stress, N/mm2

σp,Sd Design hoop stress due to hydrostatic pressure, N/mm2

σq,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:

𝑁𝑁𝑆𝑆𝑆𝑆𝑁𝑁𝑡𝑡,𝑅𝑅𝑆𝑆

≤ 1.0 [Norsok 6.3.2]

The design tension resistance, Nt,Rd, is defined as:

𝑁𝑁𝑡𝑡,𝑅𝑅𝑆𝑆 =𝐴𝐴𝑓𝑓𝑦𝑦𝛾𝛾𝑀𝑀

[Norsok 6.3.2]

2.2 Compression Check Members subjected to axial compression are checked for the following condition:

𝑁𝑁𝑆𝑆𝑆𝑆𝑁𝑁𝑐𝑐,𝑅𝑅𝑆𝑆

≤ 1.0 [Norsok 6.3.3]

The design compression resistance, Nc,Rd, is defined as:

𝑁𝑁𝑐𝑐,𝑅𝑅𝑆𝑆 =𝐴𝐴𝑓𝑓𝑐𝑐𝛾𝛾𝑀𝑀

[Norsok 6.3.3]

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, fc, is defined as:

𝑓𝑓𝑐𝑐 = ��1.0− 0.28�̅�𝜆2�𝑓𝑓𝑐𝑐𝑐𝑐 for �̅�𝜆 ≤ 1.340.9�̅�𝜆2

𝑓𝑓𝑐𝑐𝑐𝑐 for �̅�𝜆 > 1.34 [Norsok Eq. 6.3 and 6.4]

�̅�𝜆 = �𝑓𝑓𝑐𝑐𝑐𝑐𝑓𝑓𝐸𝐸

=𝑘𝑘𝑘𝑘𝜋𝜋𝜋𝜋�𝑓𝑓𝑐𝑐𝑐𝑐𝐸𝐸

[Norsok Eq. 6.5]

The characteristic local buckling strength, fcl, is defined as:

𝑓𝑓𝑐𝑐𝑐𝑐 =

⎩⎪⎪⎨

⎪⎪⎧𝑓𝑓𝑦𝑦 for

𝑓𝑓𝑦𝑦𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐

≤ 0.170

�1.047− 0.274𝑓𝑓𝑦𝑦𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐

� 𝑓𝑓𝑦𝑦 for 0.170 <𝑓𝑓𝑦𝑦𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐

≤ 1.911

𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 for𝑓𝑓𝑦𝑦𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐

> 1.911

[Norsok Eq. 6.6, 6.7, and 6.8]

𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 = 2𝐶𝐶𝑐𝑐E𝑡𝑡𝐷𝐷

For 𝑓𝑓𝑦𝑦𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐

> 0.170 the cylindrical member is a class 4 cross-section and the γM value is taken from

Norsok Section 6.3.7, equation 6.22.

2.3 Flexure Check Members subjected to bending are checked for the following condition:

𝑀𝑀𝑆𝑆𝑆𝑆

𝑀𝑀𝑅𝑅𝑆𝑆≤ 1.0 [Norsok 6.3.4]

The design moment resistance, MRd, is defined as:

𝑀𝑀𝑅𝑅𝑆𝑆 =𝑓𝑓𝑚𝑚𝑊𝑊𝛾𝛾𝑀𝑀

[Norsok 6.3.4]

The characteristic bending strength, fm, is defined as:

Flexure Check 5


𝑓𝑓𝑚𝑚 =

⎩⎪⎪⎨

⎪⎪⎧

𝑍𝑍𝑊𝑊𝑓𝑓𝑦𝑦 for

𝑓𝑓𝑦𝑦𝐷𝐷𝐸𝐸𝑡𝑡

≤ 0.0517

�1.13− 2.58�𝑓𝑓𝑦𝑦𝐷𝐷𝐸𝐸𝑡𝑡 �

��𝑍𝑍𝑊𝑊�𝑓𝑓𝑦𝑦 for 0.0517 <


≤ 0.1034

�0.94− 0.76�𝑓𝑓𝑦𝑦𝐷𝐷𝐸𝐸𝑡𝑡 �

��𝑍𝑍𝑊𝑊�𝑓𝑓𝑦𝑦 for 0.1034 <


≤ 120𝑓𝑓𝑦𝑦𝐸𝐸

[Norsok Eq. 6.10, 6.11, and 6.12]

where, W and Z are taken from the frame section property, not the code.

For 𝑓𝑓𝑦𝑦𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐

> 0.170 the cylindrical member is a class 4 cross-section and the γM value is used from

Norsok Section 6.3.7, equation 6.22.

2.4 Shear Check Members subjected to shear are checked for the following condition:

𝑉𝑉𝑆𝑆𝑆𝑆𝑉𝑉𝑅𝑅𝑆𝑆

≤ 1.0 [Norsok 6.3.5]

The design shear resistance, VRd, is defined as:

𝑉𝑉𝑅𝑅𝑆𝑆 =𝐴𝐴𝑓𝑓𝑦𝑦

2√3𝛾𝛾𝑀𝑀 [Norsok 6.3.5]

Members subjected to shear from torsional moment are checked for the following condition:

𝑀𝑀𝑇𝑇,𝑆𝑆𝑆𝑆

𝑀𝑀𝑇𝑇,𝑅𝑅𝑆𝑆≤ 1.0 [Norsok 6.3.5]

𝑀𝑀𝑇𝑇,𝑅𝑅𝑆𝑆 =2𝐼𝐼𝑝𝑝𝑓𝑓𝑦𝑦𝐷𝐷√3𝛾𝛾𝑀𝑀

[Norsok Eq. 6.14]

where,

𝐼𝐼𝑝𝑝 =𝜋𝜋

32[𝐷𝐷4 − (𝐷𝐷 − 2𝑡𝑡)4]

2.5 Hoop Buckling Check Members subjected to external pressure are checked for the following condition:

𝜎𝜎𝑝𝑝,𝑆𝑆𝑆𝑆 ≤ 𝑓𝑓ℎ,𝑅𝑅𝑆𝑆 =𝑓𝑓ℎ𝛾𝛾𝑀𝑀

[Norsok Eq. 6.15]

where,

Shear Check 6


𝜎𝜎𝑝𝑝,𝑆𝑆𝑆𝑆 =𝑝𝑝𝑆𝑆𝑆𝑆𝐷𝐷

2𝑡𝑡 [Norsok Eq. 6.16]

𝑓𝑓ℎ =

⎩⎪⎨

⎪⎧

𝑓𝑓𝑦𝑦 for 𝑓𝑓ℎ𝑐𝑐 > 2.44𝑓𝑓𝑦𝑦

0.7𝑓𝑓𝑦𝑦 �𝑓𝑓ℎ𝑐𝑐𝑓𝑓𝑦𝑦�0.4

for 2.44𝑓𝑓𝑦𝑦 ≥ 𝑓𝑓ℎ𝑐𝑐 > 0.55𝑓𝑓𝑦𝑦

𝑓𝑓ℎ𝑐𝑐 for 𝑓𝑓ℎ𝑐𝑐 ≤ 0.55𝑓𝑓𝑦𝑦

[Norsok Eq. 6.17, 6.18, and 6.19]

𝑓𝑓ℎ𝑐𝑐 = 2𝐶𝐶ℎE𝑡𝑡𝐷𝐷

[Norsok Eq. 6.20]

𝐶𝐶ℎ =

⎩⎪⎪⎪⎨

⎪⎪⎪⎧ 0.44

𝑡𝑡𝐷𝐷

for 𝜇𝜇 ≥ 1.6𝐷𝐷𝑡𝑡

0.44𝑡𝑡𝐷𝐷

+ 0.21�𝐷𝐷𝑡𝑡 �

3

𝜇𝜇4for 0.825

𝐷𝐷𝑡𝑡≤ 𝜇𝜇 < 1.6

𝐷𝐷𝑡𝑡

0.737(𝜇𝜇 − 0.579) for 1.5 ≤ 𝜇𝜇 < 0.825

𝐷𝐷𝑡𝑡

0.80 for 𝜇𝜇 < 1.5

𝜇𝜇 =𝐿𝐿𝐷𝐷�2𝐷𝐷𝑡𝑡

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:

�𝑁𝑁𝑆𝑆𝑆𝑆𝑁𝑁𝑡𝑡,𝑅𝑅𝑆𝑆

�1.75

+�𝑀𝑀𝑦𝑦,𝑆𝑆𝑆𝑆

2 + 𝑀𝑀𝑧𝑧,𝑆𝑆𝑆𝑆2

𝑀𝑀𝑅𝑅𝑆𝑆≤ 1.0 [Norsok Eq. 6.26]

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, σa,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:

𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆

𝑓𝑓𝑡𝑡ℎ,𝑅𝑅𝑆𝑆+�𝜎𝜎𝑚𝑚𝑦𝑦,𝑆𝑆𝑆𝑆

2 + 𝜎𝜎𝑚𝑚𝑧𝑧,𝑆𝑆𝑆𝑆2

𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑆𝑆≤ 1.0 [Norsok Eq. 6.34]

Axial Tension and Bending Check 7


where,

𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆 = 0.5𝜎𝜎𝑝𝑝,𝑆𝑆𝑆𝑆

𝑓𝑓𝑡𝑡ℎ,𝑅𝑅𝑆𝑆 =𝑓𝑓𝑦𝑦𝛾𝛾𝑀𝑀

��1 + 0.09𝐵𝐵2 − 𝐵𝐵2𝜂𝜂 − 0.3𝐵𝐵� [Norsok Eq. 6.35]

𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑆𝑆 =𝑓𝑓𝑚𝑚𝛾𝛾𝑀𝑀

��1 + 0.09𝐵𝐵2 − 𝐵𝐵2𝜂𝜂 − 0.3𝐵𝐵� [Norsok Eq. 6.36]

𝐵𝐵 =𝜎𝜎𝑝𝑝,𝑆𝑆𝑆𝑆

𝑓𝑓ℎ,𝑅𝑅𝑆𝑆≤ 1.0 [Norsok Eq. 6.37]

𝜂𝜂 = 5 − 4𝑓𝑓ℎ𝑓𝑓𝑦𝑦

[Norsok Eq. 6.38]

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

�𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆�𝑓𝑓𝑐𝑐𝑐𝑐,𝑅𝑅𝑆𝑆

+�𝜎𝜎𝑚𝑚𝑦𝑦,𝑆𝑆𝑆𝑆



where,

𝑓𝑓𝑐𝑐𝑐𝑐,𝑅𝑅𝑆𝑆 =𝑓𝑓𝑐𝑐𝑐𝑐𝛾𝛾𝑀𝑀

[Norsok Eq. 6.40]

If 𝜎𝜎𝑐𝑐,𝑆𝑆𝑆𝑆 > 0.5 𝑓𝑓ℎ𝑐𝑐𝛾𝛾𝑀𝑀

and 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 > 0.5𝑓𝑓ℎ𝑐𝑐, the following condition is also checked:

𝜎𝜎𝑐𝑐,𝑆𝑆𝑆𝑆 − 0.5𝑓𝑓ℎ𝑐𝑐𝛾𝛾𝑀𝑀𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐𝛾𝛾𝑀𝑀

− 0.5𝑓𝑓ℎ𝑐𝑐𝛾𝛾𝑀𝑀

+ �𝜎𝜎𝑝𝑝,𝑆𝑆𝑆𝑆𝑓𝑓ℎ𝑐𝑐𝛾𝛾𝑀𝑀

�

2

≤ 1.0 [Norsok Eq. 6.41]

where,

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

𝜎𝜎𝑚𝑚,𝑆𝑆𝑆𝑆 =�𝑀𝑀𝑧𝑧,𝑆𝑆𝑆𝑆

2 + 𝑀𝑀𝑦𝑦,𝑆𝑆𝑆𝑆2

𝑊𝑊

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

𝜎𝜎𝑎𝑎𝑐𝑐,𝑆𝑆𝑆𝑆

𝑓𝑓𝑡𝑡ℎ,𝑅𝑅𝑆𝑆+�𝜎𝜎𝑚𝑚𝑦𝑦,𝑆𝑆𝑆𝑆



Axial Tension and Bending Check 8


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:

𝑁𝑁𝑆𝑆𝑆𝑆𝑁𝑁𝑐𝑐,𝑅𝑅𝑆𝑆

+1𝑀𝑀𝑅𝑅𝑆𝑆

⎩⎨

⎧�𝐶𝐶𝑚𝑚𝑦𝑦𝑀𝑀𝑦𝑦,𝑆𝑆𝑆𝑆

1 − 𝑁𝑁𝑆𝑆𝑆𝑆𝑁𝑁𝐸𝐸𝑦𝑦

�

2

+ �𝐶𝐶𝑚𝑚𝑧𝑧𝑀𝑀𝑧𝑧,𝑆𝑆𝑆𝑆

1 −𝑁𝑁𝑆𝑆𝑆𝑆𝑁𝑁𝐸𝐸𝑧𝑧

�

2

⎭⎬

⎫0.5

≤ 1.0 [Norsok Eq. 6.27]

𝑁𝑁𝑆𝑆𝑆𝑆𝑁𝑁𝑐𝑐𝑐𝑐,𝑅𝑅𝑆𝑆

+�𝑀𝑀𝑦𝑦,𝑆𝑆𝑆𝑆

2 + 𝑀𝑀𝑧𝑧,𝑆𝑆𝑆𝑆2

𝑀𝑀𝑅𝑅𝑆𝑆≤ 1.0 [Norsok Eq. 6.28]

where,

𝑁𝑁𝑐𝑐𝑐𝑐,𝑅𝑅𝑆𝑆 =𝑓𝑓𝑐𝑐𝑐𝑐𝐴𝐴𝛾𝛾𝑀𝑀

𝑁𝑁𝐸𝐸𝑦𝑦 =𝜋𝜋2𝐸𝐸𝐴𝐴

�𝑘𝑘𝑘𝑘𝜋𝜋 �𝑦𝑦

2 [Norsok Eq. 6.29]

𝑁𝑁𝐸𝐸𝑧𝑧 =𝜋𝜋2𝐸𝐸𝐴𝐴

�𝑘𝑘𝑘𝑘𝜋𝜋 �𝑧𝑧

2 [Norsok Eq. 6.30]

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, σa,Sd, should not include the effect of the hydrostatic capped-end axial stress. The following conditions are checked:

𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆

𝑓𝑓𝑐𝑐ℎ,𝑅𝑅𝑆𝑆+

1𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑆𝑆

⎣⎢⎢⎡�𝐶𝐶𝑚𝑚𝑦𝑦𝜎𝜎𝑚𝑚𝑦𝑦,𝑆𝑆𝑆𝑆

1 −𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆𝑓𝑓𝐸𝐸𝑦𝑦

�

2

+ �𝐶𝐶𝑚𝑚𝑧𝑧𝜎𝜎𝑚𝑚𝑧𝑧,𝑆𝑆𝑆𝑆

1 −𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆𝑓𝑓𝐸𝐸𝑧𝑧

�

2

⎦⎥⎥⎤0.5

≤ 1.0 [Norsok Eq. 6.43]

𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆 + 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆

𝑓𝑓𝑐𝑐𝑐𝑐,𝑅𝑅𝑆𝑆+�𝜎𝜎𝑚𝑚𝑦𝑦,𝑆𝑆𝑆𝑆



where,

Axial Compression and Bending Check 9


𝑓𝑓𝐸𝐸𝑦𝑦 =𝜋𝜋2𝐸𝐸

�𝑘𝑘𝑘𝑘𝜋𝜋 �𝑦𝑦

2 [Norsok Eq. 6.45]

𝑓𝑓𝐸𝐸𝑧𝑧 =𝜋𝜋2𝐸𝐸

�𝑘𝑘𝑘𝑘𝜋𝜋 �𝑧𝑧

2 [Norsok Eq. 6.46]

𝑓𝑓𝑐𝑐ℎ,𝑅𝑅𝑆𝑆 =

⎩⎪⎪⎨

⎪⎪⎧1

2𝑓𝑓𝑐𝑐𝑐𝑐𝛾𝛾𝑀𝑀

�𝜉𝜉 −2𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆

𝑓𝑓𝑐𝑐𝑐𝑐+ �𝜉𝜉2 + 1.12�̅�𝜆2

𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆

𝑓𝑓𝑐𝑐𝑐𝑐� for 𝜆𝜆 < 1.34��1 −

2𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆

𝑓𝑓𝑐𝑐𝑐𝑐��−1

𝑓𝑓𝑐𝑐ℎ,𝑅𝑅𝑆𝑆 =0.9�̅�𝜆2

𝑓𝑓𝑐𝑐𝑐𝑐𝛾𝛾𝑀𝑀

for 𝜆𝜆 ≥ 1.34��1 −2𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆

𝑓𝑓𝑐𝑐𝑐𝑐��−1

⎭⎪⎪⎬

⎪⎪⎫

[Norsok Eq. 6.47 and 6.48]

𝜉𝜉 = 1 − 0.28�̅�𝜆2 [Norsok Eq. 6.49]


and 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 > 0.5𝑓𝑓ℎ𝑐𝑐, then Norsok equation 6.41 is also checked.

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

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

𝜎𝜎𝑎𝑎𝑐𝑐,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆

𝑓𝑓𝑐𝑐ℎ,𝑅𝑅𝑆𝑆+

1𝑓𝑓𝑚𝑚ℎ,𝑅𝑅𝑆𝑆

⎣⎢⎢⎡�

𝐶𝐶𝑚𝑚𝑦𝑦𝜎𝜎𝑚𝑚𝑦𝑦,𝑆𝑆𝑆𝑆

1 −𝜎𝜎𝑎𝑎𝑐𝑐,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆

𝑓𝑓𝐸𝐸𝑦𝑦

�

2

+ �𝐶𝐶𝑚𝑚𝑧𝑧𝜎𝜎𝑚𝑚𝑧𝑧,𝑆𝑆𝑆𝑆

1 −𝜎𝜎𝑎𝑎𝑐𝑐,𝑆𝑆𝑆𝑆 − 𝜎𝜎𝑞𝑞,𝑆𝑆𝑆𝑆

𝑓𝑓𝐸𝐸𝑧𝑧

�

2

⎦⎥⎥⎤0.5

≤ 1.0

[Norsok Eq. 6.50]






and 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐𝛾𝛾𝑀𝑀

> 0.5 𝑓𝑓ℎ𝑐𝑐𝛾𝛾𝑀𝑀

, then Norsok equation 6.41 is also checked.

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






and 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐𝛾𝛾𝑀𝑀

> 0.5 𝑓𝑓ℎ𝑐𝑐𝛾𝛾𝑀𝑀

, then Norsok equation 6.41 is also checked.

Axial Compression and Bending Check 10


2.8 Interaction Shear and Bending Moment Members subjected to beam shear force and bending moment are checked for the following conditions:


𝑀𝑀𝑅𝑅𝑆𝑆≤ �1.4−


for𝑉𝑉𝑆𝑆𝑆𝑆𝑉𝑉𝑅𝑅𝑆𝑆

≥ 0.4 [Norsok Eq. 6.31]


𝑀𝑀𝑅𝑅𝑆𝑆for


< 0.4 [Norsok Eq. 6.32]

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:


𝑀𝑀𝑅𝑅𝑐𝑐𝑆𝑆,𝑅𝑅𝑆𝑆≤ �1.4 −


for𝑉𝑉𝑆𝑆𝑆𝑆𝑉𝑉𝑅𝑅𝑆𝑆

≥ 0.4 [Norsok Eq. 6.33]


𝑀𝑀𝑅𝑅𝑐𝑐𝑆𝑆,𝑅𝑅𝑆𝑆≤ 1.0 for


< 0.4

where,

𝑀𝑀𝑅𝑅𝑐𝑐𝑆𝑆,𝑅𝑅𝑆𝑆 =𝑊𝑊𝑓𝑓𝑚𝑚,𝑅𝑅𝑐𝑐𝑆𝑆

𝛾𝛾𝑀𝑀

𝑓𝑓𝑚𝑚,𝑅𝑅𝑐𝑐𝑆𝑆 = 𝑓𝑓𝑚𝑚�1− 3 �𝜏𝜏𝑇𝑇,𝑆𝑆𝑆𝑆

𝑓𝑓𝑆𝑆�2

𝜏𝜏𝑇𝑇,𝑆𝑆𝑆𝑆 =𝑀𝑀𝑇𝑇,𝑆𝑆𝑆𝑆

2𝜋𝜋𝑅𝑅2𝑡𝑡

𝑓𝑓𝑆𝑆 =𝑓𝑓𝑦𝑦𝛾𝛾𝑀𝑀

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

Figure 1 - Joint geometry

T

D

g

d

t

θ

ChordBrace

Brace

Joint Geometry 12

Steel Frame Design Norsok N-004 2013 Joint Design

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

𝛽𝛽 =𝑑𝑑𝐷𝐷

𝛾𝛾 =𝐷𝐷2𝑇𝑇

𝜏𝜏 =𝑡𝑡𝑇𝑇

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, NRd, and design bending moment resistance, MRd, are defined as:

𝑁𝑁𝑅𝑅𝑆𝑆 =𝑓𝑓𝑦𝑦𝑇𝑇2

𝛾𝛾𝑀𝑀 sin𝜃𝜃𝑄𝑄𝑢𝑢𝑄𝑄𝑓𝑓 [Norsok Eq. 6.52]

𝑀𝑀𝑅𝑅𝑆𝑆 =𝑓𝑓𝑦𝑦𝑇𝑇2𝑑𝑑𝛾𝛾𝑀𝑀 sin𝜃𝜃

𝑄𝑄𝑢𝑢𝑄𝑄𝑓𝑓 [Norsok Eq. 6.53]

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

Table 1 - Strength factor, Qu

Brace Action

Joint Class

Axial Tension

Axial Compression In-plane Bending

Out-of-plane Bending

K min �

(16 + 1.2𝛾𝛾)𝛽𝛽1.2𝑄𝑄𝑔𝑔40𝛽𝛽1.2𝑄𝑄𝑔𝑔

(5 + 0.7𝛾𝛾)𝛽𝛽1.2 2.5 + (4.5 + 0.2𝛾𝛾)𝛽𝛽2.6 Y 30𝛽𝛽 min �2.8 + (20 + 0.8𝛾𝛾)𝛽𝛽1.6

2.8 + 36𝛽𝛽1.6

X 6.4𝛾𝛾(0.6𝛽𝛽2) (2.8 + (12 + 0.1𝛾𝛾)𝛽𝛽)𝑄𝑄𝛽𝛽

The geometric factor, Qβ, is defined as:

𝑄𝑄𝛽𝛽 = �0.3

𝛽𝛽(1 − 0.833𝛽𝛽) for 𝛽𝛽 > 0.6

1.0 for 𝛽𝛽 ≤ 0.6

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

Characteristic Resistances 13

Steel Frame Design Norsok N-004 2013 Joint Design

𝑄𝑄𝑔𝑔 = �1 + 0.2 �1 −

2.8𝑔𝑔𝐷𝐷

�3≥ 1.0 for

𝑔𝑔𝐷𝐷≥ 0.05

0.13 + 0.65𝜙𝜙𝛾𝛾0.5 for𝑔𝑔𝐷𝐷≤ −0.05

where,

ϕ =𝑡𝑡𝑓𝑓𝑦𝑦,𝑏𝑏

𝑇𝑇𝑓𝑓𝑦𝑦,𝑐𝑐

The chord action factor, Qf, is defined as:

𝑄𝑄𝑓𝑓 = 1.0 + 𝐶𝐶1𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆

𝑓𝑓𝑦𝑦− 𝐶𝐶2

𝜎𝜎𝑚𝑚𝑦𝑦,𝑆𝑆𝑆𝑆

1.62𝑓𝑓𝑦𝑦− 𝐶𝐶3𝐴𝐴2 [Norsok Eq. 6.54]

The parameter A is defined as:

𝐴𝐴2 = �𝜎𝜎𝑎𝑎,𝑆𝑆𝑆𝑆

𝑓𝑓𝑦𝑦�2

+ �𝜎𝜎𝑚𝑚𝑦𝑦,𝑆𝑆𝑆𝑆2 + 𝜎𝜎𝑚𝑚𝑧𝑧,𝑆𝑆𝑆𝑆

2

1.62𝑓𝑓𝑦𝑦2� [Norsok Eq. 6.55]

The coefficients C1, C2, and C3 are determined based on Norsok Table 6-4.

Table 2 - Coefficients C1, C2, and C3

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

X joints under brace axial tension loading 𝛽𝛽 ≤ 0.9𝛽𝛽 = 1.0 0

0.2 0 0

0.4 0.2

X joints under brace axial compression loading 𝛽𝛽 ≤ 0.9𝛽𝛽 = 1.0 0.2

-0.2 0 0

0.5 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:

𝑁𝑁𝑆𝑆𝑆𝑆𝑁𝑁𝑅𝑅𝑆𝑆

+ �𝑀𝑀𝑦𝑦,𝑆𝑆𝑆𝑆

𝑀𝑀𝑦𝑦,𝑅𝑅𝑆𝑆�2

+𝑀𝑀𝑧𝑧,𝑆𝑆𝑆𝑆

𝑀𝑀𝑧𝑧,𝑅𝑅𝑆𝑆≤ 1.0 [Norsok Eq. 6.57]

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 Standardization.

Standards Norway. (2013). Design of steel structures. Lysaker, Norway: Standards Norway.

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