SFD API RP 2A WSD 22nd

User Manual: SFD-API-RP-2A-WSD-22nd

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Steel Frame Design Manual

API RP 2A-WSD 22nd

API RP 2A-WSD 22nd
Steel Frame Design Manual
for

ISO SAP022217M38 Rev. 0
Proudly developed in the United States of America

February 2017

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DISCLAIMER
CONSIDERABLE TIME, EFFORT, AND EXPENSE HAVE GONE INTO THE DEVELOPMENT
AND TESTING OF THIS SOFTWARE. HOWEVER, THE USER ACCEPTS AND UNDERSTANDS
THAT NO WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE
DISTRIBUTORS ON THE ACCURACY OR THE RELIABILITY OF THIS PRODUCT.
THIS PRODUCT IS A PRACTICAL AND POWERFUL TOOL FOR STRUCTURAL DESIGN.
HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC ASSUMPTIONS OF
THE SOFTWARE MODELING, ANALYSIS, AND DESIGN ALGORITHMS AND COMPENSATE
FOR THE ASPECTS THAT ARE NOT ADDRESSED.
THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE CHECKED BY A QUALIFIED
AND EXPERIENCED ENGINEER. THE ENGINEER MUST INDEPENDENTLY VERIFY THE
RESULTS AND TAKE PROFESSIONAL RESPONSIBILITY FOR THE INFORMATION THAT IS
USED.

Contents

1 Introduction

1

1.1

Units

1

1.2

Axes Notation

1

1.3

Symbols

1

2 Member Design

4

2.1

Safety Factors

4

2.2

Tension Check

4

2.3

Compression Check

5

2.4

Flexure Check

5

2.5

Shear Check

6

2.6

Hoop Buckling Check

6

2.7

Axial Tension and Bending Check

7

2.8

Axial Compression and Bending Check

8

3 Joint Design

10

3.1

Joint Geometry

10

3.2

Allowable Capacities

11

3.3

Axial and Bending Check

13

4 References

14

i

1

Introduction

This manual describes the steel frame design algorithms in the software for API Recommended
Practice 2A-WSD 22nd Edition (American Petroleum Institute, 2014). The design algorithms in
the software for API RP 2A-WSD 22nd cover allowable stress 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 AISC ASD
9th Edition. Requirements of the code not documented in this manual should be considered
using other methods.
This manual documents the design details for cylindrical sections having thickness t ≥ 6mm, D/t
< 300. Members of other section shapes are designed in accordance with AISC ASD 9th Edition
(American Institute of Steel Construction, 1989).
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 API RP 2A-WSD design code is based on metric and imperial units. This manual is written
using imperial units, unless noted otherwise. Any units, imperial, metric, or MKS may be used
in the software in conjunction with API RP 2A-WSD 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 API RP 2A-WSD design code refers to x-x and y-y 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

Units

1

Steel Frame Design API RP 2A-WSD 22nd

Introduction

description. Where possible, the same symbol from the design code is used in this manual.
A

Cross sectional area, in2

C

Critical elastic buckling coefficient

Ch

Critical hoop buckling coefficient

Cm

Reduction factor

D

Outside diameter, in

E

Young’s modulus of elasticity, ksi

fa

Design tensile stress, ksi

Fa

Allowable compressive stress, ksi

fb

Design bending stress, ksi

Fb
Fe

Symbols

’

Allowable bending stress, ksi
Euler stress, ksi

fh

Hoop stress due to hydrostatic pressure, ksi

Fhc

Critical hoop buckling stress, ksi

Fhe

Elastic hoop buckling stress, ksi

Ft

Allowable tensile stress, ksi

fv

Design beam shear stress, ksi

Fv

Allowable beam shear stress, ksi

fvt

Design torsional shear stress, ksi

Fvt

Allowable torsional shear stress, ksi

fx

Design compressive stress, ksi

Fxc

Inelastic local buckling stress, ksi

Fxe

Elastic local buckling stress, ksi

Fy

Yield strength, ksi

g

Gap distance, in

Ip

Polar moment of inertia, in4

K

Effective length factor

l

Unbraced length, in

L

Length between stiffening rings, diaphragms, or end connections, in

M

Bending moment, kip-in

M

Geometric parameter

Ma

Allowable brace bending moment, kip-in

Mt

Torsional moment, kip-in

p

Hydrostatic pressure, ksi

2

Steel Frame Design API RP 2A-WSD 22nd

Symbols

P

Axial force, kip

Pa

Allowable brace axial load, kip

Qf

Chord load factor

Qg

Gap factor

Qu

Ultimate strength factor

Qβ

Geometric factor

r

Radius of gyration, in

SFb

Safety factor for bending

SFh

Safety factor against hydrostatic collapse

SFx

Safety factor for axial force

t

Wall thickness, in

V

Transverse shear force, kip

ν

Poisson’s ratio

θ

Angle between the chord and the brace

Introduction

3

2

Member Design

This chapter provides the details of the structural steel design and stress check algorithms that
are used for cylindrical member design and checking at each output station in accordance with
API RP 2A-WSD.
Cylindrical members subjected solely to axial tension, axial compression, bending, shear, or
hydrostatic pressure are designed in accordance with API RP 2A-WSD Sections 6.2.1 to 6.2.5,
respectively. Cylindrical members subjected to combined loads without hydrostatic pressure are
designed in accordance with API RP 2A-WSD Sections 6.3.2 and 6.3.3. Cylindrical members
subjected to combined loads with hydrostatic pressure are designed in accordance with API RP
2A-WSD Sections 6.3.4 and 6.3.5.

2.1

Safety Factors
The safety factors used in calculating allowable stresses in the following sections are defined as:
Table 1 - Safety factors
Loading

2.2

Design Condition

Axial
Tension

Axial
Compression

Basic allowable stresses
One-third increase in allowable
stresses is permitted

1.67
1.25

2.0
1.5

Bending

Hoop
Compression

𝐹𝐹𝑦𝑦 ⁄𝐹𝐹𝑏𝑏

2.0
1.5

𝐹𝐹𝑦𝑦 ⁄(1.33𝐹𝐹𝑏𝑏 )

Tension Check
Members subjected to axial tension are checked for the following condition:
𝑓𝑓𝑎𝑎
≤ 1.0
𝐹𝐹𝑡𝑡

[API 6.2.1]

The allowable tensile stress, Ft, is defined as:

Safety Factors

4

Steel Frame Design API RP 2A-WSD 22nd

Member Design

𝐹𝐹𝑡𝑡 = 0.6𝐹𝐹𝑦𝑦

2.3

[API Eq. 6.1]

Compression Check
Members subjected to axial compression are checked for the following condition:
𝑓𝑓𝑎𝑎
≤ 1.0
𝐹𝐹𝑎𝑎

[API 6.2.2]

The allowable compressive stress, Fa, is defined as:
(𝐾𝐾𝐾𝐾 ⁄𝑟𝑟)2
�1 −
� 𝐹𝐹𝑦𝑦
⎧
2𝐶𝐶𝑐𝑐2
⎪
⎪
3(𝐾𝐾𝐾𝐾 ⁄𝑟𝑟) (𝐾𝐾𝐾𝐾 ⁄𝑟𝑟)3
−
𝐹𝐹𝑎𝑎 = 5⁄3 + 8𝐶𝐶
8𝐶𝐶𝑐𝑐3
𝑐𝑐
⎨
2
⎪
⎪ 12𝜋𝜋 𝐸𝐸
⎩23(𝐾𝐾𝐾𝐾 ⁄𝑟𝑟)2

where,

for 𝐾𝐾𝐾𝐾 ⁄𝑟𝑟 < 𝐶𝐶𝑐𝑐

[API Eq. 6.2 &
Eq. 6.3]

for 𝐾𝐾𝐾𝐾 ⁄𝑟𝑟 ≥ 𝐶𝐶𝑐𝑐

0.5

2𝜋𝜋 2 𝐸𝐸
𝐶𝐶𝑐𝑐 = �
�
𝐹𝐹𝑦𝑦

𝐹𝐹𝑦𝑦
for 𝐷𝐷⁄𝑡𝑡 ≤ 60
𝐹𝐹𝑦𝑦 = �min(𝐹𝐹 , 𝐹𝐹 ) for 𝐷𝐷⁄𝑡𝑡 > 60
𝑥𝑥𝑥𝑥 𝑥𝑥𝑥𝑥

For members with D/t > 60, the yield strength, Fy, in the above equations is replaced by the
critical local buckling stress, defined as the minimum of Fxe or Fxc.
The elastic local buckling stress, Fxe, is defined as:
𝐹𝐹𝑥𝑥𝑥𝑥 = 2𝐶𝐶𝐶𝐶 𝑡𝑡⁄𝐷𝐷

[API Eq. 6.4]

where the critical elastic buckling coefficient, C = 0.3.
The inelastic local buckling stress, Fxc, is defined as:
𝐹𝐹𝑥𝑥𝑥𝑥 = 𝐹𝐹𝑦𝑦 �1.64 − 0.23(𝐷𝐷⁄𝑡𝑡)1⁄4 � ≤ 𝐹𝐹𝑥𝑥𝑥𝑥

2.4

[API Eq. 6.5]

Flexure Check
Members subjected to bending are checked for the following condition:
𝑓𝑓𝑏𝑏
≤ 1.0
𝐹𝐹𝑏𝑏

Compression Check

[API 6.2.3]

5

Steel Frame Design API RP 2A-WSD 22nd

Member Design

The allowable bending stress, Fb, is defined as:
⎧0.75𝐹𝐹𝑦𝑦
⎪
⎪

𝐹𝐹𝑦𝑦 𝐷𝐷
� 𝐹𝐹
𝐹𝐹𝑏𝑏 = �0.84 − 1.74
𝐸𝐸𝐸𝐸 𝑦𝑦
⎨
⎪
⎪�0.72 − 0.58 𝐹𝐹𝑦𝑦 𝐷𝐷 � 𝐹𝐹
𝐸𝐸𝐸𝐸 𝑦𝑦
⎩

2.5

𝐷𝐷 1500
≤
𝑡𝑡
𝐹𝐹𝑦𝑦
1500 𝐷𝐷 3000
for
< ≤
𝑡𝑡
𝐹𝐹𝑦𝑦
𝐹𝐹𝑦𝑦
3000 𝐷𝐷
for
< ≤ 300
𝐹𝐹𝑦𝑦
𝑡𝑡
for

[API Eq. 6.6,
6.7, and 6.8]

Shear Check
Members subjected to beam shear are checked for the following condition:
𝑓𝑓𝑣𝑣
≤ 1.0
𝐹𝐹𝑣𝑣

[API 6.2.4.1]

The maximum beam shear stress, fv, and the allowable beam shear stress Fv are defined as:
𝑓𝑓𝑣𝑣 =

𝑉𝑉
0.5𝐴𝐴

𝐹𝐹𝑣𝑣 = 0.4𝐹𝐹𝑦𝑦

[API Eq. 6.9]
[API Eq. 6.10]

Members subjected to torsional shear are checked for the following condition:
𝑓𝑓𝑣𝑣𝑣𝑣
≤ 1.0
𝐹𝐹𝑣𝑣𝑣𝑣

[API 6.2.4.2]

The maximum torsional shear stress, fvt, and the allowable torsional shear stress Fvt are defined
as:
𝑓𝑓𝑣𝑣𝑣𝑣 =

𝑀𝑀𝑡𝑡 (𝐷𝐷⁄2)
𝐼𝐼𝑝𝑝

𝐹𝐹𝑣𝑣𝑣𝑣 = 0.4𝐹𝐹𝑦𝑦

2.6

[API Eq. 6.11]
[API Eq. 6.12]

Hoop Buckling Check
Members subjected to external pressure are checked for the following condition:
𝑓𝑓ℎ ≤ 𝐹𝐹ℎ𝑐𝑐 ⁄𝑆𝑆𝑆𝑆ℎ

[API Eq. 6.13]

𝑓𝑓ℎ = 𝑝𝑝𝑝𝑝⁄2𝑡𝑡

[API Eq. 6.14]

The hoop stress due to hydrostatic pressure, fh, is defined as:

Shear Check

6

Steel Frame Design API RP 2A-WSD 22nd

Member Design

The critical hoop buckling stress, Fhc, is defined as:

𝐹𝐹ℎ𝑐𝑐

𝐹𝐹ℎ𝑒𝑒
⎧
⎪0.45𝐹𝐹𝑦𝑦 + 0.18𝐹𝐹ℎ𝑒𝑒
1.31𝐹𝐹𝑦𝑦
=
⎨1.15 + �𝐹𝐹 ⁄𝐹𝐹 �
𝑦𝑦
ℎ𝑒𝑒
⎪
𝐹𝐹
⎩ 𝑦𝑦

for
𝐹𝐹ℎ𝑒𝑒 ≤ 0.55𝐹𝐹𝑦𝑦
for 0.55𝐹𝐹𝑦𝑦 < 𝐹𝐹ℎ𝑒𝑒 ≤ 1.6𝐹𝐹𝑦𝑦
for
for

1.6𝐹𝐹𝑦𝑦 < 𝐹𝐹ℎ𝑒𝑒 ≤ 6.2𝐹𝐹𝑦𝑦

[API Eq. 6.18]

𝐹𝐹ℎ𝑒𝑒 > 6.2𝐹𝐹𝑦𝑦

The elastic hoop buckling stress, Fhe, is defined as:
𝐹𝐹ℎ𝑒𝑒 = 2𝐶𝐶ℎ 𝐸𝐸 𝑡𝑡⁄𝐷𝐷

[API Eq. 6.16]

The critical hoop buckling coefficient, Ch, is defined as:
0.44 𝑡𝑡⁄𝐷𝐷
⎧
⁄ )3
⎪0.44(𝑡𝑡⁄𝐷𝐷 ) + 0.21(𝐷𝐷 𝑡𝑡
𝑀𝑀4
𝐶𝐶ℎ =
⎨0.736⁄(𝑀𝑀 − 0.636)
⎪0.755⁄(𝑀𝑀 − 0.559)
⎩0.8

for

𝑀𝑀 ≥ 1.6 𝐷𝐷⁄𝑡𝑡

for
for
for

3.5 ≤ M < 0.825 𝐷𝐷⁄𝑡𝑡
1.5 ≤ 𝑀𝑀 < 3.5
𝑀𝑀 < 1.5

for 0.825 𝐷𝐷⁄𝑡𝑡 ≤ 𝑀𝑀 < 1.6 𝐷𝐷⁄𝑡𝑡

The geometric parameter, M, is defined as:
𝑀𝑀 =

2.7

𝐿𝐿
(2 𝐷𝐷⁄𝑡𝑡)0.5
𝐷𝐷

[API Eq. 6.17]

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
+ 𝑓𝑓𝑏𝑏𝑏𝑏
�𝑓𝑓𝑏𝑏𝑏𝑏
𝑓𝑓𝑎𝑎
+
≤ 1.0
0.6𝐹𝐹𝑦𝑦
𝐹𝐹𝑏𝑏

[API Eq. 6.21]

Members subjected to combined axial tension, bending, and hydrostatic pressure are checked
for the following condition:
𝐴𝐴2 + 𝐵𝐵2 + 2𝜈𝜈|𝐴𝐴|𝐵𝐵 ≤ 1.0

[API Eq. 6.26]

where,

𝐴𝐴 =
𝐵𝐵 =

𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 − (0.5𝑓𝑓ℎ )
(𝑆𝑆𝑆𝑆𝑥𝑥 )
𝐹𝐹𝑦𝑦
𝑓𝑓ℎ
(𝑆𝑆𝑆𝑆ℎ )
𝐹𝐹ℎ𝑐𝑐

Axial Tension and Bending Check

7

Steel Frame Design API RP 2A-WSD 22nd

2.8

Member Design

Axial Compression and Bending Check
Members subjected to combined axial compression and bending, without hydrostatic pressure,
are checked for the following conditions:

𝑓𝑓𝑎𝑎
+
𝐹𝐹𝑎𝑎

��

2

2

𝐶𝐶𝑚𝑚𝑚𝑚 𝑓𝑓𝑏𝑏𝑏𝑏
𝐶𝐶𝑚𝑚𝑚𝑚 𝑓𝑓𝑏𝑏𝑏𝑏
+�
𝑓𝑓𝑎𝑎 �
𝑓𝑓 �
1− ′
1 − 𝑎𝑎′
𝐹𝐹𝑒𝑒𝑒𝑒
𝐹𝐹𝑒𝑒𝑒𝑒
𝐹𝐹𝑏𝑏

2
2
+ 𝑓𝑓𝑏𝑏𝑏𝑏
�𝑓𝑓𝑏𝑏𝑏𝑏
𝑓𝑓𝑎𝑎
+
≤ 1.0
0.6𝐹𝐹𝑦𝑦
𝐹𝐹𝑏𝑏

[API Eq. 6.23]
≤ 1.0
[API Eq. 6.21]

where,

𝐹𝐹𝑒𝑒′ =

12𝜋𝜋 2 𝐸𝐸
23(𝐾𝐾𝐾𝐾 ⁄𝑟𝑟)2

[AISC H1]

The reduction factors, Cmx and Cmy are calculated according to AISC H1.
𝑓𝑓

If 𝐹𝐹𝑎𝑎 ≤ 0.15, the previous two conditions are substituted by the following condition:
𝑎𝑎

2
2
+ 𝑓𝑓𝑏𝑏𝑏𝑏
𝑓𝑓𝑎𝑎 �𝑓𝑓𝑏𝑏𝑏𝑏
+
≤ 1.0
𝐹𝐹𝑎𝑎
𝐹𝐹𝑏𝑏

[API Eq. 6.22]

Members subjected to combined axial compression, bending, and hydrostatic pressure are
checked for the following conditions:
𝑓𝑓𝑎𝑎 + (0.5𝑓𝑓ℎ )
𝑓𝑓𝑏𝑏
(𝑆𝑆𝑆𝑆𝑥𝑥 ) + (𝑆𝑆𝑆𝑆𝑏𝑏 ) ≤ 1.0
𝐹𝐹𝑥𝑥𝑥𝑥
𝐹𝐹𝑦𝑦
𝑆𝑆𝑆𝑆ℎ

𝑓𝑓ℎ
≤ 1.0
𝐹𝐹ℎ𝑐𝑐

If 𝑓𝑓𝑥𝑥 > 0.5𝐹𝐹ℎ𝑎𝑎 , the following condition is also satisfied:
𝑓𝑓𝑥𝑥 − 0.5𝐹𝐹ℎ𝑎𝑎
𝑓𝑓ℎ 2
+ � � ≤ 1.0
𝐹𝐹𝑎𝑎𝑎𝑎 − 0.5𝐹𝐹ℎ𝑎𝑎
𝐹𝐹ℎ𝑎𝑎

[API Eq. 6.27]

[API Eq. 6.28]

[API Eq. 6.29]

where,

F𝑎𝑎𝑎𝑎 =

𝐹𝐹𝑥𝑥𝑥𝑥
𝑆𝑆𝑆𝑆𝑥𝑥

Axial Compression and Bending Check

8

Steel Frame Design API RP 2A-WSD 22nd

𝐹𝐹ℎ𝑎𝑎 =

Member Design

𝐹𝐹ℎ𝑒𝑒
𝑆𝑆𝑆𝑆ℎ

𝑓𝑓𝑥𝑥 = 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 + (0.5𝑓𝑓ℎ )

Axial Compression and Bending Check

9

3

Joint Design

This chapter provides the details of the joint punching load check algorithm that is used for
tubular joints in accordance with API RP 2A-WSD Section 7.3.
API RP 2A-WSD allows the joints to be designed on the basis of nominal loads in the braces.

3.1

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

Brace diameter, in

D

Chord diameter, in

g

Gap distance, in

t

Brace thickness, in

T

Chord thickness, in

θ

Angle measured from the chord to the brace

10

Steel Frame Design API RP 2A-WSD 22nd

Joint Design

d
Brace

t
g

T

Brace
Chord

θ

D

Figure 1 - Joint geometry

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

3.2

𝑑𝑑
𝐷𝐷

𝛾𝛾 =

𝐷𝐷
2𝑇𝑇

𝜏𝜏 =

Allowable Capacities

𝑡𝑡
𝑇𝑇

The allowable brace axial load, Pa, is defined as:
𝐹𝐹𝑦𝑦𝑦𝑦 𝑇𝑇 2
𝑃𝑃𝑎𝑎 = 𝑄𝑄𝑢𝑢 𝑄𝑄𝑓𝑓
𝐹𝐹𝐹𝐹 sin 𝜃𝜃

[API Eq. 7.1]

The allowable brace bending moment, Ma, is defined as:
𝑀𝑀𝑎𝑎 = 𝑄𝑄𝑢𝑢 𝑄𝑄𝑓𝑓

𝐹𝐹𝑦𝑦𝑦𝑦 𝑇𝑇 2 𝑑𝑑
𝐹𝐹𝐹𝐹 sin 𝜃𝜃

[API Eq. 7.2]

where the safety factor, FS = 1.60.
The chord load factor, Qf, is defined as:
𝑄𝑄𝑓𝑓 = �1 + 𝐶𝐶1 �

𝐹𝐹𝐹𝐹𝑀𝑀𝑖𝑖𝑖𝑖𝑖𝑖
𝐹𝐹𝐹𝐹𝑃𝑃𝑐𝑐
� − 𝐶𝐶2 �
� − 𝐶𝐶3 𝐴𝐴2 �
𝑃𝑃𝑦𝑦
𝑀𝑀𝑝𝑝

[API Eq. 7.3]

The parameter, A, is defined as:

Allowable Capacities

11

Steel Frame Design API RP 2A-WSD 22nd

Joint Design
2 0.5

2

𝐹𝐹𝐹𝐹𝑃𝑃𝑐𝑐
𝐹𝐹𝐹𝐹𝑀𝑀𝑐𝑐
𝐴𝐴 = ��
� +�
� �
𝑃𝑃𝑦𝑦
𝑀𝑀𝑝𝑝

[API Eq. 7.4]

where the safety factor, FS = 1.20 where the 1/3 increase is applicable. Pc is the nominal axial
load and Mc is the nominal bending resultant in the chord.
2
2
𝑀𝑀𝑐𝑐 = �𝑀𝑀𝑖𝑖𝑖𝑖𝑖𝑖
+ 𝑀𝑀𝑜𝑜𝑜𝑜𝑜𝑜

[API 4.3.4]

The coefficients, C1, C2, and C3, are determined based on API Table 7.3.
Table 2 – Coefficients, C1, C2, and C3
Joint Type

C1

C2

C3

K axial
T&Y axial
X axial 𝛽𝛽 ≤ 0.9
X axial 𝛽𝛽 = 1.0
All joints moment

0.2
0.3
0.2
-0.2
0.2

0.2
0
0
0
0

0.3
0.8
0.5
0.2
0.4

The ultimate strength factor, Qu, is determined based on API Table 7.2.
Table 3 – Factor, Qu
Brace Action
Joint
Class
K
T&Y

X

Axial
Tension

Axial
Compression

(16 + 1.2𝛾𝛾)𝛽𝛽1.2 𝑄𝑄𝑔𝑔 ≤ 40𝛽𝛽1.2 𝑄𝑄𝑔𝑔
30𝛽𝛽
2.8
+ (20 + 0.8𝛾𝛾)𝛽𝛽1.6
≤ 2.8 + 36𝛽𝛽1.6
23𝛽𝛽
for 𝛽𝛽 ≤ 0.9
[2.8
+ (12 + 0.1𝛾𝛾)𝛽𝛽]𝑄𝑄𝛽𝛽
20.7 + (𝛽𝛽 − 0.9)
(17𝛾𝛾 − 220)
for 𝛽𝛽 > 0.9

In-plane
Bending

Out-of-plane
Bending

(5 + 0.7𝛾𝛾)𝛽𝛽1.2

2.5+(4.5 + 0.2𝛾𝛾)𝛽𝛽2.6

The geometric factor, Qβ, is defined as:
0.3
for 𝛽𝛽 > 0.6
𝑄𝑄𝛽𝛽 = �𝛽𝛽(1 − 0.833𝛽𝛽)
1.0
for 𝛽𝛽 ≤ 0.6

[API Table 7.2]

The gap factor, Qg, is defined as:
𝑄𝑄𝑔𝑔 = �

Allowable Capacities

1 + 0.2[1 − 2.8 𝑔𝑔⁄𝐷𝐷 ]3 ≥ 1.0 for 𝑔𝑔⁄𝐷𝐷 ≥ 0.05
0.13 + 0.65𝜙𝜙𝛾𝛾 0.5
for 𝑔𝑔⁄𝐷𝐷 < −0.05

[API Table 7.2]

12

Steel Frame Design API RP 2A-WSD 22nd

Joint Design

𝜙𝜙 = 𝑡𝑡 𝐹𝐹𝑦𝑦𝑦𝑦 ⁄�𝑇𝑇𝐹𝐹𝑦𝑦 �

3.3

Axial and Bending Check
Joints are checked for the following condition:
𝑃𝑃
𝑀𝑀 2
𝑀𝑀
≤ 1.0
� �+� � +� �
𝑃𝑃𝑎𝑎
𝑀𝑀𝑎𝑎 𝑖𝑖𝑖𝑖𝑖𝑖
𝑀𝑀𝑎𝑎 𝑜𝑜𝑜𝑜𝑜𝑜

[API Eq. 7.6]

The subscripts IPB and OPB correspond to in-plane bending and out-of-plane bending,
respectively.

Axial and Bending Check

13

4

References

American Institute of Steel Construction. (1989). Manual of Steel Construction - Allowable Stress Design
(9th ed.). Chicago, Illinois, USA: American Institute of Steel Construction.
American Petroleum Institute. (2014). Recommended Practice for Planning, Designing and Constructing
Fixed Offshore Platforms - Working Stress Design (22nd ed.). Washington, District of Columbia,
USA: API Publishing Services.

14



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