<!-- source-page: 351 -->

![](images/page-351_0caf603f214a005209919f8f3d275b6888d94ec8f2bb4e4fa46a262309d1d3d1.jpg)

<details>
<summary>scatter</summary>

| Point | x | y |
|---|---|---|
| 1 | 0.5 | 0.5 |
| 2 | 0.5 | 0.5 |
| 3 | 0.5 | 0.5 |
| 4 | 0.5 | 0.5 |
| 5 | 0.5 | 0.5 |
</details>

Default integration, beam in a plane

![](images/page-351_fd9aee3378f465911f3f13d754b1ab7759cac12b109f1d6c6d9a16ec1e30c437.jpg)

<details>
<summary>scatter</summary>

| Point | X | Y |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 1 | 2 |
| 3 | 1 | 3 |
| 4 | 1 | 4 |
| 5 | 1 | 5 |
| 6 | 1 | 6 |
| 7 | 1 | 7 |
| 8 | 1 | 8 |
| 9 | 1 | 9 |
| 10 | 1 | 10 |
| 11 | 1 | 11 |
| 12 | 1 | 12 |
| 13 | 1 | 13 |
| 14 | 1 | 14 |
| 15 | 1 | 15 |
| 16 | 1 | 16 |
| 17 | 1 | 17 |
</details>

Default integration, beam in space

# Geometric input data

Radius

# Default integration

Beam in a plane: 5 points

Beam in space: 3 points radially, 8 circumferentially (17 total; trapezoidal rule). Integration point 1 is situated at the center of the beam and is used for output purposes only. It makes no contribution to the stiffness of the element; therefore, the integration point volume (IVOL) associated with this point is zero.

# Nondefault integration input for a beam section integrated during the analysis

Beam in a plane: A maximum of 9 points are permitted.

Beam in space: Give an odd number of points in the radial direction, then an even number of points in the circumferential direction.

# Default stress output points if a beam section integrated during the analysis is used

Beam in a plane: Bottom and top (points 1 and 5 above for default integration).

Beam in space: On the intersection of the surface with the 1- and 2-axes (points 3, 7, 11, and 15 above for default integration).

# Temperature and field variable input at specific points for beam sections integrated during the analysis

Give the value at each of the points shown below.

<!-- source-page: 352 -->

![](images/page-352_bd3bf1edfe74cc070c5a516ea120d31f5841165d64d849ed6c90300b5047a826.jpg)

<details>
<summary>text_image</summary>

2
3
2
1
1
</details>

Beam in a plane

![](images/page-352_630cc84df2b4aa4eb1eac1533e4c5cece637f61e507d6d23b3686af3356b50dd.jpg)

<details>
<summary>text_image</summary>

2
3
4
2
1
1
</details>

Beam in space

# Temperature input for a frame section

Constant temperature throughout the element cross-section is assumed; therefore, only one temperature value per node is required.

# Hexagonal section

Input File Usage: Use either of the following options:

\*BEAM SECTION, SECTION=HEX   
\*BEAM GENERAL SECTION, SECTION=HEX

Abaqus/CAE Usage: Property module: Create Profile: Hexagonal

![](images/page-352_4530b423a9a811153616db254e6a4d9f7ae75a8c4b6b4369f913481c692875d8.jpg)

<details>
<summary>text_image</summary>

2
5
4
t
4
3
3
1
d
2
2
1
</details>

Default integration, beam in a plane

![](images/page-352_f6c42d4b636c9b225b1d55bcac17a6f71756e2666a74ff11e595b13fe7312ef1.jpg)

<details>
<summary>text_image</summary>

2
4
3
t
6
2
7
1
d
12
8
9
10
11
</details>

Default integration, beam in space

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# Geometric input data

d (circumscribing radius), t (wall thickness)

# Default integration (Simpson)

Beam in a plane: 5 points

Beam in space: 3 points in each wall segment (12 total)

# Nondefault integration input for a beam section integrated during the analysis

Beam in a plane: Give the number of points along the section wall, moving in the second beam section axis direction. This number must be odd and greater than or equal to three.

Beam in space: Give the number of points in each wall segment. This number must be odd and greater than or equal to three.

# Default stress output points if a beam section integrated during the analysis is used

Beam in a plane: Bottom and top (points 1 and 5 above for default integration).

Beam in space: Vertices (points 1, 3, 5, 7, 9, and 11 above for default integration).

# Temperature and field variable input at specific points for beam sections integrated during the analysis

Give the value at each of the points shown below.

![](images/page-353_ffbb944e52c6dc62eb9a9f3ebda9ea311303d04310d0014d961b9a5791f9d650.jpg)

<details>
<summary>text_image</summary>

2
3
2
2
1
1
</details>

Beam in a plane

![](images/page-353_c6de221de52373c6033f097ef5bd56c6048b1940f60b30bf1580d93af3b4d98d.jpg)

<details>
<summary>text_image</summary>

2
3
2
4
1
1
5
6
</details>

Beam in space

<!-- source-page: 354 -->

# I-section

Input File Usage: Use one of the following options: \*BEAM SECTION, SECTION=I \*BEAM GENERAL SECTION, SECTION=I \*FRAME SECTION, SECTION=I

Abaqus/CAE Usage: Property module: Create Profile: I

![](images/page-354_114ebdcdfec17990f6587d3d2f72b265be4bcfac81449784bcefd126d0cd00ce.jpg)

<details>
<summary>text_image</summary>

2
b₂
t₂
5
4
3
t₃
2
1
h
l
t₁
b₁
</details>

Default integration, beam in a plane

![](images/page-354_99bf43a93a8ac9d099e9961b904d784aaacfead822437a979b28fd9b978ae723.jpg)

<details>
<summary>text_image</summary>

2
b₂
9 10 11 12 13
t₂
8
1
t₃
7
6
t₁
1 2 3 4 5
b₁
l
h
</details>

Default integration, beam in space

# Geometric input data

$$
l, h, b _ {1}, b _ {2}, t _ {1}, t _ {2}, t _ {3}
$$

By allowing you to specify l, the origin of the local cross-section axis can be placed anywhere on the symmetry line (the local 2-axis). In the above figures a negative value of l implies that the origin of the local cross-section axis is below the lower edge of the bottom flange, which may be needed when constraining a beam stiffener to a shell.

# Defining a T-section

Input File Usage: Set $b _ { 1 }$ and $t _ { 1 }$ or $b _ { 2 }$ and $t _ { 2 }$ to zero to model a T-section.

Abaqus/CAE Usage: Property module: Create Profile: T

<!-- source-page: 355 -->

# Default integration (Simpson)

Beam in a plane: 5 points (one in each flange plus 3 in web)

Beam in space: 5 points in web, 5 in each flange (13 total)

# Nondefault integration input for a beam section integrated during the analysis

Beam in a plane: Give the number of points in the second beam section axis direction. This number must be odd and greater than or equal to three.

Beam in space: Give the number of points in the lower flange first, then in the web, and then in the upper flange. These numbers must be odd and greater than or equal to three in each nonvanishing section.

# Default stress output points if a beam section integrated during the analysis is used

Beam in a plane: Flanges (points 1 and 5 above for default integration).

Beam in space: Ends of flanges (points 1, 5, 9, and 13 above for default integration).

# Temperature and field variable input at specific points for beam sections integrated during the analysis

Give the value at each of the points shown below.

![](images/page-355_50c108cd431595107ea0fd6074c66554bf62a8bf33dbd1c7cfa5401aa65e985d.jpg)

<details>
<summary>text_image</summary>

2
3
2
1
1
</details>

Beam in a plane

![](images/page-355_7b3081e8b3e9b18a2b05bf7ee9802f1a925f7d5faba334582b40d50b4a6394a3.jpg)

<details>
<summary>text_image</summary>

2
4
5
3
1
1
2
</details>

Beam in space

For a beam in space the temperature is first interpolated linearly through the flanges based on the temperature at points 1 and 2, and then 4 and 5, respectively. It is then interpolated parabolically through the web.

<!-- source-page: 356 -->

# Temperature input for a frame section

Constant temperature throughout the element cross-section is assumed; therefore, only one temperature value per node is required.

# L-section

Input File Usage: Use either of the following options: \*BEAM SECTION, SECTION=L \*BEAM GENERAL SECTION, SECTION=L

Abaqus/CAE Usage: Property module: Create Profile: L

![](images/page-356_5504caf96f9dcdbf9d83b19b03a5a6558cdcea93806b7a2a5fe33c973b6a13c4.jpg)

<details>
<summary>text_image</summary>

2
5
4
t₂
3
b
2
1
t₁
1
a
</details>

Default integration, beam in a plane

![](images/page-356_f1c537fa9bfbc941be080f3ee6585cffbc6aaa41a101f26cb7f27cb056ab7a38.jpg)

<details>
<summary>text_image</summary>

2
9
8
7
6
5
4 3 2 1
b
t₂
t₁
1
a
</details>

Default integration, beam in space

# Geometric input data

$$
\pmb {a}, \pmb {b}, t _ {1}, t _ {2}
$$

# Default integration (Simpson)

Beam in a plane: 5 points

<!-- source-page: 357 -->

Beam in space: 5 points in each flange (9 total)

# Nondefault integration input for a beam section integrated during the analysis

Beam in a plane: Give the number of points in the second beam section axis direction. This number must be odd and greater than or equal to three.

Beam in space: Give the number of points in the first beam section axis direction, then the number of points in the second beam section axis direction. These numbers must be odd and greater than or equal to three.

# Default stress output points if a beam section integrated during the analysis is used

Beam in a plane: Bottom and top (points 1 and 5 above for default integration).

Beam in space: End of flange along positive local 1-axis; section corner; end of flange along positive local 2-axis (points 1, 5, and 9 above for default integration).

# Temperature and field variable input at specific points for beam sections integrated during the analysis

Give the value at each of the points shown below.

![](images/page-357_ca8e786b86a8cd0911bf02ad97aa593ad468745d55a1d88843f99ee6603c9568.jpg)

<details>
<summary>text_image</summary>

2
2
1
1
</details>

Beam in a plane

![](images/page-357_9ed7114f5e5455934d21edd75b2f954f79963a64a8ce5479ae0bf854c0d95c15.jpg)

<details>
<summary>text_image</summary>

2
3
2
1
</details>

Beam in space

<!-- source-page: 358 -->

# Pipe section (thin-walled)

Pipe cross-sections can be associated with beam, pipe, or frame elements.

Input File Usage: Use one of the following options:

\*BEAM SECTION, SECTION=PIPE

\*BEAM GENERAL SECTION, SECTION=PIPE

\*FRAME SECTION, SECTION=PIPE

Abaqus/CAE Usage: Property module: Create Profile: Pipe: Thin walled

![](images/page-358_37b5dc5089d5b66019d016d233f6aade0ee0677d27695249b4c4676f659470ea.jpg)

<details>
<summary>text_image</summary>

2
5
4
4
r
3
3
1
2
2
t
1
2
</details>

Default integration, beam in a plane

![](images/page-358_30efe78d0f5a4c2e0607ff366194521319d93298aa51c2d2c386578629c38f12.jpg)

<details>
<summary>text_image</summary>

2
5
4
r
7
3
1
8
2
t
</details>

Default integration, beam in space

# Geometric input data

r (outside radius), t (wall thickness)

# Default integration

Beam in a plane: 5 points (Simpson’s rule)

Beam in space: 8 points (trapezoidal rule)

# Nondefault integration input for a beam section integrated during the analysis

Beam in a plane: Give an odd number of points. This number must be greater than or equal to five.

Beam in space: Give an even number of points. This number must be greater than or equal to eight.

<!-- source-page: 359 -->

# Default stress output points if a beam section integrated during the analysis is used

Beam in a plane: Bottom and top (points 1 and 5 above for default integration).

Beam in space: On the intersection of the surface with the 1- and 2-axes (points 1, 3, 5, and 7 above for default integration).

# Temperature and field variable input at specific points for beam sections integrated during the analysis

Give the value at each of the points shown below.

![](images/page-359_92395efebd26ee2e36534361c9b5cac3364a6d8c9703baa5097d7adb072af3d4.jpg)

<details>
<summary>text_image</summary>

2
3
2
2
1
1
</details>

Beam in a plane

![](images/page-359_867d6688cc5e7ac1b5e5f35e4f5e312cf392dff58cfb2b8ef1a3dad0f58ce94c.jpg)

<details>
<summary>text_image</summary>

2
3
4
2
1
1
</details>

Beam in space

# Temperature input for a frame section

Constant temperature throughout the element cross-section is assumed; therefore, only one temperature value per node is required.

# Pipe section (thick-walled)

Thick-walled pipe cross-sections can be associated with beam or pipe elements.

Input File Usage: Use the following option:

\*BEAM SECTION, SECTION=THICK PIPE

Abaqus/CAE Usage: Property module: Create Profile: Pipe: Thick walled

<!-- source-page: 360 -->

![](images/page-360_af0cb6017072c13409870c5b615013fd9dd16a25a297de7291b2aa105bbac31c.jpg)

<details>
<summary>radar</summary>

| Point | X | Y |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 1 | 2 |
| 3 | 1 | 3 |
| 4 | 1 | 4 |
| 5 | 1 | 5 |
| 6 | 1 | 6 |
| 7 | 1 | 7 |
| 8 | 1 | 8 |
| 9 | 1 | 9 |
| 10 | 1 | 10 |
| 11 | 1 | 11 |
| 12 | 1 | 12 |
| 13 | 1 | 13 |
| 14 | 1 | 14 |
| 15 | 1 | 15 |
| 16 | 1 | 16 |
| 17 | 1 | 17 |
| 18 | 1 | 18 |
| 19 | 1 | 19 |
| 20 | 1 | 20 |
| 21 | 1 | 21 |
| 22 | 1 | 22 |
| 23 | 1 | 23 |
| 24 | 1 | 24 |
| 25 | 1 | 25 |
| 26 | 1 | 26 |
| 27 | 1 | 27 |
| 28 | 1 | 28 |
| 29 | 1 | 29 |
| 30 | 1 | 30 |
| 31 | 1 | 31 |
| 32 | 1 | 32 |
| 33 | 1 | 33 |
| 34 | 1 | 34 |
| 35 | 1 | 35 |
| 36 | 1 | 36 |
| 37 | 1 | 37 |
| 38 | 1 | 38 |
| 39 | 1 | 39 |
| 40 | 1 | 40 |
| 41 | 1 | 41 |
| 42 | 1 | 42 |
| 43 | 1 | 43 |
| 44 | 1 | 44 |
| 45 | 1 | 45 |
| 46 | 1 | 46 |
| 47 | 1 | 47 |
| 48 | 1 | 48 |
| 49 | 1 | 49 |
| 50 | 1 | 50 |
| 51 | 1 | 51 |
| 52 | 1 | 52 |
| 53 | 1 | 53 |
| 54 | 1 | 54 |
| 55 | 1 | 55 |
| 56 | 1 | 56 |
| 57 | 1 | 57 |
| 58 | 1 | 58 |
| 59 | 1 | 59 |
| 60 | 1 | 60 |
| 61 | 1 | 61 |
| 62 | 1 | 62 |
| 63 | 1 | 63 |
| 64 | 1 | 64 |
| 65 | 1 | 65 |
| 66 | 1 | 66 |
| 67 | 1 | 67 |
| 68 | 1 | 68 |
| 69 | 1 | 69 |
| 70 | 1 | 70 |
| 71 | 1 | 71 |
| 72 | 1 | 72 |
| 73 | 1 | 73 |
| 74 | 1 | 74 |
| 75 | 1 | 75 |
| 76 | 1 | 76 |
| 77 | 1 | 77 |
| 78 | 1 | 78 |
| 79 | 1 | 79 |
| 80 | 1 | 80 |
| 81 | 1 | 81 |
| 82 | 1 | 82 |
| 83 | 1 | 83 |
| 84 | 1 | 84 |
| 85 | 1 | 85 |
| 86 | 1 | 86 |
| 87 | 1 | 87 |
| 88 | 1 | 88 |
| 89 | 1 | 89 |
| 90 | 1 | 90 |
| 91 | 1 | 91 |
| 92 | 1 | 92 |
| 93 | 1 | 93 |
| 94 | 1 | 94 |
| 95 | 1 | 95 |
| 96 | 1 | 96 |
| 97 | 1 | 97 |
| 98 | 1 | 98 |
| 99 | 1 | 99 |
| 100 | 1 | 100 |
</details>

Default integration, beam in a plane

![](images/page-360_88d6c9fa99933972dbabd7199e55238a12e70d5fff9649187fdb644a777f221c.jpg)  
Default integration, beam in space

# Geometric input data

r (outside radius), t (wall thickness)

# Default integration

Beam in a plane: 3 points radially (Simpson’s rule), 5 circumferentially (trapezoidal rule)

Beam in space: 3 points radially (Simpson’s rule), 8 circumferentially (trapezoidal rule)

# Nondefault integration input for a beam section integrated during the analysis

Beam in a plane: Give an odd number of points in the radial direction, then an odd number of points (greater than or equal to 5) in the circumferential direction.

Beam in space: Give an odd number of points in the radial direction, then an even number of points (greater than or equal to 8) in the circumferential direction.

# Default stress output points if a beam section integrated during the analysis is used

Beam in a plane: Bottom and top on the pipe midsurface (points 2 and 14 above for default integration).

Beam in space: On the intersection of the pipe midsurface with the 1- and 2-axes (points 2, 8, 14, and 20 above for default integration).
