> ## Documentation Index
> Fetch the complete documentation index at: https://calcs.com/docs/llms.txt
> Use this file to discover all available pages before exploring further.

# Steel Beam Validation Examples

> Steel Beam Validation Examples

This article shows validation and design examples for steel beams per the *AISC Specification*, 2016. Note that values will vary slightly (+/- 1%) due to round-off errors.

## Example 1 - Unequal Leg Angle, Long Leg Up

Reference: Whitney McNulty, *Single Angle Design Manual*, 2008, **Example 4.5, p. 4-66**

In this example, we find the flexural capacity of an unequal leg angle with the long leg up. Note that in the reference, no loads are calculated, only capacity. A uniformly distributed load is assumed. Only nominal loads are looked at thus the distinction between ASD or LRFD does not matter here. Strength calculations are based on the principal axis, and at the end converted to the geometric X-axis.

### Inputs

| Parameter                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         | Value            |
| ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------- |
| Cross-section                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | L6x4x3/8         |
| Angle Orientation                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | Long leg up      |
| Yield Strength $F\_y$                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | 36 ksi           |
| Length $L$                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | 8'               |
| Lateral Bracing                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   | Unbraced         |
| Support Conditions                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | Simply Supported |
| <img src="https://mintcdn.com/clearcalcs/wCKMGQrVqWo51C47/images/migrated/a835586a9043-file-tnwfftmvfu.png?fit=max&auto=format&n=wCKMGQrVqWo51C47&q=85&s=a11106fde6ff0cefbc7e7261d04be375" alt="" width="225" height="299" data-path="images/migrated/a835586a9043-file-tnwfftmvfu.png" /><br /> |                  |

### Outputs

| Result                                                                           | Example      | Calcs.com    |
| -------------------------------------------------------------------------------- | ------------ | ------------ |
| Major Principal Axis Yield Moment                                                | 136.4 kip-in | 136.2 kip-in |
| Major Principal Axis Leg Local Buckling Moment                                   | 199.3 kip-in | 199.2 kip-in |
| Major Principal Axis Elastic Lateral-Torsional Buckling Moment ($C\_b$ = 1.14)\* | 326.5 kip-in | 328.0 kip-in |
| Major Principal Axis Nominal LTB Moment Capacity                                 | 158.8 kip-in | 158.8 kip-in |
| Minor Principal Axis Plastic Moment                                              | 68.0 kip-in  | 68.0 kip-in  |
| Minor Principal Axis Leg Local Buckling Moment                                   | 125.1 kip-in | 125.0 kip-in |
| Nominal Moment Capacity in Gravity Loading                                       | 85.2 kip-in  | 85.2 kip-in  |
| Total Deflection Under a 0.53 kip/ft Load (Vector Sum)\*\*                       | 0.27 in      | 0.27 in      |
|                                                                                  |              |              |

\*The formula for the elastic LTB moment changed slightly between the 2005 AISC Specification (used in the example) and the 2016 AISC Specification (used by Calcs.com), which is the reason for the differences here.

\*\*The example splits deflection components in their horizontal and vertical components, while Calcs.com currently only reports the vector sum of the components.

## Example 2 - Unequal Leg Angle, Short Leg Up

Reference: Whitney McNulty, *Single Angle Design Manual*, 2008, **Example 4.8, p. 4-85**

In this example, we find the flexural capacity of an unequal leg angle with the short leg down. Note that in the reference, no loads are calculated, only capacity. A uniformly distributed load is assumed. Only nominal loads are looked at thus the distinction between ASD or LRFD does not matter here. Strength calculations are based on the principal axis, and at the end converted to the geometric X-axis.

### Inputs

| Parameter                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   | Value            |
| ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------- |
| Cross-section                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               | L6x4x3/8         |
| Angle Orientation<br />                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | Short leg up     |
| Yield Strength $F\_y$                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       | 36 ksi           |
| Length $L$                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  | 8'               |
| Lateral Bracing                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | Unbraced         |
| Support Conditions                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | Simply Supported |
| <img src="https://mintcdn.com/clearcalcs/0BKfHfJWdoXOtU8o/images/migrated/e9784216e439-file-mcm6tmwjnl.png?fit=max&auto=format&n=0BKfHfJWdoXOtU8o&q=85&s=c80ec0b1ec06e33490489abec0f45298" alt="" width="226" height="194" data-path="images/migrated/e9784216e439-file-mcm6tmwjnl.png" /> |                  |

### Outputs

| Result                                                                           | Example      | Calcs.com    |
| -------------------------------------------------------------------------------- | ------------ | ------------ |
| Major Principal Axis Yield Moment                                                | 136.4 kip-in | 136.2 kip-in |
| Major Principal Axis Elastic Lateral-Torsional Buckling Moment ($C\_b$ = 1.14)\* | 627.9 kip-in | 632.1 kip-in |
| Major Principal Axis Nominal LTB Moment Capacity                                 | 187.5 kip-in | 187.5 kip-in |
| Minor Principal Axis Plastic Moment                                              | 68.0 kip-in  | 68.0 kip-in  |
| Minor Principal Axis Leg Local Buckling Moment                                   | 125.1 kip-in | 125.0 kip-in |
| Nominal Moment Capacity in Gravity Loading                                       | 64.1 kip-in  | 64.1 kip-in  |
| Total Deflection Under a 0.40 kip/ft Load (Vector Sum)\*\*                       | 0.426 in     | 0.427 in     |
|                                                                                  |              |              |

\*The formula for the elastic LTB moment changed slightly between the 2005 AISC Specification (used in the example) and the 2016 AISC Specification (used by Calcs.com), which is the reason for the differences here.

\*\*The example splits deflection components in their horizontal and vertical components, while Calcs.com currently only reports the vector sum of the components.
