Beams

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

Outputs

Result	Example	ClearCalcs
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 ClearCalcs), which is the reason for the differences here.

**The example splits deflection components in their horizontal and vertical components, while ClearCalcs 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	Short leg up
Yield Strength $F_y$	36 ksi
Length $L$	8'
Lateral Bracing	Unbraced
Support Conditions	Simply Supported

Outputs

Result	Example	ClearCalcs
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 ClearCalcs), which is the reason for the differences here.

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