Lateral Torsional Buckling (LTB) Inputs

Lateral Torsional Buckling (LTB) occurs when a beam bends about its major axis and the compression flange is not restrained, causing the member to twist sideways under bending. The inputs in this section let you define restraint conditions, effective lengths, and modification factors so the design checks match your real structure.

Effective length (Le, K-factors):
Defines the unbraced length for LTB

Le End 1: Effective length factor for the start (lower node-numbered) end of the beam.
- With the fully restrained option set, this will be reflected in the calculation outputs, and the lateral restraint input will have no effect on the design.
- Where the beam is not fully restrained for LTB, then the restraint positions are defined in the 📄 Lateral Restraints Tab
Le End 2 as 1: Check this box to use the same effective length at end 2 (higher node-numbered).
- If un-checked the additional Le End 2 input is presented and the software will average the two factors.

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End fixity is a key driver of LTB capacity. A beam with both ends fully fixed against rotation will have a shorter effective LTB length (higher capacity) than one with pinned ends. Typical values:

Fixed–fixed: 0.7
Pinned–pinned: 1.0
Cantilever: 2.0

Loading Type

Control over shape of BM used for; C1,2,3 factor calculation and Table B.3 in EC design; Table 18 m_LT in BS 5950:2000 design
- Pre MasterSeries 2025
- MasterSeries 2025+
If set to Autoselect, MasterSeries automatically picks the curve appropriate to the member type and loading.

Major Axis Stress

The new inputs in MasterSeries 2024 allow you to explicitly tell the software which part of the section is in compression (or tension) from the major axis moment, affecting section classification and lateral torsional buckling checks.

Unequal Angles:

Long Leg in Compression:
Short Leg in Compression:

In BS 5950:2000 design, controls the sign of the monosymmetric index value B.9.3 used in the calculation of the buckling slenderness faction 'v'.

Symmetrical I sections:

Top Flange in Tension:
Top Flange in Compression:

In MasterSeries 2024 and below, this setting used to control the Zj value used in Mcr and section classification of asymmetrical I sections. In MasterSeries 2025 for asymmetrical I section that have moment this input is not enabled as the flange that is in compression is automatically controlled by the sign of moment. When double curvature bending is detected both flanges are seem to be in compression, and the most critical section classification is chosen. In addition both compression flange side buckling checks are performed, with the most critical chosen.

T sections:

Flange in Tension:
Flange in Compression:

In BS 5950:2000 design, controls the sign of the monosymmetric index value B.2.8 used in the calculation of the buckling slenderness faction 'v'. This method of calculating the dimensionless slenderness ratio for lateral torsional buckling λ_LT used also used in Eurocode design.

Other Sections:

Top in Tension:
Top in Compression:

More generally, this setting also influences the additional flange plate projection classification (on I sections, Channel Sections and RHS/RHS hollow sections) by dictating if the plate is in compression or tension from the major axis moment.

Minor Axis Stress

This is used for Channel and PFC shaped sections to dictate sense of force created in the web from minor-axis bending moment.

Web in Tension:
Web in Compression:

Influences the Minor axis Plastic Moment Capacity values in the presence of axial loading. Influences section classification by dictating sense of force created in the web from minor axis moment, however member axial force is also used to calculate value of compression stress in the web.

Cantilever / Non-Cantilever:
Captures Warping Condition at supports

MasterSeries tests the geometry to see if the beam qualifies as a cantilever. The dropdown will update automatically, but can be adjusted manually

Non-Cantilever
- BS5950:2000 General Case for beams Table 18
- EC3: Equivalent Uniform Moment factor C1 default values can be overwritten in the EC3 Mcr Factors below
Cantilever - Warping Free: End allows twist without restraint. This is common at free ends.
- BS5950:2000 For cantilevers without intermediate lateral restraint: mLT = 1.00
- EC3: Equivalent Uniform Moment factor C1 taken from NCCI SN006
Cantilever - Warping Fixed: End prevents twist, e.g. by stiffeners, deep connections, or diaphragm action.
- BS5950:2000 For cantilevers without intermediate lateral restraint: mLT = 1.00
- EC3: Equivalent Uniform Moment factor C1 taken from NCCI SN006

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Cantilevers are more prone to LTB, especially if warping is unrestrained. Confirm your input matches your structural intent.

Warping fixity is rare in practice unless specifically detailed. Assume Warping Free unless you are confident the detail provides full torsional restraint.

See:
SCI P360 Section 3.2
NCCI SN006a Elastic critical moment of cantilevers

Eurocode factors (C1–C3):EC3 Only - Refine Mcr calculations to reflect bending diagram and load application

Eurocode modification factors used in the elastic critical moment equation.
Depend on the shape of the bending moment diagram.
Value is automatically determined by the software.
- When Cantilever is specified, values can not be amended on analytical cantilevers
- When Non-Cantilever is specified, values can be amended

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Leave as default '0' values (calculated by software) unless you have a special case. If overriding, ensure your values come from reliable references (e.g. SCI guides or EN 1993 worked examples).

zg Factor

Height of load application above the beam’s shear centre (in mm).
Positive value = load applied above shear centre (destabilising).
Default = 0 (assumes load passes through shear centre).

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This matters for beams with eccentric loading, e.g. roof purlins applying load above the top flange. Entering zg ensures destabilising effects are captured in the LTB check.

Equivalent Uniform Moment Factors

In structural steel design under Eurocode 3 (specifically when calculating the elastic critical moment, Mcr), C1, C2, and C3 are equivalent uniform moment and correction factors used to account for non-uniform bending moment diagrams, load height effects, and section asymmetry.

C1

Accounts for the shape of the bending moment diagram between lateral restraints. It modifies the baseline Mcr calculation to reflect whether the member is subjected to uniform bending, a triangular moment diagram, or reverse curvature.

C2

Accounts for the load height position (zg) relative to the member's shear center. It works directly with the zg term (as seen in the Mcr formula component C2.zg) to capture destabilizing or stabilizing effects when loads are applied above or below the shear center (such as top-flange crane loads).

C3

Accounts for cross-section mono-symmetry (ie. symmetrical in one axis only). It works with the zj term (as seen in the Mcr formula component C3.zj) for heavily asymmetric sections where the top and bottom flanges have unequal stiffness.

Load Height Position

The load height position zg represents the vertical distance between the point of load application and the cross-section's shear center. In lateral-torsional buckling (LTB) calculations under Eurocode 3, zg is a critical parameter used to evaluate how the vertical position of a load affects a beam's stability.
In MasterSeries, zg is a user-defined value because the software needs to know the exact physical elevation of the load relative to the shear axis of the compound or built-up section.

Top-Flange Loading (Destabilizing): When loads are applied to the top flange of a beam (generally above the shear center) zg is positive. As the beam begins to twist laterally under bending, a top-flange load will shift sideways, creating an additional twisting torque. This destabilizing effect of this lowers the elastic critical moment (Mcr).
Bottom-Flange Loading (Stabilizing): Conversely, if loads are applied below the shear center, they create a restoring torque that resists twisting, acting as a stabilizing effect.
Role in the Mcr Equation: zg interacts directly with the equivalent uniform moment factor C2 inside the core buckling expression (typically appearing as the C2.zg term), scaling the magnitude of the load-height penalty.

Mono-symmetry Parameter

The zj factor is the cross-section mono-symmetry parameter used in lateral-torsional buckling (LTB) calculations under Eurocode 3. It quantifies the degree of cross-sectional mono-symmetry by measuring the distance-related shift between a section's centroid and its shear center.
While zg handles the height of the applied loads, zj handles the geometry of the beam itself. If a section is recognized by the software as mono-symmetric, a non-zero zj value is computed and factored into the final buckling resistance.

Measures Cross-Sectional Asymmetry: For a standard, doubly-symmetric I-beam (where the top and bottom flanges are identical), the section is symmetrical, meaning the centroid and the shear center align, and zj = 0mm. However, when you create a compound section or use an asymmetric section (ASB), the top and bottom flanges have unequal stiffness, resulting in a non-zero zj value.
Role in the Mcr Equation: zj is multiplied by the equivalent uniform moment factor C3 inside the core LTB expression, forming the (C2.zg - C3.zj) term.
Accounting for Torsional Behavior: Mono-symmetric sections behave differently under bending and torsion compared to symmetric sections. The C3.zj term adjusts the elastic critical moment (Mcr) to account for the destabilizing or stabilizing effects caused by this geometric asymmetry when the beam twists.

Equation F.2

In the complete Mcr equation F.2 (see below), C2 and C3 combine with load height and section properties in the interaction term to adjust the critical buckling threshold for asymmetric and eccentrically loaded members. Masterseries applies this equation with one caveat, taking (KLTB / kw) = 1 as per SCI NCCI: Elastic critical moment for lateral torsional buckling SN003a.

DD ENV 1993-1-1:1992 Annex F (Clause F.1.2) Equation F.2

The load height position (zg) must be entered manually. Additionally, you can override any of the software-calculated values for C1, C2, or C3 by inputting your own non-zero values directly into the list.

Positve zg values assume that the load is acting towards shear center (destabilizing), and negative zg values assume that the load is acting away from the shear center (stabilizing).
Because the software models the structural frame and members independently of how local dead/live loads physically interface with the flanges, it defaults zg to 0mm (assuming the load passes straight through the shear center), and the engineer must manually specify zg to account for destabilizing or stabilizing load-height effects.

Note, when zg is zero, C2.zg = 0 and C2 will not be calculated by MasterSeries, similarly C3 and zj will only be calculated for mono-symmetric sections.