Applying Local Bow Imperfection in MasterSeries 2025

Introduction – Local Bow Imperfections in MasterSeries

In real structures, compression members are never perfectly straight. Small initial out-of-straightness (known as local bow imperfections) can significantly influence the buckling behaviour of slender members under axial load.

In Eurocode design, these imperfections are typically accounted for implicitly through the use of buckling curves and reduction factors in Clause 6.3 of EN 1993-1-1. Alternatively, the code allows imperfections to be considered explicitly at the analysis stage by introducing a small initial member curvature and carrying out a second-order (geometric non-linear) analysis.

When Local Bow Imperfections are enabled in MasterSeries, the software follows this second approach. A small geometric imperfection is applied to the member and the resulting second-order effects are captured during analysis. This allows the buckling behaviour of the member to be represented directly in the structural analysis rather than relying solely on the implicit buckling curve method at the design stage.

Local Bow analysis benefits Structural Design Engineers by providing:

• A more realistic second-order simulation of local member instability

• Better accuracy for slender or heavily-axially loaded members

• Improved insight into how axial load amplifies imperfections

• Safer, clearer identification of critical members

• A modern analysis capability that complements EC3 buckling curves rather than replacing them

It bridges the gap between conventional code-based design and advanced geometric-nonlinear analysis, giving engineers a more robust and reliable assessment of member stability, especially in cases where traditional buckling curves may not fully reflect the member’s behaviour.

This is an approach that accounts for in-member geometric non-linearity, also known as small P-delta effects. Here is a guide on when and how to apply it.

When to Apply Local Bow Imperfection Loading

The application of local bow imperfection loading is required when the applied axial force (NEd) is greater than 25% of the member's elastic critical buckling load (Ncr).

Note the 0.25 * Ncr is rearrangement of EN 1993-1-1:2005 eqn 5.8, but is also how this presented in EN 1993-1-1:2022.

• In MasterKey Steel design - Axial+ Moment Design brief, this check is performed for both the major and minor axes of the member.
• A warning will be issued if this condition is met but the local bow imperfection loads have not been applied. For instance, the software might indicate that for the minor axis, NEd is greater than 0.25 * Ncr, and warn that local bow loads haven't been applied. 
• Note that in steel design the Ncr values for major and minor axis for this check use the unfactored length (hinged ends) as per EN 1993-1-1:2005 5.3.2 (6).
• • The Ncry (major axis) is based on the member length or the Ly manual input in design brief if specified.
  • The Ncrz (minor axis) is based on the laterally restrained portion length or the Lz manual input in the design brief if specified.

The engineer should ensure the appropriate lengths are being used before taking further action to implement local bow imperfection loads + P-Delta analysis.

It is crucial to understand that Local Bow imperfection loads are only applied during a second-order P-Delta analysis. If P-Delta analysis is not used for a loading case, the local bow loads will not be applied, even if the attribute is assigned to the member.

What is 'Local Bow' designing for

Member axial flexural bucking is normally empirically designed for using member buckling reduction factors in the design code in EN 1993-1-1:2005 6.3.1. The 'Local Bow' check is an second-order P-delta analytical approach to capturing this buckling behaviour in more heavily axially loaded and more slender members. By subdividing the member with internal nodes and by apply the local bow load in induce geometric imperfection, the second-order P-Delta analysis can capture the local member geometric non-linearity in a more sophisticated fashion at analysis time.

How does the design approach change?

When local bow imperfection is required and applied, this means the member flexural buckling in accounted for at design time. Hence in accordance with EN1993-1-1:2005 5.2.2. (3) & (7), the flexural buckling check in 6.3.1.1 do not need to be applied. The following changes are made to the final axially load + moment interaction buckling equations.

• Equation EN1993-1-1:2005 6.61 is omitted. This is more explicitly stated in 2nd generation EN1993-1-1:2022 7.2.2 (7b) M4 analysis method.
• In Equation EN1993-1-1:2005 6.62 the χz flexural axial buckling reduction factor is taken as 1.0. χt (axial torsional buckling) and where relevant χtf (axial torsional flexural buckling) is used in place of χz in equation 6.62.

How to Apply the Local Bow Imperfection Attribute

You can apply the local bow imperfection loading by assigning the 'Local-Bow' member attribute in the software.

This can be found within Properties -> Member Attributes and under 'More Attributes'.

The attribute has two inputs:

1. Axis Selection: The first input specifies the axis for the imperfection loading.

   • Enter '0' for the major axis.
   • Enter '1' for the minor axis.

2. Length Override (L): The second input allows you to override the member length used to calculate Ncr and the imperfection value e0.

   • If you use the default value of '00.000', the physical length of the member is used for the calculation.
   • You can enter a specific value to account for any unmodeled restraints. For example, if a 3.5m member has a mid-point restraint for the minor axis, you could override the length Lz to be 1.75m, which would increase the Ncr value and might resolve the need for the imperfection loading.

If local bow loads are required for both axes, you must apply two separate Local-Bow member attributes to the member, one for each axis. In this case it is not necessary to apply the local bow imperfection load to both axis simultaneously, hence the 'UT' load group (global common) should not be used, and each axis local-bow load group should be separated. E.g. 

​N1 Local-Bow 0 00.000

​N2 Local-Bow 1 00.000

Where the N1 and N2 load group can be activated separately in different load cases. This may involve some repetition of load cases, in a similar manner to global sway type equivalent horizonal notional loads being applied separately in different horizontal directions.

The direction of the applied load is determined automatically to increase any existing bending in the member. These loads do not observe the load factor of the load group they are in, but will be activated by any factor greater than zero. It is recommended to include them in the UT (user-defined template) load group so they are present in all loading cases.

Prerequisites for a Successful Analysis

For the local bow loading and the associated small P-delta effects to be included correctly, the physical member needs to be subdivided into smaller analytical members.

• It is recommended to have three evenly distributed internal nodes, which creates four analytical parts.
• This subdivision can be generated automatically if you use the 'Modify Geometry > Modal Auto-Connect and Clean Up' feature with the correct settings enabled for automatic subdivision.
• This ensures that the small P-delta effects from the imperfection are properly captured in the analysis. The software will still treat it as a single physical member for design purposes.
• If manual internal nodes need to be generated use the 'Modify Geometry> Split Member' geometry function in MasterFrame, ensuring to use the 'Insert analytical node only' option.

Final Steps and Considerations

After applying the attribute and ensuring member subdivision, you must activate a P-Delta analysis for the relevant load cases.

Note when local bow imperfection is handled in this way the steel design combined Axial and Moment Checks are modified in that equation EN 1993-1-1:2005 6.61 is omitted (as per 2022 equation 8.88). EN 1993-1-1:2022 is more explicit on this (7.2.2 (7) b) Method M4), but 2005 alludes to it in 5.2.2. (3) & (7). 

Opting Out

There is an option in the 'Axial with Moment' design brief to not check local bow, which must be used at the engineers discretion.

In Summary 

1. Perform the Steel Design Axial +Moment members checks and examine the Local bow imperfection check results
2. In MasterFrame, apply the 'Local-Bow' attribute for the required axis.
3. Ensure analytical subdivision is in place, for example, by using 'Model Auto-Connect', which may also be automatic.
4. Activate P-Delta analysis for the load cases where the NEd > 0.25 * Ncr condition is met.

Be aware that applying these loads and running a second-order analysis will introduce additional forces and moments, which might cause a previously passing member to fail. In many cases, engineers might prefer to increase the section size to avoid this complex analysis.