Steel Bracing Design For Limit State

Design for the Limit State Steel members of all types - struts, ties, beams and columns - are covered in most Design Codes as Limit State Design of Steel members. Of course, steel bracing members are no exception. Check out our Design Guide for Limit State Member Design of Steel Members to AS 4100 here. 
The design codes that cover basic steel limit state design are:
AS4100: Steel Structures (Australia)
AISC 360-10: Specification for Structural Steel Buildings (USA)
BS EN 1993-1-1:2005 Design of Steel Structures (Eurocode and UK)
Steel braces are typically more slender than columns and beams since they are only subject to axial loading. Thereby, yielding longer spans. 
Since compressive braces are subject to buckling, it is important to consider the slenderness ratio during the initial design stage. General design heuristics are a good place to start to understand their stiffness performance.  As it stands, the higher the slenderness ratio, the higher the probability buckling will occur under significant compression loads.  
Global Deflectional and Drift LimitsDeflection It is the degree to which an element of structure changes shape when a load is applied. There can be changes in distance or angle and they can be visible or invisible, depending on the load intensity, material and shape of the component. 
﻿
Global and local deflection
Deflection can be of two types:
Global Deflection
Local Deflection
Drift Limits Building drift is the maximum deflection of the upper floor relative to the lateral deflection of the bottom floor for a given story. 
Drift limits are mainly considered for façades to limit inter-storey drift due to their stricter requirements regarding deflections. Any damage in the façade post construction will be visible and are often very difficult to fix. On that note, the most common material used for facades is glass, which is a brittle material and you can imagine what happens when there is excessive movement in the structure. 
﻿
Building drift
Standards recommend drift provisions for serviceability and ultimate limit states. The design codes that cover basic drift limits include:
AS 1170.4:2007 Structural Design Actions (Australia)
AS 3600:2018 Concrete Structures (Australia)
ASCE 7-16:2017 Minimum Design Loads and Associated Criteria for Buildings and Other Structures (USA)
BS EN 1993-1-1:2005 Design of Steel Structures Clause 7.2.2 (Eurocode)
﻿
BS EN 1993-1-1:2005 Clause 7.2.2 [5]
﻿
BS EN 1990:2002+A1:2005 A1.4.3 [6]
﻿
NA to CYS EN 1993-1-1:2005 Table NA2 [7]
Effects of Frame Geometric Imperfection (Eurocode)Buildings are never constructed perfectly vertical. There is therefore extra moments in our columns and walls. "Geometric imperfections" take into account this non-verticality. 
The Eurocode explicitly includes the effects of geometric imperfections, whereas the Australian standard does not and is instead captured in the robustness clauses.
To transform sway imperfections to an equivalent horizontal load (ΔH), sway imperfections (ɸ), which can generally be taken conservatively as 1/200, are multiplied by the total vertical loading of a floor. This equivalent horizonal load is added to the horizontal load on that floor.
﻿
Equivalent sway imperfection (BE-EN-1993-1-1)
Other imperfections also mentioned in the Design Code that must be considered:
Floor Diaphragm Imperfections
Splice Imperfections
Bow Imperfections
Second-Order EffectsAll frames, no matter if they are braced or unbraced, will deflect laterally under vertical loads. This now means the vertical load is being applied at an eccentricity and if the frame then continues to displace, it is "unstable". The addition of moments caused by the eccentric vertical load as the frame deflects is referred to as second-order effects. 
There are two main types of second-order effects: 
P-Δ effect
Change in axial force in a member as it deflects.
P-δ effect
Curvature of a member as it deflects, causing a moment in the member.
Global second-order effects are more pronounced in tall buildings since they have a sizeable height-to-width ratio. Local second-order effects occur in compression members and frames where the lateral restraint element is not stiff enough. 
﻿
First and second-order effects of pinned braced frame [8]
Nonlinear (buckling) analysis in Finite Element Analysis packages is typically used to understand the extent and impact of second-order effects. If second-order effects are deemed significant, they result in an amplification of your design horizontal loads.
﻿
﻿
CalcTreeCalcTree, the app you're reading this one is a calculation management platform. You can sign-up and build hosted, shareable web apps (complete with an API and a web publishing module) with tools like Python and Spreadsheets. Learn more here!
﻿
References[1] Standards Australia & Standards New Zealand. (2007). Structural Design Actions, Part 4: Earthquake actions in Australia  (AS/NZS ISO 1700.4:2007). SAI Global. https://www.saiglobal.com/ 
[2] Standards Australia & Standards New Zealand. (2007). Concrete Structures (AS/NZS ISO 1700.4:2007). SAI Global. https://www.saiglobal.com/
[3] American Society of Civil Engineers. (2017). Minimum Design Loads and Associated Criteria for Buildings and Other Structures (ASCE/SEI 7-16:2017). SAI Global. https://www.saiglobal.com/
[4] International Code Council. (2016). International Building Code (IBC:2016). International Code Council, Inc. 
[5] European Union. (2005). Eurocode 3: Design of Steel Structures (BS EN 1993-1-1:2005). SAI Global. https://www.saiglobal.com/ 
[6] European Union. (2005). Eurocode: Basis of Structural Design (BS EN 1990:2002+A1:2005). SAI Global. https://www.saiglobal.com/ 
[7] Cyprus National Annex. (2005). CYS National Annex to CYS EN 1993-1-1:2005 (NA to CYS EN 1993-1-:2005)
[8] Brown, D., Iles, C., Yandzio, E. (2009). Steel Building Design: Medium Rise Braced Frame. https://www.steelconstruction.info/images/8/86/SCI_P365.pdf
﻿