Load paths, stability and bracing of steel structures in Dubai

How loads travel to the foundations

Part F asks for measures that keep the building stable under the design-basis loads and, where necessary, under the maximum credible loads for which the collapse limit state might be chosen as applicable.¹ Every feature with a critical influence on overall stability has to be identified and included in the design, including all members that restrain critical members in compression.¹ The structure has to provide continuous load paths that carry each action from its point of application to the ground.¹

The Code’s Figure F.2, adapted from ACI 318-19 and drawn as a multi-storey concrete building, shows gravity and inertial loads, diaphragms with collectors, walls, a moment frame, an inclined column, a transfer slab and basement walls acting as one system.¹¹

Connections carry the path

AISC 360 designs connections to Chapters J and K, with forces and deformations consistent with the intended behaviour and the analysis.¹² Beams, girders and trusses need restraint against rotation about their longitudinal axis at supports unless analysis shows otherwise.¹² Simple connections may be modelled as pinned but need enough rotation capacity; fully restrained ones allow no relative rotation.¹² Partially restrained connections need their force-deformation response in the analysis, and diaphragms and collectors are designed to Chapters C to K.¹³

Page F29 lists connection requirements: lifetime strength; stresses from restrained creep, shrinkage and temperature change; durability and fire resistance matching the connected elements; checks for all load scenarios, including horizontal earthquake and wind; and positive ties for precast members unless seating exceeds the maximum expected movement.¹⁴ The list continues F.6.4.6 on precast concrete connections, not the steel clause F.6.5 printed beside it.¹⁵²

Bolted steel connections follow the AISC steel construction manual and the specification for structural joints using ASTM A325 or A490 bolts; welding follows AWS D1.1 or BS EN ISO 15614.¹⁶ Site welding should not be undertaken; if it is unavoidable, a method of work with certificates and tests must be submitted for approval for approval and accredited welders are used.¹⁶ No connection may rely on welds and bolts acting together.¹⁶

Structures resist self-straining forces from expansion and contraction, and relieving details may be used where practical if they do not break an assumed load path.¹⁷ For steel members and members exposed to the sun, a range equal to the maximum temperature swing is appropriate; ±25 °C may be used for protected steel, and exposed steelwork is assessed case by case.¹⁷

What keeps a steel frame stable

AISC 360 requires the structure and its elements to be designed for stability to Chapter C.¹³ Stability is required of the whole structure and of every element, taking account of member and connection deformations, second-order P-Δ and P-δ effects, geometric imperfections, stiffness loss from partial yielding and residual stresses, and uncertainty in strength and stiffness.³ They are calculated at LRFD or 1.6 times ASD combinations, and any rational method covering all of them is permitted.³

When a frame or a member needs bracing

Under the direct analysis method, flexural buckling is checked on the unbraced length unless rational analysis justifies less, and bracing that defines an unbraced length must have enough stiffness and strength to control movement at the braced points.⁷ A user note points to Appendix 6, which does not apply to bracing in the lateral force-resisting system.⁷ Appendix 6 gives the minimum strength and stiffness to create a braced point in a column, beam or beam-column.⁸

A beam has to be restrained against twist at its supports. Between supports, a braced point needs lateral or torsional bracing, or both, to stop relative movement of the flanges; an inflection point is a braced point only if braced.¹⁹ Lateral bracing goes at or near the compression flange, except at a cantilever’s free end (top flange) and at the brace nearest an inflection point in double curvature (both flanges).¹⁹ These rules cover doubly and singly symmetric I-shaped members bent in a plane of symmetry with zero net axial force.¹⁹ Torsional bracing may be attached anywhere on the section; a user note gives cross-frames, moment-connected beams and vertical diaphragms as point braces, and slabs or decks as continuous bracing.²⁰

The effective length method of Appendix 7 is the alternative. In braced-frame and shear-wall systems it takes K = 1.0 unless a smaller value is justified; in moment frames, K or the buckling stress of the columns that provide lateral stiffness comes from a sidesway buckling analysis, and other columns take K = 1.0; an exception permits K = 1.0 for all columns where the second-order to first-order drift ratio, for LRFD or 1.6 × ASD combinations, is 1.1 or less in every storey.²¹

Designing for stability: the direct analysis method

The direct analysis method is permitted for all structures; with elastic analysis, required strengths come from C2 and available strengths from C3.³ Members and connections are then checked to Chapters D to K with no further check of overall stability.⁷

The analysis includes all deformations that contribute to displacement, uses the C2.3 reduced stiffnesses, and is second-order, covering P-Δ and P-δ.⁴ P-δ may be left out of the overall response only when gravity is carried mainly by nominally vertical members, the ratio of maximum second-order to first-order drift, for LRFD or 1.6 × ASD combinations with C2.3 reduced stiffness, is 1.7 or less in every storey, and moment-frame columns carry no more than one-third of the gravity load in the direction considered; members in compression and bending still include P-δ.⁴ Appendix 8’s approximate method is permitted, and all loads that influence stability are included,⁴ including, a user note says, leaning-column loads.¹⁸ ASD analyses run at 1.6 times the ASD combinations, with results divided by 1.6.¹⁸

System imperfections, chiefly column out-of-plumbness, are either modelled directly, which is always permitted, at the largest amount considered and in the most destabilising pattern, or represented by notional loads.¹⁸ Notional loads may be used where gravity is carried mainly by nominally vertical members: lateral loads at every level, added to the other lateral loads in all combinations except as C2.2b(d) allows, of Ni = 0.002 α Yi (Eq. C2-1), with α = 1.0 for LRFD and 1.6 for ASD and Yi the gravity load at level i, spread like that load in the most destabilising direction.⁵ A user note adds that the fictitious base shear can be corrected at the base, but the extra overturning is real.⁵ Another says that for most buildings two orthogonal directions, each in both senses and in the same direction at all levels, satisfy the direction rule in gravity-only combinations, and the resultant lateral-load direction otherwise.⁶

The 0.002 coefficient reflects an out-of-plumbness of 1/500 and may be scaled for a different justified maximum; a user note identifies 1/500 as the Code of Standard Practice column tolerance and warns that tolerances on the plan position of columns can require tighter plumbness.⁶ Where gravity is carried mainly by nominally vertical members and the drift ratio, for LRFD or 1.6 × ASD combinations with C2.3 reduced stiffness, is 1.7 or less in every storey, modelled imperfections and notional loads may both be confined to gravity-only combinations.⁵⁶

Stiffnesses that contribute to stability are factored by 0.80, which may be applied to all stiffnesses, and the flexural stiffness of members contributing to stability by a further τb.⁶ For noncomposite members τb = 1.0 when αPr/Pns is 0.5 or less (Eq. C2-2a), otherwise τb = 4(αPr/Pns)[1 − (αPr/Pns)] (Eq. C2-2b), with Pns = FyAg for nonslender sections.⁷ Where C2.2b applies, τb = 1.0 may be used for all noncomposite members if an extra 0.001 α Yi is applied at all levels, in the C2.2b(b) direction, in all combinations and whatever the drift ratio.⁷ Non-steel components take any larger reductions their own codes require.⁷

When the effective length or first-order method may be used

Chapter C also permits two elastic alternatives in Appendix 7, the effective length method and the first-order analysis method, within that appendix’s limits.⁴ The C1 requirements still apply to both.²⁴

The effective length method needs gravity carried mainly by nominally vertical columns, walls or frames and a ratio of maximum second-order to first-order drift, for LRFD or 1.6 × ASD combinations, of 1.5 or less in every storey, with stiffness not reduced under C2.3; a user note allows the ratio to be taken as B2 from Appendix 8.²⁴ Its analysis uses nominal stiffness and C2.2b notional loads.²⁴ A user note says those loads are needed only in gravity-only combinations, and an exception in 7.2.3 permits K = 1.0 for every column where that drift ratio, on the same basis, is 1.1 or less in every storey.²¹

The first-order analysis method needs the same gravity condition, the same 1.5 limit with unreduced stiffness, and αPr no greater than 0.5Pns (Eq. A-7-1) in every member whose bending stiffness contributes to lateral stability.²⁵ Every combination then includes an extra lateral load at each level of Ni = 2.1 α (Δ/L) Yi, at least 0.0042 Yi (Eq. A-7-2), where Δ/L is the largest first-order storey drift ratio, spread like the gravity load in the most destabilising direction.²⁵ Member moments are amplified by B1, and flexural buckling uses the unbraced length unless a smaller value is justified by rational analysis.²⁶

Sizing a stability brace: AISC 360 Appendix 6

One bracing system serving several members is designed for the sum of their required strengths, and the stiffness it provides includes its connections and anchoring details.⁸ A user note distinguishes panel bracing, which limits relative sideways movement between braced points, point bracing, which controls movement at its own point, and continuous bracing.⁸ Brace members and connections must provide the required strength and stiffness unless analysis justifies less, and braced members may then use Lc and Lb equal to the distance between braced points.⁸

Alternatively, the brace strength and stiffness may come from a second-order analysis that satisfies Chapter C or Appendix 1, with the brace points displaced in the most demanding pattern; or the stiffness may be taken as 2/φ (LRFD) or 2Ω (ASD) times the ideal stiffness from a buckling analysis, with the brace strength still taken from 6.2 to 6.4. Either route allows Lc and Lb shorter than the distance between braced points.²⁷

Column bracing is assumed to act at the shear centre; a user note warns that bracing that does not prevent twist leaves the column open to torsional buckling under E4.²⁷ Panel bracing needs Vbr = 0.005Pr (Eq. A-6-1) and βbr = (1/φ)(2Pr/Lbr) for LRFD or Ω(2Pr/Lbr) for ASD (Eq. A-6-2a and b),²⁸ and its connection to the column needs the strength of a point brace.²⁷ Point bracing needs Pbr = 0.01Pr (Eq. A-6-3) and βbr = (1/φ)(8Pr/Lbr) or Ω(8Pr/Lbr) (Eq. A-6-4a and b), with φ = 0.75 and Ω = 2.00.²⁸ Pr is the largest required axial strength either side of the brace, the larger Pr/Lbr sets the stiffness, and for intermediate point bracing of an individual column Lbr need not be taken below the longest effective length at which the column still carries Pr.²⁸

For I-shaped beams, panel bracing needs Vbr = 0.01(MrCd/ho) (Eq. A-6-5) and βbr = (1/φ)(4MrCd/(Lbr ho)), with Ω in place of 1/φ for ASD (Eq. A-6-6a and b).¹⁹ Point bracing needs Pbr = 0.02(MrCd/ho) (Eq. A-6-7) and βbr = (1/φ)(10MrCd/(Lbr ho)), likewise (Eq. A-6-8a and b), with φ = 0.75 and Ω = 2.00; ho is the distance between flange centroids, and Cd is 1.0, or 2.0 for the brace nearest the inflection point in double curvature.²⁰

A torsional point brace needs Mbr = 0.02Mr (Eq. A-6-9) and a stiffness combining the brace system requirement with the web’s distortional stiffness (Eq. A-6-10 to A-6-12), with φ = 0.75 or Ω = 3.00.²⁹ A user note warns that a web with too little distortional stiffness makes the torsional bracing ineffective.²² For continuous torsional bracing such as a deck, the strength per unit length is Eq. A-6-9, with Mr the maximum throughout the span, divided by the maximum unbraced length permitted under Mr, and the stiffness uses Eq. A-6-10 and A-6-11 with L/n = 1.0 and Eq. A-6-13.²²

For a beam-column, the axial and flexural requirements are added, panel with panel and point with point, using the actual unbraced length without the minimum-length relaxations.²²³⁰ Where axial force and bending together put both flanges into compression, both flanges have to be restrained.³⁰

Robustness and structural integrity

Part F makes robustness against disproportionate collapse mandatory by one of two approaches: direct design, which checks progressive collapse explicitly by the tie-force, alternate-path or enhanced-local-resistance method, with details in UFC 4-023-03; or indirect design, which provides minimum levels of strength, continuity and ductility.⁹ It recommends direct design, and Table F.2 links the checks to risk category: nothing specific for category I; the indirect approach or either of two direct options for II; and combinations of alternate-path and enhanced-local-resistance checks for III and IV, with tie forces added for IV.⁹

Where the building code requires structural integrity design, AISC 360 B3.9 sets minimum nominal tensile strengths: column splices at least D + L for the tributary area between that splice and the next splice or base beneath; beam and girder end connections two-thirds of the required vertical shear (LRFD) or the full required shear (ASD), and not less than 10 kips, a value printed without an SI equivalent.¹³ That is about 44.5 kN (our conversion). End connections of members bracing columns need 1% of two-thirds of the column’s required axial strength at that level (LRFD), or 1% of that strength (ASD).³⁶ These checks stand apart from other strength checks and permit bearing bolts in short-slotted holes parallel to the force and inelastic connection deformation.³⁶

Stability during construction

The design has to allow for safe fabrication, transport, handling and erection.²³ Minimum construction loads follow ASCE 37, which is not held here.¹⁰ The Engineer includes construction-stage loads, including stresses locked in by the sequence, states the construction-load assumptions on the detailed design drawings, verifies every stage; any departure from those assumptions by the Contractor’s construction sequence has to be assessed.¹⁰

AISC 360 requires column bases to be set level with full bearing and the frame to be carried up true and plumb within the Code of Standard Practice limits.³⁷ As erection proceeds the structure has to be secured for the loads expected, with temporary bracing left in place as long as safety requires.³⁷

Part F requires drift and deformation to be assessed over the structure’s whole life, including construction,³⁸ with deviation from plumb under permanent gravity load verified against Section 7 of ACI 117-10, which is not held here.³⁸ Differential vertical shortening should be assessed by a nonlinear static construction-sequence analysis, which the Engineer and/or Contractor has to perform, at a minimum, for multi-storey buildings with different core and perimeter stresses, asymmetric plans or massing, stepped setbacks or outriggers.³⁸

Drift limits for the lateral system

Wind drift is assessed under F.7.12.4, and seismic movement under Section 12.12 of ASCE/SEI 7-16, which is not held here.³⁸ F.7.12.4 sets overall and inter-storey displacement limits under 10-year return wind pressures in Table F.11;³⁹ the serviceability guide gives the values and discusses the clause’s wording.

What to record in the design basis

The Code requires the features critical to stability to be identified and included in the design,¹ the construction-load assumptions to be stated on the detailed design drawings,¹⁰ one robustness approach to be used,⁹ and analysis and design software approved by the Authority to be used.²³

Scope and limits