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Introduction
Background
Rectangular hollow sections (RHS) are widely used in structures because of • A high structural efficiency in compression and bending• A high strength and stiffness in torsion• An aesthetic appeal• A reduced exposed area• A reduced drag coefficient in fluid flow• Reduced complexity of manufacturing the connections over
circular sections.
Finite element model
Conclusions & future work
References[1] J. Packer, J. Wardenier, X.L. Zhao, G. van der Vegte & Y. Kurobane. Design guide 3 – for RHS joints under predominantly static loading, CIDECT, 2009. [2] J. Becque& T. Wilkinson. Tubular structures XV, CRC Press, 2015, 419-426. [3] J. Becque & S. Cheng. J. Struct. Eng. 2016 (under review). [4] S. Cheng & J. Becque. Eng. Struct. 2016 (under review). [5] S. Cheng & J. Becque. SDSS 2016, 30th May – 1st June, 2016, Romania.
Design methodology [4, 5]
Reliability analysis [4]
Theoretical model (elastic buckling)The chord side wall was idealized as [4, 5]
• an infinitely long plate • simply supported along both longitudinal edges • subjected to longitudinal chord loading and
transverse patch loading
First order reliability method (FORM) and Monte-Carlo simulations were applied to ensure the proposed design equations possess the required level of safety.
Reliability analysis was conducted for both Eurocode (target 𝛽𝛽 = 3.8) and AISI specifications (target 𝛽𝛽 = 3.5) .
Prediction 2 is recommended as it is simpler in application. A partial safety factor of 𝛾𝛾𝑀𝑀 = 1.6 was recommended for
Eurocode and a resistance factor of ∅ = 0.55 was recommended for AISI specification.
Satisfactory and consistent reliability level has been achieved across the full slenderness range, and for different ratios of live to dead load.
A design method for side wall buckling of equal-width RHS truss X-jointsShanshan Cheng1 and Jurgen Becque2
1 Lecturer in Civil Engineering, Plymouth University. Email: [email protected] Lecturer in Structural Engineering, University of Sheffield. Email: [email protected]
Design in two steps:
• Check the member in tension or compression
• Check the connection resistance according to the CIDECT rules
Current CIDECT design rule [1]:
Design as a column:
The current CIDECT design rule:
• ignores the 2D character of the side wall buckling as a plate
• is conservative for higher wall slenderness values
• Recognizes that design should be based on the buckling load
• Buckling load = min{Pult, P3%bo} – invalidated by experiment
• Test results
22
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uctio
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χ(=
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Slenderness λ
Elastic buckling No chord load25%fy chord load 50%fy chord load75%fy chord load Proposed design
Prediction 2: • ignores chord pre-load
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Prediction 1 / CIDECTPrediction 2 / CIDECT
Experimental programme [2,3]
• 5 tests• SHS
100x100• t = 3mm• t = 4mm• t = 5mm• t = 6mm• t = 8mm
• S355
Displacement control
Load control
Fig. 2 X1: axial load vs. axial shortening
Fig. 3 X5: axial load vs. axial shortening
Determination of buckling load:
Specimen X1 (t = 3 mm):
Specimen X5 (t = 8 mm):
Aim: To present a new design methodology for equal-width RHS X-joints failing by side wall buckling.
Methodology: •Derive elastic buckling stress of chord side wall.•FE verification of equal-width X-joints tests. •Carry out FE parametric studies for various levels of chord pre-load. •Develop design model based on column buckling equations in Eurocode.•Carry out reliability analysis to ensure a sufficient safety level.
Rayleigh-Ritz approach was used to obtain the critical buckling stress
Exponential Gauss function was chosen to represent the shape of buckle.
Fig. 6 Reliability levels of all X-joints using 𝛾𝛾𝑀𝑀 = 1.6 for a load ratio 𝜅𝜅 = 5(b) 75% chord pre-load(a) No chord pre-load
Fig. 7 Reliability levels of all X-joints using ∅ = 0.55 for a load ratio 𝜅𝜅 =5
(b) 75% chord pre-load(a) No chord pre-load
A new design method for side wall buckling of equal-width RHS X-joints is presented.
The effect of the compressive chord pre-load is investigated. The approach employs a slenderness parameter based on
the theoretical elastic buckling stress of the side wall subjected to patch loading
The new method strongly outperforms the current CIDECT design rule.
A partial factor of 𝛾𝛾𝑀𝑀 = 1.6 was proposed for use in the Eurocode and a resistance factor of ∅ = 0.55 was proposed for design using the AISI specifications.
Fig. 8 Reliability levels of specimen X1 using Prediction 2
(b) AISI (∅ = 0.55)(a) Eurocode (𝛾𝛾𝑀𝑀 = 1.6)
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α = 0.08
2 1thP crcr σ×=
0.0
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0.6
0.9
1.2
0.0 1.0 2.0 3.0
Red
uctio
n fa
ctor
χ(=
Pb/P
y)
Slenderness λ
Elastic buckling No chord load25%fy chord load 50%fy chord load75%fy chord load Proposed design
Prediction 1:
Fig. 5 Comparison with CIDECT design
• Use elastic critical buckling stress in definition of slenderness. • Factor of 1.2 in yield load definition accounts some load
follows an alternative load path through the chord top and bottom faces and then spreads out into the chord side walls.
(a) Load vs. axial shortening (b) Load vs. lateral deflection
3%bo limit
Fig. 1 Test results of all five specimens
(a) No chord pre-load (b) 50% chord pre-loadFig. 4 X4: determination of buckling load
