THE ANALYSIS OF SPLICE JOINT BEHAVIOUR IN HEAVILY LOADED TENSILE CHORDS OF WARREN TRUSSES

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1 PANACM st. Pan-American Congress on Computational Mechanics An IACM Special Interest Conference THE ANALYSIS OF SPLICE JOINT BEHAVIOUR IN HEAVILY LOADED TENSILE CHORDS OF WARREN TRUSSES Lilita Ozola Asoc. Prof., Dr.Sc.ing. Department of Structural Engineering Latvia University of Agriculture 19 Akademijas Str Jelgava, LV-3001, LATVIA Department of Structural Engineering Latvia University of Agriculture Lilita.Ozola@llu.lv

Problem Comprehensive design practice entails some risk when the most unfavourable loading situations for the whole structure or stress-strain relationships are not analysed.

2 Problem Comprehensive design practice entails some risk when the most unfavourable loading situations for the whole structure or stress-strain relationships are not analysed. Tolerance of this risk varies widely among countries and emerges from the legal code system and content, and clarity in definitions of criteria for the acceptability of construction products, and even more from the intelligence of professionals disputable topics in the truss design area deal with the conformity between design model links and a realistic behaviour phenomena of a system

The Objectives of a Study: 1) suggestions for modelling of splice joint in tensile chord considering additional stresses induced by bending moment; 2)

3 The Objectives of a Study: 1) suggestions for modelling of splice joint in tensile chord considering additional stresses induced by bending moment; 2) drawing up the methodology for analysis and numerical examples of end-plate joint design considering elastically deformed tensioned bolts and stiffness on end-plate

4 The Method selected The specified method used is the phenomenological approach to the splice joint behaviour problem illustrated by the results of numerical analysis based on a real design solution.

The benefit to be expected: to perfect the knowledge in structural design deepening the understanding in designing and promoting an extensive

5 The benefit to be expected: to perfect the knowledge in structural design deepening the understanding in designing and promoting an extensive judgement of structural solutions accepted, especially when the hard-loaded structures have been designed for covering the spans of public building areas

6 End-plate joint types under discussion a) a) With extended end-plates b) b) With hidden fasteners between flanges

7 [124.1] 22.4 [5] , [1.8] [7'-10.49"]...used in tensile chord of Warren truss [39'-3.46"] HEA320 HEA260 CHS160 HEA [9'-6.17"] 3000 [9'-10.11"] 3000 [9'-10.11"] 1575 [5'-2.01"] 1500 [4'-11.06"] q= kn/m [3.08 kip/ft] A , D g= 0.68 kn/m [0.05 kip/ft] A [112699] 64.4 [47499] [16743] ,9 D 0,2 [74.8] 78.5 [137.8] [10.7] 88.4 [65200] kn; knm [kipf; lbf*ft] [306.7] [306.7] [18] [288.8] [18] [307.9]

8 Middle bar effect in countour u1 u u = 48.5 mm 2 u = 40.5 mm HEA q= 65 kn/m CHS160 u'1 u'2 u ' = 44.6 mm 1 u ' = 44.4 mm 2

9 Models effect on values of internal forces in Warren truss heavily loaded elements

10 Splice joint with extended end-plates Assembly Loading scheme

11 Consideration on Behavior of Connection Due to the coexistence of bending moment and axial force in continuous chord sections there will be regions of distinctive stress concentrations, even though the mean stress across the section remains well below yield. Thus, the end-plate is modelled as a continuous beam on discrete elastically deformed supports (representing tying bolts), and loaded by concentrated forces transferred by flanges and the web of I section. Clapeyron s theorem of three moments has been used at the first step assuming bolts as rigid supports for continuous end-plate, and reactive forces expected to be acting in bolts has been determined.

12 In reality some axial deformation of the bolts takes place under tensile forces according to Hooke s law. So, at the next step a model of a continuous beam on elastic supports has been examined taking into account the additional rotations (ψ -ψ ) due to differences of support n+1 n displacements. The condition of continuity of a deformed axis may be expressed by the following equation: 6EJ n n M 4 M M ψ ψ τ τ 0 n 1 n n 1 n 1 n r l Design model of extended end-plate: beam on discrete elastic supports Deformed axis of endplate modelled Primary system for analysis

13 Algorithm for extended end-plate joint analysis Input Data: h o, A s, A f, A w, W y, W yo, A b, l, N td, M d, σ td, F tu, F tb, q w Compilation of three-moment equation systemslide 22 Defining the fictive reactionsslide 23 Finding the support moments solving the equation systemslide 24 Determination of the support reactions Slide 25 Determination of elongation value of an individual boltslide 26 Equation system for continuous beam on elastic supportsslide 27 Solution of the system and determination of reactions in bolts Differences 0 M B, i 1 B, i B, i M B, i M 0; M M C, i 1 C, i C, i M C, i 0; M M D, i 1 D, i D, i M D, i 0 No Yes End

14 Bolt row location Results of approximation A A A Elastic B B B Rigid C C C Elastic Rigid D D D E E E Force, kn Force per bolt row, kn

15 Analysis of joint behavior with hidden fasteners Three moment equation Five moment equation

16 Moments in end-plate sections and reactive forces in bolts for joint variant with hidden fasteners (1-st approximation- rigid supports)

17 Bolt row location Results of analysis of joint behavior with fasteners hidden between flanges A B B B C C C Elastic Rigid D D D E Force, kn Force per bolt row, kn

18 Summary of Results Bending moments generated in the tensile bottom chord sections even of reasonably moderate values itself affects significantly the force distribution between the bolts depending on a location. It has been found that in the case of variant with closed fasteners solution the overloading of bolts near flanges exceed 2,5 times in comparison with the bolts of variant with extended end-plates at the same position. No experimental tests have been carried out to prove the results of this study. Significant effects on the behaviour and force distribution in a real structure may be expected due to friction surfaceon-surface, imperfections, some lateral actions, plastic deformations possibly accumulated during previous extreme loading cycles and other factors.

19 Force transferred, kn Anticipated force distribution between bolt rows depending on location A B C D E Bolt row location Variant I, elastic supports Variant II, elastic supports Variant I, rigid supports Variant II, rigid supports

20 CONCLUSIONS Design models that disregard some portion of the stresses or strains in comparison with real structural behaviour, may be assessed as overly simplified and insufficient for the design of bearing structures. It is potentially dangerous to assess or design truss structures without thorough analysis of possible models taking into account more unfavourable loading situations, the stresses generated and the deformations developed.

21 The continuous beam model on elastically settled supports may be advisable for the analysis of end-plate joint behaviour in heavily loaded tensile chords The end-plate joint solution with fasteners arranged between flanges (variant with closed fasteners) may be assessed as hazardous with regard to collapse Despite the proper account of code conditions in the practical design it would be reasonable to consider the potentials of a structure when subjected to overloading and/or unfavourable service conditions.

22 Russia Thanks for your attentation! Latvia Jelgava Riga Latvia University of Agriculture

JUT!SI I I I TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER:

JUT!SI I I I TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER: COURSE: Tutor's name: Tutorial class day & time: SPRING