the analysis of splice joint behaviour in heavily …clapeyron’s theorem of three moments has been...

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

PANACM 2015 1st. Pan-American Congress on Computational Mechanics

An IACM Special Interest Conference

Department of

Structural Engineering

Latvia University of Agriculture

19 Akademijas Str

Jelgava, LV-3001, LATVIA

E-mail :

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.

• 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

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

The Objectives of a Study:

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 judgement of structural

solutions accepted, especially when

the hard-loaded structures have

been designed for covering the spans

of public building areas

End-plate joint types under discussion

a) With extended

end-plates

b) With hidden

fasteners

between flanges

a)

b)

...used in tensile chord of Warren truss

A

280

A

g= 0.68 kN/m [0.05 kip/ft]

332.8

[137.8]

47.5 [10.7]

22

.4 [

5]

55

2.0

5 [

12

4.1

]

1364.1 1364.1

7.9

7.9

22.7

88.4

[112699]

[47499]

HEA260

CHS160

HEA260

HEA320

q= 44.95 kN/m [3.08 kip/ft]

239.

2

1157.2815.0332.8

618.85

613.1

567.

4

364.3

55

2.0

5

390.

1

1024,8

245.9

82.6

1284.7

1329.7

68.7

55

2.0

5

1369.51284.8

78.5

[18]

1.7 0,2

1,0

1.7

D

7.9

7.9

[1

.8]

22.7 [16743]

7.9

3000 [9'-10.11"] 3000 [9'-10.11"]

1575 [5'-2.01"]

2900 [9'-6.17"]

1500 [4'-11.06"]

24

00

[7

'-1

0.4

9"]

11975 [39'-3.46"]

kN; kNm [kipf; lbf*ft]

[74.8]613.1

152.864.4

[65200]

[307.9][288.8]

78,9

[18]

[306.7] [306.7]

D

Middle bar effect in countour

u 1u 2

u' 1

u' 2

12000

1500

q= 65 kN/m

HEA320

CHS160

u = 48.5 mm

u = 40.5 mm

1

2

u = 44.6 mm

u = 44.4 mm1

2

'

'

Models effect on values of internal forces in Warren

truss heavily loaded elements

Splice joint with extended end-plates

Assembly

Loading scheme

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.

Design model of extended

end-plate: beam on

discrete elastic supports

Deformed axis of end-

plate modelled

Primary system for

analysis

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 (ψn+1-ψn) due to differences of support

displacements. The condition of continuity of a deformed axis may be

expressed by the following equation:

01116

nlτ

nrτnψnψnMnM4nM

EJ

Input Data: ho, As, Af, Aw, Wy, Wyo, Ab, ℓ, Ntd, Md, σtd, Ftu, Ftb, qw

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

Yes End No

Algorithm for extended end-plate joint analysis

;0,

,1,

,

iB

iBiB

iBM

MM;0

,

,1,

,

iC

iCiC

iCM

MM0

,

,1,

,

iD

iDiD

iDM

MM

-200 -100 0 100 200 300 400 500 600

E

D

C

B

A

Force, kN

Bo

lt r

ow

lo

cati

on

Elastic Rigid

Results of approximation

E

A

Force per bolt row, kN

D

C

B

A

B

C

D

E

Rigid

Elastic

100 200 300 400 500 600 0 -100

Analysis of joint behavior with hidden fasteners

Three moment equation

Five moment equation

Moments in end-plate sections and reactive forces

in bolts for joint variant with hidden fasteners (1-st

approximation- rigid supports)

-1000 -500 0 500 1000

E

D

C

B

A

Force, kN

Bo

lt r

ow

lo

cati

on

Elastic Rigid

Results of analysis of joint behavior with

fasteners hidden between flanges

Force per bolt row, kN

D

C

B B

C

D

0 500 1000 -500 -1000

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 surface-

on-surface, imperfections, some lateral actions,

plastic deformations possibly accumulated during

previous extreme loading cycles and other factors.

Anticipated force distribution between bolt rows

depending on location

-1000

-500

0

500

1000

1500

A B C D E

Bolt row location

Forc

e tr

ansf

erre

d,

kN

Variant I, elastic supports Variant I, rigid supports

Variant II, elastic supports Variant II, rigid supports

• 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.

CONCLUSIONS

• 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.

Latvia Riga

Jelgava

Ru

ss

ia

Latvia University of Agriculture

Thanks for your attentation !