Design Of Glass Column 1y4fd

ADVANCED DESIGN OF GLASS STRUCTURES Design of glass column Viorel Ungureanu European Erasmus Mundus Master Course

Sustainable Constructions under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC

Objectives of the lecture Objectives Composite section Non-composite section Accidental situation

Worked example

•

1) Assess the resistance of a glass column made of bundled tubes, ing a roof, as shown in the figure. Tubes are attached together by the use of adhesive which enables them to work as: a) a single composite section; b) a non-composite section. L= c1 4000 mm tube outside diameter d = 135 mm thickness t = 6 mm Design value of glass strength: in compression fcd = c2 400 MPa in tension ftd = 50 MPa

Design of glass column

a) Section A - A

L b) Section A - A after failure

116,91 184,41

67,5

2) Assess the resistance of the same column with two broken tubes - see the figure. 2

Composite section Objectives

Accidental situation

• tube outside diameter

d = 135 mm

• thickness

t = 6 mm

• area of one tube

A0



2

 d 2  d  2t  A0  4

y



• moment of inertia of one tube



z

67,5

Non-composite section

Tubes are attached by use of adhesive which enables them to work as a single composite section

116,91

Composite section

 d 4  d  2t 4 I0  64

67,5

I0



• Moment of inertia of composite section Iy ,Iz



I y  3I 0  4 I 0  A0  r12



 r = 116,91mm 1

 

I z  I 0  4 I 0  A0  r22  2 I 0  A0  r32



r2 = 67,5mm r3 = 135,0mm

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Composite section Objectives Composite section Non-composite section Accidental situation

• Maximal resistance in compression without buckling

N max   cd  7 A0 • Critical force

N cr ,comp

 2 EI  2 Lcr

• “safety factor” – restriction for capacity by Ncr/4

N Rd ,1 

N cr ,comp 4

4

Non-composite section Objectives Composite section

Tubes without connection, each tube share axial load equally • Critical force of one tube

Non-composite section Accidental situation

N cr , 0

 2 EI 0  2 Lcr

• Capacity of the column

N Rd , 2

7  N cr , 0  4

5

Accidental situation Objectives Composite section Non-composite section Accidental situation

2) Accidental situation – two broken tubes • New location of gravity axis

yT 

3  A0 184,41  2  A0  67,5 5  A0

yT

116,91 184,41

67,5

• Moment of inertia IyT of 5 tube – composite section 2

2

I yT  3I 0  3 A0 184,41  yT   2 I 0  2 A0  yT  67,5 • Distance to the tensioned fibres dt • Distance to the compressed fibres dc • Critical force

N cr , yT

 2 EI yT  L2cr

yT 116,91 184,41

67,5

tensioned fibres

• Eccentricity of force

e  184,41  yT

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Accidental situation Objectives Composite section Non-composite section Accidental situation

a) axial force + moment – tensioned fibres

I yT

W y ,tension 

• Cross-section modulus

dt

• maximal allowed force for tensioned fibres

f td 

N Ed N e  Ed 5 A0 W y ,tension

 N Ed  

b) axial force + moment – compressed fibres • Cross-section modulus

W y ,compression 

I yT dc

• maximal allowed force for compressed fibres

N Ed N Ed  e f cd   5 A0 W y ,compression Conclusion:



N Ed  

Preliminary resistance of glass column

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