Future Work

1. Introduction

5.6 Future Work

This investigation dealt with plastic failure of straight, non-composite, symmetrical cellular beams. There is scope for further work investigating the behaviour of cellular beams which are curved, composite or asymmetric.

CHAPTER 6 REFERENCES

1. Trinchero, Paolo E. Serviceability Limit States of Composite Beams, MSc Thesis, University of the Witwatersrand, Appendix A, pp A.6 - A.7, 1993

2. Neubert, H.K.P., Strain gauges, Kinds and Uses, Macmillan, London, 1967.

3. Window, A.L. and Holister, G.S., Strain Gauge Technology, Applied Science publishers, London, 1982.

4. Redwood, RG and McCutcheon, JO Beam Tests with Unreinforced Web Openings. Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, January 1968, pp 1-17.

5. Nethercot, DA and Kerdal, D Lateral-torsional Buckling of Castellated Beams.

The Structural Engineer, Volume 60B, No 3, September 1982, pp53-61.

6. Maalek, S and Burdekin, FM Weld Quality Requirements for Castellated Beams.

The Structural Engineer, Volume 69, No 13,2 July 1991, pp243-254.

7. Hosain, MU and Speirs, WG Experiments on Castellated Steel Beams. Welding Research Supplement, August 1973, pp329-342.

8. Okubo, T and Nethercot, DA Web post strength in castellated steel beams.

Procedures of the Institute of Civil Engineers, Part 2, 1985,79, September,pp533- 557.

9. Westok. Cellular Beams. Information and beam section properties brochure, January 1993

10. Ward, JK. Design of Composite and Non-Composite Cellular Beams. SCI publication 100. The Steel Construction Institute, 1990.

11. Dougherty, B K. Castellated Beams: A state of the art report. South African Institute of Civil Engineers Journal, Second Quarter 1993, pp 12-20.

12. Redwood, RG Design of beams with web holes. Canadian Steel Industries Construction Council, Ontario, Canada, 1973.

13. Dougherty, BK. Ultimate load tests on beams with rectangular web openings.

Struct Engr, Vo158, No 3, Sept 1980.

14. Westok. Cellular Beams. Information and beam section properties brochure, July 1997

15. Ravinger, J and Lascekova, P. Experimental Verification of Thin-walled Girders with Circular Holes. Journal o/Constructional Steel Research 0143-974 X, 1989, pp301-316

At - Laboratory Tests

CHAPTER 7 APPENDICES

Detailed drawings of the test beams.

8-0-0-0 0

^{; I1}

, _Smm PLATE STIFFENER

BEAM 1A

Bmm PLATE STIFFENER

203 x 133 x 25 US

T

Smm PL~~E STIFFENER

ttOQ-O-O-O- OlOD-O - OO o j ,o ^{00- 00} Oll

-6mm PLATE STIFFENER

6mm PLATE STIFFENER

203 x 133 x 25 US

BEAM 1B

6rnm PLATE STIFFENER

Smm PLATE S~IFFENER

, 300

[t OOO 0 oc)[)- oo o ^{0 0}

^{1 1}

6mm PLATE STIFFENER

uO

! 3uu . .:.:

6mm PLATE STIFFENER

BEAM 2A

203 x 133 x 25 UB -

'_00 _ _ - - - -

jOO _---.---'~ ro

6mm PLATE STIFFENER

[fooo 00

^;

^{otOooo-o 0[0 0 00} 0011

6mm PLATE STIFFENER

203 x 133 x 25 UB - - _- 6mm PLATE STIFFENER

BEAM 2B

6mm PLATE

STIFFENER 6mm PLATE -

STIFFENER

If. 0

\

'- -Bmm PLATE \ STIFFENER

- 305 x 102 x 25 US

100

' - -Bmm PLATE STIFFENER

1-125

Bmm PLATE- - STIFFENER

lOOOoJJ

10mm PLATE STIFFENER

BEAM 3A

t

6~'5

Bmm PLATE STIFFENER

"" I C=_'--.,..-__

Bmm PLATE - -~

STIFFENER

BEAM 3B

305 x 102 x 25 US

~I-

Bmm PLATE - STIFFENER

J

...

o 00

1 toO oooooooo~ooooooooo ^II

8mm PLATE

~

6mm PLATE STIFFENER 6mm PLATE

STIFFENER .~ 305 x 102 x 25 UB STIFFENER

BEAM 4A

w..&.-_ _ _ _ P'

IIOD,,-I ---""",-0 _+---=---,---'-'''-_ -'=----I-~~ ^{- '}

-- 000000 000000 000000 /

L a " " , PLATE

~

^,102,25U

~a""'PLATE

^{LammPLATE BmmPlATE~} STIFFEI'£R

STlFFEr€R 305 _STIFFENER STIFFEflER

BEAM 4B

Key

'" Strain gauge rosette

Ci>

Dial gauge

- Three straight strain gauges

...-

...- o

Beam IB

Beam 2B

Beam 3A

Beam 3B

Beam 4B

-

,

Beams with m idpo in t lo a ding p

o ^{0-0 ( )0}

,11

_OOOOC

Lateral support

/

BEAM 1A

p

,v

D -

1 \

OO- OOC D-O OO()OOO -

BEAM 2A

I-

I'

>-

...

Vl

\0 tJoddns IOJ8 tO

l

--

if

-

~ 0 0 0

_{I ,}

0 - ODe

^{1 - - --}

d

Beams with th irdpoint load ing

P

P/2 P/2

Lateral support

BEAM 1B

P

P/2 P/2

00 0000 - 0 - 0 0

BEAM 2B

0 0 0

...

...

-.J

00 -

P/2 P/2

- 0 - 0 00

' - - - Lateral support

BEAM 3B

000

Diagram (a)

oc)o

Diagram (b)

BEAM 4B

...

...

00

Appendix A2 - Ultimate load behaviour

Stress strain curves used for FEA material properties ^I

steel stress vs strain curves are plotted for SF and SP in Figs.A.3 & A.4.

350

300

250 ...

&'200

-

~ ^III III

~ 150

III

100

50

0 0

(1600;310)

~~g;;;;;;;;-"!!' ..

^__

~_:":":

^__

~_!"!:"-

^{_:;_;:; __ ;:;;_;; __ ;: __}

;;_~

^{__ ;:;;_:;_} -;::::::::===("(1;9400;350)

..

, I

,

2,000 6,000 10,000

mlcrostraln

--. SP flange

- SF flange

- simplified curve for FEA

14,000 18,000

FIG.A.3. - stress vs strain of flange, specimen SF & SP 350 ,,-===--a:;-,;.;--;.:,-;,;--_--iioii-,;,;--;;,;!,;;,!!-~!!I!!e!!!!!!!!!!!!!!!~~==~~:!!:!' (19500;340)

300 (1700;330)

-

^Cl '1.200 250

-

~ ^{III In}

~ 150

-

^III

100

50

--. SP web - SF web

- simplified curve for FEA

O~---r---r---.---r--~--~--~--~--~~~

o

^{2,000 6,000 10,000}

mlcrostraln

14,000 18,000

FIG.A.4. - Stress vs strain of web, specimen SF & SP

Beam lA

N o

--

N N

Beam 2B

Beam3B

Beam4B

Graphical comparisons between theoretical and experimental stresses

Beam lA

250

ro

200

0...

~ 150

l:l

¹⁰⁰

(j) ~ 50

o

Comparison with FEA

Beam 1 A - web post stresses

v

~ ~

v ^....

L."...o

V

i--'""

~

V

^V

--

V-~

o

20 40 60 80 100 120 140 Load (kN)

- -FEA - -Experimental

Comparison with FEA

Beam 1 A - opening centre stresses 400

l.

³⁰⁰

~

';; 200

IJ)

~ 100

(J)

o

v

^V

. /

-

v.:: ^{~ v ...}

h.::: ^~

V V

^V

o -

^{20 40 60 80 100 120 140}

Load (kN)

- -FEA - -Experimental

400

;f

300 :2 ~ 200

Cl)

~ 100

Cl)

o

Comparison with FEA

Beam 1 A - opening side stresses

li

r--

^{~ ~}

-

I -

-

^!--

l -^f.---

/"""

o

^{20 40 60 80 100 120 140}

Load (kN)

400

..--...

~

300

~

-200

_Cl)

Cl)

~ 100

Cl)

o

--FEA - - Experimental

Comparison with FEA

Beam 1 A - flange stresses ....,- -

v ...

^{/ ...-}

../" ~ ~

;:::::-.

~ ~ po-

,.Pr'"

:e

^~

~ ~

-

^{~ !-}c

I. -

...

o ^{20 40 60 80 100 120 140}

Load (kN)

--- 10 FEA -- 11 FEA -- 12 FEA

--- 10 Exp --- 11 Exp -- 12 Exp

Beam IB

400

~

³⁰⁰

:2 -;;; 200

I/)

~ 100

Cl)

o

500

ro

⁴⁰⁰

CL

e-

³⁰⁰

~ 200

(l)

.!:J 100

Cl)

o

Comparison with FEA

Beam 1 B - web post stresses

v - ^v

~ ^~

... ~ :::---

-

^f-'

-

^f-'

--

^~

o

20 40 60 80 100 120 140 Load (kN)

---FEA ---Experimental

Comparison with FEA

Beam 1 B - load opening stresses

/

1/ -~

..,.

~

~ ^:.-- .-"

-

.--f-""

o

20 40 60 80 100 120 140 Load (kN)

---FEA ---Experimental

Comparison with FEA

Beam 1 B - centre opening stresses

400

~

³⁰⁰

~

-;;; 200

I/)

~ 100

Cl)

o

^.-

...-... /

v

....

:,...-...

... ^....

~

~ i-""'"

o

^{20 40 60 80 100 120 140}

Load (kN)

-

400

~ 300

~

-- 200

_en

~

en

100

Cl)

o

- -FEA ... Experimental

Comparison with FEA

Beam 1 B - flange stresses

"j

~ - - ' " ~

~ ^~

~ ~

...

^~

- ^i--'

.-

^~

-

/"" r-^JO

o ^{20 40 60 80 100 120 140}

Load (kN)

-- 10 FEA -- 11 FEA -- 12 FEA

-&- 10 Exp

^{- 9 -}

11 Exp --- 12 Exp

Beam 2A

Comparisons with FEA

Beam 2A - Web post stress

300

ro

a... 200

~ ' - "

f/)

:3

¹⁰⁰

...

W o

400

~

³⁰⁰

~ --;; 200

f/)

~ 100

Cl)

o

... ~ ,,-/

V

...

^~

~

-

~

i,....--" ^~

-- ^v

o

^{20 40 60 80 100 120 140}

Load (kN)

- -FEA --- Experimental

Comparison with FEA

Beam 2A - Flange stresses

V

, /

V ...-I--""

/ ~

~

---

~ ~

~ I-'

--

^{/ '}

/ " ~

o

^{20 40 60 80 100 120 140}

Load (kN)

- -FEA - -Experimental

Beam 2B

300

ro

250

~ 200 -;; 150

:fl

100

U5

'- 50

o

500

ro

400

Il...

e.

³⁰⁰

::l

200

Q)

!:; 100

Cl)

o

Comparison with FEA

Beam 2B - web post stresses

--

I-:: :;:..-

^f-

~

:::::

^V

--- ^----

v ----

V--

...

o

^{20 40 60 80 100 120 140}

Load (kN)

- -FEA --- Experimental

Comparison with FEA

Beam 2B - load opening stresses

o

L V

V --

^{~ ~}

.;? ^v~

"""

v .---

.-V ---

20 40 60 80 100 120 140 Load (kN)

- -FEA ---Experimental

Comparison with FEA

Beam 2B - centre opening stresses

400

;f

300

~

:;; 200

If)

~ 100

Cl)

o

-400

co

a..300

~

';200

en ~100

--

(J)

0

... ^...- . / .&~

,

^~ ~ /'"

,/ ' "

.-^{/ '}

o

20 40 60 80 100 120 140 Load (kN)

- -FEA - - Experimental

Comparison with FEA

Beam 2B - flange stresses

L_

~

^~

."""

~ ^~ P"'"

~

--- ^--- -

---

..

^~

o 20 40 60 80 100 120 140

Load (kN)

~ 10FE~ 11 FE~ 12FEA -e-

10 Exp -- 11 Exp- - 12 Exp

Beam3A

250

ro

²⁰⁰

a.. ~ 150

::l

100

U5

~ 50

o

ro

600 ⁵⁰⁰

~ 400 ';; 300 :G 200

...

U5

100

o

Comparison with FEA

Beam 3A - web post stresses

~ .--"

....- -

....-

^,...-

~

---

~ r-

--

f-

o

^{25 50} 75 100 125 150 175 200 Load (kN)

-.-FEA - -Experimental

Comparison with FEA

Beam 3A - opening centre stresses

...

...:::

...

- -

...

~

---

o

^{25 50} 75 100 125 150 175 200 Load (kN)

-.-FEA - -Experimental

400

~300

~

-;;; 200

If)

~ 100

Cl)

o

Comparison with FEA

Beam 3A - opening side stresses

I

V

-

^,..-

^v

d'

... ..-

~ I - I -

--

o

^{25 50} 75 100 125 150 175 200

500 --400

_co

a..

~

300

-- _{~ 200}

Q) ...

...

Cl)

100

o

Load (kN)

--FEA --Experimental

Comparison with FEA

Beam 3A - flange stresses

/

V

I

. / ~

I L.

^~

.... ,

---

^~

..,.

^~

~ ~

....-" ^~

f--"

o ^{25 50} 75 100 125 150 175 200

Load (kN)

- -10 FEA - -11 FEA - - 12 FEA - - 10 Exp - - 11 Exp -e- 12 Exp

Beam3B

250

ro

²⁰⁰

a.. ~ 150

~ 100

en

~ ⁵⁰

o

Comparison with FEA

Beam 3B - web post stresses

~

lA'

~

~

~

~ V

!p"

v

/ ' , /

o

^{50 100 150 200}

Load (kN)

~FEA ..-Experimental

Comparison with FEA

Beam 3B - opening centre stresses

400

~300

~

';; 200

Cl)

~ ¹⁰⁰

Cl)

o _o ----

...-"

...

....-.;;::'

v ...

./~

.~

..-v

50 100 150 200

Load (kN)

~ FEA - -Experimental 250

250

m

²⁵⁰ 300

~ 200 ';; 150

~ 100

(7)

50

o

400

~

300 :2 ';; 200

Cl)

~ 100

U)

o

Comparison with FEA

Beam 3B - opening side stresses

/

--

/

...

..--

... ~

...

...

o

^{50 100 150 200}

Load (kN)

---FEA - - Experimental

Comparison with FEA

Beam 3B - flange stresses

~

,,/'

~

V

----

.-::

::::::---

---

^f-'

--

^,....-

o

50 100 150 200

Load (kN)

---FEA - -Experimental

250

250

Beam4A

200

~

150

~

-;; 100

If)

~ 50

U5 o

500

ro

⁴⁰⁰

a..

e-

³⁰⁰

~ 200

Q)

.!:; 100

Cl)

o

Comparison with FEA

Beam 4A - web post stresses

v

~"

v

--:/

~ /"'"

,./

/~

/ '

o

^{20 40 60 80 100 120}

Load (kN)

~ FEA --Experimental

Comparison with FEA

Beam 4A - opening centre stresses

/ ~

1/ ^,/

/ ^{, , /}

/'"

-

~

~ , , /

o

^{20 40 60 80 100 120}

Load (kN)

~FEA --Experimental

500

m

⁴⁰⁰

a.. ~300

~ 200

Q)

~ 100

Cl)

o

Comparison with FEA

Beam 4A - opening side stresses

7

/ ~

/

~ !'--

~ V l.--- l.---

--

^I--

~

o

^{20 40 60 80 100 120}

500

rn- ⁴⁰⁰

CL ~

300

' - "

~

200

~

Ci5 100

o

Load (kN)

---FEA - -Experimental

Comparison with FEA

Beam 4A - flange stresses

'" ^~

~

...

~ ::.,....-

~ ^/

~

~

.J' ~

~

. /

..-'

~

o ^{20 40 60 80 100 120}

Load (kN)

-- 10 FEA --- 11 FEA -- 12 FEA

--e- 10 Exp -- 11 Exp -- 12 Exp

Beam 4B

300

ro

250

~ 200 ';; 150

~ 100

~ 50

o

500

ro

400

0...

~300

~ 200

Q)

.!:; 100

Cl)

o

Comparison with FEA

Beam 4B - web post stresses ,.,.

...

..

I-:::

? '

...

...

o

^{~ ~ W 00 100 1~ 1~ 1W}

Load (kN)

- -FEA ^-M-Experimental

Comparison with FEA

Beam 4B -load opening stresses

o

~

,-

~ ...

'f'IY I--"

V ...-

20 40 60 80 100 120 140 160 Load (kN)

- -FEA -M-Experimental

Comparison with FEA

Beam 4B - centre opening stresses 500

co

400

CL

5

³⁰⁰

~ 200

<l.l

.!:; 100

Cl)

o ^-- - -

...

....

~

~ p- I.---""

o

^{20 40 60 80} 100 120 140 160

- m 300 400

0.. ~

'-"200

_(/)

(/)

~ 100

Cl)

o

Load (kN)

---FEA - - Experimental

Comparison with FEA

Beam 4B - flange stresses

/~ ^~

-"~ ^IY

~ ~

~

"""

v

~

...

- ^...

-

.,...

o ^{20 40 60 80} 100 120 140 160

Load (kN)

-- 10 FEA -- 11 FEA -- 12 FEA

-&- 10 Exp -- 11 Exp -- 12 Exp

Appendix A3 - Deflections

Graphical comparisons between theoretical and experimental results

Steel Construction Institute method

... 16

~

¹²

§ 8

:.;::;

()

~

4

ID

o 0

...

50 E

40

~30

E

U o

20

ID

'Q) 10

o 0

Comparison with SCI

Beam 1 A - vertical deflections

/

V

/ ^~ L---

- ^{v--- -~}

^p

-

---:

^{~ ~}

::..-

^~

...:::::

^{~ ~ ~}

~

...

f.--

--

o

^{20 40 60 80 100 120}

o

Load (kN)

---V1 Exp ... V2 Exp-+- V3 Exp

-a- V1 SCI-9- V2 SCI-&-V3 SCI

Comparison with SCI

Beam 1 B - vertical deflections

~

~

~ ^p

~

^~

V

_I--^~

~

v ---

~

^~

^t:--

^{I-- ~}

~ ~ _~ ~ -~ F::;... I----"

20 40 60 80 100 120

Load (kN)

---V1 Exp ... V2 Exp-+- V3 Exp

-a-V1 SCI-9- V2 SCI-&- V3 SCI

..-

25

E 20 E --; 15

U

o 10

;;:::: 5

(]) _(])

o 0

50

..-

E 40

--

E _c:: ^en

³⁰

+::

o

20

<.>

(])

ID

10

o o

o

o

Comparison with SCI

Beam 2A - vertical deflections

~

-

~ ./

v---

^.-:;::; !of""

v ____

~ ~

~ ~ ^{f--"_ ~}

..

~ ~ I-" ....-I ~

-~

-

20 40 60 80 100 120

Load (kN)

---V 1 Exp --.-V2 Exp -+- V3 Exp

-a-V1 SCI-'i'-V2 SCI -&--V3 SCI

Comparison with SCI

Beam 2B - vertical deflections

V

l-::::::: ~

....,~ ~ I--"

~ ^~~ ,::::;-

~ ^~ ...

~

.::;:::;;- - ^....--

~ F"""

-

/

~

..-

20 40 60 80 100 120

Load (kN)

---V1 Exp--.-V2 Exp-+-V3 Exp

-a- V1 SCI-'i'-V2 SCI --e--V3 SCI

---

20

~

¹⁵

...

§

10

U

~

5

ID

o 0

--- _~

20

... 15

§

¹⁰

:.;::;

(,)

~ 5

o

Q)

o

Comparison with SCI

Beam 3A - vertical deflections

/ •

~

Z

....

^~

- v

^~

...-

^~ ~ ~ f...--^f-" ~

:! -

^{~ ~}

...

:::::::::

o

^{20 40 60 80} 100 120 140 160 Load (kN)

---V1 Exp ... V2 Exp ... V3 Exp

-i3-V1 SCI-9-V2 SCI-&- V3 SCI

Comparison with SCI

Beam 3B - vertical deflections

...:

...-~

~ ~..--:: ~

~ ~ ^~

~ ~

~ ^~

~

....

o

^{50 100 150 200}

Load (kN)

---V1 Exp ... V2 Exp ... V3 Exp

-i3-V1 SCI -9-V2 SCI-&-V3 SCI

50 ...-E 40 '-"'30 E _c:

U o

20

ID

'$

10

o o

50 E40 '-"'30

E

_c

U o

20

ID

'$

10

o o

Comparison with SCI

Beam 4A - vertical deflections

...:::"

~ ...

...

^~

- ^,.

,;"'"

-

^~

~ i-""'" ,,;r'

...- ..

^~

---- ^--:....

^-*"

f.::::: I---'"

o -

^{10 20 30 40 50 60 70}

Load (kN)

~ V1 Exp ... V2 Exp ~ V3 Exp

-er V1

sel

-9- V2

sel

~ V3

sel

Comparison with SCI

Beam 4B - vertical deflections

~ ~ ^{, . /}

/ . ~ le::?

~ ;:::;---...,.-:: ~

~ ~

v

~ ^~

...

::S

~~

....

---

^P'"

~ ~

^- -- ^---

.-

V

-

o

^{20 40 60 80 100 120}

Load (kN)

---V1 Exp ... V2 Exp ~ V3 Exp

-er V1 SCI-9-V2 SCI ~ V3 SCI

Simplified SeI method

Comparison with simplified SCI

Beam 1 A - vertical deflections

. -16

E

E 12

--

^rJ) _c

₈

:;::; o

~ 4

c;:::::

o

Q)

0

o

.".

. /

~ . / ^{~ ~} i::::=

-

^{~ ~ ~ l -}

V --

^~

^-

^I--!---

...-::: ~ ~ :'---1-

--

20 40 60 80 100 120

Load (kN)

---V 1 Exp -.-V2 Exp ---V3 Exp

~ V1

sel s

^-'0'-V2

sel s

^-e-V3

sel s

Comparison with simplified SCI

Beam 1 B - vertical deflections

. -

50 E

40

~30

E

U o

²⁰

Q)

'W

10

o 0

o

v

~ t7

~ ~ I---

~.~ ~

...-J;:; ~ ~

~ ~

. -.-.

^~

~ ~ ...:: j;iiIP"

20 40 60 80 100 120

Load (kN)

---V 1 Exp -.-V2 Exp ---V3 Exp

~ V1

sel s

^{- 9 -}V2

sel s

^-e-V3

sel s

Comparison with simplified SCI

Beam 2A - vertical deflections

- 25

L/ ^'IF

---

^-"

I,....e' ~

-

^{V l---" L..--F}

~ :::;",.... ~-^{~ __ r-}

--

^I.-

~ ~

E 20

~ E 15

U o

10

CL>

'Q)

5

o 0

o

^{20 40 60 80 100 120}

Load (kN)

---V1 Exp ~ V2 Exp ~ V3 Exp -e-V1

sel s

^-Si'-V2

sel s

^-e-V3

sel s

Comparison with simplified SCI

Beam 2B - vertical deflections

..-

50 E

40

~30 E

U o

20

CL>

~ 10

o o o

/ ' l / : ^:,/

--

^{~ :~}

-

...-::::: ~ ~

~ t;:::;:::::~

~ ~ ~ - --'

""""

~ ~

..." ~

20 40 60 80 100 120

Load (kN)

---V1 Exp ~ V2 Exp ~ V3 Exp -e-V1

sel s

^-Si'-V2

sel s

^-e-V3

sel s

Comparison with simplified SCI

Beam 3A - vertical deflections

20

...-...

E 15

- E _§

₁₀

:;:;

<..>

~ 5

o

Q)

o

7

•

V-

?

--~

^{~ ~}

.-

^~ I#"" ~ ^{~ I.---}

r:.---

~

k

^{.-::; I-" I-" I,...r}

-

^I--

...

V

---

^{~ P-}

o

^{20 40 60 80} 100 120 140 160 Load (kN)

---V1 Exp -.- V2 Exp ....-V3 Exp

-e- V1

sel s

- 9 -V2

sel s

--e-V3

sel s

Comparison with simplified SCI

Beam 3B - vertical deflections

...-... 25

E

20 -15

E

_c

:g

o 10

Q)

'ID

5

o o o

v -

~ '7'

---

^{II" ~ L--}

.-:::;::. ~~ ^~

~ ~

~ ;,.,.--.-'f'

~

"""""""

50 100 150 200

Load (kN)

---V1 Exp -.- V2 Exp ....-V3 Exp

-e-V1

sel s

^{- 9 -}V2

sel s

^--e-V3

sel s

Comparison with simplified SCI

Beam 4A - vertical deflections

... 50 E 40 -30 E _c

:g o

20

ID

'(j) 10

o o

.-

. , /

... ^..

v..

^~

~ W" ... f*' _~ I--' W

~ pr .-1--'"" ~

~ 1-""...-I--" ~

. L ~ -:; ^.->

-

^I--

~ ~ ~ -~

~

~

^~

o

^{10 20 30 40 50 60 70}

Load (kN)

~ V1 Exp -.-V2 Exp ~ V3 Exp

-e-V1

sel s

^-'i'-V2

sel s

~ V3

sel s

Comparison with simplified SCI

Beam 4B - vertical deflections

60 ...

E

-S40

c

o

:.;::::;

~ 20

c;:::::

o

ID

o o

--

--- ^~

~

~ ~

^?

V

^~

~ ~ t:::-

^{I.-- I -}

--- -

~ ^~

^::..--

~

...& ~

20 40 60 80 100 120

Load (kN)

~ V1 Exp -.-V2 Exp ~ V3 Exp

-e-V1

sel s

^-'i'-V2

sel s

~ V3

sel s

Vierendeel method

Comparison with Vierendeel method Beam 1 A - vertical deflections

16

,.-...

~ ¹²

- _§

₈

:.;:;

()

ID

to=:

4

o

ID

o o

.,It

.--- ./'

/ ^~

--

^~

^v

- ^V

^{~ ~ ~}

-

^I-

~ ~ ^~

- --

^{~ e-}

~ ~ ^~

- ^...

20 40 60 80 100 120

Load (kN)

--- V1 Exp -.- V2 Exp --- V3 Exp

--a--

V1

vier ^{- 9 -}

V2

vier ~

V3

vier

Comparison with Vierendeel method Beam 1 B - vertical deflections

50

,.-...

E

40 -30 E

_c

U o 20

ID

Q)

10 o o

o

/

.?

7

...-

^~

~ ~...-:

::::..-

~ ^{~ v}

.6" ~

-

.-

---

...:::

^:::;..-

...: ~

20 40 60 80 100 120

Load (kN)

--- V1 Exp -.- V2 Exp --- V3 Exp

--a--

V1

vier - 9 -

V2

vier ~

V3

vier

Comparison with Vierendeel method Beam 2A - vertical deflections

- E 25 20 -15 E

_c

U

o

10

Q)

'ID 5

o o

o

/

"

V ...£ ,....

....--:

^{f--:::::; ...}

~

---- - --

~ :::::::--.-...-

r::::- - _---

...r:. _~

---- ^....

-

^::;::;.-

20 40 60 80 100 120

Load (kN)

--- V1 Exp --.- V2 Exp ...- V3 Exp

-e-

V1

vier ~

V2

vier ~

V3

vier

Comparison with Vierendeel method Beam 2B - vertical deflections

50 E40 E -30

_c

U o 20

Q)

'ID 10

o o

/

/..

^~

~

r -

... ...-:: ~

/ ... ^~

-

~

....-

^{~ :.-}

-

-""

~ ^::::--

-- ^-

o ^{20 40 60 80 100 120}

Load (kN)

--- V1 Exp --.- V2 Exp ...- V3 Exp

-e-

V1

vier ~

V2

vier ~

V3

vier

Comparison with vierendeel method Beam 3A - vertical deflections

20 ....-.

E 15 ...

E

o

j

•

~

z

~

--:::::

^{~ ~}

.... -

.---.

^~ ~ ~

--- - ^,,;-

..AI: ~

:::::::;

::::::::::: _~ ^~

... -- -

~ ~ ~ ^:;..-

o

^{20 40 60 80} 100 120 140 160 Load (kN)

---V 1 Exp ---.-V2 Exp ---V3 Exp

-e-V1 vier ^--9-V2 vier ^-&-V3 vier

Comparison with Vierendeel method Beam 3B - vertical deflections

....-. 20

~

¹⁵

§

10

:;:.

Q) u

tt=

5

o

Q)

o

^~

o

~

~ ^~

~

50

"..::::::

~ ~

~

100 Load (kN)

...-:

...-: ~

V-

^~ _~

...

~

~

150

---V1 Exp ---.-V2 Exp ---V3 Exp

-e-V1 vier ^--9-V2 vier ^-&-V3 vier

200

Comparison with Vierendeel method Beam 4A - vertical deflections

-- ^{E 40} 50 -30 E

_c

U o 20

ID

'Q)

10

Cl

o

..-:::::~

~ r---

...-: ^~

~ -"" ~~

~ ~ I,..-r I""'"

",..

Jlf--"

..,

^.... .JP'"'

---

.-::::: ^r....-

~

o ^{10 20 30 40 50 60 70}

Load (kN)

--- V 1

Exp --..-

V2

Exp.-.-

V3

Exp

.

-e-

V1

vier ^-'9'--

V2

vier -e-

V3

vier

Comparison with Vierendeel method Beam 4B - vertical deflections

-- ^{E 40} 50 -30 E

_c

U

o

²⁰

ID

'Q)

10

Cl

o o

/

...

~ .-

-

~ ~

,.&:11 ~ ~

""

^{~ ~}

~ ~

....

^~ i""""

--

~ ~

- -

^!---"

20 40 60 80 100 120

Load (kN)

--- V1

Exp--..-

V2

Exp.-.-

V3

Exp

-e-

V1

vier ^-'9'--

V2

vier -e-

V3

vier

Finite Element Analysis method

...-..

20

~

¹⁵

' - '

§ 10

U

~

5

Q)

o 0

60

..--.

E 540

c

o

:;:;

~

20

tt= Q)

o o

Comparison with FEA

Beam 1 A - vertical deflections

, , /

v

./" l--

/

~

^e--

-;::::. ^::...--

^,../'

~ ~

^I--

k-::: :..--

-- --

1 I

::::::::

^{,...-f-;::: ::.--}

-- _{... V}

f::::::: -

~

o ^{20 40 60 80 100 120 140}

Load (kN)

-- V1 FEA-- V2 FEA-- V3 FEA

-e-

V1 Exp -- V2 Exp -- V3 Exp

Comparison with FEA

Beam 1 B - vertical deflections V

./

(f

1

. /

~

^~

^/'" I

~

~ ^~ v I

:::::::..;; ,.... ^b,...R

-

^--'

~

~ ~ ^~

~

o ^{20 40 60 80 100 120 140}

Load (kN)

-- V1 FEA-- V2 FEA-- V3 FEA

-e-

V1 Exp -- V2 Exp -- V3 Exp

--

E 30 -S20

c o

:.;::::;

~ 10

;:;::::

o

Q)

o

..-60

E

-S40

c

o

:.;::::;

~ 20

;:;::::

Q)

o 0

Comparison with FEA

Beam 2A - vertical deflections ) 1 1

/ ,

/ '

~ v / /

~

~

^~

- ^~ ---

~

^{~ ~}

-

^~

^v

~

--- -

~~

o

^{20 40 60 80 100 120 140}

Load (kN)

- -V1 FEA---- V2 FEA- -V3 FEA ---V1 Exp ---.-V2 Exp - -V3 Exp

Comparison with FEA

Beam 2B - vertical deflections

v

^~

~

~

^{~ /}

...- ^..:::;:

^{~ ~}

---

k:::::::: ~

--

...,

-

^~

^-

^f--f-'e"

)/

'}

l-.I

o

^{20 40 60 80 100 120 140}

Load (kN)

---V1 FEA---.-V2 FEA- -V3 FEA - - V1 Exp ----V2 Exp - -V3 Exp

20

-

^{E 15}

E c:: o 10

:;:;

U '+= ID

ID 5

o

o

-30 E E :::- 20

_c

<1>

E ~

10 co

Q.

o

(1)

0

Comparison with FEA

Beam 3A - vertical deflections

1 I / I 1 ,

/ ' ~

'j I 1

v

_~ ^10'"

~

. /

~

~

~

^I...-

/ V

. / '

~ ~ V - --- ^....

^{1--' ... I---'}

~ ~

f-"" ~ ~

...-: r:;r

~

~ v

o

25 50 75 100 125 150 175 200

o

Load (kN)

- -2 FEA ~ 3 FEA - -4 FEA -e- 2 Exp __ 3 Exp --- 4 Exp

Comparison with FEA

Beam 3B - vertical deflections

...

I 1 L.I/ /

~

^{~ 1-/}

--

^~

~ ~ ^i-'" .... 11'

~ ^{p -}

50 100 150 200

Load (kN)

-- V1

FEA~

V2 FEA-- V3 FEA

-e-

V1 Exp -- V2 Exp --- V3 Exp

- E 150 E 100

...

c

o

:;::::;

~ 50

;;::

o

ID

.-.50 E E 40

...

C 30

ID

~ 20

u ro

10

Q.

f/)

i:5

0

o

o

Comparison with FEA

Beam 4A - vertical deflections

/ I f /

!

I

~ !

/ /

^/

^{~ I}

-- ^{~ r: ---} ---

^~

^/

~

k::::::::

r:::-- -

~

o ^{20 40 60 80 100 120}

Load (kN)

-- V1 FEA -- V2 FEA-- V3 FEA

-e-

V1 Exp -- V2 Exp -- V3 Exp

Comparison with FEA

Beam 4B - vertical deflections

",-

~ V I b::? ^{./" IT} I

./.~ ~ I

~...,: ~ l"

, / . / p--

-

^~

~ .-/' _~ ~

-"/ ^~

,..-

h ~

- --

~ ~

20 40 60 80 100 120 140 160

Load (kN)

-- V1 FEA-- V2 FEA-- V3 FEA

-e-

V1 Exp -- V2 Exp -- V3 Exp