1. Towards The
Columns
Design of
Super
Prof. AbdulQader Najmi

2. Description:  Tubular Column – Square or Round  Filled with Concrete
 Provided with U-Links welded to its Walls as shown in
Figure 1

3. Compression Specimen
U-Links are
used to
Confine
Concrete

4. What is a Super Column?  Large Forces  Sustains Large Axial Strains
 Has A Unique Type of Failure

5. Super Column Failure:  By Plastic Buckling of the steel Tube.
 Not by the Crushing of Concrete.
 Concrete does not fail
 In fact: Concrete deforms inside the buckled tube shape depicting its exact inside shape with no signs of cracking!!!

6. 3 Million pounds Apparatus – Newmark Lab
- University of Illinois at Urbana Champaign
Author among professors from Civil and Mechanical
Engineering Departments.

7. Test Specimen fitted with all sorts of
measuring devices

8. Concrete reshaped –
No signs of cracks

9. Summary of Test Results f m a x . f c = 30 MPa f c = 23.7 MPa
Square Specimens
Group-1
Circular Specimens
Group-2
Circular
Specimens
Group-3
Rectangular Specimens
group-4
Specimen
C1-
000
C1-
040
C1-
030
cc-
000
cc-
040
cc-
030
cc-
020
C2C
-000
C2C-
020
REC-
000
REC
-045
REC-
035
Spacing of
U-Links
(mm) - 40 30 - 40 30 20 - 20 - 45 35
Ultimate
Load (kN)
1104
1568
1620
1230
1693
1744
1947
2270
3290
1900
2280
2306 '
0.85
1.73
1.83
0.86
1.87
1.98
2.43
0.78
1.77
0.85
1.58
1.63
f m a x .
f c
f c = 30 MPa '
A  m m 2
f (shell) =320 MPa
Dia. of U-link = 8 mm
f (link) = 335 MPa
f c = 23.7 MPa '
A  m m 2
f (shell) = 355 MPa
Dia. of U-link = 8 mm
f (link) = 335 MPa
f c = 27.1 MPa '
A  m m
f (shell) = 454
MPa
Dia. of U-link =
10mm
f y (link) = 486
2 A  m m 2 '
f (shell) = 367 MPa
Dia. of U-link = 10 mm
f (link) = 486 MPa
f c = 23.4 MPa c c c c y y y y y y y
Summary of
the results.

10.          
Test Results at Newmark Laboratories
Control
Specimen
1222
kips
#2 (Control)


tra ns verse strain

         
average axial strain

concrete a xial s train

average overall s train

Avg rebar
Avg axial
Avg trans
Avg overall Fig. 14 : Load ‐ Axial Strain Steel Tube, Axial strain of concrete (imbedment), Transverse
 strain of tube, Average overall strain of specimen (Control Specimen)

Applied load, P (kips)
Strain, 
1222 kips
Imbedment


11.          
3/8” U-Links
250 kips ksi added =20%
#3 (3/8" rebar)


 average axial stra in
         
 embedment s train

average overall s train

Imbedment kips
Avg rebar
 Avg axial
Avg trans
Avg overall e mbe dment strain (concrete), a verage overall strain


Applied load, P (kips)
ave
rage transverse s rtain
in, 
Stra
Fig. 15: Lo a d ‐ a
verage tra nsverse
strain, a verage axial
strain (tu be),

12.          
½ “ U-Links
281 kips ksi added =23%
#4 (1/2" rebar)



         



Imbedment
Avg rebar
 Avg axial
Avg trans
Avg overall

1503 kips

Applied load, P (kips)
Strain, 

13.          
5/8” U-Links
360 kips ksi added =30%
#5 (5/8" rebar)



         



Imbedment
Avg rebar
 Avg axial Avg trans Avg overall


Applied load, P (kips)
Strain, 
1582 kips

14. Filled Composite Rectangular Columns AISC Specifications
P  P  F A  0.85f ' A
P   P   0.75 no p y s
c c u
c n c
P  P  Pp Py    2
 r p 
P  F A  0.7f ' A
  b / t  E Fy
  b / t  E Fy
b / t  E no p
   2 p p r Fy y y s
c c
P  F A  0.7f ' A
F  9E s
 t 
Pno  2.25 Pe y cr s
c c
 Pno 
 
Pu  0.75  0.877Pe cr
 b 
  2
Pu  0.75Pno 0.658 Pe 
EI eff .  E s I s  C 3E c I c
 As 
 Ac  As 
E  w f '
C 3  0.6  2 
  0.9 c c c
P   2 EI ef f . e
 KL 2

15.   2 EI ef f . Pu  0.75Pno 0.658 Pe     KL 2
Pno 
Pu  0.75Pno 0.658 Pe   
(1)
P  P  F A  0.85f
' A
(2)
no p y s
  2 EI ef f .
c c
Where: P
(3) e
 KL 2
EI eff .  E s I s  C 3 E c I c
 As 
C 3  0.6  2  A
  0.9
 c s 
 A
Pno Pe Ac
E c
EI eff
E s Fy
I s K L
 nominal strength
 elastic buckling load
 area of concrete
 modulus of elasticity of concrete
 effective stiffness of composite section
 modulus of elasticity of steel
 minimum yield sress of steel
 moment of inertia of steel shape
 effective length factor
 laterally unbraced length
 concrete grade
 weight of concrete per unit volume
 coefficient related to filled composite compression member
 Pno for compact sections
 area of steel shape
 0.75 f ' c
w c
C 3 Pp As c

16. Compact section AISC Equation I2-9b Page 16.1-87
AISC Code
Calculations –
AISC
Eqn. 12-9b
f 'c 
B 
t des 
B i 
E s 
Fy 
HSS 8  8 1 / 2
Leff .  1.7 ft
7.84 8
0.465
7.07
29000 46
t  0.93  1  0.465" 2 E
p  b / t  F
Ac 
I c 
des .
f c Unconfined  '
49.98
208.21 y 2
A  13.5 in P Pe
7.84
56.75
P   2 EI eff .
 K L  no 
1.00
  b / t  14.2
P  P  F A  0.85f ' A
Compact section AISC Equation I2-9b Page e 2
0.009 no p
y s
c c
I  125 in 4 s '
E c  w f c
954.10 P
Pn  Pno  
  
no  Pe
5144
950.6
Effective Stiffness
EI eff .  E s I s  C 3E c I c
 A 
C 3  0.6  2  A  A   0.9 s
 c s 
C 3 
1.55
0.900
Newmark Lab -Illnois
1582
EI eff . 
1503
1472 #3
1222
1.20
U‐Link 3/8 inches spacing 1.5 inches ‐ added 250 kips

17.  y  Fy E  E s 1  1st secant modulus of steel (E steel ) f c  f''
 
"  enhanced stress attained of concrete f ' c c
n  E s 1
 E  2nd secant modulus of steel at n
E s 2
s 2 y f '
E c 2  2nd secant modulus of concrete at n y c n
AT Fy n
 E s 1 ,
 E s 1 ,  A E N 
F  f
' A
s 2 n
 Ac
E c 2
s y c c
 2 E I
 As 1
 s 2 T A
... (steel units), A
.... (steel units),
P   L 2 cT N
s 2 n n
  2 E
AT  AcT  As 2 (steel units)
I s 2  (steel units), I cT 
 s A
  L 
  2 T I
(b  2t ) (b  2t )3 s 
...(steel units)  n N 12
  r
T  I
(b  2t )4 I
 s 
...(steel units) T
n N
A (b  2t )2 A
 s 
....(steel units) T n N
r  I T (steel units) T AT

18. Non-Linear Transformation
Calculations
Applies to: Linear, plastic and Strain Hardening Stages
U 3  8
HSS 8
HSS 8  8 1/2
n  E s 1
E s 2 Fy
E s 1
As 1 b t
Ac 2
Acs 1 E ''
s 2  f
 c '
f c
E cs 2 75
387 46
29000
13.5 8
0.465
50.0
0.25
f ' c
I s 2
As 2
 b 2t  2
2.172
7.84
143 E
s 1  AT
I T N  r A
125 y
0.18 T
cs 1 N
EcT
I s 1
0.0016
0.43
2.69
2.51
0.25
202.60 E
 I s 2  b 2t  (b  2t ) 3
1.67 
s 1 I nF
 2 (E ) I T n N 12 y P
Pn 
s T
b 2t 4
I 
12N
9.11 n L2
A b  2t  2 E
1472
1472
cs 1
A 
s 2 
L  
s 1 rT
22.89
1472
1.03 T
n N y nF P
A F ' P  n 
s y 
f A c c
f '
E cs 2  n c
L (ft)
1.91 y
Co l
umns: Pn  AT   n
n [ 
[  Fy
 constant ]
 E s 1
Beams:   
    y y
E s2

19. Multi-Cell Column Cross-sections Figure :9
Four Cell Cross-Section
Four Cell Cr
oss-Section
Five Cell Cross-Section
Three Cell Cross-Section
Figure :9
Suggested Layouts of the multi-Cell Columns
Two Cell Cross-Section

20. CONCLUSION
 The strength of a compression cell is linked to the U-Links provided, the use
of square tubes ensures a uniform confinement of concrete.
 The ultimate strains attained in the compression cells together with the
large inertia properties of multi-cell cross-sections results in high design
moments close to plastic moments when considering large unsupported
lengths.
 The failure of such columns will tend to be linked to plastic buckling of steel
tubes rather than of crushing in concrete.