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

Transcription

1 Towards The Design of Super Columns 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 Square Specimens Circular Rectangular Specimens Group-1 Circular Specimens Specimens group-4 Group- Group-3 Specimen C1- C1- C1- cc- cc- cc- cc- CC CC- REC- REC REC Spacing of U-Links (mm) Ultimate Load (kn) f m a x. f c f c = 30 MPa f c = 3.7 MPa f c = 7.1 MPa f c = 3.4 MPa A m m A m m c c c c A m m A 0 m m f f y (shell) =30 MPa (shell) = 355 MPa y f (shell) = 454 y y f (shell) = 367 MPa Dia. of U-link = 8 mm Dia. of U-link = 8 mm MPa Dia. of U-link = 10 mm f (link) = 335 MPa f Dia. of U-link = (link) = 335 MPa y y y 10mm f (link) = 486 MPa f y (link) = 486 MPa Summary of the results.

10 Test Results at Newmark Laboratories Control Specimen 1 kips # (Control) tra ns verse strain average axial strain Strain, concrete a xial s train average overall s train Imbedment Avg rebar Avg axial Avg trans Avg overall 1 kips 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)

11 Stra 3/8 U-Links 50 kips ksi added =0% #3 (3/8" rebar) ave rage transverse s rtain average axial stra in embedment s train in, Imbedment average overall s train 147 kips Avg rebar Avg axial Avg trans Avg overall Fig. 15: Lo a d a verage tra nsverse strain, a verage axial strain (tu be), e mbe dment strain (concrete), a verage overall strain Applied load, P (kips)

12 ½ U-Links 81 kips ksi added =3% #4 (1/" rebar) Strain, Imbedment Avg rebar Avg axial Avg trans Avg overall 1503 kips Applied load, P (kips)

13 5/8 U-Links 360 kips ksi added =30% #5 (5/8" rebar) Strain, Imbedment Avg rebar Avg axial Avg trans Avg overall 158 kips Applied load, P (kips)

14 Filled Composite Rectangular AISC Specifications Columns P P F A 0.85f A no p y s c c P P 0.75 u c n c P P P p P y no p p r p p b / t.6 E F y r b / t 3.00 E F y b / t 5.00 E F y P F A 0.7f A y y s c c P no.5 P F A 0.7f A y cr s c c P e F 9E s b t cr P u P no 0.75P no Pe P u P e EI eff. E s I s C 3 E c I c A s C A c A s E w 1.5 c c f c P EI ef f. e KL

15 Where: P u 0.75P no Pe P no A c c (1) P P F A 0.85f () no p y s EI ef f. P (3) e KL EI eff. E s I s C 3 E c I c C A A s 0.9 A c s P no P e A c E c EI eff E s F y I s K L f c w c C 3 P p A s c 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 P no for compact sections area of steel shape 0.75

16 AISC Code Calculations AISC Eqn. 1-9b HSS / L eff. 1.7 t " des. s ft p b / t.6 no p y s c c f c B t des B i E s F y F E y A c I c P no A P in EI eff. e P e b / t 14. P P F A 0.85f K L A I 15 in 4 E c w 1.5 f c Compact section AISC Equation I-9b Page P no P Pe n P no Effective Stiffness EI eff. E s I s C 3 E c I c A C s A A 0.9 c s f c Unconfined C Newmark Lab -Illnois 158 EI eff #3 U Link 3/8 inches spacing 1.5 inches added 50 kips

17 F y y E s 1 E s 1 1st secant modulus of steel (E steel ) f c f " enhanced stress attained of concrete f c n E s 1 E E s c c s nd secant modulus of steel at n y f E c nd secant modulus of concrete at n y n A T F y n E s 1, E s 1, A E N F f A n E c A E I c A s 1 A... (steel units), A... (steel units), P s T ct s n L N n A E T A ct A s (steel units) s A T I (b t ) (b t ) L I s...(steel units), I ct 3 s...(steel units) n N 1 r T s s y c c I (b t ) 4 I s T...(steel units) n 1N A (b t ) A s T...(steel units) n N r T I T...(steel units) A T

18 Non-Linear Transformation Calculations Applies to: Linear, plastic and Strain Hardening Stages U 3 8 f c f c HSS 8 8 1/ s f c E cs I s A s s 1 A T I T r A N y cs E b t T N E ct I s E 3 s I nf T b t 4 I s b t (b y (E s 1 ) I T t ) n N 1 P P n 9.11 n L I cs 1 1N A b t E s s 1 A L r T T n N nf y HSS 8 n E s 1 E s F y E s 1 A s 1 b t A c A cs 1 f c E cs L (ft) 1.91 n y E P n A F s y f c A c Beams: Coumns: P n A T l n y n [ y F y E s 1 E s constant ]

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