Abstract
Experimental and theoretical research on the rotational behavior of Multi-cell shaped concrete-filled steel tubular (MCFST) connection under low-period cyclic load is performed. The experimental results showed that the design parameters had significant effects on the elastic rotational stiffness of the connection, and affected the sequence and position of the plastic hinges appearance at the column and beam ends. Furthermore, the damage mechanism of the plastic hinge lines is obtained, and the simultaneous yielding for the plastic hinges results in the rapid increase of the beam end rotation. In order to handle the problem with irregular geometry boundary and uneven distribution of tightening-ring stresses a differential element of an unified material is proposed considering the effective tightening-ring stresses of special-shaped steel tube on confined concrete, which can be used to analyse the whole mechanical and damage performance of the connection. Combining unified design theory and experimental results, the calculation for the elastic bending rigidity of the connection is obtained. Finally, the moment-rotation relation model of the connection is proposed by regression analysis on experimental results, and the theoretical results are observed to agree well with the experimental results.
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Abbreviations
- A c, A s (mm2):
-
Sectional areas of confined concrete and steel tube
- A c1, A c2 (mm2):
-
Total areas of confined concrete in effective constraint region of limbs parallel and vertical to beams
- a f(mm):
-
Length of confined concrete of limbs vertical to beam in web direction
- As1, A s2 (mm2):
-
Total areas of limbs parallel and vertical to beams in model of equivalent concrete-filled circular steel tube
- a wn1, a fn1 (mm):
-
Lengths of steel webs of limbs parallel and vertical to beams on left side of neutral axis u
- a wn2, a fn2 (mm):
-
Length of steel webs of limbs parallel and vertical to beams on right side of neutral axis u
- b w, b f (mm):
-
Vertical lengths of confined concrete of limbs parallel and vertical to beams
- D, F :
-
Calculation parameters for elastic modulus of unified material composed of special-shaped steel tubulars and confined concrete in compressive region
- dϕ :
-
Differential element in model of equivalent concrete-filled circular steel tubular
- E c, E s (MPa):
-
Elastic moduli of confined concrete and steel tube
- E ′s , E ″s (MPa):
-
Second and third modulus of steel material
- E sc (MPa):
-
Elastic modulus of unified material composed of special-shaped steel tubulars and confined concrete in compressive region
- E scm (MPa):
-
Elastic moment resisting modulus of joint at event I
- E scm I sc0 :
-
Composite bending rigidity of joint at state I
- f(β):
-
Influence coefficient of height to thickness ratio of column section on elastic bending rigidity of joint
- H (mm):
-
Height of column
- H b (mm):
-
Height of beam cross section
- H f (mm):
-
Width of steel tube of limbs vertical to beam
- H w1, H w2 (mm):
-
Widths of flange 1 and 2
- I c (mm4):
-
Moment of inertia of confined concrete
- I s (mm4):
-
Moment of inertia of special shaped steel tube
- I sc (mm4):
-
Modified composite moment of inertia for joint
- I sc0 (mm4):
-
Composite moment of inertia for joint
- k :
-
Influence parameters of cross-section shape and height to thickness ratio of column section on shape characteristic of Mj-θr curves
- K e (kN·m):
-
Elastic bending rigidity of joint
- L w, L f (mm):
-
Depths of steel tube of limbs parallel and vertical to beams
- M e, M y (kN·m):
-
Bending moments at state points I and II
- M j (kN·m):
-
Bending moment of panel zone
- M uj (kN·m):
-
Ultimate bending moment of joint
- N (kN):
-
Axial pressure force on top of column
- N (kN):
-
Load applied to column
- n :
-
Axial compression ratio of column
- n s :
-
Parameter related to shape of Mj-θr curves
- p (N/mm2):
-
Constraint reaction stresses on steel tubes of limbs parallel and vertical to beams
- p cw, p cf (N/mm2):
-
Tightening-ring stresses of confined concrete in effective constraint region of limbs parallel and vertical to beams
- p e (N/mm2):
-
Equivalent tightening-ring stresses of confined concrete in model of equivalent concrete-filled circular steel tube
- p ecw, p ecf (N/mm2):
-
Equivalent tightening-ring stresses of confined concrete in effective constraint regions of limbs parallel and vertical to beams in model of equivalent concrete-filled circular steel tubular
- p hf, p vf (N/mm2):
-
Horizontal and vertical constraint reaction stresses on steel tubes exerted by confined concrete in limbs vertical to beam
- p hw, p vw (N/mm2):
-
Horizontal and vertical constraint reaction stresses on steel tube exerted by confined concrete in limb parallel to beam
- Q (kN):
-
Intersection point between starting point of para-curve corresponding to web limb and y-axis
- S (mm2):
-
Ineffective restraint area of confined concrete
- t b, t d (mm):
-
Thicknesses of flanges of beam and internal diaphragm
- t f1, t f2 (mm):
-
Thicknesses of flanges of limbs parallel and vertical to beams
- t w1, t w2 (mm):
-
Thicknesses of steel webs of limbs parallel and vertical to beams
- u :
-
Neutral axis of column section
- V (kN):
-
Lateral load on top of column
- α 1 :
-
Ratio of steel content of limb parallel to beam
- α 2 :
-
Ratio of steel content of limbs vertical to beam
- α E :
-
Ratio of modulus elastic of steel tube to that of confined concrete
- α s1, α s2 :
-
Stiffness reduction ratios at yield point and plastic stiffness reduction point
- β :
-
Height to thickness ratio of column section
- γ :
-
Ratio of moment of inertia of steel tube to that of confined concrete
- δ :
-
Relative angle between plastic hinges at beam and column ends
- δ m (mm):
-
Horizontal displacement of panel zone
- δ u (mm):
-
Horizontal displacement of column
- θ b :
-
Rotation of beam end
- θ c :
-
Rotation of column end
- θ e, θ y, θ r :
-
Rotations at state points I, II and III
- θ e :
-
Reference rotation which is ratio of ultimate bending moment ofjoint to elastic bending rigidity of joint
- θ r :
-
Relative rotation between ends of column and beam
- λ :
-
Ratio of sectional area of steel tube to that of confined concrete
- ξ :
-
Confinement coefficient of whole unified material constituted by limbs parallel and vertical to beams
- ξ f :
-
Confinement coefficient ξf of limbs vertical to beam
- ξ w :
-
Confinement coefficient of limb parallel to beam
- σ cB (N/mm2):
-
Axial compressive strength of confined concrete
- σ sw, σ sf (N/mm2):
-
Transverse tension stresses of steel webs of limbs parallel and vertical to beams
- σ sy, σ sr, σ sB (N/mm2):
-
Stress at yield point, plastic stiffness reduction point, and ultimate point
- φ :
-
Initial angle of para-curve at intersection point
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Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant No.: 51808195), and the National Natural Science Foundation of China (Grant No.: 50978217). The financial support is highly appreciated.
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Chen, X., Xue, J., Li, H. et al. Performance-based Analysis of Elastoplastic Rotational Behavior of Multi-cell Shaped Concrete-filled Steel Tubular Connection. KSCE J Civ Eng 27, 4300–4322 (2023). https://doi.org/10.1007/s12205-023-0390-8
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DOI: https://doi.org/10.1007/s12205-023-0390-8