Materials and Structures

, 51:160 | Cite as

Seismic performance and prediction equations of sandwich beam-column joints subjected to skew cyclic loads

  • Liqun Hou
  • Xinzheng Lu
  • Hong Guan
  • Weiming Yan
  • Shicai Chen
Original Article


To study the seismic performance of sandwich beam-column joints constructed with high strength concrete column and normal strength concrete floor system and joint regions, four specimens with different column to beam concrete strength ratios (α) were tested under skew cyclic loads. The performance indices of the specimens including the failure mode, ductility, energy dissipation were compared and analyzed. The results show that the failure modes of the sandwich joints are in form of joint shear failure after yielding of the beam, while the ductility coefficient is found to be greater than 3.0. Compared to the joints with low concrete strength ratios α, the specimen with a high concrete strength ratio α features larger deformation at the joint. Based on the softened strut-and-tie model, a set of shear strength prediction equations for the sandwich beam-column joint, taking into account the effects of the concrete strength ratio α, floor slabs and plastic region of beams, is proposed. Comparison of the present tests against the published literature confirms that the shear strength of the sandwich joints can be well predicted by the proposed model.


Sandwich beam-column joints Cyclic loads Failure mode Shear strength 

List of symbols


Gross-sectional area of the column

As, \(A_{\text{s}}^{{\prime }}\)

Sectional areas of the top and bottom reinforcement of the beam, respectively


Reinforcement area in the tension zone of the beam


Reinforcement area of the floor slab located within the beam effective flange width

\(A_{\text{sst}}^{{\prime }}\)

Area of the diagonal strut


Total sectional area of transverse reinforcements within the effective width of the joint core zone in the loading direction

\(a_{\text{s}}^{{\prime }}\)

Distance between the centroid of resultant forces of longitudinal compressive steel reinforcements and the extreme compression face of the beam

as, bs

Depth and width of the diagonal strut, respectively

bb, hb

Beam width and depth, respectively

bc, hc

Column width and depth, respectively

bj, hj

Effective width and height of the core zone of the joint, respectively

cb, cc

Depth of the compression zone of the beam and column, respectively

\(h_{\text{b}}^{\prime \prime }\), \(h_{\text{c}}^{\prime \prime }\)

Distances between the extreme longitudinal reinforcement in the beams and columns, respectively


Effective depth of beam

\(h_{\text{b}}^{\prime }\)

Distance between the centroids of upper and lower beam reinforcement


Height of column


Length of the plastic hinge region of the beam


Spacing of the transverse reinforcements along the beam axis


Thickness of the floor slab

\(f_{\text{cb}}^{{\prime }}\), \(f_{\text{cc}}^{{\prime }}\)

Compressive strengths of concrete of the beam and the column, respectively

\(f_{\text{c}}^{{\prime }}\)

Cylinder strength of concrete

\(f_{\text{ce}}^{{\prime }}\)

Effective compressive strength


Design tensile strength of concrete


Design strength of shear reinforcement

fyh, fyv

Yield strength of the joint hoop reinforcement and intermediate column bars, respectively

fyb, fyp

Yield strength of the beam reinforcement and slab reinforcement, respectively


Design axial force


Axial force acting on the column


Horizontal joint shear strength predicted by ACI 318-14


Horizontal joint shear strength predicted by CSA A23.3-04


Horizontal joint shear strength when the beam reinforcement yields


Horizontal shear strength of type 1 joint


Horizontal joint shear strength predicted by chinese design code for concrete structures


Horizontal joint shear strength of the softened strut-and-tie model

\(V_{\text{sst}}^{{\prime }}\)

Horizontal joint shear strength of the modified softened strut-and-tie model


Measured shear strength


Energy dissipated in each load cycle


Energy dissipation of an equivalent elastic cycle


Strut-and-tie index

M/(V h)

Shear span ratio


Concrete strength ratio


Angle between the diagonal strut and horizontal axis


Seismic adjusting factor

γh, γv

Fractions of diagonal compression transferred by the horizontal ties in the absence of the vertical ties and the vertical ties in the absence of the horizontal ties, respectively

\(\overline{{F_{\text{h}} }}\), \(\overline{{F_{\text{v}} }}\)

Balanced forces of the horizontal ties and vertical ties, respectively

\(\overline{{K_{\text{h}} }}\), \(\overline{{K_{\text{v}} }}\)

Indexes of the horizontal and vertical ties, respectively


Lateral deformation at the top of the column


Longitudinal strain of the beam reinforcement in the plastic hinge region of the joint


Tensile strain of the beam at yielding

εr, εd

Average principal tensile and compressive strains in the joint, respectively


Average concrete strain in the center of the joint


Equivalent hysteretic damping ratio


Confinement effect factor of the orthogonal beams


Softening coefficient of the concrete


Strength reduction ratio


Rotation angle of the column

ϕpmp, ϕpmn

Positive and negative plastic rotational angles, respectively



This work was financially supported by the National Natural Science Foundation of China (No. 51778341) and the National Key R&D Program (No. 2017YFC0702902).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© RILEM 2018

Authors and Affiliations

  • Liqun Hou
    • 1
  • Xinzheng Lu
    • 2
  • Hong Guan
    • 3
  • Weiming Yan
    • 4
  • Shicai Chen
    • 4
  1. 1.Beijing Engineering Research Center of Steel and Concrete Composite StructuresTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Department of Civil EngineeringTsinghua UniversityBeijingPeople’s Republic of China
  3. 3.Griffith School of EngineeringGriffith University Gold Coast CampusSouthportAustralia
  4. 4.Department of Civil EngineeringBeijing University of TechnologyBeijingPeople’s Republic of China

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