Introduction to
1.5-Layer Space
FramesPei-Shan Chen Dr.Eng
Professor
Department of Civil Engineeringand Architecture
Graduate School
Hachinohe Institute ofTechnology
Peishan Chen Dr.Eng., Hachinohe Tech.

Qingming Shanghe Tu

528cm in length ,24.8cm in width
Northern Song Dynasty (A.D. 960-1127)
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The Study Model
Four members arch
Horizental member
Three members arch

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Elevation Section
Horizontalmember

Four members archThree membersarch

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Model of Hongiqao

The Deformation

 ma x max  0.23mm

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Distribution of Axial Forces
7.7kN

9.6kN

10.1kN

13.8kN
12.4kN

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Distribution of Moments
1.3kN･m

0.9kN･m

1.28kN･m
1.73kN･m

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Model for Structural Analysis

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Application to Modern Structural Design

A cylindrical frame with Lap-Beams
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Cone-Shaped Lap-BeamPeishan Chen Dr.Eng., Hachinohe Tech.

Application to Modern Structural Design

Lap-Beam Dome (Zaru Dome) Peishan Chen Dr.Eng., Hachinohe Tech.

ザル・ドーム

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A Zaru Dome

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From Basket Meshing to Space Frame

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Definition of A 1.5-Layer Space Frame

A 1.5-Layer Space Frame is a
structure composed by bars pinedwith two layers of joints, and there isno member linking two or more joints
in one certain layer.

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The key parts and basic units(b) Lap- units(a) Key parts(c) Crossing- units

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Lap- units

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Lap-units in Curved Shape

added members

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Crossing- units

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On the Stability

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On the Stability
AA’
B’

B

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Kutzbach-Gruebler Equation

F=6(n-1)-

𝑘 (6 − 𝑘)fk

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Demonstrate the stability by linear analysis

Rank(Stiffness Matrix) → DOF
Linear static solution → Stable structureAnalytical model => flat/planar frames

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Demonstrate the stability by linear analysis
Plane frame, Steel, Span: 33.0m, Vertical members H=1.5m, A = 100cm2 , P= 18kN
Max. Vertical disp.: 4.70cm
Peak member forces:+255kN-558kN

Lap- units
Max. Vertical disp.: 7.45cm
Peak member forces:+332kN-473kN

Crossing- units
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Versatility for Form Design

Planar frames

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Versatility for Form Design

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Hybrid Frame System
1.5-Layer Space Frames + Double Layer Space Frames

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Free Grid

Random grids generated fromChinese window grilles

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Classification of Space Frames• Single Layer• Double Layers
multi-Layers• 1.5-Layer
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Peishan Chen Dr.Eng., Hachinohe Tech.

Conclusion• The 1.5-Layer Space Frame is a new structure system
inspirited from the Hongqiao bridge painted inQingming Shanghe Tu.
• The system has versatility for form design.
• Further researches are required to demonstrate Its
mechanical characteristics and develop the structuraldesign methods.
• The author promotes to re-classify the types of spaceframes into: 1) Double and multi-Layers, 2) 1.5-Layer,and 3) Single Layer Space Frames.
Peishan Chen Dr.Eng., Hachinohe Tech.

八户工业大学

S-Art 研究会

Thank you !!
Peishan Chen, Hachinohe Tech.