Axial Forces of a Half-spherical Space Truss Structure with Opening

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 11 | Nov 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 660
Axial Forces of a Half-spherical Space Truss Structure with Opening
Lilya Susanti1*, Muammar Kadhafi2, Gunawan Prayitno3, Adyatma Andhika Atmaja1
1Civil Engineering Department, Universitas Brawijaya, MT Haryono 167 Malang-65145 East Java Indonesia
2Faculty of Fisheries and Marine Science, Universitas Brawijaya, Veteran Malang-65145 East Java Indonesia
3Urban and Regional Planning Department, Universitas Brawijaya, MT Haryono 167 Malang-65145 East Java
Indonesia
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract – A half-spherical space truss has a beautiful
architectural view that can be applied as a roof on an
aesthetic building such as a floating resort, bungalow, etc. For
some cases, placing an opening such as a door or window can
change the space truss structural configuration. A regular
space truss structure has a good stability but changing the
structural layout resulting some structural problems. This
paper investigated the effect of placing an opening on the
maximum axial forces of a half-sphericalspacetrussstructure.
The result indicated that the gap can increase the axial forces
by more than ten times the regular system. Hence, some
structural treatments should be conducted to maintain the
truss capacity.
Key Words: Axial force, Design, Opening, Space-truss
1. INTRODUCTION
Some architects prefer a half-spherical space truss because
of its beautiful view, aerodynamic and easy to assemble the
structural system. Truss is famous for its lightweight,
effective cost, and easy preparation. Itcanbeappliedtolarge
area with a few interior supports.Somereferencesdiscussed
how to design and analyze the space truss structures. A
report by H. Klimke and J. Sanchezintroducedthedesign and
analysis of the space structure, including the 3D modeling,
continuum analogy, structural reliability, and the load
carrying behavior [1]. At the same time, other paper
discussed about the design of truss structuresthrough reuse
[2].
The truss structure is easy to be modified. Various types of
truss models have been made. Recent advanced types of the
truss structures have developed significantly with a lot of
research have discussed their properties and behavior such
as the compressive behavior of tetrahedral lattice truss
structures [3], mechanical properties of a hierarchical octet-
truss structure [4], the nail ductility on the load capacity of a
glulam truss structure [5] and also the stability and load
capacity of an elasto-plastic pyramidal truss [6]. Structural
failure behavior was also discussed by the previous studies
as the progressive collapse of space truss structures during
earthquake [7], dynamic analysis for progressive failure of
truss structures considering inelastic post-buckling cyclic
behavior [8], evaluation method for predicting dynamic
collapse of double layer latticedspacetrussstructuresdue to
the earthquake motion [9] and also failure and energy
absorption characteristics of advanced 3D truss core
structures [10].
As a development of recent truss model variation, the
present study used a half-spherical space truss. This truss
model, next, will be applied as a wall-roof structure on the
floating resort bungalow. An ordinary roof structure does
not need an opening. As a wall application, there always be
an opening, such as a door or window. This opening
placement resulted in changes of the truss structural
configuration. Irregularity in the structural system can
significantly affect the structural capacity, mainly the axial
forces. Hence this paper discussed the axial forces of a half-
spherical space truss structure with anopeningcomparedto
the regular truss.
2. METHODOLOGY
A half-spherical space truss model was chosen. The present
analysis used a STAAD.Pro finite element software [11] to
arrange the model and find the axial forces of the truss
members. Two models were investigated, a regular half-
spherical space truss and a half-spherical spacetrusswithan
opening. The regular space truss model is shown in Fig-1,
while the structure with an opening is shown in Fig-2. Four
main transverse frames were used with an angle between
each frame at 45 degrees. In order to find suitable structural
integrity and stability, a basic triangular shape was used.
This configuration enables the structure to ignore the
bending moment contribution, as the truss structure can
only resist the axial forces. A total of 33 nodes and 88 truss
beam members were made.

Fig -1: A regular half-spherical truss model
Fig -2: A half-spherical truss model with opening
The truss structure was arranged using a pipe 4/3 SCH40
(USA) steel profile. The material and structural properties of
a presently used profile is written in Table-1. Each bottom
node of the truss structurewassupportedbypinnedsupport
as the truss structure can only carry shear and axial forces.
Table -1: Material and structural properties of pipe 4/3
SCH40
Description Symbol Magnitude Unit
Elastic Modulus E 205000 MPa
Specific gravity γ 7833 Kg/m3
Poisson’s ratio φ 0.3 -
Yield stress fy 253 MPa
Ultimate stress fu 407 MPa
Outside diameter OD 1.05 inc
Inside diameter ID 0.94 inc
Area A 110.918 mm2
Moment of inertia I 16649.26 mm4
Radius of gyration r 12.251 mm
Three load types, dead load (DL), live load (LL), and wind
load (WL), were applied to the structure with the directions
shown in Fig-3. The dead load was applied using automatic
STAAD.Pro menu. The live loadwasdeterminedaccordingto
Indonesian Standard – minimum load for designingbuilding
and other structures SNI 1727-2020 [12] as 100 kg applied
on each node. Finally, wind load was calculated using the
basic load as 25 kg/m2 (for the non-coastal area), then
converted to 21 kg on the half-structure nodes in a
horizontal direction.
(a) Live load (LL)
(b) Wind load (WL)
Fig -3: Live and wind loads of truss model

Load combinations were also made according to SNI 1727-
2020 as follows:
 1.2 DL + 1.6 LL
 1.2 DL + 1.0 LL + 1.0 WL
 1.2 DL + 1.0 LL + 1.0 WL
The axial forces output was taken from the maximum value
of those three load combinations, whichconsistofmaximum
tension and axial compression forces. The result was then
compared between the regular structure and the truss
structure with opening so that the opening influence on the
maximum structural forces could be understandable.
3. RESULT AND DISCUSSION
The result of axial forces from the present regular half-
spherical truss system is written in Fig-4. Here, the
maximum tension axial force of 523.702 kg was found in
beam number 9 while the maximum compression force
found in beam number 17 was -105.234 kg.
(a) Beam number
(b) Maximum tension and compression axial forces
Fig -4: Beam axial forces for regular truss
If the used beam steel profile as pipe 4/3 SCH40 (USA) was
checked to control the structural capacity, it needs to divide
the examination for two types of axial forces which are
tension and compression. For tension structural safety
examination, the maximum tension axial force from
STAAD.Pro software is compared to themaximumallowable
structural tension capacity using the yield stress data
multiplied by the steel cross-section area. From the data
shown in Table-1, the maximum allowable force is
calculated as 2806.2 kg, which is larger than the maximum
tension force as 523.702 kg, which means that the steel
profile has fulfilled the safety requirement. For the
compression force examination, it is necessary to check the
beam slenderness because the structural compression
capacity is significantly influenced by the slenderness ratio.
The slenderness ratio can be calculatedbydividingthebeam
length and the radius of gyration. From the slenderness
calculation as 211.5, the beam is categorized as a slender
beam because the beam’s slenderness is more significant
than 200. The slender beams collapse due to buckling. The
buckling load (Pcr) can be determined using the Euler
equation as follows, where E is the elastic modulus, I is the
moment of inertia, and L is the beam length. From the
calculation, the beam buckling load of 501.4 kg islargerthan
the maximum compression axial forces of 105.234 kg which
means that the truss also fulfils the safety requirement.

A half-spherical truss system with an opening that was
analyzed using similar steps to the regular one. The result of
analysis using STAAD.Pro software for the truss with an
opening is shown in Fig-5. From this figure, it was found that
the maximum tension of 6642.362 kg occurred in beam 71,
while the maximum compression axial force of -7857.023 kg
occurred in beam 77.
(a) Beam number
(b) Maximum tension and compression axial forces
Fig -5: Beam axial forces for truss with opening
As it has been calculated for the allowablestructuralcapacity
of pipe 4/3 SCH40 steel profile as 2806.2 kg and 501.4 kg for
tension and compression forces, respectively, the actual
tension and compression forces as 6642.362 kg and -
7857.023 kg is much larger, which means that this does not
fulfill the safety requirement. For that, it needs to check
which beams from the truss system that result in the axial
forcesmoresignificantthantheallowablestructuralcapacity.
From the examination, then somebeamswithoverlimitaxial
forces need to be replaced using the more extensive steel
profile until the analysis meets the safety requirement. From
the investigation, then some beams that have over-axial
forcesare shown in Fig-6. The beams with theredcolorwere
then replaced using the larger dimension of the steel profile
as pipe 2-1/2 SCH 40. The material and structural properties
of this profile are written in Table-2. The structural dead
load (DL) is automatically adjusted by STAAD.Pro software
when steel profile is replaced.
Fig -6: The structural parts that need steel profile
replacement
Table -2: Material and structural properties pipe 2-1/2
SCH 40
Elastic Modulus E 205000 MPa
Specific gravity γ 7833 Kg/m3
Poisson’s ratio φ 0.3 -
Yield stress fy 253 MPa
Ultimate stress fu 407 MPa
Outside diameter OD 2.88 inc
Inside diameter ID 2.69 inc
Area A 536.2485 mm2
Moment of inertia I 603535.5671 mm4
Radius of gyration r 33.548 mm
Indeed, replacingsomeofthetrussstructuralpartsisdifficult
to be applied in real fields. But it is very economical because
there will be only a slight difference in the maximum axial

forces compared to whole steel profile replacement. Using
steel profile pipe 2-1/2 SCH 40, the maximum allowable
structural capacitiesas 13567,09 kg(tension)and-18178,11
kg (compression) resulted. If it then is compared to the
maximum actual axial forces as 6642.362 kg (tension) and -
7857.023 kg (compression),bothofthemhavemetthesafety
requirement. The structural components need to be
examined for safety and convenience. For the convenience
requirement,structuraldisplacementisneededtobechecked
against the allowable displacementaccordingtothestandard
requirement.
4. CONCLUSION
The present study discussed the comparison between a
regular half-spherical truss structure andthetrussstructure
with opening to investigate the influence of placing an
opening on the space truss system to the structural actual
axial forces. Two models were analyzed using STAAD. Pro
software. From the results that are mentioned in the
previous chapter, it can be concluded that placing the
opening resulted in a significant increase in the maximum
axial forces. For this case, the increase reached more than
ten times compared to a regular truss structure. Therefore,
the opening placement disturbs the structural integrity,
stability and regularity. To improve the structural capacity,
some beam members with large forces should be replaced
using the larger profile dimension. If the safety requirement
has been fulfilled, then the structuresneedto be evaluated in
the convenience requirement.
REFERENCES
[1] H. Klimke and J. Sanchez, “Design, Analysis and
Construction of Space Structures,” The Mero Legacy,
2020.
[2] J. Brutting, J. Desruelle, G Senatore and C. Fivet,”Design
of Truss Structures Through Reuse,”Structures18,April
2019, pp. 128-137, doi: 10.1016/j.istruc.2018.11.006.
[3] G. W. Kooistra, V. S. Deshpande and H. N. G.
Wadley,”Compressive Behavior of Age Hardenable
Tetrahedral Lattice Truss Structures Made From
Aluminium,” Acta Materialia 52(14), August 2004, pp.
4229-4237. doi: 10.1016/j.actamat.2004.05.039.
[4] L. Weitao, D. Li and L. Dong, “Study on Mechanical
Properties of a Hierarchical Octet-truss Structure,”
Composite Structures 249, October 2020, doi:
10.1016/j.compstruct.2020.112640.
[5] L. Stehn and K. Borjes,”The Influence of Nail Ductilityon
The Load Capacity of A Glulam Truss Structure,”
Engineering Structures 26(6), May 2004, pp. 809-816,
doi: 10.1016/j.engstruct.2004.01.012.
[6] M. V. B.Santana, P. B. Goncalves and R. A. M. Silveira,
“Stability and Load Capacity of an Elasto-plastic
Pyramidal Truss,” International Journal of Solids and
Structures 171, October 2019, pp. 158-173, doi:
10.1016/j.ijsolstr.2019.04.011.
[7] H. D. Zeng and J. Fan,”Analysis of The Progressive
Collapse of Space Truss Structures During Earthquakes
Based on a Physical Theory Hysteretic Model,” Thin-
Walled Structures 123, 2018, pp. 70-81.
[8] R. B. Malla, P. Agarwal and R. Ahmad,”Dynamic Analysis
Methodology for Progressive FailureofTrussStructures
Considering Inelastic Postbuckling Cyclic Member
Behavior,” Engineering Structures 33(5), May 2011, pp.
1503-1513, doi: 10.1016/j.engstruct.2011.01.022.
[9] K. Ishikawa, S. Okubo andS. Kato,”EvaluationMethodfor
Predicting Dynamic Collapse of Double Layer Latticed
Space Truss Structures due to Earthquake Motion,”
International Journal of Space Structures 15(3),
December 2020, doi: 10.1260/0266351001495099.
[10] I. Ullah, M. Brandt and S. Feih,”Failure and Energy
Absorption Characteristics of Advanced 3D Truss Core
Structures,” Materials & Design 92, February 2016, pp.
937-948, doi: 10.1016/j.matdes.2015.12.058.
[11] Bentley, STAAD.Pro V8i Technical Reference Manual.
[12] Ministry for public works and housing, SNI 1727-2020
Minimum Load for Designing Building and Other
Structures, 2020.
BIOGRAPHIES
Dr. Eng. Lilya Susanti is a teacher
and researcheratCivil Engineering
Department. She focused on
research about the structural
mechanics of steel and concrete,
structural modeling, and dynamic
analysis.
1’st
Author
Photo

Axial Forces of a Half-spherical Space Truss Structure with Opening

More Related Content

Similar to Axial Forces of a Half-spherical Space Truss Structure with Opening (20)

More from IRJET Journal (20)

Recently uploaded (20)

Axial Forces of a Half-spherical Space Truss Structure with Opening