The study aims to analyze the geometric characteristics of the pointed arches proposed by Al-Kāshī in his book "Miftāḥ al-Ḥisāb" (Key of Arithmetic) and investigate their planning principles, architectural application, and typological characteristics. Al-Kāshī completed this significant work in 1427 and dedicated it to Ulugh Beg, a Timurid Sultan in Samarkand. In the ninth chapter, titled "Al-‘Imārāt wa al-Abnīya" (Amīr’s Mansion and Building), Al-Kāshī sought to measure the surface areas and volumes of barrel vaults (Azaj) and domes (Qubba). To achieve this, he proposed five kinds of pointed arches (Ṭāq) and analyzed their drawing methods and composition principles. The Īwān and Qubba structures, which are curved architectural elements, hold significant importance in Islamic architecture. However, previous research has predominantly focused on comparing the drawings in Al-Kāshī's book with historical buildings, neglecting the inherent characteristics of the drawings themselves. This study intends to contribute to a deeper understanding of Al-Kāshī's remarkable work and shed light on the geometric aspects of monumental structures in the Timurid Period.

The seismic behaviors of the arch structure vary according to the rise-span ratio of the arch structure. In this study, the rise-span ratio (H/L) of the example arch structure was set to 1/4, 1/6, and 1/8. And the installation angle of the seismic isolator was set to 15°, 30°, 45°, 60° and 90°. The installation angles of the seismic isolator were set by analyzing the horizontal and vertical reaction forces according to the rise-span ratio of the arch structure. Due to the geometrical and dynamic characteristics of the arch structure, the lower the rise-span ratio, the greater the horizontal reaction force of the static load, but the smaller the horizontal reaction force of the dynamic load. And if the seismic isolator is installed in the direction of the resultant force of the reaction forces caused by the seismic load, the horizontal seismic response becomes small. Also, as the installation angle of the seismic isolator increases, the hysteresis behavior of the seismic isolator shows a plastic behavior, and residual deformation appears even after the seismic load is removed. In the design of seismic isolators for seismic response control of large space structures such as arch structures, horizontal and vertical reaction forces should be considered.

When an unexpected excessive seismic load is applied to the base isolation of arch structure, the seismic displacement of the base isolation may be very large beyond the limit displacement of base isolation. These excessive displacement of the base isolation causes a large displacement in the upper structure and large displacement of upper structure causes structural damage. Therefore, in order to limit the seismic displacement response of the base isolation, it is necessary to install an additional device such as an anti-uplift device to the base isolation. In this study, the installation direction of the base isolation and the control performance of the base isolation installed anti-uplift device were investigated. The installation direction of the base isolation of the arch structure is determined by considering the horizontal and vertical reaction forces of the arch structure. In addition, the separation distance of the anti-uplift device is determined in consideration of the design displacement of the base isolation and the displacement of the arch structure.

If an excessive displacement occurs in the base isolation system, the structure will be damaged due to overturning of the upper structure. In this study, we analyze the behavior of base isolation by applying earthquake to base isolation with anti-uplift device. In the case of structures that generate horizontal reaction forces such as arch structures, horizontal reaction forces must be considered in the design of the base isolation and structural members. And anti-uplift device for preventing the excessive displacement of the base isolation system is needed.

This research investigates the effects of trench installation methods with expanded polystyrene (EPS) geofoam on the behavior of buried corrugated steel arch structure. A universal finite element analysis program, ABAQUS, was used to model and analyze the structure. For this study, the S275 corrugated steel with a profile of 152x51mm and the arch has fixed boundary condition. The structure was analyzed for three different configurations, namely; without EPS geofoam, imperfect trench installation (ITI), and embedded trench installation (ETI). ITI and ETI cases were further divided depending on the width and height of EPS geofoam. The width of EPS geofoam varies from the span of the arch up to a 30% increase of the span of the arch while its height varies from the rise of the arch upto 100% increase of the rise of the arch. The results from the finite element analysis revealed that the ETI reduced the wall stresses by at least 53.95%. It is recommended to conduct further study regarding ETI to validate the results and to further improved the design criteria of buried corrugated steel arch as it is expected to bring about cost reduction and stability for buried structures.

In order to solve the limitation of the long span arch structures, a numerical analysis was carried out to investigate the effects of embedded trench installation technique to the earth pressure of an underground arch-rib shaped structure. For the arch-rib shape, the parabolic curve and the circular shape were analyzed according to the span-rise ratio varying from 0.1 to 0.5. The finite element analysis program, ABAQUS (2016), was used to consider the soil - structure interaction. The results from the analysis was verified through comparison with the existing Geofoam application technique.

In order to reduce the seismic response of the spatial structure, a seismic isolation system with sufficient flexibility is used. The natural period of structure with seismic isolation system got be long to avoid prominent period. In this study, The seismic response of the truss-arch structure, which is modeled in three types according to the rise-span ratio is analyzed on El-centro, Northridge and Artificial Earthquake and compared with the seismic response of the truss-arch structure with lead rubber bearing(LRB). When seismic load is applied to the truss arch with isolation system, the horizontal acceleration response of the truss arch is reduced and vertical seismic response is also reduced. The application of the seismic isolation system is effective in controlling the seismic response.

Large spatial structures can not easily predict the dynamic behavior due to the lack of construction and design practices. The spatial structures are generally analyzed through the numerical simulation and experimental test in order to investigate the seismic response of large spatial structures. In the case of analysis for seismic response of large spatial structure, the many studies by the numerical analysis was carried out, researches by the shaking table test are very rare. In this study, a shaking table test of a small-scale arch structure was conducted and the dynamic characteristics of arch structure are analyzed. And the dynamic characteristics of arch structures are investigated according to the various column cross-section and length. It is found that the natural vibration periods of the small-scaled arch structure that have large column stiffness are very similar to the natural vibration period of the non-column arch structure. And in case of arch structure with large column stiffness, primary natural frequency period by numerical analysis is very similar to the primary natural frequency period of by shaking table test. These are because the dynamic characteristics of the roof structure are affected by the column stiffness of the spatial structure.

Long span arch structure is composed of arch as relatively flexible structure and column as relatively rigid structure. In this study, the characteristic of dynamic response is analyzed according to the natural frequency ratio between arch and columns. The result of analysis for arch as relatively vertical vibration mode is dominant, the influence of columns mainly appears at relatively high frequency band according to increase of 1st mode frequency in column. However, the dynamic characteristic of arch structure is expected to vary with not only frequency ratio but interaction between vibration modes of arch and columns.

Spatial structures have the different dynamic characteristics from general rahmen structures. Therefore, it is necessary to accurately analyze dynamic characteristics and seismic response of spatial structure for seismic design of spatial structure. An arch structure is used as an example structure because it has primary characteristics of spatial structures. Multiple support excitation may be subjected to supports of a spatial structure because ground condition of spatial structures is different. In this study, the response analysis of the arch structure under multiple support excitation and simple support excitation is studied. By means of the pseudo excitation method, the seismic response is analyzed for long span spatial structure. It shows that the structural response is divided into two parts, ground displacement and structural dynamic response due to ground motion excitation. It is known that the seismic response of spatial structure under multiple support excitation and simple support excitation are the different in some case. Therefore, it has to be necessary to analyze the seismic response of spatial structure under multiple support excitation because the spatial structure supports may be different.

공간구조물은 높이-경간비 또는 개각과 같은 아치의 형상비에 따라 상이한 동적거동특성을 나타내며, 이러한 공간구조물은 지진의 영향을 직접적으로 받는 하부구조의 강성 및 그 접합부에 따라 상이한 지진응답특성을 나타낸다. 따라서 본 연구에서는 수직진동모드와 수평진동모드의 영향이 다른 단층아치구조에 하부기둥의 강성과 접합부에 따른 지진응답특성을 분석하고자 한다. 하부기둥의 영향으로 단층아치구조는 수직방향 응답이 더 많은 영향을 받으며, 기둥의 접합부 회전강성에 있어서는 활절을 제외하고는 큰 영향이 없는 것으로 나타난다.

공간구조물은 일반 라멘구조와는 다른 동적특성을 가지고 있으며 이런 동적특성에 관해 많은 연구가 수행되고 있다. 그러나 대부분의 연구는 특정 형태의 공간구조물에 대해 수행되었으며 내진설계를 위해 직접적으로 이용 가능한 연구결과는 매우 제한적이다. 본 연구에서는 공간구조물의 기본적인 동적특성을 내재한 트러스-아치구조물을 대상으로 양단의 기둥의 길이가 다른 경우에 트러스 아치구조물의 지진응답변화를 분석하고자 한다. 양단 기둥 길이의 차이에 따라 가속도 응답이 수평방향에 비해 수직방향에서 더 많은 영향을 받는다. 따라서 상부구조물을 지지하는 하부구조물의 강성이 다른 경우에 공간구조물의 내전설계에 있어서 수직방향 응답에 대한 고려가 더욱 많이 요구된다.

기존에 공간구조물의 동적거동에 관한 대부분의 연구는 수치해석적 방법을 이용하여 지붕구조의 동적거동 파악을 위주로 하고있다. 그러나 실제 공간구조물의 지붕구조는 기둥 또는 벽체와 같은 하부구조에 의해 지지되므로 지진발생시 상부구조의 동적거동은 하부구조에 따라서 많은 영향을 받는다. 본 연구에서 아치구조물에 대한 하부 기둥구조의 재질을 황동과 폴리카보네이트로 하고 각각의 단면 및 길이 변화와 상부 지붕구조의 추가질량에 따른 고유주기 변화특성을 파악하고자 한다. 기둥의 강성 및 추가질량의 변화에 대하여 고유주기의 변화율이 상대적으로 크게 나타났다. 즉 하부 기둥구조의 강성이 상부 지붕구조의 강성과 비교하여 매우 큰 경우에 기둥구조의 강성변화나 지붕구조의 질량변화에 따른 공간구조물의 고유진동수 변화가 거의 없다.

지진에 의한 구조물의 응답을 저감시키기 위하여 내진, 면진, 제진 등 다양한 장치가 사용되고 있으며 그 중에서 면진장치는 구조물로 전달되는 지진에너지를 최소화하기 위한 시스템으로 그 주된 목적은 구조물의 주기를 길게 만들어 지진파의 탁월주기를 벗어나게 하는 것이다. 본 연구에서는 대공간구조물의 기본적인 동적특성을 가지고 있으며 동시에 가장 간단한 구조이기도 한 아치에 납-고무면진장치와 마찰진자면진장치를 적용하여 지진거동을 분석하였다. 대공간구조물의 지진거동은 일반적인 골조구조물의 지진거동과 달리 수평지진에 의하여 수직방향으로 큰 지진응답이 나타나고 있다. 면진장치를 대공간 구조물에 적용할 경우에 수평지진하중에 의하여 수평방향 지진응답이 저감되는 것은 물론 면진장치의 수직강성으로 인하여 수직응답도 현저하게 저감되는 것을 알 수 있었다.

본 연구에서는 국내에서 국가 건설기반 시설물로 이용되는 지하차도를 소형의 프리캐스트 박스구조물을 개량하여 대단면을 가지면서 개착식 터널과 같은 공법에 적용하기 위해 아치형 단면을 이용하여 암거 및 지하차도를 개발함에 그 목적을 두고있다. 본 연구를 위해 3힌지 프리캐스트 아치 구조시험체를 제작하였으며, 콘크리트의 내구성 증진을 위해 고로슬래그 미분말을 50%적용하여 실험을 실시하였다. 실험결과 아치부 압축력으로 균열발생하중이 높은 것으로 나타났으며, 하중-처짐 결과 높은 하중에 따른 복원력이 우수하였으며, 우수한 연성거동을 확보하였다. 하중 800kN에서 다수의 균열이 발생 되었으며, 사용하중 DB-24의 바퀴하중에 해당되는 약 226.4kN에서 균열폭이 0.32mm발생되었다. 본 연구에서는 프리캐스트 콘크리트 3힌지 아치형 구조물을 제작하여 이에 대한 휨 실험을 통하여 아치단면의 우수성을 고찰하고자하였으며, 실험결과 높은 토피고에 대해 적용할 수 있는 아치형 구조물의 상부 아치단면이 가지는 특성으로 그 영향이 높은 것으로 생각되며, 아치형상의 프리캐스트로 제작하여 설치하면 상재 토압에 대한 내력이 우수하여 기존 사각형상의 현장 타설 공법에 비해 경제적인 단면 설계가 가능, 또한 운송/조립/설치가 빠름으로써 공사기간을 대폭 단축할 수 있는 장점을 가지고 있다.