土木建築工程施工，以支撐系統安全為首要；如發生倒塌失敗，常造成人員財物之重大損失。本文探討三維系統支撐架在不同邊界條件下之桿件受力行為，以支撐架施工可能遇到之組搭邊界條件為例，以三維有限元素數值計算分析方法，分析桿件在不同邊界條下之受力行為，並就不同邊界條件下之桿件受力情形，加以比較闡釋，探討邊界條件對支撐架桿件受力之影響程度等，以掌握系統支撐架結構力學行為，使有利於系統支撐架極限承載力分析計算之應用參考。
研究內容為建立系統支撐架三維有限元素分析之結構總體勁度矩陣模型，以數值計算方法，利用MATLAB程式語言工具建立執行程式，進行線性分析，並以單座三層單排單跨系統支撐架為例，探討在不同邊界條件下之桿件受力行為，為進一步以程式語言數值計算方法，進行三維構架非線性分析之研究建立基礎。
本研究以150cmx150cm之三層單排單跨系統支撐架為例，以三維有限元素幾何線性理論分析方法，建立系統支撐架三維有限元素數值分析模型，將支撐架按不同類型桿件分類及離散化後，以有限元素法建立剛接模式及半剛接模式之系統支撐架三維總體勁度矩陣，再利用力與位移關係及邊界條件，進行數值分析，並就結果探討在不同邊界條件下，桿件之受力變化情形。

During the construction of buildings and bridges, the safety of template supporting system is the most important key. A failure of scaffold structures has sometimes happened, which causes series problems of properties and human live. Thus, the main purpose of this thesis is to evaluate the ultimate bearing capacity of steel scaffold structures using three different level steel experiments and mathematical simulations, discuss the steel behavior with external forces loaded in different boundary conditions. Using MATLAB language to develop three-dimensional nonlinear finite-element analysis models.
Three common ledger lengths frequently used in the domestic construction sites were utilized to build the “three-story one-row one-bay” scaffold system specimens, including the row length and bay length of 1.5mx1.5m, for the loading tests to understand the bay length and row length influences to load capacity by using three-dimensional nonlinear finite-element analysis models, uses discretize, a whole ring scaffold system of the rigid-connection beam and the semi-rigid connection beam methods therefore can be developed. Then uses the relation between load and displacement as well as the boundary conditions to calculate the loading force of the ring scaffold system.

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