一般鋼筋混凝土設計手冊均忽略拉力側混凝土所提供之張力強度,易導致荷重-彎矩關係的錯估,低估了鋼筋混凝土結構物能承受之最大彎矩。本研究將SOFO光纖簡支梁作為分析對象,利用結構及鋼筋混凝土力學理論,發展一套力學理論數值分析模式,運用MATLAB數學軟體編寫程式,建立力學理論數值分析模式,並藉由設定之鋼筋與混凝土的組合律,模擬鋼筋混凝土簡支梁施加雙點載重,評估梁試體中鋼筋與混凝土的應變與應力,藉由比對簡支梁載重-理論彎矩與MATLAB數值分析結果的載重-彎矩,結果顯示,MATLAB數值分析結果與理論解相同,驗證本研究發展之力學理論數值分析模式的正確性。再者,針對純彎矩斷面,將MATLAB數值分析的載重-變形模擬結果與簡支梁試體中綁扎於鋼筋之光纖感應器應變量測結果相互比對,結果顯示,MATLAB數值分析結果與光纖感測器量測值之鋼筋壓應變相當吻合,但是,鋼筋張應變卻有所偏差,且載重越大,偏差之差距越大。 因本研究發展之力學理論數值分析模式與光纖感測器量測結果比對有所偏差,因此,後續使用FLAC 3D三維有限差分軟體,建立鋼筋與混凝土網格,輸入鋼筋與混凝土的組合律,模擬鋼筋混凝土簡支梁承受雙點加載。最後,將FLAC 3D使用之參數,輸入MATLAB數值分析模式中,比對FLAC 3D、MATLAB數值分析與光纖量測值在彈性階段的結果,結果顯示,FLAC 3D、MATLAB數值分析與光纖量測值在彈性階段相當吻合,驗證本研究發展之力學理論數值分析模式在彈性階段的準確性與適用性。
Reinforced concrete design manual generally ignores the contribution from concrete tensile strength, this will underestimate the capacity of maximum bending moment of reinforced concrete structure. This study will develop a mechanical theory numerical analysis model, using the MATLAB mathematical software implemented with the constitutive relations of concrete and reinforcement bar to analyze the tensile and compressive strains of reinforcement bar of a simple supported beam under two-point load. The calculated strains are compared with the experimental results measured form SOFO fiber sensors attached to the reinforcement bars in a reinforced concrete beam. The calculated moments along the beam are identical to the theoretical solution, this indicate this numerical analysis model is functioning well. Furthermore, for the pure bending section, the calculated compressive strains are in good agreement with the measured strains. However the calculated tensile strains are somewhat offset from the measured values. In addition, FLAC3D, a finite difference software, is used to analyzed the same instrumented beam, in which Mohr Coulomb is used to model concrete and linear elasticity is used to model reinforcement bar. When applied load is smaller than 1150kg, the calculated strains from FLAC3D are in good agreement with the results from mechanical theory numerical analysis model as well as experimental results.