中空鋼筋混凝土梁與實心預力混凝土梁之扭力分析

Torsional Analyses of Hollow RC Members and Solid PC Members

陳哲昇(Je-Sheng Chen)

指導教授 ： 鄭全桓

共同指導教授 ： 邱浩然

國立暨南國際大學/科技學院/土木工程學系/碩士(2010年)

摘要

本論文依據適用於實心斷面鋼筋混凝土梁受純扭力(pure torsion)之分析模式SMMT-RC-S (Softened Membrane Model for Torsion for Solid Reinforced Concrete Members)，由此分析模式修正得到適用於中空斷面鋼筋混凝土梁與實心斷面預力混凝土梁的新分析模式SMMT-RC-H (SMMT for Hollow Reinforced Concrete Members)及SMMT-PC (SMMT for Prestressed Concrete Members)，將這兩個新分析模式應用於由文獻蒐集之實驗試體，比較分析結果並律定修正，使新分析模式能獲致更準確的分析結果。
本研究共蒐集53組中空斷面鋼筋混凝土梁試體及65組實心斷面預力混凝土梁試體並進行檢核。對中空斷面鋼筋混凝土梁試體進行壁厚過大之檢核，最終採用通過檢核試體共21組；對實心斷面預力混凝土梁試體進行鋼筋量不足、箍筋間距過大以及混凝土保護層厚度不足或過厚篩檢，最終採用通過檢核試體共42組。
將SMMT-RC-H模式應用於中空斷面鋼筋混凝土梁試體的扭力分析，針對混凝土張力彈性模數放大係數(λ)與混凝土開裂應變放大係數(μ)進行參數研究，發現使用λ=μ=1.2可得到與實驗數據最吻合之混凝土開裂扭矩。
將SMMT-PC模式應用於實心斷面預力混凝土梁試體的扭力分析，將分析結果與實驗值比較後，發現分析之極限扭矩受預力施加量影響而偏大，且預力施加量越大造成之偏差越大。由預力施加量與極限扭矩之實驗值對分析值比值的關係，得到修正係數G及G’(G=1-0.88 ∙σ/f’c；G’=1-0.93∙σ’/f’c；∙σ/f’c及σ’/f’c代表預力施加量)。修正後得到很接近實驗值之分析結果。

關鍵字

扭力 ； 扭矩-扭轉角曲線 ； 開裂扭矩 ； 中空斷面 ； 鋼筋混凝土 ； 預力混凝土

並列摘要

A new rational theoretical model called the Softened Membrane Model for Torsion (SMMT) was developed to predict the entire torque-twist response of solid reinforced concrete (RC) members, and is referred to as SMMT-RC-S in this thesis. The SMMT-RC-S has recently been modified and extended to analyze the torsion of hollow RC members and solid prestressed concrete (PC) members. In this thesis, these modified models are referred to as SMMT-RC-H (SMMT for hollow RC) and SMMT-PC (SMMT for PC), respectively. This study applies the SMMT-RC-H and SMMT-PC to analyze tested hollow RC and solid PC beam specimens, quantifies the model parameters, and validates the SMMT-RC-H and SMMT-PC.
This study collects a total of 53 hollow RC specimens and 65 solid PC specimens in the literature. Some of the collected hollow RC specimens with excessive wall thickness are excluded and the other 21 specimens are adopted for comparison. Some solid PC specimens are excluded based on three criteria: insufficient reinforcement, excessive stirrup spacing, and insufficient or excessive thickness of concrete cover; the rest of the other 42 solid PC specimens are adopted for comparison.
The amplification factorsλ and μ for the pre-cracking modulus and the cracking strain, respectively, of the tensile stress-strain relation of concrete are quantified by systematically comparing the SMMT-RC-H analytical results of the 21 hollow RC specimens with test data. It is found that the values of λ=μ=1.2 give predicted cracking torques that best correlate with the test values.
Comparison of the SMMT-PC analytical results of the 42 solid PC specimens with tests indicates that the prestressing generally causes the predicted ultimate torque to be larger than test value; and further, the greater the level of prstressing is, the greater the difference between predicted ultimate torque and test value may become. Hence, two reduction factors G and G^' (G=1-0.88∙σ⁄(f_c^' )；G^'=1-0.93∙σ^'⁄(f_c^' )；σ⁄(f_c^' ) and σ^'⁄(f_c^' ) both represent level of prestressing) are derived by regression of the comparison between predicted ultimate torques and test values. The predicted ultimate torques multiplied by G or G^' agree with the test values very well.

並列關鍵字

Torsion ； torque-twist curve ； cracking torque ； hollow ； reinforced concrete ； prestressed concrete.

參考文獻

1. ACI Committee 318, Building Code Requirements for Structural Concrete（ACI 318-05）and Commentary（ACI 318R-05）, American Concrete Institute, pp. 147-191.

2. Belarbi, A. and Hsu, T. T. C.,1994, Constitutive Laws of Concrete in Torsion and Reinforcing Bars Stiffened by Concrete, ACI Structural Journal, Vol. 92, No. 5, Sept.-Oct., pp.562-573.

3. Baumann, T.,1972, Zur Frage der Netzbewehrung von Flachentragwerken, Der .Bauingenieur, vol. 47, No. 6, pp. 367-337.(in German).

4. Bredt, R.,1986 July 18, Kritische BemerKungen zür Drehungselastizitat, Zeitschrift des Vereines Deutscher Ingenieure, Band 40, No. 28, July 11, pp.785-790; No. 29,, pp.813-817 (in German).

5. Collins, M. P.,1973, Torque-twist Characteristics of Reinforced Concrete Beams,Inelasticity and Non-Linearity in Structural Concrete, Study No. 8, University of Waterloo Press, Waterloo, Ontario, Canada, pp. 221-232.