Al-Ta'a: Softened Truss Model Theory for the Analysis of Fibre Reinforced Concrete Deep 21 Softened Truss Model Theory for the Analysis of Fibre Reinforced Concrete Deep Beams and Corbels S. A. Al-Ta’an, Professor N. S. H. Al-Husaini, Assistant lecturer Department of Civil Engineering, Dept. of Building and Construction, Mosul University, IRAQ Technical Engineering College, Mosul Corresponding author, S. A. Al-Ta’an, Email: saad.altaan@yahoo.com Abstract Reinforced concrete members may be subjected to axial load, bending moment, shear and torsion. However the behaviour of these members under shear or combined shear and torsion is a complex phenomenon. In this study the softened truss model theory is applied for the analysis of fibre reinforced concrete deep beams and corbels. The theory is more promising than the strut and tie model which satisfies the equilibrium conditions and to some extent materials constitutive relationships. While this theory, considers the equilibrium, compatibility, materials constitutive relationships and the degrading effect of the diagonal tension cracks on the compressive strength of cracked reinforced concrete element when subjected to biaxial compression-tension stresses. The previously developed algorithms for the analysis were modified by incorporating the effect of short discrete steel fibres on the behaviour and strength of concrete subjected to shear. Fibre reinforced concrete deep beams and corbels were analyzed using the adopted algorithm and materials constitutive relationships. The predicted effects of the shear span / depth ratio, volume fraction of steel fibres and the longitudinal steel ratio on the shear strength of fibre reinforced concrete deep beams and corbels showed good agreement with published experimental results. Keywords: corbel, deep beam, reinforced concrete, shear, softened truss, steel fibres. تائفϜالϭ ΔϘيϤ العΔحϠسϤ الΔيϔيϠ الΔسانيήΨ الΕاΒ العتيلϠين لتحϠم الϨسϤ الΝΫϮϤ نΔيή نظ ϥعاτي الϠ عΪ.سعΩ.΃ / Ϋستا΃ يϨ الحسيϱΪ سعΓϭΪ ن/ Ϊ مساعαέΪ م صلϮϤ الΔ / جامعΔنيΪϤ الΔسΪϨϬ قسم الصلϮϤ / الΔيϨϘ التΔيϠϜ / الΕ΂إنس΃ϭ تاءΒ قسم ال ΔاصΨ ال νήتع تΪ قΔحϠسϤ الΔسانيήΨء الاπ اأعϰ إلحتاء تπ اأعϩά هϙϮϠ لي. سϡϭΰعϭ قصϯϮاء، قϨΜ انϡϭΰ، عΔيέϮ محϝاϤح΃ صϘ الϯϮ قή تأثيϭ قصϯϮ قϭ΃ .ΓΪϘ معΓήاهυ ϥϮϜ ييϠ الϡϭΰ ع Ψ استΔاسέΪ الϩά في هيلϠين لتحϠم الϨسϤ الΝΫϮϤ نΔيήمت نظΪ ϩάتائف. هϜالϭ ΔϘيϤ العΔحϠسϤ الΔيϔيϠ الΔسانيήΨ الΕاΒ العت ϩάا هϤϨ. بيΩاϮϤϠ لΔيϨيϮϜ التΕقالعا ا ماΪ حϰالϭ ϥίاϮ التρϭήق شϘي تحالتϭ ρباήالϭ ΔعامΪ الΝΫϮϤ نل منπف΃ ΔيήظϨ ال ϥίاϮ التρϭή شά تأخΔيήظϨ ال ، الافقϮ تΔيϨيϮϜ التΕقالعااϭ ρغاπان اΔمϭاϘ مϰϠ عΔيήτϘ الΪ الشϕϮϘ شήتأثيϭ ΩاϮϤϠ ل ρغاπ انΕاΩاϬ اجاϬضή تعΪϨ عΔϘϘتشϤ الΔحϠسϤ الΔسانήΨϠ ل- .έϮحϤ الΔائيϨ ثΪ ش ΔضήعϤ الΔسانήΨ الΔمϭاϘمϭ ϙϮϠ سϰϠ عΓήيμϘ الΔيΫاϮϔف الأليا اή تأثيϝخاΩيل بإϠتحϠا لϘ سابΓέϮτϤ الΕمياίέاϮΨ الΕέϮ ح ϰ إل قص.ϯϮ ق يلϠ تم تحή. تأثيΩاϮϤϠ لΔيϨيϮϜ التΕقالعااϭ ΔحήتϘϤ الΕمياίέاϮΨ الϝاϤكتائف باستعϭ ΔحϠ مسΔيϔ ليΔϘيϤ عΔسانيή خΕاΒ عت ΕήϬυ΃ تائفϜالϭ ΔϘيϤ العΕاΒعتϠص لϘ الΔمϭاϘ مϰϠلي عϮτيح الϠ التسΔΒنسϭ ΔيΫاϮϔف الألياق، حجم اϤص/ العϘء الاπ ف ΓέϮشϨϤ الΔيϠϤئج العتاϨا مع الΪا جيϘافϮ ت Received: 28 – 6 - 2013 Accepted: 7 – 01 - 2013