الفهرس 
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Abstract
This thesis investigated the effects of tension flange restraints on the LTB moment capacity of web-tapered steel I-beams. Beams used in the study are welded built-up sections. The cross-section dimensions of smaller end are equal to standard rolled shapes (IPE-HEA-HEB), and the cross-section dimensions of larger end are equal to standard rolled shapes (IPE-HEA-HEB) except that the web height is equal to the web height of smaller end multiplied by tapering ratio. Also, Prismatic beams were studied.
ABAQUS v14 software was utilized to build up a 3D FE models that represent the behavior of studied beams. A non-linear finite element analysis is performed where non-linearity in material, initial imperfections and initial residual stresses were considered. The FE models were verified using two different experimental research works. The FE model was verified with design equations in specifications.
A comprehensive parametric study was conducted using the FE models. Four different configurations of tension flange restraints were studied (L – 0.5L – 0.25L – 0.1L). Many parameters were studied such as tapering ratio, beam length, moment gradient and cross-section properties.
A proposed design method was utilized to consider the beneficial effect of tension flange restraint. It was proposed based on results from FE models. The proposed method is compatible with the design procedure of AISC DG25 (2nd Ed.).
8.2 Conclusion
Based on the analysis of FE models of web-tapered steel I-beams with tension flange restraint, several models were analyzed with different parameters, the behavior of such beams was analyzed to propose a simplified design method to determine the moment capacity of such beam taking into consideration the effect of tension flange restraints. from the analysis, the following conclusions could be withdrawn:
1. There is very good agreement between results of LTB moment capacity from ABAQUS v6.14 and LTBeamN software with discrepancies less than 2%.
2. Tension flange restraint has a beneficial effect on the moment capacity of both prismatic and web-tapered steel I-beams.
3. The enhancement due to tension flange restraint is significant in the case of long beams falling in the elastic LTB zone.
4. Increasing the number of tension flange restraint has a small effect on the enhanced LTB moment capacity. Adding only one tension flange restraint in the middle will result in increment around 70% to 80% overall gain in case of (0.1L) restraint.
5. The modification of the LTB moment capacity in AISC DG25 (2nd Ed.) make the results more accurate and dependable if compared to FE results.
6. AISC DG25 (2nd Ed.) accurately predicts the moment capacity of web-tapered steel I-sections for different tapering ratios and beam lengths in most cases.
7. The LTB moment capacity according to AISC DG25 (2nd Ed.) is conservative in case of high tapering ratio that perform slender web. The torsional constant value equal to zero (J = 0) for a slender web is not applicable for the tapered section when only a small portion of web is slender while the remaining web is not.
8. As tapering ratio increases, strength to weight ratio increases and the beneficial effect of tension flange restraint decreases. The increase due to adding tension flange restraint is about 6% in the case of HEA section, while it ranges from 10% up to 12% in case of (HEB and IPE) sections. The highest enhancement is in the case of prismatic beams.
9. As beam length increases, LTB moment capacity decreases and the beneficial effect of tension flange restraint increases. It reaches a maximum value of 40% in case of IPE beam with length 12.0m
10. Moment gradient has slight change on the effect of tension flange restraint. The increase due to adding tension flange restraint ranges from 2% up to 5% in the case of HEA section, while it ranges from 4% up to 7% in case of (HEB and IPE) sections. The highest increase is for case of moment gradient () = 0.5, and tapering ratio (α=2).
11. For different cross-section dimensions, as the ratio (bf*d/ tf) decreases, the effect of tension flange restraint increases.
12. Adding a full depth stiffener to a beam with tension flange restraint at the same locations has a greater effect on the LTB moment capacity of web-tapered steel I-beams than using tension flange restraint only.
13. Taking the residual stresses effect into consideration in FE modelling reduces the moment capacity of web-tapered steel I-beams by maximum value of 13%. An average value of (5%-7%) may be considered in most cases.
14. The enhancement of tension flange restraint on the moment capacity of steel beams while taking the residual stresses into consideration differs slightly compared to case of neglecting residual stresses.
15. The proposed design method offers an accurate, practical, and simple method to take the effect of tension flange restraint on the moment capacity into consideration. It is also compatible with the procedure of AISC DG25 (2nd Ed.).
16. We recommend using one tension flange restraint at middle for short beams, and two equally spaced tension flange restraints for beams long beams to consider the enhancement effect of tension flange restraint. In fact, these recommended values are valid for the practical wise in most cases.
17. The results of the nominal moment resistance from BS5950-1:2000 is not compatible with FE model results. The results from BS5950-1:2000 is highly conservative in long beams. BS5950-1:2000 is not accurate in calculating the moment capacity of web-tapered beams while taking the tension flange restraint into consideration.
8.3 Recommendations for Future Studies
1- The effect of tension flange restraint may be extended to beam-column.
2- Extend the study of adding full depth vertical stiffeners at the locations of tension flange restraints.
3- Studying the effect of tension flange restraint on partially web-tapered beam.
4- Studying the tension flange restraint stiffness on the moment capacity of web-tapered steel I-beams.
5- Studying the effect of tension flange restraint in case of using lateral and rotational restraint.