الفهرس 
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Abstract
The main aim of this study is to investigate the behavior of concrete beams reinforced in flexure and shear with CFRP bars and subjected to pure torsion. Accordingly, seven half-scale RC beams are tested experimentally under pure torsion. One beam is reinforced in flexure only with CFRP to evaluate the concrete contribution to the torsional resistance. The objective of the experimental program is to investigate the effect of concrete compressive strength, stirrup spacing and stirrup size on cracking and ultimate torsional moment. 3D models are developed using the non-linear finite element program ATENA to simulate the behavior of RC beams. To check the validity of the models, the test results presented in chapter 4 are compared to their counterparts modeled with non-linear program ATENA. The comparison showed a good agreement between experimental and numerical results. A parametric study is conducted to investigate the effect of the following parameters: concrete compressive strength, beam depth-to-width ratio, stirrup spacing, stirrup size and longitudinal reinforcement on cracking and ultimate torsional moments. Finally, proposed design models are introduced to predict both cracking and ultimate moments for RC beams subjected to pure torsion.
Conclusion
In this section, the experimental findings can be summarized and concluded. The conclusion is extended to include the numerical investigation along with the proposed model.
Experimental Investigation
Seven half-scale RC beams are constructed and tested under pure torsion. All beams had a rectangular cross-section with 150mm width and 300 mm depth and with an overall length of 3000 mm. The concrete clear cover is maintained constant at 25mm around all specimens. One beam is tested without transverse reinforcement to determine the concrete contribution to torsional capacity. The experimental program investigated the effect of concrete compressive strength, stirrup spacing, and stirrup bar size on the torsional capacity of concrete beams reinforced in flexure and shear with CFRP bars.
Based on the test results, The effect of previously mentioned parameters on the torsional strength can be concluded in the following:
The cracking torsional moment for RC beam with concrete compressive strength of 42.5 MPa is higher than that of the beam with concrete compressive strength of 30 MPa by 20%, while the ultimate torque increased by 23%.
The variation in concrete compressive strength from 30 to 42.5 MPa increases the torsional stiffness after cracking (K_cr) by 27%.
It is observed that ultimate torque increased with the decrease of stirrup spacing. The cracking torque for RC beams with stirrup spacing 170, 125, and 85 mm, respectively are almost equal while the ultimate torque for previously mentioned beams is higher than the beam without stirrups by 31%, 56%, and 77%, respectively.
The twisting rotational angle corresponding to the ultimate torque increased with the increase of stirrup spacing. The twisting angle for RC beams with stirrup spacing 170, 125, and 85 mm, respectively is 0.046, 0.058 and 0.064 Rad/m, respectively.
The decrease in stirrup spacing enhances the torsional stiffness after cracking 〖 (K〗_cr) by 39% and 58%, respectively for beams with spacing between stirrups equal 125 mm and 85 mm than that of 170 mm spacing.
The ultimate strength of tested specimens increased with the increase of stirrup bar size by 28% and 45% for sizes 9.5 mm, and 11.5 mm, respectively compared to the beam with stirrup bar size of 7.5 mm.
The increase of stirrup bar size improves the torsional stiffness after cracking〖 (K〗_cr) by 71% and 80% for sizes 9.5 mm, and 11.5 mm, respectively than that of 7.5 mm.
Numerical Investigation
A numerical investigation is conducted using non-linear finite element (FE) program ATENA. 3D models are developed to simulate the behavior of concrete beams reinforced in flexure and shear with CFRP bars and subjected to pure torsion. To check the validity of the numerical models, a comparison was held between numerical results and their counterparts experimentally tested and mentioned in chapter 4. The comparison also extended to include results of the numerical results and compared to their counterparts experimentally tested and gathered from literature. The comparison showed good agreement between experimental and numerical results. Accordingly, a parametric study is conducted to investigate the effect of the following parameters such as: concrete compressive strength, beam depth-to-width ratio, stirrup spacing, stirrup size and longitudinal reinforcement on cracking and ultimate torsional moments.
The numerical investigation of concrete beams reinforced in flexure and shear with CFRP bars and subjected to pure torsion can be concluded in the following:
Effect of Concrete Compressive Strength
The cracking and ultimate moments are obtained from numerical models for groups A, B, C, D, and E with beam depth-to-width ratios 1.0, 2.0, 2.67, 3.33, and 4.0, respectively. The cracking moment for groups (A, B, C, D, E) increased by about 37%, 28%, 34%, 27% and 35%, respectively for each group with the increase of concrete compressive strength from 25 to 50MPa. The ultimate moment for groups (A, B, C, D, E) increased by about 17%, 28%, 35%, 40% and 47%, respectively with the increase of concrete compressive strength from 25 to 50MPa.
It can be concluded that the concrete compressive strength has a significant effect on both cracking and ultimate moments where the cracking and ultimate moment increased by increasing concrete compressive strength.
Effect of beam depth-to-width Ratio
The effect of beam depth-to-width ratio is conducted on RC beams with different values of beam depth (t) varying from 150mm to 600mm. The effect of beam depth-to-width ratio is investigated in 6 groups with different concrete compressive strength varying from 25MPa to 50MPa. The cracking torsional moment increased by about 448% by increasing the beam depth-to-width ratio from 1.0 to 4.0. The torsional stiffness before cracking increased by about 6% with the increase of beam depth-to-width ratio ratio from 1.0 to 4.0.
The ultimate moment increased by about 619%, 678%, 735%, 780%, 812% and 801%, respectively for each group with the increase of beam depth from 150mm to 600mm at different values of concrete compressive strength varying from 25MPa to 50MPa. The torsional stiffness after cracking increased by about 14%, respectively with the increase of beam depth-to-width ratio from 1.0 to 4.0. Finally, the beam depth-to-width ratio affected as expected on both cracking and ultimate moments.
Effect of spacing between Stirrups
The effect of stirrup spacing is conducted for beams with different stirrup spacing varying from 50 to 300mm and compared with control beam without stirrups. The effect of stirrup spacing is conducted on RC beams with different depth-to-width ratio varied from 2.0 to 4.0. The cracking moment is almost the same for each group. The ultimate moment for all groups with different depth-to-with ratio is higher than the beam without stirrups by 210%.
The results indicated that stirrup spacing has an insignificant effect on cracking moment, while the ultimate moment increased by using closer stirrup spacing. The ultimate moment also increased as expected by increasing the beam depth-to-width ratio.
Effect of Stirrup Bar Size
The effect of stirrup size appeared in ratio of transverse reinforcement (A_ft) that equal 0.45, 0.56, 0.70 and 1.0% for beams with stirrup diameters 8, 9, 10 and 12mm, respectively. The cracking and ultimate moments along with torsional stiffness before and after cracking are obtained from numerical models for groups A, B, C and D with beam depth-to-width ratios 2.0, 2.67, 3.33 and 4.0, respectively. The cracking moment and torsional stiffness before cracking are almost the same for each group. The ultimate moment for previously mentioned groups increased by about 23%, 25%, 19% and 17% with increase stirrup size from 8mm to 12mm. The torsional stiffness after cracking for previously mentioned groups also increased by 161%, 103%, 77% and 45%, respectively with increase stirrup size from 8mm to 12mm.
It can be concluded that the stirrup size has an insignificant effect on cracking moment, while the ultimate moment and torsional stiffness after cracking increased with the increase of stirrup size.
Effect of Longitudinal Reinforcement Ratio
The cracking and ultimate moments are obtained from numerical models for groups A, B, C and D with beam depth-to-width ratios 2.0, 2.67, 3.33 and 4.0, respectively. All beams had a longitudinal reinforcement ratio with ratio varying from 0.76% to 2.93% and without stirrups. The cracking moment was almost the same for all groups. The ultimate moment for groups with depth-to-width ratios 2.0, 2.67, 3.33, and 4.0 increased by about 16%, 30%, 22% and 43% with the increase of longitudinal reinforcement from 0.76% to 2.93%.
It is found that the longitudinal reinforcement ratio has an insignificant effect on cracking moment and the cracking moment is almost the same for each group. The results indicated that the ultimate moment increased with the increase of longitudinal reinforcement. Using top and bottom reinforcement provided higher twist capacity than distributed bars around the concrete section.
Proposed Models
The proposed models are introduced based on the regression analysis of the numerical results. The proposed models are used to predict both cracking and ultimate moments for concrete beams reinforced in with CFRP bars with CFRP and subjected to pure torsion. The predicted results using proposed models are compared to their counterparts either from experimental work or data gathered from literature for verification purposes. The numerical results are in good agreement with their counterparts predicted by proposed models. The predicted models improved predicting both cracking and ultimate moments and the mean values of numerical-to-predicted are 1.016 and 1.08, respectively.
Future work
The following are suggestions for future research on topics related to the present research:
Models should be conducted on flanged RC beams with L and T sections to investigate the effect of geometry for RC beams under pure torsion. The behavior of flanged beams can be compared to the corresponding results of R-section.
Studying the effect of concrete compressive strength, spacing between stirrups, stirrups diameter and longitudinal reinforcement on the behavior of RC beams with (L/T) sections and subjected to pure torsion.
The behavior of concrete beams reinforced with CFRP and subjected to flexure, shear and torsion should be investigated.
Investigating the effect of concrete compressive strength, spacing between stirrups, and (Max/Min) transverse and longitudinal reinforcement ratio for flanged beams subjected to flexure, shear, and torsion.
Examining the influence of various types of reinforcing FRP materials on the torsional capacity of RC beam with (R / T) sections and subjected to flexure, shear, and torsion.