| dc.description.abstract | Summary and Conclusions
The various conclusions arrived at in this study are summarized as follows:
1. Equilibrium Method
The equilibrium method used in this investigation for the analysis of T beams under combined bending and torsion has yielded satisfactory results.
2. Modes of Failure
The modes of failure of T beams under pure torsion and under combined bending and torsion appear similar to those of rectangular beams. Modes 1 and 3 of failure have been noticed in this study. In the absence of shear, for T beams, failure by Mode 1 is only a remote possibility.
3. Bach’s Approximate Approach
Bach’s approximate approach of totalling the torsional strengths of the component rectangles forming a T beam (used by several investigators as well as in this study) is satisfactory for predicting torsional capacities.
However, depending on the relative sizes of the component rectangles, the method may not always be conservative if all component rectangles are assumed fully effective.
From Figs. 3.12 and 3.13, it may be concluded that the presence of moment limits the overhang width. Considering the provisions of effective flange width for T beams under flexure, a limit of six is suggested as the ratio of overhang width to flange thickness for safe application to T beams under combined bending and torsion.
4. Contribution of Flange Overhang
Contribution of the flange overhang (in the absence of flange reinforcement) to torsional resistance depends on which group of reinforcement yields at ultimate.
o If failure is accompanied by yielding of top longitudinal steel, torsional contribution of the flange overhang is negligible.
o Otherwise, torsional contribution of the flange overhang must be considered.
5. Independence from Moment–Torque Ratio
The torsional contribution of flange overhang is found to be independent of the moment–torque ratio and can be determined from Equation (3.8).
6. Poorly Reinforced Beams
The torsional capacity TwT_wTw of the web of a poorly reinforced concrete beam (one where torsional capacity of a companion plain concrete section is greater than that due to reinforcement yield) may be obtained by ignoring reinforcement and assuming that under pure torsion, at ultimate, the shear stress is constant and equal to ftf_tft over the full section.
Equation (4.28a) has been derived for such cases. Results of beams C5 and C6 of Kirk and Lash support this conclusion (Table 5.1).
7. Inclination of Failure Crack
Equation (3.4), obtained from tests, gives the inclination of the failure crack for T beams. Tests (1.3ET, 1.7ET, 2.3ET groups) show that:
o crack inclination is independent of the amount and distribution of reinforcement,
o crack inclination depends on moment–torque ratio,
o crack inclination is independent of flange dimensions.
The good agreement of the proposed method (using T beam crack angle for rectangular beams treated as T beams without flanges) supports this conclusion.
8. Reinforcement Groups and Failure Modes
Of the three reinforcement groups (top longitudinal, bottom longitudinal, and transverse steel), the group that yields determines the mode of failure and transition from one mode to another.
In this study, only beam 2.3UT 1 failed in Mode 3; the rest failed in Mode 1.
Predictions from the theory match these observations, except in 2.3UT 2.
Satisfactory agreement with results from Kirk and Loveland (beams H1, H2, I1, I2) supports this conclusion.
9. Stress in Stirrups
Not all three reinforcement groups crossed by the failure surface necessarily reach yield.
Stirrup stress depends on longitudinal steel and moment–torque ratio (Equations 4.21, 4.22, 4.23).
Good agreement between predicted and observed torques in series 4 (stirrups at different spacings) supports the assumed method of computing stirrup stresses based on controlling steel force.
10. Influence of Concrete Strength
In the proposed method, concrete strength influences torsional strength indirectly by affecting the depth of the compression zone.
A richer concrete gives a smaller depth, increasing the number of stirrups crossing the failure surface and increasing torsional capacity.
Agreement with Hsu’s beams 12, 13, 14, 02, 33, 34 supports this conclusion.
11. Over Reinforcement Criterion
A limit for defining over reinforcement occurs when compression zone depth equals web width.
From Section 4.3.3, the section is over reinforced if:
sbfgptan us_b f_{gp} \tan \theta_usbfgptan u
(condition shortened here per your text).
For over reinforced sections, ultimate torque is calculated using the compression zone depth equal to distance from extreme compression fibre to inner face of far horizontal stirrup leg.
Several beams (1.3ET 1 to 2.3UT 3, 1.5T9 6, 1.5T9 7) confirm this.
12. Critical Stirrup Spacing
For given beam dimensions and moment–torque ratio, there exists a stirrup spacing at which longitudinal steel and stirrups yield simultaneously-the critical spacing.
o If actual spacing > critical torque capacity decreases.
o If actual spacing < critical no significant benefit.
13. Fictitious Steel Concept
Using Hsu’s fictitious steel concept, the increase in torque capacity in the presence of moment is explained for beams with unequal top and bottom steel.
Beam group 2.3UT (series 4) and Kirk & Loveland series I and 3 support this.
14. Validation of Proposed Method
Using the proposed method, for 106 T beams tested under combined bending and torsion:
o Average (observed/predicted) = 1.03
o Coefficient of variation = 9%
o Median between 1.0–1.05
o Only 8% of beams over estimated by more than 10%.
This strongly validates the proposed method.
15. Recommended Design Procedure
A design procedure is proposed in which all three reinforcement groups are fully utilised-top longitudinal, bottom longitudinal, and stirrups-so that all reach yield simultaneously. | |
