146 REINFORCED CONCRETE CONSTRUCTION 



the top of the web. Using these limiting values as approxi- 

 mations for the true ones ; 



M c =l/2f c bt(d-l/2 (a) 



M 



or <** = (/s)( ^ 1/20 0>) 



The errors involved in these approximations are on the side of 

 safety. 



Since a T-beam will usually have ample strength in compression 

 for any ordinary depth of beam likely to be selected, the design 

 of the stem of the T, or the beam below the slab, is therefore 

 largely a question of providing sufficient concrete to take care 

 of the shearing stresses and to give a good layout of the tension 

 rods. The manner of providing reinforcement for shearing 

 stresses in T-beams is similar to that already described for 

 rectangular beams. In T-beams, however, the reinforcement 

 for shear should run well up into the slab in order to tie the 

 beam and slab together. Results from tests for both shear and 

 moment in T-beams agree quite closely with theoretical results. 

 It also appears that the shearing strength of a T-beam is about 

 the same as that of a rectangular beam of the same depth and 

 a width equal to the width of the stem of the T. 



All re-entrant angles in concrete are points of weakness and 

 such angles should, therefore, be avoided. Also, T-beams should 

 not be made too deep in proportion to the width of stem as 

 such forms are relatively weak at the junction of stem and 

 flange. The width should preferably be from one-third to one- 

 half the depth in ordinary cases. For large beams the width 

 may be "made one-third to one-fourth the depth. 



Deflection formulas for T-beams are given in Art. 51. 



In the following problems and also in those problems to be worked out 

 by the student, the working stresses recommended by the Joint Committee 

 for a 2000-lb. concrete will be assumed; namely, 



/ c = 650, /, = 16,000, n = 15. 



In the illustrative problems following Art. 50 in which the above-mentioned 

 allowable stresses were used, the following values were determined: 

 p = 0.0077, k = 0.378, / = 0.874. 



