SLABS, CROSS-BEAMS, AND GIRDERS 159 



The cases which may be met with in practice, with the method 

 of solution in each instance indicated, are as follows: 



(1) To determine b and d. 



Assume p, p f , and -7- 



d . 



Solve for k. 



Substitute value of k in formulas for L and K. 



Substitute L and K in formulas for M c and M 8 respectively. 



Solve for bd 2 in each case and accept larger value. 



(Remember in this case M c = M s = exterior bending 



moment.) 



(2) To determine moment of resistance. 



d' 

 Compute p, p', and -,- 



Solve for k. 



Substitute value of k in formulas for L and K. 



Substitute L and K in formulas for M c and M s respectively. > 



Solve for M c and M s and take the smaller. 



(3) To determine fiber stresses. 



Obtain p, p r , and -v 



Solve for k. 



Substitute value of k in formulas for L, K, and I/'. 



Solve directly the formulas for/ c ,/ s , and/%. 



(Note. When using formula for shear or for bond stress along 

 horizontal tension rods of beams double-reinforced, an average 

 value of / = 0.85 may be taken.) 



63. Design of a Continuous Beam at the Supports. The 

 formulas given in the preceding article apply directly to the 

 design of continuous beams at the supports. If possible, half of 

 the rods on each side should be bent up and extend along the 

 top of the beams over the supports. The other rods should 

 extend horizontally through the supporting columns. 



In the design of continuous T-beams at the supports the 

 student should realize that the flange being under tension, the 

 stress in the concrete is negligible above the neutral axis and a 

 rectangular section may be considered at such points. The 

 method of design is thus similar to the design of a double-rein- 



