RECTANGULAR BEAMS 45 



Theoretically, a plain concrete beam will fail by cracks opening 

 up along the zigzag lines which are shown in Fig. 16. This is 

 found to be true in tests on this type of beam. A plain concrete 

 beam will always fail in tension due to the low ultimate strength 

 of concrete in tension as compared to its strength in compression. 



The exact direction of the maximum tensile stress at any point 

 in a beam depends only upon the relation between shear and 

 bending moment. Hence by means of the formulas given above, 

 the student should be able to trace the general direction of the 

 stresses in a beam with the loading other than uniform. The 

 introduction of steel into a concrete beam, however, changes 

 the direction of the stress lines somewhat. The exact effect of 

 adding steel will be taken up later. 



The student should have some idea of the variation of the 



^Compression A 



"tension 

 FIG. 18. 



maximum tensile stress throughout a vertical cross-section. Of 

 course, in studying this variation of stress, it should be remem- 

 bered that the direction of the stress is not normal to the ver- 

 tical section at the different points. Maximum tensile stresses, 

 as we have already shown, are normal to a vertical section only 

 when the section is taken where the shear is zero. In other 

 sections these stresses are normal only along the lower fibers of 

 the beam. Fig. 18 1 shows the variation in the maximum tensile 

 stress on a section such as XX' ', Fig. 17. The variation of the 

 normal and shearing stresses is also shown. 



It should now be clear that the steel reinforcement in a con- 

 crete beam for uniform loading should have the general direc- 

 tions shown in Fig. 19 in order to take the tension in the beam 

 and prevent' the cracks starting along the lines indicated. Fig. 

 20 is the simplest method of reinforcement and quite often used 

 for light loads. In beams highly stressed, the student can 

 appreciate the reason for curved reinforcement in addition to 

 the horizontal rods. The most common method is to use 

 several rods for the horizontal reinforcement and then to bend 



1 From Turneaure and Maurer's "Principles of Reinforced Concrete Construction," 

 2nd edition, page 50. 



