RECTANGULAR BEAMS 79 



fleets, and failure soon occurs by the crushing of the concrete. 



The ultimate shearing strength of a beam having no web 

 reinforcement may be taken at 100 to 150 Ib. per square inch, 

 for a 1:2:4 concrete, calculated as average shearing stress on the 

 cross-section. The stresses here considered relate to shearing 

 stresses involving large diagonal tensile stresses. Where such 

 tensile stresses are not developed to any extent, as in punching 

 shear, a value of at least one-half the compressive strength (as 

 previously mentioned) may be employed. However, it is almost 

 impossible in practice' to avoid altogether such tensile stresses, 

 and it is not advisable to raise the first value given any consider- 

 able amount. The student must continually bear in mind that 

 the kind of failure denoted as a shear failure is so called for con- 

 venience; they are diagonal tension failures brought about by 

 large shearing stresses and hence may be measured by the shear- 

 ing forces present. The average shearing stress on a vertical 

 section at failure is the value always given. While the maximum 

 shearing stress is 12 to 15 per cent greater than this, the average 

 stress is practically as good a standard of measure and is much 

 more readily calculated. 



The following is taken from "Principles of Reinforced Con- 

 crete Construction" by Turneaure and Maurer: "As already 

 stated the amount of horizontal steel has a direct bearing on 

 shear failures for the reason that large areas of steel with low 

 unit stresses permit less extension of the concrete than small 

 areas with high working stresses. This effect is shown in a 

 marked manner in a series of tests made at The University of 

 Wisconsin on small mortar beams of 1:3 mixture. The beams 

 were 3 in. X4 1/2 in. in cross-section and 4 ft. span length. 

 Loads were applied at two points a varying distance apart. Only 

 straight reinforcement was used, amounting to 1.41 per cent. 

 The tensile strength of the material was high, being 490 Ib. per 

 square inch. The results were as follows: 



Distance apart of loads Average shearing stress 



Inches Lb. per sq. in. 



Center load 177 



12 200 



24 220 



32- 316 



36 512 



40 850 



44 1035 



