REINFORCED CONCRETE STRENGTH OF BEAMS. 653 



It is well known, however, that combination of shearing- stresses 

 with the horizontal stresses produces in the body of the beam oblique 

 tensions and compressions similar to those which tend to buckle the 

 webs of steel plate gii'ders. 



To determine these oblique tensions and compressions and the 

 angles of their inclination we may use the formula — 



Where p is tension or compression, according to the sign which 

 is adopted — that is to say, if /' is tension the + sign gives us the 

 maximum oblique tension and the — sign the oblique compression 

 at right angles to it; on the other hand, if f is compressive, the sign 

 gives us the maximum compression. 



The angle of obliquity is given by 



tan 20 = ^ . 



It is not easy to determine where p becomes a maximum; the 

 best plan is to calculate for several points and draw a curve. 



With shallow girders the sheai'ing stresses will be small and 

 dangerous tensions will occur at the extreme fibres where reinforce- 

 ment is already provided; with deep girders it may be that heavy 

 shearing stresses will produce tensions near the neutral axis, neces- 

 sitating reinforcement. 



Continuous beams often have the heaviest horizontal stresses at 

 the supports where the shear is also large. 



It is usual to specify that the shear in a beam shall not exceed 

 50 or 60 lb. per square inch. This seems strange when the shearing 

 strength of concrete is about half its compressive strength, or, say, 

 1.200 lb. per squai'e inch. This low stress is really intended as a 

 safeguard against diagonal tension. A logical plan would be to 

 determine the actual diagonal tensions as far as possible and provide 

 reinforcement for them, if necessary. 



A point which should be examined in an ordinary beam is one 

 adjacent to the reinforcement just about the point where tension 

 reaches 200 lb. per square inch in the concrete, and where the shear 

 is of considerable amount. In a tee beam we should examine the 

 Aveb at junction with table for shear, but the principal oblique stress 

 will be there a compressive one, except in the special case of a tee 

 beam continuous over supports. 



It is a very common practice to subject reinforced concrete con- 

 structions to tests of one and a half or more times the working load. 



The effect of this is probably to raise the neutral axis and 

 enlarge the zone of fracture. The method of calculation which 

 neglects the tensile strength is then nearer the truth and still on the 

 safe side. 



In conclusion, I would like to point out what is perhaps not 

 realised by most Australian engineers, and that is the weakness of 

 reinforced concrete as compared with our own hardwoods. 



For example, to carry 1 ton per lineal foot over a span of 20 ft. 

 requires a concrete beam 12 in. wide by ."ft. deep, while an ii-onbark 

 or spotted gum beam 12 in. by 18 in. (exactly half the size) is more 



