INTERNAL FORCES 77 



of sufficient size to carry the load, the total amount of shear the 

 beam is good for should be equal to or exceed the maximum reac- 

 tion. Thin webs act like long slender columns and may fail by 

 crippling. The crippling strength of the beams is also given in the 

 tables and this should be equal to or exceed the maximum reaction. 

 Fig. 61 is a very old illustration used by many writers to explain 

 shearing action in a beam. Let (a) represent a beam assumed 

 __________ to be composed of a 



*JLr number of planks not 

 (b > fastened together. 



Pig. 61 Illustration of Horizontal Shear When loaded the 



planks bend and slide on each other as shown. This sliding action 

 is horizontal shear, which is zero at the top and bottom edges 

 and a maximum along the neutral plane where the tensile stress 

 changes to compressive stress. 



Spike the planks together (6) and they will not separate when 

 the beam bends under load. The sliding stress is pure shear 

 on the spikes connecting the planks. The spikes act by bearing on 

 the planks into which they are driven, and in this manner some 

 tension is carried from outer to inner planks. The resultant force 

 is called diagonal tension. 



Imagine a beam of any material divided into a great number of 

 horizontal layers. Along the imaginary joints shear exists which 

 is resisted by the tensile strength of the material. In beams of 

 steel or iron, in which materials the tensile strength is equal in 

 all directions, the diagonal tension thus developed may be strong 

 enough to tear the web along a diagonal line extending upward 

 from the support. The web must be thick enough to resist the 

 diagonal shear or, in the case of a plate girder, be strengthened 

 by stiffeners. 



Reinforced-concrete beams fail similarly in diagonal shear. 

 This may be resisted by making the stem of the beam thick or, 

 if it is desirable to use little concrete in the stem, stirrups are 

 added to resist diagonal tension. There are other theories which 

 endeavor to account for the diagonal cracks which appear some- 

 times in reinforced-concrete beams, but the generally accepted 

 method for proportioning stirrups is based on shear expressed as 

 diagonal tension, and since the desired result is accomplished and 

 the computations are readily performed this method it is believed 

 will persist. 



