76 PRACTICAL STRUCTURAL DESIGN 



Shearing Resistance 



A beam may be strong enough to carry the load without a 

 bending failure, which will crush the fibers at the top or pull them 

 apart at the bottom, yet it may fail in shear. The direct shearing 

 stress at any section on a beam is found by dividing the shear at 

 the section by the area of the beam at the section. The direct 

 shear, however, is seldom operative, this action being best repre- 

 sented by a punch making holes in a plate or by a large shear 

 cutting a plate. The shearing stress which breaks a beam is di- 

 agonal tension resulting from the combined action of the horizontal 

 and vertical shearing stresses. 



The direct vertical end shear is equal to the maximum reaction. 

 The horizontal shear is equal in amount and acts along the neutral 

 plane where the fiber stress in bending changes from tension to 

 compression, the stress being in reality a sliding of the fibers where 

 they have no bending stress. The diagonal tension is the com- 

 ponent of these two actions. (Fig. 60.) Referring again to the 

 statement that the area of the shear diagram between any sec- 

 tion and the nearest support, for a beam resting on two, or more, 

 supports, equals the bending moment at the section, the unit 

 shear at any section amounts to 



V M l -M 2 



s = TJ = ^ ' 

 jd jd 



in which s = unit shear in pounds per square inch, 



V = shear at the section in pounds, 

 Mi = moment in inch pounds at one side of section, 

 Mz = moment in inch pounds at the other side of section, 

 jd = moment arm in inches. 



The allowable shearing stress in steel is 

 10,000 Ibs. per square inch. After obtain- 

 ing the size of beam to carry a 'certain load, 

 divide the maximum reaction by the web 

 thickness multiplied by the depth of the 

 beam. This will give the shearing stress in 



Pig go Relation be- pounds per square inch. If it exceeds 10,000 



tween Moment and Ibs. a larger beam is required. In the steel 



Shear handbooks the total amount of shear for 



which a beam is safe is given in the tables of " Properties of 



Sections." For example, in taking out from the tables a beam 



