CHAPTER IX 

 BENDING AND DIRECT STRESS 



74. Theory in General. Consider any given section of a 

 beam or column and locate its center of gravity. Now, if the 

 resultant of the forces on one side of the section does not pass 

 through this center of gravity, bending will result, and the 

 distribution of stress normal to the section will not be uniform. 

 Bending may result from lateral pressure; or it may be due to the 

 eccentric application of a force in the direction of the axis; or 

 it may be due to the two combined. 



If the structure considered is a beam and is acted upon by 

 forces which are all normal to its length, then the stresses 

 resulting are due to simple bending and the formulas already 

 deduced may be employed. If, however, any of the forces acting 

 throughout the length of a beam be inclined, or if additional 

 forces be applied at the ends, then our beam formulas for simple 

 bending will not apply. Likewise, in columns, if the load be 

 eccentrically applied or if lateral pressure be exerted, both 

 bending and direct stresses will result and the ordinary column 

 formulas cannot be used. 



The same combination of stresses occurs also in arch rings and 

 may occur in special cases. The formulas to be derived can be 

 employed in any type of reinforced concrete structure provided 

 the normal component of the resultant thrust on the given section 

 acts with a lever arm about the center of gravity of the section. 

 In long beams and columns, the deflection resulting from flexure 

 should be given consideration when determining the eccentricity 

 of the axial and inclined forces. 



Let us first consider structures of homogeneous material, as 

 structures of plain concrete. The distribution of pressure on 

 any section due to a resultant pressure acting at different points 

 will be explained. Consider a section represented in projection 

 by EF, Fig. 84. When the resultant, R, acts at the center of 

 gravity, 0, the intensity of stress is uniform over the section 

 and is equal to the vertical component of R divided by the area 



W 

 of section, or -j- If R acts at any other point, as N, and if 



A. 



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