STRENGTH OF MATERIALS 301 



COMBINED STRESSES 



Bending Combined with Compression or Tension. Assume 

 that P is the axial force acting on the beam; M, the maximum 

 bending moment to which the beam is subjected; A, the cross- 

 sectional area of the beam; /, its moment of inertia; and c, 

 the distance from the neutral axis of the most distant fiber, 

 having the same kind of stress (tension or compression) as that 

 caused by P. Then, the working stress should not exceed 

 P Me 



*-A+T 



In case of compression, s should, in addition, be reduced by 

 one of the compression formulas previously given. 



The preceding formula for 5 is the one commonly used in 

 practice, but it is only approximate. When more accurate 

 results are required, the following formula should be used, 

 P Me 



Here, I is the span; E, the modulus of elasticity, and k, a 

 constant having the following values: 



Value of k 

 For a cantilever loaded at end .................... 



For a cantilever loaded uniformly ................. J 



For a beam supported at both ends and loaded at 

 center ..................................... r ^ 



For a beam supported at both ends and loaded uni- 

 formly ...................................... ^ 



For a beam fixed at both ends and loaded at center . . ^ 

 For a fixed beam uniformly loaded ................ Jj 



The minus sign before k is for the case when the direct stress 

 is compressive, and the plus sign, when it is tensile. 



