STRUCTURES EXAMPLE BEAM ANALYSIS

Reactions

Shear

Find x, where shear = 0 and bending = maximum:

Vbr-w2 x = 0;  x = Vbr/w2 = 2000/200      x = 10 ft

Moment 

Section modulus 

Bending stress

Shear stress

Note: stress is figured, using absolute maximum bending and shear, regardless if positive  or negative.  Lumber sizes are nominal, yet  actual sizes are used for computation.   Actual sizes are ½ in. less for lumber up to 6 in. nominal and ¾ in. less for larger sizes:  4x8 nominal is 3½x7¼ in. actual. 

Note: in the above two beams shear stress is more critical (closer to the allowable stress)  than bending stress, because negative cantilever moments partly reduces positive  moments.