STRUCTURES EXAMPLE BEAM DESIGN

V   Shear diagram.
M  Bending diagram.
∆   Deflection diagram. 
I    Inflection point (change from + to - bending).

Reactions

  R= 400plf (24)/2      R = 4800 lbs

Shear 

Moment

Try 4x10 beam  

Bending stress  

f b = Mmax/S= 5000 (12)/50      f b = 1200 psi
                                                  1200 < 1450, ok

Shear stress  

f v = 1.5V/bd=1.5(2800)/[3.5(9.25)]       f v = 130 psi
                                                               130 > 95, not ok

Try 6x10 beam  
f v = 1.5V/bd=1.5 (2800)/[5.5 (9.25)]      f v= 83 psi
                                                                83 < 95, ok

Note: increased beam width is most effective to reduce shear stress; but increased depth  is most effective to reduce bending stress.