Strategy for Analyzing Shearing Flow in Beams

In a Nut Shell:   Shear flow, q , depends directly on the shear force, V, at the section

of the beam where it is to be calculated, on the first moment of area, Q,  at the location

of the shear flow, and inversely on the moment of inertia of area, I, of the entire

cross section about its neutral (centroidal) axis.

q  =  VQ/I

Common units for shear flow are  lb/in,   lb/ft,   N/mm,  N/m   (English/Metric)

 Strategy for analyzing shearing stress involves five key steps as detailed in the table below. Step 1 Determine the centroid of the beam's cross-section. Step 2 Determine the moment of inertia of area of the beam's entire cross-section about its neutral (centroidal) axis.  This step may involve use of the parallel axis theorem.   Recall for a rectangular cross-section of width  b  and height  h the moment of inertia of area, I, about its centroidal  axis is (1/12) bh3 .  Voids of area contribute negative values of moments of inertia. Step 3 Determine the distribution of shear force across the length of the beam. This step involves plotting the shear force distribution along the length of the beam.  Pick the maximum shear force, V. Step 4 Calculate, Q, the first moment of area at the location where the shear flow is to be calculated.  Q is the product of the area, A, from where the shear flow is zero to the location where the shear flow is to be calculated times the distance, ybar, from the neutral axis to the centroid of of this area, A. Step 5 Finally, calculate the shear flow, q,  using:                                    q =  VQ/I   Note:  Shear flow is independent of the width of the beam's cross-section.