Shear (V)

Shear (V) is the tendency for one part of a beam to slide past another part. The magnitude of the shear at any section is equal to the algebraic sum of loads and reactions acting perpendicular to that section.



SIGN CONVENTION
If the tendency of the section to the left of the cut is to move upward, the shear is positive; if it has a tendency to move down, it is negative.




For simplicity in obtaining the correct sign, one may say that it is equal to the algebraic sum of loads and reactions to the left of the cut. Note that the internal shear on the end of the FBD acts in the opposite direction of the algebraic sum of the loads and reactions in order to balance these forces (SV = 0).

A shear diagram is a graphic representation of the shear at every point along the length of a member.

To plot a shear diagram on a beam, the shear must be calculated at each point along the length of the beam. One way is to simply plot the shear as the algebraic sum of the loads and reactions acting perpendicular to the beam at the left side of each increment along the length of the beam. Positive values are shown above and negative values below a reference axis.

How to draw a SHEAR DIAGRAM
Start at the left end and plot the external shear values with regard to the following:

• The shear diagram is the graphic representation of the shear force at successive points along the beam. Forces acting upward are assumed positive and downward forces negative. 
• The shear force (V) at any point is equal to the algebraic sum of the external loads and reactions, perpendicular to the beam, to the left of that point. 
• Since the entire beam must be in equilibrium (sum of V = 0), the shear diagram must close to zero at the right end. 
• Consider the loading for increments along the length of the beam in order to determine the shape of the curve.
  
  

  if there is no change in the load along the incremental length under consideration, the shear curve is a straight horizontal line (or a curve of zero slope). The slope at any point is defined as the tangent to the curve at that point.
  
  if a load exists, but does not change in magnitude over successive increments (uniformly distributed), the slope of the shear curve is constant and non-horizontal.
  
  if a load exists, and increases in magnitude over successive increments, the slope of the shear curve is positive (approaches the vertical); if the magnitude decreases, the slope of the shear curve is negative (approaches the horizontal).

• Abrupt changes in loading cause abrupt changes in the slope of the shear curve. Concentrated loads produce vertical lines (a jump) in the shear curve.