Boundary Conditions and Sign Conventions:

Boundary Conditions

Boundary conditions are referring to the known values of deflection & slope at particular values of x. The y and dy/ dx are invariably known at the supports. dy′ / dx might also be ascertained from symmetry of bent shape of beam central line. For instance,

 (a) At simple supports, y = 0, dy/ dx  ≠ 0 .

 (b) At fixed supports, y = 0, dy/ dx  = 0 .

 (c) At centre of SS beam loaded either by a single central or Udl over entire length y ≠ 0, dy/ dx  = 0 .

Sign Conventions

1.      x is +ve towards right.

2.      y is +ve upwards.

3.      Anticlockwise slopes are +ve.

4.      Sagging BM are +ve.