Unsymmetrical Bending of Beams • Unsymmetrical Bending occurs in beams with unsymmetrical Cross section. • Assumptions are same as that of symmetrical Bending. • Symmetrical bending will become special case of unsymmetrical Bending. Sign Conventions and Notations Notations and sign conventions • C/s of the beam is in XOY Plane. Z-axis is longitudinal axis of the beam. • M: Bending Moments, • S: Shear Forces /loads, • P: Axial or direct loads • T: Torque • W: Intensity of distributed loads • u, v, w: displacements in X, Y & Z-directions resp. Notations and sign conventions • Sx & Sy: Shear loads in X & Y direction. Positive along positive directions. • Mx: Bending moment about X-axis or in vertical plane. Positive when it induces tension in 1st quadrant of the beam. • My: Bending moment about Y-axis or in horizontal plane. Positive when it induces tension in 1st quadrant of the beam. • Wx, Wy: Intensity of distributed loads in X & Y directions. Resolution of Bending Moment Direct or Bending Stress Distribution due to Unsymmetrical Bending • This is the governing equation for direct or bending stress distribution due to unsymmetrical Bending. • In above equation, if cross section is symmetrical about at least one axis i.e. Ixy = 0, and only Mx is applied, i.e My = 0, Then It becomes a specific case of symmetrical bending about Xaxis.
