7.2 Superposition
        Normal Stresses | Shear Stresses | Beam Deflection

» Normal Stresses
Consider a section of a beam subjected simultaneously to both an Axial Force, P, and Moment, M. The Method of Superposition can be used to determine the normal stresses acting on a cross-section of the beam:

Click below to see the Normal Stress Distribution due to:

1) The Axial Force, P;
2) The Moment, M;
3) The Axial Force, P and the Moment, M.

» Shear Stresses
Consider a circular cross-section of a beam subjected simultaneously to both an Transverse Shear Force, V, and Torque, T. The Method of Superposition can be used to determine the stear stresses acting on a cross-section of the beam:

Click below to see the Shear Stresses at points 0, 1, 2, 3, and 4 due to:

1) The Transverse Shear Force, V;
2) The Torque, T;
3) The Transverse Shear Force, V and the Torque, T.

(Image at right is face of beam looking in the negative x direction)

» Beam Deflection
The Method of Superposition is also useful in determining the Bending Stress and Deflection in a beam when two or more separate loads are acting on a beam. Take for example a rectangular Cantilevered Beam with a Distributed Load (w) and a Point Force (P) acting at the tip:

Click below to see the Moment and Deflection in the Beam due to:

1) The Point Force (P);
2) The Distributed Load (w);
3) The Point Force (P) and the Distributed Load (w).