» Combined Loading
In the previous chapters, various formulas were developed for obtaining the normal and shear stresses in axial members (bars), torsional members (shafts), and beams. However, in many cases, machine parts and structural members are simultaneously subjected to both normal stresses (axial and bending) and shear stresses (due to shear forces and torques). When two or more types of loads contribute to the stress state at a point, we have what is called COMBINED LOADING. Some examples of Combined Loading are (click on description to see):

A Shaft subjected to an axial force and a torque A Shaft subjected to a transverse shear force and a torque A Beam subjected to a transverse shear force and an axial force

» Superposition
The principal method of solving problems of Combined Loadings is through the METHOD of SUPERPOSITION. In a nutshell, the Method of Superposition involves:

1) Break the problem into parts where only one type of load acts;
2) Solve for the stresses resulting from the load;
3) Assemble the solutions to solve for the whole problem.

Several rules must be considered when applying the Method of Superposition:

• You can only add Like Stresses (i.e., two normal stresses; do not add a shear stress to a normal stress);
• You can only add stresses like forces when they act over the same physical area;
• The Method of Superposition only works if the system remains LINEAR, that is, the material must not exceed the yield condition;
• There must not be an interaction effect among independently applied loads - stresses due to one load are not affected by the presence of other loads;

The Method of Superposition is covered in more detail on the following pages.