7a. Combined Loads  (SSES Ch. 7.0)
Combined Loading • Superposition  
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Combined Loading

In earlier chapters, formulas were developed to obtain the stresses in axial members (bars), torsional members (shafts), pressure vessels, and beams. Each type of component was subjected to one type of load, which caused one type of stress at a material point, e.g., torque causes shear stress.

In general, engineering systems are simultaneously loaded by axial forces, torques, bending moments and shear forces - combined loading - as illustrated in the image below.

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Axial forces and bending moments cause normal stresses (axial stress and bending stresses).

Torques and shear forces cause shear stresses (due to torsion and shear).

When two or more types of loads contribute to the stresses at a cross-section, determining the stress state at any point on the cross-section may seem like a daunting task. However, by breaking the problem down into two or more basic problems, and then superimposing the results of the basic problems, the overall solution can be found.


Combined loading problems are solved using the Method of Superposition:

  1. Break the problem into easier problems where only one type of load acts.
  2. Solve for the stresses on a cross-section resulting each individual load.
  3. Superimpose (combine) the individual stress solutions at various (critical) points.

Several rules must be considered:

  • Only combine like stresses (i.e., two normal stresses) that act on the same face of a stress element.
  • Superposition only works if the system remains LINEAR. For Strength of Materials problems, this means that material must obey Hooke's Law; i.e., it does not yield.
  • 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.

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Updated: 05/24/09 DJD