### 3.3. Load, Flow and Stress

Reference: Abbott, Richard. Analysis and Design of Composite and Metallic Flight Vehicle Structures 3 Edition, 2019

Fundamental to structures analysis are the ideas of load, flow and stress.

• Load is a measure of force, a moment (which is regarded as a type of applied load) is a measure of twisting or bending force.
• inlb (Moment)
• Flow is a measure of load or moment per length or width
• inlb/in (Moment Flow)
• Stress is a measure of load per area – or stress can be thought of as flow per thickness.
• lb/in2

The assessment of the effect of loads and moments on a structure, the derivation of relevant flows and stresses, and comparing these with appropriate failure criteria is the process of structures analysis.

The difference between load flow and stress is a useful distinction when interpreting hand analysis and finite element model results.

Using a cantilever shear beam as an example:

Consider a shear beam loaded with ‘V’. The beam has a width (or depth) of ‘W’ and a thickness of ‘t’.

Note that this example is statically determinate. i.e. the load transfer through the structure is not affected by stiffness.

The reaction load, V is not changed by either W or t .

The Shear Load Flow V/W  is affected by the width of the beam but not the thickness.

And finally, the average shear stress:

is affected by both the width and the thickness.

Conversely:

• The reaction load is unaffected by changes in both the width and the thickness
• The Flow is unaffected by the thickness

This is particularly important when the engineer is dealing with a finite element model using plate elements. If the engineer uses plate elements (and the model is ‘reasonably’ statically determinate) the model need not be re-run to consider webs of different thicknesses if load flow results are used from the model – because the load flow is unaffected by the thickness.

### 3.3. Load, Flow and Stress

Reference: Abbott, Richard. Analysis and Design of Composite and Metallic Flight Vehicle Structures 3 Edition, 2019

Fundamental to structures analysis are the ideas of load, flow and stress.

• Load is a measure of force, a moment (which is regarded as a type of applied load) is a measure of twisting or bending force.
• inlb (Moment)
• Flow is a measure of load or moment per length or width
• inlb/in (Moment Flow)
• Stress is a measure of load per area – or stress can be thought of as flow per thickness.
• lb/in2

The assessment of the effect of loads and moments on a structure, the derivation of relevant flows and stresses, and comparing these with appropriate failure criteria is the process of structures analysis.

The difference between load flow and stress is a useful distinction when interpreting hand analysis and finite element model results.

Using a cantilever shear beam as an example:

Consider a shear beam loaded with ‘V’. The beam has a width (or depth) of ‘W’ and a thickness of ‘t’.

Note that this example is statically determinate. i.e. the load transfer through the structure is not affected by stiffness.

The reaction load, V is not changed by either W or t .

The Shear Load Flow V/W  is affected by the width of the beam but not the thickness.

And finally, the average shear stress:

is affected by both the width and the thickness.

Conversely:

• The reaction load is unaffected by changes in both the width and the thickness
• The Flow is unaffected by the thickness

This is particularly important when the engineer is dealing with a finite element model using plate elements. If the engineer uses plate elements (and the model is ‘reasonably’ statically determinate) the model need not be re-run to consider webs of different thicknesses if load flow results are used from the model – because the load flow is unaffected by the thickness.