Elastic Section Modulus can also be defined as the first moment of area.

In order to consider all these factors in terms of one descriptor, the section modulus (cm3/m) is used.

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.

The section modulus combines all the important geometric information about a beam's section into one quantity.

For the case where a beam is doubly symmetric, and we have one section modulus .

For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.

The plastic section modulus is used to calculate the plastic moment, M, or full capacity of a cross-section.

Design formulae for the shear area and section modulus for a wide range of icebreakers have been established.

Often the equation is simplified to the moment divided by the section modulus (S), which is I/y.

The plastic section modulus depends on the location of the plastic neutral axis (PNA).

The Plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior is assumed to be an acceptable limit.

Typically, and in this case, the struts are oriented such that the trunnion friction stress is applied to the weak axis of the struts (see Section modulus).

There are two types of section moduli, the elastic section modulus (S) and the plastic section modulus (Z).

The mechanical strength of the bone can be accurately predicted by the section modulus, which is defined as the cross-sectional moment of inertia divided by half of the subperiosteal width.

Though generally section modulus is calculated for the extreme tensile or compressive fibres in a bending beam, often compression is the most critical case due to onset of flexural torsional buckling.

Note that the ultimate strength of a beam in bending depends on the ultimate strength of its material and its section modulus, not its stiffness and second moment of area.

He correctly assumed a central neutral axis and linear stress distribution from tensile at the top face to equal and opposite compression at the bottom, thus deriving a correct elastic section modulus of the cross sectional area times the section depth divided by six.

The plastic section modulus is then the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:

There may also be a number of different critical cases that require consideration, such as there being different values for orthogonal and principal axes and in the case of unequal angle sections in the principal axes there is a section modulus for each corner.

In the case of T-sections if there are tensile fibres at the bottom of the T they may still be more critical than the compressive fibres at the top due to a generally much larger distance from the neutral axis so despite having a higher allowable the elastic section modulus is also lower.

In CSA S16-01 Limit states design of steel structures, there is a disconnect in moment capacity of laterally supported members between Classes 2 and 3: when the section crosses the Class 2 boundary, its calculated capacity drops in the ratio of the elastic to plastic section modulus.

Backfill soil properties, soil – steel pile interface friction angle, depth of the water table from the top of the sheet pile wall, total depth of embedment below the dredge line, yield strength of steel, section modulus of steel sheet pile, and anchor pull are all treated as random variables.